NAVIGATING UNCERTAINTY IN WILDLIFE MANAGEMENT: 
AN EMPIRICAL EVALUATION OF A REGULATION CHANGE AND SUBSEQUENT IMPACTS ON 
MICHIGAN WHITE-TAILED DEER POPULATIONS 

By 

Steven Matthew Gurney 

A THESIS 

Submitted to 
Michigan State University 
in partial fulfillment of the requirements 
for the degree of 

Fisheries and Wildlife – Master of Science 

2023 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT 

Assessing changes in population abundance is important when evaluating the 

effectiveness of conservation and management for wildlife. However, both observational and 

structural uncertainty affect the reliability of abundance estimates and may limit the ability to 

assess temporal or spatial differences in abundance. Further, evaluating a conservation or 

management action on a free-ranging population presents challenges with partial 

controllability. Recently, wildlife managers in Michigan sought to understand whether a specific 

harvest regulation had the intended consequences on a white-tailed deer (Odocoileus 

virginianus) population. I used a camera-trap study design to evaluate the effects of an antler 

point restriction (APR) regulation change on a white-tailed deer population in the south-central 

Lower Peninsula of Michigan, USA, 2019–2022. In my first chapter, I used a subset of camera-

trap data to evaluate the sensitivity of abundance estimates to alternative sampling strategies 

that modified sampling frequency, sampling duration, and camera distribution. Results indicated 

that an N-mixture model generated reasonably reliable estimates (i.e., precise and accurate), 

irrespective of data modifications, and that precision was sensitive to modifications. My results 

emphasized the importance of sampling relevant to animal activity and highlighted viable ways 

to improve sampling efficiency. In my second chapter, I evaluated potential population-level 

changes over time and space following an APR change in a before-after-control-impact design. I 

found weak evidence for APRs affecting the relative abundance by sex-and-age classes. In both 

APR and Non-APR treatment areas, I consistently observed increasing trends in Legal and Sub-

legal Male deer relative abundance over time and found no evidence supporting change in 

Female and Fawn relative abundance. 

 
 
ACKNOWLEDGEMENTS 

This research is the culmination of years of hard work that would not have been possible 

without an ecosystem of people and their kindness. First and foremost, I thank my partner, 

Haley. Her unconditional love, compassion, support, and unwavering belief in me is the 

foundation of my life. I am eternally grateful for her patience, for tolerating my sporadic 

absences, for working a second job so we could live more comfortably, and for carrying 

additional weight around home throughout my endeavors as a wildlife professional. I truly could 

not have done this without her. Many thanks to my family. Their support, encouragement, and 

love are the reasons I am who I am today—I owe much of my work ethic and personal character 

to them. I also want to thank my family’s construction company, Apex Roofing, for playing an 

integral role in my success story and allowing me to work as needed to make ends meet. To 

Haley and the rest of my family, I love you all more than I can express. 

I extend my utmost appreciation to my advisor, Dr. Sonja Christensen, for taking me on 

as her first graduate student, and for guiding me throughout this process with unwavering 

support, positivity, and trust. I am especially grateful for her confidence in my abilities, as they 

surpassed my own at times. I credit her with pushing me to reach my potential (and then some), 

from which I have certainly become a better researcher, leader, and wildlife professional. I also 

thank my committee members, Dr. Scott Winterstein and Dr. Rique Campa, for their time, 

expertise, and insightful feedback that improved the rigor of this project. Extra thanks to Dr. 

Rique Campa, who has never stopped encouraging me and supporting me since day one as an 

undergraduate. I owe many thanks to Dr. David Williams, who helped kickstart the modeling 

efforts in this study and, many years ago, taught me to appreciate ecology as a quantitative 

iii 

discipline. Much appreciation goes to Dr. Rose Stewart for providing years of project support 

and helping me overcome many obstacles. I extend sincere appreciation to Dr. Neil Gilbert, for 

his interest and involvement in this research and for exposing me to the satisfaction of tackling 

quantitative puzzles. His natural ability for teaching combined with his friendship resulted in a 

truly positive learning experience.  

This research would not have been possible without the support and partnership of the 

Michigan Department of Natural Resources. I extend sincere appreciation to Dr. Dwayne Etter, 

Dr. Sarah Mayhew, Dr. Mauri Liberati, Melissa Nichols, and Chad Stewart, whose contributions 

were paramount to the development, support, and completion of this research project—

including helping in the field when I was shorthanded. Special thanks to all of them for their 

support, mentorship, friendship, and encouragement over the years. 

I owe an enormous debt of gratitude to the many private landowners who allowed this 

research to be conducted on their property. Without their generosity and assistance, I would 

not have the data necessary to address the questions posed in this research—and I truly 

appreciate the friendship and experiences we shared. I want to offer my special thanks to all 

those who helped collect and process data, including Erin Zimmer, Tristan Swartout, Laura 

Warner, Abby Thiemkey, Erin Stiede, Shana Altus, Rachel Correia, Bonnie Walgamot, Jazmyn 

Toombs, Veronica Clark, Kevin Lovasik, Samantha Greenlee, Katie King, Amber Ng, Arika 

Hawkins, Caitlin Boon, Katie Farinosi, Julie Melotti, Addison Pletcher, Samantha Racicot, Sofia 

Galvan, Taylor Gross, Cheyanne Boucher, Cameron Brown, Brady Yokom, Kevin Schutte, Sam 

Kneibel, Cooper Krueger, and Miranda Strasburg. Extra thanks to Rachel Correia for her 

leadership in the final field season and commitment to helping the team. My experiences with 

iv 

these people made for a fun and much more fulfilling learning experience than I could have 

ever anticipated from an intellectual pursuit alone. 

I am grateful to the Michigan Department of Natural Resources and Michigan State 

University Joint Wildlife Disease Initiative, the U.S. Fish and Wildlife Service through the 

Pittman-Robertson Wildlife Restoration Act Grant MI W-155-R, the former Boone & Crockett 

endowed Quantitative Wildlife Center at Michigan State University, The Hal and Jean Glassen 

Conservation Medicine Fellowship, Michigan State University Department of Fisheries and 

Wildlife’s Joseph Laurence Maison Fellowship, The Wildlife Center’s Wildlife Conservation 

Scholarship, and the Safari Club International Michigan Involvement Committee’s Joseph G. 

Schotthoefer Memorial Student Award for financial support and assistance in completing this 

project.  

Lastly, I would like to acknowledge my MSU family during my time in graduate school, 

including Jonathan Trudeau, Nick Jaffe, Noelle Thompson, Samantha Courtney, Nick Alioto, Jack 

Magee, Rachel Correia, and Miranda Strasburg. Special thanks for their collegiality, countless 

laughs, insightful discussions, constructive feedback, and constant encouragement. Extra thanks 

to Miranda Strasburg for her mentoring and a much-needed perspective at critical times during 

my graduate program. To these people, and to all those who have supported me in this 

endeavor, thank you. You have truly made this a wonderful, memorable experience.  

v 

 
 
TABLE OF CONTENTS 

GENERAL INTRODUCTION ........................................................................................................... 1 
LITERATURE CITED .............................................................................................................. 7 

CHAPTER 1: CAMERA-TRAP SAMPLING STRATEGIES AFFECT ABUNDANCE ESTIMATION FOR 
AN UNMARKED DEER POPULATION ......................................................................................... 12 
INTRODUCTION ................................................................................................................. 12 
STUDY AREA ...................................................................................................................... 16 
METHODS .......................................................................................................................... 19 
RESULTS............................................................................................................................. 32 
DISCUSSION ....................................................................................................................... 47 
LITERATURE CITED ............................................................................................................ 59 

CHAPTER 2: ASSESSING THE EFFECT OF A DEER HARVEST REGULATION CHANGE ON RELATIVE 
ABUNDANCE: AN EXPERIMENTAL APPROACH ......................................................................... 67 
INTRODUCTION ................................................................................................................. 67 
STUDY AREA ...................................................................................................................... 76 
METHODS .......................................................................................................................... 82 
RESULTS............................................................................................................................. 93 
DISCUSSION ..................................................................................................................... 113 
LITERATURE CITED .......................................................................................................... 123 

CONCLUSIONS AND MANAGEMENT IMPLICATIONS .............................................................. 135 

APPENDIX 1A: CAMERA-TRAPPING PROTOCOL ...................................................................... 138 

APPENDIX 1B: PHOTO-REVIEW PROTOCOL ............................................................................ 147 

APPENDIX 1C: EXPLORATORY DATA ANALYSIS REPORT ......................................................... 154 

APPENDIX 2A: MEGADETECTOR DATA-PROCESSING PROTOCOL .......................................... 202 

APPENDIX 2B: STATIC BINOMIAL N-MIXTURE MODEL STUDY ............................................... 220 

APPENDIX 2C: CODE FOR YEAR-STRATIFIED N-MIXTURE MODEL .......................................... 235 

APPENDIX 2D: CODE FOR MARGINAL EFFECTS AND CHANGE IN ABUNDANCE ..................... 239 

APPENDIX 2E: MEGADETECTOR ACCURACY ........................................................................... 242 

APPENDIX 2F: MICHIGAN DEER-HARVEST TRENDS ................................................................ 243 

APPENDIX 2G: APR-CWD SIMULATION STUDY ....................................................................... 247 

vi 

GENERAL INTRODUCTION 

Chronic wasting disease (CWD) is a fatal disease caused by a prion that infects cervids 

(family Cervidae), including white-tailed deer (Odocoileus virginianus; Williams 2005). The 

disease is a major management challenge as CWD is transmissible through animal-to-animal 

contact and acts as an environmental contaminant. Shed prions can remain infectious for years 

in the environment and further contribute to the maintenance of the disease (Miller et al. 

2004). Described as the most important disease threatening North American cervids, CWD 

poses a serious threat to both the sustainability of free-ranging and captive cervids and 

conservation nationwide (Gillin and Mawdsley 2018). In areas where CWD is established, it has 

emerged as a major threat, reducing the health of wild cervid populations, and potentially 

causing long-term population decline (Gross and Miller 2001, Manjerovic et al. 2014, Edmunds 

et al. 2016, DeVivo et al. 2017). In addition to population-level impacts, CWD can discourage 

hunters from harvesting deer in and around affected areas (Needham et al. 2004, Vaske and 

Lyon 2011). This is problematic because funding for state wildlife agencies comes from hunting-

related expenditures and license sales (Jacobson et al. 2010). Deer hunters account for the 

largest portion of the hunting public and generate a substantial portion of conservation dollars 

(Hewitt et al. 2015). Consequently, CWD-driven declines in deer hunting and deer-hunting 

revenue can destabilize the overall economic well-being of wildlife conservation.  

Deer hunting regulations and hunter harvest are the primary levers used by state 

wildlife agencies for managing deer populations and disease. Management actions are often 

intended to manipulate the total abundance or sex-and-age composition of targeted deer 

populations (Demarais et al. 2000). As it relates to disease, some studies have shown that 

1 

reducing deer densities has been successful at maintaining low prevalence of CWD (~1–2%; 

Manjerovic et al. 2014, Mateus-Pinilla et al. 2013), whereas other research has established that 

different sex-and-age classes of free-ranging deer have different prevalence rates of the disease 

(Miller and Conner 2005, Grear et al. 2006, Osnas et al. 2009, Rees et al. 2012, Jennelle et al. 

2014). Due to changes in the sex-and-age composition, harvest strategies that target specific 

sex-and-age classes may be useful for CWD management (Mysterud and Edmunds 2019).  

Wildlife management agencies often alter harvest regulations to change the 

composition and structure of harvests with the expectation that the alteration will result in 

population-level changes in abundance, composition, and structure (Carpenter 2000, Demarais 

et al. 2000). For example, mortality from hunting antlerless deer (including females) is a 

common approach for managing white-tailed deer abundance (Woolf and Rosenberry 1998, 

Diefenbach et al. 2021). Harvest can provide an effective tool for managing populations, and 

management decisions can greatly influence the targeted population. For example, sex- and 

age-specific hunting can alter the composition and structure of targeted populations, which in 

turn can affect various demographic processes (Ginsberg and Milner-Gulland 1994, Milner et al. 

2007). Historically, male-biased harvesting regimes have been applied to North American 

cervids (McCullough 2001). This type of harvest strategy can lead to a female-biased sex ratios 

in populations (Noyes et al. 1996, Nilsen and Solberg 2006). With regards to age, 

disproportionate harvests of young animals can limit animals from advancing to older age 

classes and skew a population’s age structure (Milner et al. 2007).  

Mandatory antler-point restrictions (APRs) are an example of a deer harvest regulation 

intended to change the sex-and-age composition of harvests. Antler point restrictions are based 

2 

on antler size (i.e., number of antler points), and antler size generally increases with the age of 

the animal (Strickland and Demarais 2000). Specifically, APRs are designed to limit the harvest 

of younger antlered deer and thus increase recruitment of male deer into older age classes 

(Carpenter and Gill 1987, Frawley 2017, Hansen et al. 2017, Wallingford et al. 2017). APRs may 

also decrease deer abundance in an APR area which could reduce contact rates and thus overall 

spread of CWD. These decreases can result from indirect effects of APRs on harvest, like shifting 

harvest pressure to antlerless deer (Cornicelli et al. 2011, Hansen et al. 2017, Wallingford et al. 

2017, Hansen et al. 2018), although this has not been observed in all places with APRs (Hansen 

et al. 2017, Cain et al. 2022). Overall, natural resource agencies have limited information on 

how deer harvest regulations affect the abundance and sex-and-age composition of the true 

state of the population (as opposed to the harvested segment; Brown et al. 2000, Carpenter 

2000, Riley et al. 2003, Giles and Findlay 2004, Morina et al. 2021). This limitation is relevant 

because CWD transmission rates are related to the sex-and-age composition of the population, 

thus different harvest regulations could have different implications for CWD transmission. 

White-tailed deer are an important game species, and the accurate estimation of 

population parameters is essential for the evaluation of management actions (Ludbow et al. 

1996, Gibbs 2000, Furnas et al. 2018). Further, precise abundance estimates by sex-and-age 

class can offer a more rigorous assessment needed for relevant disease management. This need 

is especially relevant in areas where population-management actions are aimed at mediating 

the spread of CWD in free-ranging deer. However, estimating abundance and composition can 

be logistically difficult, with traditional methods often involving live capture and marking 

animals (O’Connell et al. 2011, Burton et al. 2015, Wearn and Glover-Kapfer 2019). Most state 

3 

agencies instead rely on estimated or enumerated harvest for population monitoring efforts 

(Roseberry and Woolf 1991, Skalski et al. 2005, Hansen 2011, Ryder 2018, Diefenbach et al. 

2021). Although useful, sex-and-age data of the harvested population may be 

nonrepresentative of the true state of the population (Carpenter 2000, Demarais et al. 2005, 

Collier and Krementz 2007).  

Camera trapping has become an increasingly common method for monitoring wildlife 

over large spatial scales and represents an alternative to more intensive methods (O’Connell et 

al. 2011, Burton et al. 2015, Parsons et al. 2017, Wearn and Glover-Kapfer 2019). Likewise, 

camera trapping has emerged as a valuable tool for gathering count data for monitoring cervid 

populations (DeYoung 2011). Camera-trap data have been used to estimate population 

parameters for numerous cervids (Furnas et al. 2018, Moeller et al. 2018, Furnas et al. 2020), 

including white-tailed deer (Jacobson et al. 1997, Roberts et al. 2006, Petroelje et al. 2014, Haus 

et al. 2019). Camera-trap based population estimates can be compared across time and space 

to monitor changes in populations and, by extension, can be used to test hypotheses about the 

effects of management actions. However, one major challenge with camera-trap approaches is 

the labor required to review high numbers of photographs (DeYoung 2011, Pierce et al. 2012), 

and it is not uncommon to collect large quantities of camera-trap data. This often forces wildlife 

managers to compromise between the quality of data and the sampling strategies used 

(Marcon et al. 2019). Solutions to the photo-reviewing issue include increasing efficiency of 

data management (Price Tack et al. 2016) or decreasing survey intensity, such as reducing the 

survey duration or number of camera sites. However, these modifications may also influence 

the precision and accuracy of abundance estimators and thus need to be critically evaluated 

4 

before formal application. Therefore, methodological assessments for data collection and 

parameter estimation are needed to maximize the utility of camera-trap approaches. 

In Michigan, CWD was first identified in free-ranging deer in 2015 (Stewart et al. 2016) 

and has now been detected in 3 primary areas (southwest Upper Peninsula, and south-central 

and southeast Lower Peninsula). The south-central Lower Peninsula area is considered a CWD 

hotspot, where the disease is established in Kent and Montcalm County. In addition to changes 

in state and peninsula-wide deer harvest regulations designed to mediate potential spread of 

disease, the Natural Resource Commission implemented APRs in select counties in the south-

central Lower Peninsula as part of experimental management. This action was coupled with 

research aimed to evaluate the efficacy of APRs as a tool for managing CWD (hereafter, APR 

study). To address this, camera traps were used to collect data on white-tailed deer populations 

over 4 consecutive years (2019–2022) within a 5-county area (Ionia, Kent, Mecosta, Montcalm, 

and Newaygo counties).  

The overarching goals of my thesis are to evaluate the consequences of camera-trap 

sampling design and estimate potential population-level changes following the implementation 

of an APR in an area with CWD. The first goal was developed to identify sampling strategies that 

minimize financial and human resources to attain precise and reliable estimations of deer 

abundance using N-mixture models (Royle 2004). The second goal was developed to help fill 

critical knowledge gaps about the effects of APRs on deer abundance by sex-and-age. 

In Chapter 1, I leveraged a subset of camera-trap data from the APR study to conduct a 

post hoc methodological assessment focusing on survey design and abundance estimation. My 

objectives were to evaluate the sensitivity of abundance estimation to modifications in 1) 

5 

sampling frequency, 2) sampling duration, and 3) camera distribution. Specifically, for these 

three vital aspects of camera-trap study design, I investigated how modifications affected 

estimates of abundance, detection probability, and model performance. Further, the 

development of reliable sampling strategies and statistical techniques in Chapter 1 were critical 

to informing abundance-estimation efforts in Chapter 2.  

In Chapter 2, I used the APR study’s 2019–2022 camera-trap data to estimate annual 

white-tailed deer abundance by sex-and-age class in areas with varying harvest treatment (APR 

and Non-APR). My objectives were to empirically evaluate two, prevalent APR hypotheses: 1) 

that APRs increase the abundance of adult males, and 2) that APRs decrease overall deer 

abundance. Finally, the conclusion section at the end of my thesis provides a summary of my 

findings and general conclusions, including recommendations for practitioners modeling 

abundance with N-mixture models and camera-trap count data, and for managers considering 

alternative harvest regulations to achieve management goals.

6 

LITERATURE CITED 

Brown, T., S. Riley, J. Enck, T. Lauber, P. Curtis, and G. Mattfeld. 2000. The future of hunting as a 
mechanism to control white-tailed deer populations. Wildlife Society Bulletin 28:797–807. 

Burton, A. C., E. Neilson, D. Moreira, A. Ladle, R. Steenweg, J. T. Fisher, E. Bayne, and S. Boutin. 
2015. Wildlife camera trapping: a review and recommendations for linking surveys to 
ecological processes. Journal of Applied Ecology 52:675–685. 

Cain, R. L., D. M. Williams, and W. F. Porter. 2022. The effectiveness of antler point restrictions 

to achieve management goals. Wildlife Society Bulletin 46:e1359. 

Carpenter, L. H., 2000. Harvest management goals. Pages 192–213 in S. Demarais and P. R. 

Krausman, P. R. editors. Ecology and Management of Large Mammals in North America. 
Prentice-Hall, Upper Saddle River, New Jersey, USA. 

Carpenter, L. H., and R. B. Gill. 1987. Antler point regulations the good, the bad, and the ugly. 

Transactions of the Western Association of Game and Fish Commissioners 67:94–107. 

Collier, B. A., and D. G. Krementz. 2007. Uncertainty in age-specific harvest estimates and 
consequences for white-tailed deer management. Ecological Modeling 201:194–204. 

Cornicelli, L., D. C. Fulton, M. D. Grund, and J. Fieberg. 2011. Hunter perceptions and 

acceptance of alternative deer management regulations. Wildlife Society Bulletin 35:323–
329. 

Demarais, S., K. V. Miller, and H. A. Jacobson. 2000. White-tailed deer. Pages 601–628 in S. 
Demarais and P.R. Krausman, editors. Ecology and Management of Large Mammals in 
North America. Prentice Hall, Upper Saddle River, New Jersey, USA. 

Demarais, S., B. Strickland, and L. Castle. 2005. Antler regulation effects on white-tailed deer on 

Mississippi public hunting areas. Proceedings of the Annual Conference of the 
Southeastern Association of Fish and Wildlife Agencies 59:1–9. 

DeVivo, M. T., D. R. Edmunds, M. J. Kauffman, B. A. Schumaker, J. Binfet, T. J. Kreeger, B. J. 

Richards, H. M. Schätzl, and T. E. Cornish. 2017. Endemic chronic wasting disease causes 
mule deer population decline in Wyoming. PLoS ONE 12:e0186512. 

DeYoung, C.A., 2011. Population dynamics. Pages 160–193 in D. G. Hewitt, editor. Biology and 

Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

Diefenbach, D. R., W. M. Know, and C. S. Rosenberry. 2021. The future of managing ungulate 
species: white-tailed deer as a case study. Pages 327–339 in K. L. Pope and L. A. Powell, 
editors. Harvest of Fish and Wildlife: New Paradigms for Sustainable Management. CRC 
Press, Boca Raton, Florida, USA. 

7 

Edmunds, D. R., M. J. Kauffman, B. A. Schumaker, F. G. Lindzey, W. E. Cook, T. J. Kreeger, R. G. 
Grogan, and T. E. Cornish. 2016. Chronic wasting disease drives population decline of 
white-tailed deer. PLoS ONE 11:e0161127. 

Frawley, B. J. 2017. Evaluation of antler point restrictions in deer management units in the 

northwest Lower Peninsula. Michigan Department of Natural Resources Wildlife Division 
Report 3638, Lansing, Michigan, USA. 

Furnas, B. J., R. H. Landers, S. Hill, S. S. Itoga, and B. N. Sacks. 2018. Integrated modeling to 
estimate population size and composition of mule deer. The Journal of Wildlife 
Management 82:1429–1441. 

Furnas, B. J., R. H. Landers, R. G. Paiste, and B. N. Sacks. 2020. Overabundance of black-tailed 

deer in urbanized coastal california. The Journal of Wildlife Management 84:979–988. 

Gibbs, J.P. 2000. Monitoring populations. Pages 213‒252 in L. Boitani and T.K. Fuller, editors. 
Research Techniques in Animal Ecology. Columbia University Press, New York, New York, 
USA. 

Giles, B. G., and C. S. Findlay. 2004. Effectiveness of a selective harvest system in regulating deer 

populations in Ontario. Journal of Wildlife Management 68:266–277. 

Gillin, C. M., and Mawdsley, J. R. (eds.). 2018. AFWA Technical Report on Best Management 
Practices for Surveillance, Management and Control of Chronic Wasting Disease. 
Association of Fish and Wildlife Agencies, Washington, D. C. 111 pp. 

Ginsberg, J. R., and E. J. Milner-Gulland. 1994. Sex-biased harvesting and population dynamics 
in ungulates: implications for conservation and sustainable use. Conservation Biology 
8:157–166.  

Grear, D. A., M. D. Samuel, J. A. Langenberg, and D. Keane. 2006. Demographic patterns and 
harvest vulnerability of chronic wasting disease infected white-tailed deer in Wisconsin. 
Journal of Wildlife Management 70:546–553.  

Gross, J. E., and M. W. Miller. 2001. Chronic wasting disease in mule deer: disease dynamics and 

control. The Journal of Wildlife Management 65:205–215.  

Hansen, L., 2011. Extensive management. Pages 409–451 in D. G. Hewitt, editor. Biology and 

Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

Hansen, L. P., E. B. Flinn, J. A. Sumners, X. Gao, and J. J. Millspaugh. 2017. Effects of an antler 
point restriction on harvest of white-tailed deer in Missouri. Wildlife Society Bulletin 
41:516–522. 

8 

Hansen, L. P., J. A. Sumners, R. Reitz, Y. Bian, X. Gao, and J. J. Millspaugh. 2018. Effects of an 
antler point restriction on deer hunter perceptions and satisfaction in Missouri. Wildlife 
Society Bulletin 42:607–615. 

Haus, J. M., T. B. Eyler, and J. L. Bowman. 2019. A spatially and temporally concurrent 
comparison of popular abundance estimators for white-tailed deer. Northeastern 
Naturalist 26:305–324.  

Hewitt, D. G. 2015. Hunters and the conservation and management of white-tailed deer 

(Odocoileus virginianus). International Journal of Environmental Studies 72:839–849.  

Jacobson, H. A., J. C. Kroll, R. W. Browning, B. H. Koerth, and M. H. Conway. 1997. Infrared-

triggered cameras for censusing white-tailed deer. Wildlife Society Bulletin 25:547–556.  

Jacobson, C. A., J. F. Organ, D. J. Decker, G. R. Batcheller, and L. Carpenter. 2010. A conservation 

institution for the 21st century: implications for state wildlife agencies. Journal of Wildlife 
Management 74:203–209.  

Jennelle, C. S., V. Henaux, G. Wasserberg, B. Thiagarajan, R. E. Rolley, and M. D. Samuel. 2014. 
Transmission of chronic wasting disease in Wisconsin white-tailed deer: implications for 
disease spread and management. PLoS ONE 9:e91043. 

Lubow, B. C., G. C. White, and D. R. Anderson. 1996. Evaluation of a linked sex harvest strategy 

for cervid populations. The Journal of Wildlife Management 60:787–796.  

Manjerovic, M. B., M. L. Green, N. Mateus-Pinilla, and J. Novakofski. 2014. The importance of 
localized culling in stabilizing chronic wasting disease prevalence in white-tailed deer 
populations. Preventive Veterinary Medicine 113:139–145. 

Marcon, A., D. Battocchio, M. Apollonio, and S. Grignolio. 2019. Assessing precision and 

requirements of three methods to estimate roe deer density. PLOS ONE 14:e0222349.  

Mateus-Pinilla, N., H.-Y. Weng, M. O. Ruiz, P. Shelton, and J. Novakofski. 2013. Evaluation of a 
wild white-tailed deer population management program for controlling chronic wasting 
disease in Illinois, 2003–2008. Preventive Veterinary Medicine 110:541–548. 

McCullough, D. R. 2001. Male harvest in relation to female removals in a black-tailed deer 

population. The Journal of Wildlife Management 65:46–58.  

Miller, M. W., and M. M. Conner. 2005. Epidemiology of chronic wasting disease in free-ranging 

mule deer: spatial, temporal, and demographic influences on observed prevalence 
patterns. Journal of Wildlife Diseases 41:275–290. 

Miller, M. W., E. S. Williams, N. T. Hobbs, and L. L. Wolfe. 2004. Environmental sources of prion 

transmission in mule deer. Emerging Infectious Diseases 10:1003–1006. 

9 

Milner, J. M., E. B. Nilsen, and H. P. Andreassen. 2007. Demographic side effects of selective 

hunting in ungulates and carnivores. Conservation Biology 21:36–47. 

Moeller, A. K., P. M. Lukacs, and J. S. Horne. 2018. Three novel methods to estimate abundance 

of unmarked animals using remote cameras. Ecosphere 9:e02331. 

Morina, D. L., C. P. Hansen, L. P. Hansen, and J. J. Millspaugh. 2021. The efficacy of antler harvest 
regulations in meeting management objectives. Pages 263–282 in K. L. Pope and L. A. 
Powell, editors. Harvest of fish and wildlife: new paradigms for sustainable management. 
CRC Press, Boca Raton, Florida, USA. 

Mysterud, A., and D. R. Edmunds. 2019. A review of chronic wasting disease in North America 

with implications for Europe. European Journal of Wildlife Research 65:26. 

Needham, M. D., J. J. Vaske, and M. J. Manfredo. 2004. Hunters’ behavior and acceptance of 

management actions related to chronic wasting disease in eight states. Human Dimensions 
of Wildlife 9:211–231. 

Nilsen, E. B., and E. J. Solberg. 2006. Patterns of hunting mortality in Norwegian moose (Alces 

alces) populations. European Journal of Wildlife Research 52:153–163. 

Noyes, J. H., B. K. Johnson, L. D. Bryant, S. L. Findholt, and J. W. Thomas. 1996. Effects of bull 

age on conception dates and pregnancy rates of cow elk. The Journal of Wildlife 
Management 60:508–517. 

O’Connell A., J. D. Nichols, and K. U. Karanth, editors. 2011. Camera traps in animal ecology: 

methods and analyses. Springer Science & Business Media, Tokyo, Japan.  

Osnas, E. E., D. M. Heisey, R. E. Rolley, and M. D. Samuel. 2009. Spatial and temporal patterns of 
chronic wasting disease: fine-scale mapping of a wildlife epidemic in Wisconsin. Ecological 
Applications 19:1311–1322. 

Parsons, A. W., T. Forrester, W. J. McShea, M. C. Baker-Whatton, J. J. Millspaugh, and R. Kays. 
2017. Do occupancy or detection rates from camera traps reflect deer density? Journal of 
Mammalogy 98:1547–1557. 

Petroelje, T. R., J. L. Belant, D. E. Beyer, G. Wang, and B. D. Leopold. 2014. Population-level 
response of coyotes to a pulsed resource event. Population Ecology 56:349–358.  

Pierce, B.L., R. R. Lopez, and N. J. Silvy. 2012. Estimating animal abundance. Pages 284–310 in N. 

J. Silvy, editor. The Wildlife Techniques Manual: Research. Volume 1. Seventh edition. The 
Johns Hopkins University Press, Baltimore, Maryland, USA.  

Price Tack, J. L., B. S. West, C. P. McGowan, S. S. Ditchkoff, S. J. Reeves, A. C. Keever, and J. B. 
Grand. 2016. AnimalFinder: a semi-automated system for animal detection in time-lapse 
camera trap images. Ecological Informatics 36:145–151. 

10 

Rees, E. E., E. H. Merrill, T. K. Bollinger, Y. T. Hwang, M. J. Pybus, and D. W. Coltman. 2012. 

Targeting the detection of chronic wasting disease using the hunter harvest during early 
phases of an outbreak in Saskatchewan, Canada. Preventive Veterinary Medicine 104:149–
159. 

Roberts, C. W., B. L. Pierce, A. W. Braden, R. R. Lopez, N. J. Silvy, P. A. Frank, and D. Ransom Jr. 
2006. Comparison of camera and road survey estimates for white-tailed deer. The Journal 
of Wildlife Management 70:263–267. 

Roseberry, J. L., and A. Woolf. 1991. A comparative evaluation of techniques for analyzing white-

tailed deer harvest data. Wildlife Monographs 117:3–59. 

Riley, S. J., D. J. Decker, J. W. Enck, P. D. Curtis, T. B. Lauber, and T. L. Brown. 2003. Deer 

populations up, hunter populations down: Implications of interdependence of deer and 
hunter population dynamics on management. Écoscience 10:455–461. 

Royle, J. A. 2004. N-Mixture models for estimating population size from spatially replicated 

counts. Biometrics 60:108–115.  

Ryder, T., editor. 2018. State Wildlife Management and Conservation. Johns Hopkins University 

Press, Baltimore, Maryland, USA. 

Skalski, J. R., K. E. Ryding, and J. J. Millspaugh. 2005. Wildlife demography: analysis of sex, age, 

and count data. Elsevier Academic Press, San Diego, CA. 656 pp. 

Stewart, C., M. Cosgrove, and J. Melotti. 2016. 2015-2016 Michigan chronic wasting disease 
management and surveillance report. Unpublished report. Michigan Department of 
Natural Resources, Lansing, USA. 

Vaske, J. J., and K. M. Lyon. 2011. CWD prevalence, perceived human health risks, and state 

influences on deer hunting participation. Risk Analysis 31:488–496. 

Strickland, B. K. and S. Demarais. 2000. Age and regional differences in antler size and body 
mass of white-tailed deer in Mississippi. Journal of Wildlife Management 64: 903−911. 

Wallingford, B. D., D. R. Diefenbach, E. S. Long, C. S. Rosenberry, and G. L. Alt. 2017. Biological 
and social outcomes of antler point restriction harvest regulations for white-tailed deer: 
antler point restrictions. Wildlife Monographs 196:1–26. 

Wearn, O. R., and P. Glover-Kapfer. 2019. Snap happy: camera traps are an effective sampling 
tool when compared with alternative methods. Royal Society Open Science 6:181748. 

Williams, E. S. 2005. Chronic wasting disease. Veterinary Pathology 42:530–549. 

Woolf, A., and J. L. Roseberry. 1998. Deer management: our profession’s symbol of success or 

failure? Wildlife Society Bulletin (1973-2006) 26:515–521.

11 

CHAPTER 1: CAMERA-TRAP SAMPLING STRATEGIES AFFECT ABUNDANCE ESTIMATION FOR AN 
UNMARKED DEER POPULATION 

INTRODUCTION 

Population abundance measures are crucial to ecological studies and form the 

foundation of effective wildlife-monitoring programs. Whether studying threatened species, 

invasive species, or game species, an understanding of abundance is important for evaluating 

the impact of conservation and management efforts (Kidwai et al. 2019, Schlichting et al. 2020, 

Christensen et al. 2021). However, meaningful assessments are only realized when the 

methodology is sensitive enough to detect population trends. Suboptimal sampling strategies 

can limit precision, accuracy, and the ability to identify temporal or spatial differences in 

abundance, which can then lead managers to incorrect inference and flawed decisions. 

Obtaining precise estimates of animal abundance can be logistically difficult, time-consuming, 

and costly (Pierce et al. 2012), requiring wildlife managers to balance the quality of results and 

the sampling strategy implemented (Marcon et al. 2019). Given the limited resources available 

for monitoring wildlife populations, there is a need for reliable and cost-effective methods 

sensitive enough to detect population trends needed by wildlife management agencies. 

Remote cameras, also known as camera traps, have become a standard non-invasive 

method for monitoring wildlife populations. Their ease of use, cost-effectiveness, and capability 

to survey large geographic areas have made them a valuable and powerful tool in wildlife 

research (O’Connell et al. 2011, Burton et al. 2015, Parsons et al. 2017). Camera-trap data are 

typically categorized based on number of individuals and sometimes by physically 

distinguishable characteristics like sex and age. Once characterized, camera-trap data can be 

used to estimate population parameters, including density, abundance, and relative abundance 

12 

 
indices (Burton et al. 2015). These estimates can be compared over time and space to monitor 

population changes and test hypotheses about the effects of conservation and management 

actions. Most camera-trap studies to date have focused on estimating population abundance 

using individually recognizable, or "marked," animals (Gilbert et al. 2021). Consequently, 

abundance estimation of unmarked populations remains a significant frontier in camera 

trapping.  

The application of camera traps as a wildlife population monitoring tool offers a myriad 

of advantages, albeit accompanied by the challenge of managing and processing image data 

(DeYoung 2011). With the surge in popularity of camera trapping and advancements in 

technology and data management, large quantities of image data (e.g., millions of images) are 

becoming more common, requiring time-consuming and labor-intensive efforts to process. To 

address this challenge, several potential solutions have been proposed, including improving 

data management efficiency (Price Tack et al. 2016), using artificial intelligence for photo 

processing (Vélez et al. 2022), and altering sampling strategies. Different sampling strategies 

that vary the survey duration or number of camera sites can have different travel and field-

labor costs, but they may also affect precision and accuracy of abundance estimators. Sampling 

strategies must therefore be critically evaluated before formal application. Ultimately, 

understanding how sampling strategies influence abundance estimation is important for 

designing effective and efficient monitoring programs (Si et al. 2014). 

A suite of models are available to estimate the abundance of unmarked animals based 

on camera-trap data, including site-structured models (see review by Gilbert et al. 2021). These 

analytical frameworks offer a unique advantage in that they incorporate ecological and 

13 

observational processes (Kéry and Royle 2015). By accounting for imperfect detection, these 

models can provide a more accurate picture of wildlife populations. Site-structured models are 

subject to critical assumptions, including population closure (i.e., no individuals leave or enter 

the population via birth, immigration, death, or emigration), detection probability is equal for 

all individuals, absence of false-positive detections (i.e., no misidentifications or double 

counting of individuals), and detections of individuals are independent of one another (Royle 

2004). Deviations from these assumptions can affect the validity of the estimates produced by 

these models (Barker et al. 2018, Link et al. 2018). Consequently, if the underlying assumptions 

are not satisfied, it is advisable to interpret estimates as relative abundance indices instead of 

absolute values (Barker et al. 2018, Gilbert et al. 2021).  

N-mixture models (Royle 2004) are site-structured models and have been successfully 

applied to numerous species, including birds (Lyons et al. 2012, Jakob et al. 2014, McCaffery et 

al. 2016, Zou et al. 2019), amphibians (Ficetola et al. 2018, Costa et al. 2020), reptiles (Ward et 

al. 2017, Barão-Nóbrega et al. 2022), and large mammals (Belant et al. 2016, Haus et al. 2019, 

Kidwai et al. 2019, Christensen et al. 2021, Brack et al. 2023). N-mixture models can be used to 

estimate site abundance and thus produce relative abundance indices (Burton et al. 2015). 

Implementing N-mixture models with camera-trap data has been found to be an effective 

approach for estimating size of unmarked white-tailed deer (Odocoileus virginianus) 

populations (Keever et al. 2017, Haus et al. 2019). Haus et al. (2019) found that this approach 

achieved greater precision compared to road-based distance sampling techniques that used 

spotlight or forward-looking infrared surveys. Keever et al. (2017) conducted a study using a 

known population of enclosed white-tailed deer and demonstrated that N-mixture models 

14 

accurately estimated population size. Additionally, the authors identified strategies for resource 

optimization by minimizing the necessary number of survey days. Although shorter surveys may 

reflect lower costs and reduced data-processing, estimates of free-ranging populations may be 

sensitive to such manipulations in sampling design (Haus et al. 2019). Further, the required 

sampling intensity may vary over the species’ range, highlighting study-area specificity of 

camera-trap approaches (DeYoung 2011). Although N-mixture modeling has been applied 

successfully to camera-trap studies of white-tailed deer, there is still limited information on 

how different sampling strategies can affect abundance estimation of free-ranging populations. 

An important consideration when applying N-mixture models to camera-trap surveys is 

the designation of sampling frequency, survey duration, and number of camera sites for survey 

design and abundance estimation. To address this matter, I used an existing camera-trap 

dataset from a Michigan study aimed to assess potential changes of a white-tailed deer 

(hereafter, deer) population following a harvest regulation change. That study generated a high 

volume of images (>2.6 million) that I leveraged and subset to conduct a post hoc 

methodological assessment. The goal of my study was to evaluate the consequences of 

sampling design and provide methodological recommendations to researchers and 

practitioners. My objectives were to evaluate the sensitivity of abundance estimation to 

modifications in sampling frequency, sampling duration, and camera distribution. For these 

three vital aspects of camera-trap study design, I investigated how modifications affected 

estimates of relative abundance, detection probability, and model performance. In the absence 

of knowledge about the true state of the deer population, I used a data-simulation approach to 

evaluate the robustness of my statistical inferences. I hypothesized there would be sampling 

15 

strategies that balanced precision of relative abundance estimates with high detection 

probability and model performance. The outcomes of my study allowed me to offer 

methodological recommendations for camera-trap survey design. More specifically, my results 

identified sampling strategies that minimize financial and human resources to attain precise 

and reliable estimations of deer relative abundance using N-mixture models and highlight the 

importance of sampling relevant to animal activity.  

STUDY AREA 

The study took place in the south-central Lower Peninsula of Michigan in a 5-county 

area (Newaygo, Kent, Mecosta, Montcalm, and Ionia County; hereafter, 5-County Area) that 

included a known chronic-wasting-disease hotspot (Kent and Montcalm County; Figure 1.1). In 

2019, an antler point restriction (APR) was implemented in a portion of the 5-County Area and 

a study was designed to evaluate its effect on the abundance and sex-and-age composition of 

deer populations in the area. Specifically, the APR prohibited hunters from harvesting antlered 

deer that did not have at least 4 antler points on one side. A paired-comparison study design 

was implemented to monitor deer populations in APR and non-APR areas (i.e., experimental 

and control areas, respectively). A robust before-after-control-impact (BACI) study design 

(Green 1979) was employed to monitor potential population-level changes, over 3 consecutive 

years (2020–2022), following the regulation change. This design was intended to allow 

researchers to identify changes in population abundance and composition in the treatment 

area (APR Zone) relative to the control area (Non-APR Zone) over the course of the study. 

The study implemented a camera-trap sampling design restricted to 8 townships within 

the 5-County Area, encompassing an area of approximately 749 km2 (Figure 1.1). In the APR 

16 

Zone (4,845-km2), antlered deer with at least four points on one antler could be taken with a 

valid license (a legal point was defined as ≥ 2.54 cm [1 inch] long as measured from its tip to the 

nearest edge of antler beam). In the Non-APR Zone (4,488-km2), any antlered deer with an 

antler ≥7.62 cm (3 inches) in length could be taken. Apart from the APR regulation, all other 

deer-hunting regulations were comparable between the APR and Non-APR Zones (Frawley 

2020, 2021, 2022). Deer hunting occurred every fall and regulations were similar between 

zones prior to the 2019 APR-regulation change. Natural predators included coyote (Canis 

latrans) with the addition of bobcat (Lynx rufus) and American black bear (Ursus americanus) in 

the northernmost stretches of the study area.  

The 5-County Area spanned a floristic tension zone and multiple ecoregions, including 

the Lansing loamy plain ecoregion in the south and Newaygo barrens and Cadillac hummocky 

moraines ecoregions in the north (Barnes and Wagner 2004, EPA 2010). Consequently, the study 

area was a fragmented mosaic composed of different land-use and land-cover types. The 

southern region was flat and dominated by large expanses of agricultural land (primarily corn, 

soybeans, wheat, alfalfa), fragmented woodlots, and development (Albert 1995). The southern 

region was distinguished from the northern by warmer annual temperatures and a longer, less 

variable growing season (Barnes and Wagner 2004). At higher latitudes, the landscape 

transitions to sandy rolling hills, greater forest cover (Albert 1995), and an increased conifer 

presence in uplands and wetlands (Barnes and Wagner 2004). Across the study area, average 

elevation is approximately 268 m with a range of 182–411 m. Overstory vegetation in the study 

area varied by ecoregion but included northern hardwood (dominated by maple [Acer spp.], oak 

[Quercus spp.], and hickory [Carya spp.]) and pine (Pinus spp.) with scattered hardwood-conifer 

17 

swamps (Albert 1995). The 5-County Area was approximately 9,332 km2 and 40% was used for 

agriculture, 30% was forested, 15% wetland, and 12% was developed (Dewitz and USGS 2021). 

Monthly mean temperatures ranged from -6.1–21.1 °C, with a mean annual precipitation of 84 

cm, including 165 cm of snowfall (NOAA 2021). 

Figure 1.1. Study area in the south-central Lower Peninsula of Michigan, USA, in a designated 5-
county area that included a known chronic-wasting-disease hotspot. Mandatory antler point 
restrictions (APRs) were implemented in 2019 in the experimental area (APR Zone) and not in 
the control area (Non-APR Zone). Townships were paired (A–D) between zones, and remote 
cameras were placed in each township to monitor white-tailed deer (Odocoileus virginianus) 
populations over a duration of four years (2019–2022). Maps created in ArcGIS Pro (version 
2.7.1; ESRI 2020).

18 

 
METHODS 

Site selection 

The study area was longitudinally divided instead of latitudinally to minimize the effects, 

other than APRs (e.g., land-use and land-cover types), on deer populations. Landscape 

compositional analyses (e.g., % forest, % public hunting land) were completed for each 

township in the 5-County Area to identify similar townships for pairing. Additional pairing 

criteria included geological features (e.g., rivers), human density, and apparent CWD presence 

(Table 1.1). Eight townships were systematically selected and paired between the APR Zone and 

Non-APR Zone to compare deer populations over time at a scale that was achievable with 

camera-traps while also reflecting the variation within the 5-county study area (Figure 1). A 

stratified-random design (at the township-section scale) was used to select 144 camera sites 

evenly across the 8 townships using generalized random-tessellation stratification (GRTS; 

Stevens and Olsen 2004). The GRTS sampling design is advantageous because it maintains 

statistical qualities of a random draw when removing intractable samples (i.e., no land access), 

while yielding a spatially balanced set of points (Stevens and Olson 2004). Random camera 

placement was selected with the intent of providing the least biased approximation of 

population structure. Sample sites were located on both public and private land, the latter 

necessitating landowner permission.  

19 

 
Table 1.1. Criteria used to determine township pairings (A, B, C, D) between experimental and 
control areas zones (APR and Non-APR Zones, respectively) for a before-after-control-impact 
study design. Eight townships were paired based on similarities including land-cover features, 
geographic features, and apparent presence of chronic wasting disease. Pairings were applied 
to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.  

Pairing 

A 
B 
C 
D 

APR Zone 
township 
Sheridan 
Easton 
Bushnell 
Douglass 

Non-APR Zone 
township 
Sherman 
Tyrone 
Bowne 
Nelson 

Pairing criteria 

Heavily forested, public lands 
Mixed cover, large rivers, public lands 
Agriculturally dominated 
Agriculture-forest mix, CWD detected 

20 

 
 
 
Camera-trap setup and data collection 

Eighteen infrared cameras (Strike Force HD Pro X®, Browning Trail Cameras, 

Birmingham, AL) were deployed in each of the 8 selected townships. Camera make and model 

were selected to balance cost and trigger speed. To minimize potential bias, camera sites were 

nonbaited (Koerth and Kroll 2000, McCoy et al. 2011, Newbolt et al. 2017) and placed as close 

to the generated GRTS sample locations as possible (Kays et al. 2009). In exceptional 

circumstances cameras were placed within 100 m of the point. In such situations, exact camera 

location was selected to avoid locations with a high risk of theft, open water, road rights-of-

way, close proximity to human dwellings, and to maintain a clear field of view. Cameras were 

oriented north to minimize direct sunlight exposure, false triggers caused by exposure to the 

sun’s rays (Wilton 2021), and observer bias in placement. Cameras were placed on a straight 

tree and secured with a security box, cable, and lock. If no suitable trees were available, a steel 

T-post was used to mount the camera. Cameras were mounted so that the center of the lens 

was 36–41 cm (14–16 inches) above the ground and the horizon was centered in the field of 

view (guidance provided by Moll et al. 2018). The selected camera height was intended to 

detect all age groups of deer and allow overhanging vegetation (e.g., branches) to be reached 

and removed from the field of view. Ground vegetation and debris were cleared 5 m in front of 

the camera to minimize false triggering and allow for an unobstructed field of view.  

Cameras were active for 63 days on 24-hour capture mode with a 5-sec delay, taking a 

burst of 3 photographs per motion-triggered event. Since camera sites were not baited, 

cameras were programed to rapid fire (0.3 sec between each image within a burst) and fast-

motion infrared flash to maximize clear images of mobile deer. Photo data were collected 

21 

during what was considered a 9-week closure period (i.e., no immigration or emigration) from 

15 July to 15 September for four consecutive years (2019–2022). Each camera site was visited 

for maintenance (e.g., check batteries, change memory cards, clear vegetation) approximately 

every two weeks over the duration of the data-collection period. Camera surveys were used to 

create detection histories for each site. If a camera was not functional for some time, these 

occurrences were treated as missing data in the detection history (Furnas et al. 2020). 

All photos were entered into Colorado Parks and Wildlife Photo Warehouse, a Microsoft 

Access application designed to facilitate camera-trap photo processing (Newkirk 2016). Deer 

were counted in each image and classified as Fawns, Does (yearling and adult females), Sub-

legal Males (antlered deer that did not meet the APR criteria), Legal Males (antlered deer that 

met the APR criteria), or Unknown Deer. Deer were classified as Unknown when it was 

impossible to determine the sex and age of an individual (e.g., unable to see head). To minimize 

misidentifications, all photos were processed by two independent observers that received 

species-specific image training (Newbolt and Ditchkoff 2019, Elliot et al. 2022). Photo data was 

considered validated when photo classifications matched between the two observers (e.g., 1 

Doe and 2 Fawns in the photo). If there was a discrepancy on the identification of a deer in an 

image, then a third observer served as a referee. Discrepancies were judged by an experienced 

referee to maintain consistent and accurate classification of photographs (Newbolt and 

Ditchkoff 2019, Elliot et al. 2022). See the Appendix for detailed camera-trap and photo-review 

protocols (Appendix 1A, Appendix 1B, respectively).  

22 

Abundance modeling 

In this study, I used relative abundance of deer as an index, assuming it was functionally 

related to population size. Specifically, I summed site-level abundances to derive an estimated 

total study-area abundance, where total abundance related to the number of deer within the 

total area of all 1.24-km2 effective sampling areas in the study area (e.g., 144 camera sites = 179 

km2 [69 mi2]; Figure 1.2). Hence, my abundance estimates reflect relative abundance, not 

absolute, as I did not infer site-level abundances for areas beyond the total surveyed area (i.e., 

total effective sampling area). Since the larger study included baseline data, and intended to 

look at change over time, the use of relative abundance as an index was deemed sufficient. 

To account for imperfect detection, I estimated population parameters with a closed N-

mixture model (Royle 2004) applied to camera surveys of unmarked deer. As described by Kéry 

and Schaub (2012), I implemented a Bayesian hierarchical framework using software program 

JAGS (Plummer 2003) in program R (version 4.1.2; R Core Team 2021) with the jagsUI package 

(Kellner 2015). I chose this Bayesian approach because of its ease of use for fitting hierarchical 

models and it allowed me to build a custom model that embodied complex ecological processes 

while accounting for uncertainty of population parameters. Essentially, the N-mixture model 

consists of two linked generalized linear models. The first generalized linear model is the 

ecological process. The ecological process yields the latent state and the spatial variation of 

abundance at site 𝑖, 𝑁𝑖, for a group of sites with a mean 𝜆 (Kéry and Schaub 2012). Since 

properly modeling error maximizes the utility of N-mixture models (Joseph et al. 2009), it was 

important to select a mixing distribution that best fit the underlying data. An exploratory data 

analysis was conducted using data from this study and included an evaluation of N-mixture 

23 

models with alternative mixing distributions, including Poisson, zero-inflated Poisson, negative 

binomial, and Poisson lognormal (Appendix 1C). Results from those explorations indicated that 

the Poisson mixing distribution best fit the data (Appendix 1C). Using these results as guidance, 

I opted to use the Poisson distribution in my ecological-process model. To extract more 

information from the data and better allocate variance, I built on the ecological model to 

include township as a random effect on abundance, thus 𝜆 was described as 𝜇𝜆 (i.e., a 

distribution of distributions): 

𝑁𝑖 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 (𝜇𝜆𝑖) 

I assumed site abundances reflected the number of deer within a 1.24-km2 (0.48-mi2) 

circular buffer around each camera-trap site, which represents an effective sampling area 

(Figure 1.2) equivalent to the average summer home range size of a rural female deer (𝑛 = 22) 

in the south-central region of the Lower Peninsula, Michigan (Trudeau et al., unpublished data). 

Agriculture was the dominant land-cover class in the study area and is considered an important 

driver of demographic variation in abundance (Nixon et al. 1991, Nixon et al. 1994, Nixon et al. 

2001) and antler growth (Felix et al. 2002, Strickland and Demarais 2008). Further, exploratory 

data analyses identified agricultural cover as a valuable predictor of abundance (Appendix 1C). 

For these reasons, I included agriculture cover as a covariate in the ecological-process model. I 

calculated the proportion of agricultural cover using effective sampling areas and the National 

Land Cover Database (Dewitz and USGS 2021) land-cover classification layer (30-m2 resolution) 

in ArcPro (ESRI 2020). This approach allowed me to extract values and collapse 3 NLCD land-

cover types (herbaceous, hay/pasture, cultivated crops) into a single agriculture classification. I 

incorporated the effects of the agriculture covariate into the ecological model, associated with 

24 

abundance through a log-link function, and described by a nonlinear relationship with percent 

agricultural cover as a site-specific covariate. Additionally, I included a random intercept 𝜅 into 

the log-link function, which allowed township to act as a random effect on abundance: 

𝑙𝑜𝑔(𝜇𝜆𝑖) =  𝜅(𝑇𝑜𝑤𝑛𝑠ℎ𝑖𝑝𝑖) +  𝛽2(%𝐴𝑔𝑟𝑖𝑐𝑢𝑙𝑡𝑢𝑟𝑒)2 

The second generalized linear model of the N-mixture framework is the observational 

process. The observational process yields the observed counts 𝑦𝑖,𝑗 (given 𝑁𝑖) at site 𝑖 and during 

replicate survey 𝑗, and are described by a binomial distribution with sample size 𝑁𝑖 and 

detection probability 𝑝 (Kéry and Schaub 2012): 

𝑦𝑖,𝑗 | 𝑁𝑖 ~ 𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙 (𝑁𝑖,  𝑝[𝐶𝑜𝑣𝑒𝑟𝑖]) 

Cover data were collected during camera-trap setup and was defined as far cover or the 

majority of cover in a 100-m radius of the camera (open or closed). Note that I included cover in 

the observational-process model as it may be important to the presence and detectability 

components of detection probability. Further, an exploratory data analysis evaluated the value 

of alternative covariates and identified cover (far cover) as important to the detection process 

(Appendix 1C). To incorporate this covariate on detection probability, I used a logit-link 

function, described by a linear relationship with site-specific cover: 

𝑙𝑜𝑔𝑖𝑡(𝑝𝑖) =  𝛼 +  𝛽1(𝐶𝑜𝑣𝑒𝑟𝑖) 

With regards to the Bayesian framework, I assumed vague prior distributions for all 

analyses to express the absence of prior information about estimated parameters. For my 

Markov Chain – Monte Carlo (MCMC) approach, I ran 3 parallel chains for 50,000 iterations, 

discarded the first 3,000 iterations as burn-in, and thinned the remaining iterations by 1 in 5, 

resulting in 28,200 draws of the posterior distribution for inference. Parameters monitored 

25 

included total 𝑁, 𝑝, 𝛼, 𝛽 values, and 𝜅 values. I monitored model convergence by evaluating 

posterior distributions, visual inspection of MCMC trace plots, and using the Gelman-Rubin 

convergence diagnostic (R-hat or 𝑅̂; Gelman 2006).  

(A) 

(B) 

Figure 1.2. Camera-trap study design used to estimate relative abundance of unmarked white-
tailed deer (Odocoileus virginianus) where (A) the effective sampling areas for individual 
cameras are functions of animal movement and survey length, and (B) relative abundance 
measures the number of deer at one camera site compared with another. Relative abundance 
was used as an index assumed to be functionally related to population size. This study produces 
relative abundance estimates for the effective sampling area (green) of independent cameras 
and aggregations of cameras (𝑛 = 18) within each township (orange). Township abundances 
were aggregated to produce a single population estimate. Revised images from Gilbert et al. 
2021. 

26 

 
 
Sensitivity analyses 

I conducted a post hoc sensitivity analysis to evaluate the sensitivity of parameter 

estimates to sampling strategies that modified daily-sampling frequency (i.e., counts per day), 

sampling duration (i.e., number of days in sampling period), and the distribution of camera sites 

(i.e., number of camera sites per township). I simulated these scenarios using my N-mixture 

modeling approach and evaluated the sensitivity of relative abundance, detection probability, 

and model performance to alternative sampling strategies. Sensitivity was calculated as the 

relative change of the output quantity (e.g., relative change of precision). To standardize 

precision of abundance estimates for meaningful comparisons across treatments, I calculated 

the percent coefficient of variation (%CV) by multiplying the quotient of standard deviation (SD) 

divided by the mean (𝑥̅) by 100: 

%𝐶𝑉 = (

SD
𝑥̅

) ∗ 100 

 For my sensitivity analyses I used a subset of validated photo data from the 2019 field 

season. Since I was interested in using the product of this research to detect potential 

population-level changes over time, final sampling approaches recommended will maximize 

precision of relative abundance estimates while considering detection probability and model 

performance. 

Data simulation and model diagnostics 

Since truth was unknown for the deer population in my study, I used a modeling 

approach to explicitly simulate ‘true’ scenarios of deer abundance (i.e., scenarios of known 

abundance). To supplement my sensitivity analysis, simulations allowed me to investigate the 

performance and accuracy of my N-mixture model under alternative-sampling strategies (i.e., 

27 

sampling frequency, sampling duration, camera distribution). For each sampling strategy, I 

generated 50 unique datasets per scenario to capture variability in random draws and produce 

a comparable number of data points. Using program R (version 4.1.2; R Core Team 2021), I 

simulated ‘true’ scenarios of deer abundance as Poisson distributed. The Poisson distribution 

was selected based on recommendations provided by an exploratory data analysis (Appendix 

1C). I also incorporated parameters estimated from empirical data into simulations, including 

mean site abundance by township (random effect), coefficient values for the percent-

agriculture covariate on abundance (𝛽2, 𝛽3), and mean detection probability. For each set of 

simulations, I defined the scenario-specific number of camera sites and counts (e.g., 9 camera 

sites per township and 63 counts per site). 

To enable comparisons among sampling strategies, I used root-mean-square error 

(RMSE) as a metric to evaluate model performance, complemented by relative bias (RB) 

analysis (Duarte et al. 2018). Specifically, I used RMSE as a measure of overall accuracy and RB 

to assess the directionality of biases in model output. I calculated RMSE as the average distance 

between simulated truth and predicted data values by taking the square root of the mean-

squared difference between simulated abundance and predicted abundance (i.e., the square 

root of the variance of the residuals): 

𝑅𝑀𝑆𝐸 = √

2

𝑛
𝑖=1

∑  (𝑁𝑖 − 𝑁̂𝑖)
𝑛

Using RMSE as a model-performance metric allowed me to aggregate the magnitudes of errors 

in predictions into a single measure of predictive power on the same scale as the unit being 

predicted (i.e., site abundance). RMSE values are always non-negative and although unlikely, a 

28 

  
value of zero indicates a perfect fit of the data. Thus, I considered scenarios with lower RMSE 

values as having more predictive power.  

I calculated RB by subtracting simulated abundance (𝑁) from predicted abundance (𝑁̂) 

divided by simulated truth (Doser et al. 2022), for each camera site (𝑖), summed across the total 

number of camera sites (𝑛): 

𝑅𝐵 =  

∑  (𝑁𝑖 −  𝑁̂𝑖)
𝑛
𝑖=1
∑  (𝑁𝑖)

𝑛
𝑖=1

Relative bias values that approximated and were centered around zero represented no bias 

between simulated truth and predicted abundance. Negative and positive RB values indicated 

an under and over estimation of abundance, respectively.  

I estimated parameters for each simulated dataset using my N-mixture modeling 

approach, but since model convergence improved under simulated scenarios, I reduced MCMC 

settings to 12,000 iterations and a burn-in of 2,000 (resulting in 6,000 draws total) to accelerate 

simulations. To further reduce computation time, I used supercomputing resources at Michigan 

State University’s High Performance Computing Center. For each sampling scenario, I obtained 

parameter (𝛽2, 𝛽3, RMSE, RB) summary statistics by integrating the 50 distinct posterior 

distributions and calculating mean and 95% quantile values (Q95%; Doser et al. 2022) from the 

associated 300,000 data points. Sensitivity analyses also incorporated these model-

performance metrics. I monitored coefficient (𝛽2, 𝛽3) and quantile values to determine if 

results were reasonable given the ‘true’ parameter values (i.e., overlapping error).  

29 

 
Daily-sampling frequency 

I evaluated how population parameters were affected by different daily-sampling 

frequencies (i.e., counts per day), including 1, 2, 3, and 4 times per day and at crepuscular 

hours. I accomplished this by systematically sampling within distinct daily time intervals 

throughout the sampling period. Counts were restricted to the maximum number of individuals 

(aggregated by class) observed in a single image, per unit of time (Haus et al. 2019, Zou et al. 

2019). To better align with deer activity, standard time was rescaled to local solar time. For 

daily sampling frequencies 1, 2, 3 or 4 times per day, I divided the day into 1–4 even time 

intervals and sampled within each interval. For example, a daily frequency of 2 generated 2 

samples per day (2 counts), one for the first half of the day and another for the second half of 

the day (solar noon = midday). Crepuscular sampling generated 2 samples per day (2 counts) 

using 2-hr intervals around sunrise and sunset (i.e., 1 hour before and after sunrise and sunset). 

I estimated parameters using my N-mixture abundance modeling approach and summarized 

parameters by mean and 95% Bayesian credible intervals (95% BCI). I concluded that scenarios 

generated different estimates if there was no 95% BCI overlap. 

Sampling duration and camera distribution 

I simulated reductions in sampling intensity by reducing the number of days in the 

sampling period and the number of camera sites distributed. The sampling-duration and 

camera-distribution scenarios were modeled independently from one another. I evaluated the 

sensitivities of these reductions on parameter estimation to determine if subsampling could 

produce sufficient precision. My approach included comparing parameter estimates from 

reduced datasets to parameter estimates from the full dataset. For the sampling-duration 

30 

scenario, I reduced days from the full sampling period (63 days) by 7-day steps to simulate 

sampling durations of 56, 49, 42, and 35 days. Sampling durations did not specifically include 

sequential blocks of days, but instead days were selected at random within the 63-day window 

of the full sampling period (15 July to 15 September). My intent of this random approach was to 

identify sampling durations (i.e., total number of days) that performed well regardless of 

calendar date. For distribution of camera sites, the number of camera sites corresponded to the 

number distributed in each of the 8 townships surveyed (1 township = 93 km2 [36 mi2]). I 

reduced the number of camera sites from 18 by steps of 3 to simulate camera distributions of 

15, 12, and 9 per township. Individual camera sites were randomly selected from the 18 pre-

established sites within each township. I opted to choose camera sites randomly rather than 

relying on specific data metrics (e.g., land cover) to capture an unbiased snapshot of 

populations and ensure alignment with model assumptions (e.g., equal detectability). To 

capture variability in random-sampling approaches, I generated 10 unique datasets for each 

sampling-duration and camera-distribution scenario (e.g., 10 random datasets for the 35-day 

treatment). Additionally, I replicated the 100%-data scenario (63 days with 18 sites per 

township) 10 times to produce a comparable number of datapoints to the treatments (𝑛 = 

282,000). I simulated random datasets and estimated parameters using my N-mixture 

abundance modeling approach. Final count data were determined using the best performing 

daily-sampling frequency identified during my initial analysis. For each sampling scenario, I 

obtained parameter summary statistics by integrating the 10 distinct posterior distributions and 

calculating mean and 95% quantiles (Q95%; Doser et al. 2022) from the associated 282,000 

31 

datapoints. I concluded that scenarios generated different estimates if there was no Q95% 

overlap. 

RESULTS 

Data collection and processing 

The data subset from 2019 included photo data from 144 camera traps deployed for 63 

days, which resulted in a total survey effort of 8,772 trap days. Including camera operation 

failures, average camera deployment period was 61 days (SD = 5.9; range = 27–63 days). 

Twenty-four cameras were not fully operational during deployment due to memory cards filling 

up (from false triggering), camera malfunctioning, and vandalism. Camera density was 

approximately 1 per 5.2 km2 (1 per 2.0 mi2) within each township and cameras averaged 1.4 km 

(SD = 0.7) between nearest neighbor camera sites. 

Camera traps collected 797,407 images during the 2019 survey period, including 

275,794 images with deer in the field of view (≥1 deer in each image). The APR Zone accounted 

for 414,626 images, including 155,111 with deer. The Non-APR Zone accounted for 382,781 

images, including 120,683 with deer. All but 5 cameras detected deer throughout the sampling 

period. Most deer photos included Does in the field of view (𝑛 = 146,145; Table 1.2). With the 

exception of Unknown Deer (𝑛 = 16,161), Legal Males were photographed the least (𝑛 = 20,039; 

Table 1.2). Deer were photographed most frequently around sunrise and sunset, with most 

detections occurring between 0.2 and 0.35 (24-hr time rescaled 0–1; Figure 1.3).

32 

Table 1.2. Summary of white-tailed deer (Odocoileus virginianus) image classifications by sex 
and age class, zone, and study area. Note that a single image could include multiple 
classifications (e.g., doe and fawn in image). Images were collected using a camera-trap study 
design in the south-central Lower Peninsula of Michigan, USA, 2019.  

Photo classification 
Doe 
Fawn 
Sub-legal Male 
Legal Male 
Unknown Deer 

APR Zone 
84,205 
57,416 
24,649 
14,404 
9,627 

Non-APR Zone 
61,940 
54,456 
15,392 
5,635 
6,534 

Study area total 
146,145 
111,872 
40,041 
20,039 
16,161 

Figure 1.3. White-tailed deer (Odocoileus virginianus) diel activity pattern of each sex-age class 
(Doe, Fawn, Legal Male, Sub-legal Male, Unknown Deer) during 15 July–15 September 2019 
camera-trap surveys in the south-central Lower Peninsula, Michigan. Deer detected (≥ 1 
individual) in photographs were used as an index for activity. Standard time was rescaled to 
local solar time (0–1). Dashed vertical lines indicate sunrise and sunset times.

33 

 
 
 
 
 
Abundance modeling  

For all sampling scenarios with empirical data, N-mixture models converged with 𝑅̂ 

values <1.1 (Gelman and Rubin 1992) and adequate mixing based on visual inspection (Gelman 

2006). Similarly, successful convergence was achieved with simulated datasets. Simulated 

datasets also yielded estimates of 𝛽2 and 𝛽3 coefficients comparable (i.e., overlapping error) to 

those estimated with the empirical data. Collectively, these results indicated that the MCMC 

sampler reached stationary distributions and that the predictor of abundance (% agriculture) 

performed consistently among sampling scenarios.  

Daily-sampling frequency 

The sensitivity analysis indicated that selected daily-sampling frequency had a significant 

effect on most parameter estimates. For frequencies 1, 2, 3, and 4 per day, I found that mean 

relative abundance increased as daily-sampling frequency increased (Figure 1.4). Crepuscular 

sampling produced significantly lower relative abundance estimates than all other frequencies 

(x̅ = 1,374; 95% BCI = 1,286–1,471; Figure 1.4). The precision of abundance estimates were 

relatively insensitive to changes in sampling frequency with CVs approximating 3% for all 

scenarios (Figure 1.4). I found a negative relationship between daily-sampling frequency and 

mean detection probability, with detection probability decreasing as sampling frequency 

increased (Figure 1.5). The 1-per-day frequency produced significantly higher detection 

probabilities than all other scenarios (x̅  = 0.073; 95% BCI = 0.062–0.085; Figure 1.5). Apart from 

the 1-per-day frequency, crepuscular sampling produced detection probabilities (x̅  = 0.028; 

95% BCI = 0.023–0.034) similar to all other scenarios (Figure 1.5). 

34 

My sensitivity analysis also indicated that selected daily-sampling frequency influenced 

model performance. The accuracy of the abundance estimator was highest (lowest RMSE) with 

the 1-per-day (x̅  = 3.07; 95% BCI = 2.02–5.91) and crepuscular (x̅  = 2.54; 95% BCI = 1.83–4.69) 

sampling strategies and lowest (highest RMSE) with 3 per day (x̅  = 3.60; 95% BCI = 2.12–8.48; 

Figure 1.6). On average, all sampling frequencies produced relatively unbiased abundance 

estimates (i.e., RB approximated and centered around 0; Figure 1.6). However, error intervals 

(Q95%) suggested slight underestimation, especially with the 3-per-day sampling frequency 

(Figure 1.6).

35 

Figure 1.4. Estimates of (A) relative white-tailed deer (Odocoileus virginianus) abundance and (B) associated percent coefficient of 
variation (%CV) by alternative daily-sampling frequencies (i.e., counts per day). Relative abundance was used as an index and 
assumed to be functionally related to population size. Crepuscular sampling generated 2 counts per day using 2-hr intervals around 
sunrise and sunset. Error bars indicate a 95% Bayesian credible interval. Estimates were obtained using an N-mixture modeling 
approach applied to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.  

36 

 
 
Figure 1.5. Mean white-tailed deer (Odocoileus virginianus) detection probability by alternative 
daily-sampling frequencies (i.e., counts per day). Crepuscular sampling generated 2 counts per 
day using 2-hr intervals around sunrise and sunset. Error bars indicate a 95% quantile interval. 
Estimates were obtained using an N-mixture modeling approach applied to a camera-trap study 
design in the south-central Lower Peninsula of Michigan, USA, 2019. 

37 

 
 
Figure 1.6. (A) Root-mean-square error and (B) relative bias of white-tailed deer (Odocoileus virginianus) abundance estimates by 
alternative daily-sampling frequencies (i.e., counts per day). Error bars indicate a 95% quantile interval. The dashed, orange 
horizontal line represents zero or no bias between simulated truth and predicted abundance. Crepuscular sampling generated 2 
counts per day using 2-hr intervals around sunrise and sunset. Estimates were obtained using empirical and simulated data with an 
N-mixture modeling approach applied to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.

38 

 
 
Sampling duration 

The sensitivity analysis with the 1-per-day sampling frequency indicated that sampling 

duration had a significant effect on relative abundance estimates. I found a positive relationship 

between the number of days in the sampling period and relative abundance (Figure 1.7). Both 

the 56-day (x̅ = 1,956; Q95% = 1,828–2,094) and 63-day (x̅ = 2,046; Q95% = 1,920–2,181) 

scenarios produced relative abundance estimates significantly higher than the 35-day scenario 

(x̅ = 1,618; Q95% = 1,459–1,796; Figure 1.7). Further, I found that precision improved (i.e., %CV 

decreased) with more days sampled with a CV ranging from 5.41% (35-day scenario) to 3.26% 

(63-day scenario; Figure 1.7). I found an inverse relationship between the number of days in the 

sampling period and mean detection probability (Figure 1.8). Mean detection probabilities 

ranged from 0.074 (63-day scenario; Q95% = 0.062–0.086) to 0.092 (35-day scenario; Q95% = 

0.077–0.108) and were comparable among all scenarios (Figure 1.8).  

My sensitivity analysis with the 1-per-day sampling frequency also indicated that 

sampling duration had a slight influence on the accuracy of the abundance estimator. 

Specifically, I found that model error (RMSE) was the highest with the 56-day scenario (x̅ = 3.13; 

Q95% = 2.00–6.63; Figure 1.9). The model produced relatively unbiased abundance estimates 

across all scenarios (i.e., RB approximated and centered around 0) with some higher 

underestimation occurring with the 56-day and 63-day scenarios (Figure 1.9). 

39 

 
Figure 1.7. Estimates of (A) relative white-tailed deer (Odocoileus virginianus) abundance and (B) associated percent coefficient of 
variation (%CV) by number of days in sampling period. Relative abundance was used as an index and assumed to be functionally 
related to population size. Counts were restricted to the maximum number of individuals observed in a single image per day (daily-
sampling frequency = 1). Error bars indicate a 95% quantile interval. Estimates were obtained using an N-mixture modeling approach 
applied to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.

40 

 
 
Figure 1.8. Mean white-tailed deer (Odocoileus virginianus) detection probability by number of 
days in sampling period. Counts were restricted to the maximum number of individuals 
observed in a single image per day (i.e., a daily-sampling frequency of 1). Error bars indicate a 
95% quantile interval. Estimates were obtained using an N-mixture modeling approach applied 
to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.

41 

 
 
Figure 1.9. (A) Root-mean-square error and (B) relative bias of white-tailed deer (Odocoileus virginianus) abundance estimates by 
number of days in sampling period. Counts were restricted to the maximum number of individuals observed in a single image per 
day (daily-sampling frequency = 1). Error bars indicate a 95% quantile interval. The dashed, orange horizontal line represents zero or 
no bias between simulated truth and predicted abundance. Estimates were obtained using empirical and simulated data with an N-
mixture modeling approach applied to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.

42 

 
 
Camera distribution 

I used a 1-per-day sampling frequency and found that relative abundance estimates 

were sensitive to modifications in camera distribution. Relative abundance estimates increased 

as the number of sites increased, and most scenarios were significantly different from one 

another (Figure 1.10). The 9-site scenario produced the least precise mean relative abundance 

estimate (8.53%) with a CV 2.6 times greater than the 18-site scenario (3.26%; Figure 1.10). 

However, I found that mean detection probability was relatively insensitive to changes of 

camera distribution and approximated 0.07 for all scenarios (Figure 1.11).  

The sensitivity analysis with a 1-per-day sampling frequency also indicated that camera 

distribution influenced model performance. The accuracy of the abundance estimator grew 

poorer (i.e., higher RMSE) for camera distributions less than 18 sites (x̅  = 2.97; Q95% = 1.97–

5.75) and was poorest with the 12-site scenario (x̅  = 3.78; Q95% = 2.09–10.68; Figure 1.12). All 

camera distributions produced relatively unbiased abundance estimates (i.e., RB approximated 

and centered around 0), but the 18-site scenario had the least variable estimates (x̅  = -0.01; 

Q95% = -0.35–0.25, Figure 1.12). 

43 

 
Figure 1.10. Estimates of (A) relative white-tailed deer (Odocoileus virginianus) abundance and (B) associated percent coefficient of 
variation (%CV) by number of camera sites. Relative abundance was used as an index and assumed to be functionally related to 
population size. The number of camera sites corresponds to the number of camera sites distributed in each of the 8 townships 
surveyed (1 township = 93 km2 [36 mi2]). Counts were restricted to the maximum number of individuals observed in a single image 
per day (daily-sampling frequency = 1). Error bars indicate a 95% quantile interval. Estimates were obtained using an N-mixture 
modeling approach applied to a camera-trap study design in the south-central Lower Peninsula of Michigan, USA, 2019.

44 

 
 
Figure 1.11. Mean white-tailed deer (Odocoileus virginianus) detection probability by the 
number of camera sites used. The number of camera sites corresponds to the number of 
camera sites in each of the 8 townships surveyed (1 township = 93 km2 [36 mi2]). Counts were 
restricted to the maximum number of individuals observed in a single image per day (i.e., a 
daily-sampling frequency of 1). Error bars indicate a 95% quantile interval. Estimates were 
obtained using an N-mixture modeling approach applied to a camera-trap study design in the 
south-central Lower Peninsula of Michigan, USA, 2019.

45 

 
Figure 1.12. (A) Root-mean-square error (RMSE) and (B) relative bias of white-tailed deer (Odocoileus virginianus) abundance 
estimates by number of camera sites. The number of camera sites corresponds to the number of camera sites in each of the 8 
townships surveyed (1 township = 93 km2 [36 mi2]). Error bars indicate a 95% quantile interval. The dashed, orange horizontal line 
represents zero or no bias between simulated truth and predicted abundance. Estimates were obtained using empirical and 
simulated data with an N-mixture modeling approach applied to a camera-trap study design in the south-central Lower Peninsula of 
Michigan, USA, 2019.

46 

 
DISCUSSION 

In this study, I presented an assessment of sampling strategies for N-mixture models to 

assist camera-trap study designs for estimating deer abundance. This included a post-hoc 

methodological assessment of different treatments of sampling frequency, sampling duration, 

and camera distribution. To my knowledge, this is the first sensitivity analysis of sampling 

strategies of free-ranging deer with camera traps and an N-mixture model. My results 

supported my hypothesis that each sampling strategy could balance precision of relative 

abundance estimates with high detection probability and model performance. 

First, I found that the precision of abundance estimates was relatively insensitive to 

modifications in sampling frequency. However, among scenarios that modified sampling 

frequency, sampling duration, and camera distribution, I found detection probability was most 

sensitive to modifications in sampling frequency. The 1-per-day frequency provided relatively 

precise and accurate abundance estimates with the lowest amount of bias (Figure 1.4, Figure 

1.6). Further, the 1-per-day frequency produced detection probabilities significantly higher than 

other frequency scenarios (Figure 1.5). For these reasons, the 1-per-day sampling strategy was 

selected as best performing and was used for subsequent analyses as a method for counting 

deer. Moreover, I found scenarios that decreased the sampling duration or reduced camera 

distribution compromised the precision of the results, thus were deemed inadequate for the 

broader scope of my study. 

I found that the precision of abundance estimates was more sensitive to modifications 

in sampling duration than sampling frequency (Figure 1.4, Figure 1.7). Of the sampling-duration 

scenarios, the 63-day scenario produced the most precise (CV = 3.3%; Figure 1.7) and relatively 

47 

 
 
 
accurate abundance estimates with the lowest degree of bias (x̅ = -0.01, Q95% = -0.35–0.24; 

Figure 1.10), thus was identified as the best performing sampling duration. Despite having 

similar detection probabilities among scenarios (Figure 8), the 63-day scenario (maximum 

duration) produced a significantly different mean relative-abundance estimate 1.26 times 

higher and 0.40 times more precise than the 35-day scenario (minimum duration; Figure 1.7). 

These differences were likely attributed to differences in sample size, with shorter sampling 

durations less likely to detect higher counts of deer and thus not representative of the 

population of interest over the period of study. Keever et al. (2017) evaluated sampling 

duration and obtained reliable population estimates of a known, enclosed white-tailed deer 

population (174 ha) in as little as 5 days. It is worth noting that shorter surveys could help 

alleviate any privacy concerns the public may have regarding cameras on public land (R. Campa, 

Michigan State University, personal communication). Shorter surveys can also substantially 

reduce survey costs, but free-ranging deer with potentially more variable detection 

probabilities showed that reductions in sampling duration also reduced precision.  

As suggested by the 63-day scenario, longer surveys can capture a more representative 

sample that better reflects characteristics of a free-ranging population during the summer 

season in the south-central Lower Peninsula of Michigan. However, sampling deer more than 

63 days in this system would not be appropriate because of a high likelihood of violating the N-

mixture model’s population closure assumption. The 63-day sampling duration corresponded to 

summer months during the post-fawning period when large-scale deer movements are limited 

(Beier and McCullough 1990, Rosenberry et al. 1999, Nixon et al. 2007, Long et al. 2008, Skuldt 

et al. 2008, Hiller et al. 2009), which was confirmed by GPS-collar data from deer in the area 

48 

(Trudeau et al., unpublished data). Further, shorter sampling periods may lead to small sample 

sizes of rare animals (e.g., Legal Males in this study system) or fail to detect them altogether (Si 

et al. 2014, Kays et al. 2020). For long surveys where closure violation is a concern, an extension 

of the N-mixture model could be implemented to relax the assumption and produce an open 

population model (e.g., Dail and Madsen 2011).  

Among the scenarios that modified sampling frequency, sampling duration, and camera 

distribution, I found precision of relative abundance estimates were most sensitive to the 

number of camera sites (Figure 1.4, Figure 1.7, Figure 1.10). These were comparable with 

previous research by Schlichting et al. (2020), where the authors demonstrated that increasing 

the number of camera sites used for estimating wild pig populations improved precision of 

estimates. Also consistent with their findings, the mean detection probability from my analysis 

was relatively insensitive to changes of camera distribution, and uncertainty grew as sites 

decreased. As expected, I found that relative abundance estimates decreased as the number of 

camera sites decreased. This relationship can be explained by a reduced geographic area 

covered by the effective sampling areas, which led to a corresponding alteration in the 

population-level of inference (i.e., total abundance associated with a smaller geographic area). 

Overall, the 18-camera-site scenario produced the most precise abundance estimates of all 

camera-distribution scenarios (CV = 3.26%; Figure 1.10). Further, the 18-camera-site scenario 

produced the most accurate abundance estimates with the lowest RMSE (x̅  = 2.97; Q95% = 

1.97– 5.75) and RB (x̅  = -0.01; Q95% = -0.35–0.25, Figure 1.12). Given these results, the 18-

camera-site scenario was considered the best performing camera distribution.  

49 

 
Although precision and accuracy increased with more camera sites, I do not recommend 

camera distributions >18 sites per township (1 per 5.2 km2 [1 per 2.0 mi2]) in this study system. 

Higher camera densities would have a higher chance of violating the assumption of site 

independence and detection of an individual animal at multiple sites within a sampling period 

(i.e., violation of the closure assumption; Royle 2004). Violating this assumption could result in 

double counting individuals and consequently, abundance estimates that are biased high. As a 

standard practice in camera-trapping studies, I calculated a 1.24-km2 (0.48 mi2) effective 

sampling area based on average home range size (Suwanrat et al. 2015, Wilton 2021) using data 

from GPS-collared deer in the area (𝑛 = 22 rural female deer; Trudeau et al., unpublished data). 

The effective sampling areas for individual cameras are functions of both animal movement and 

survey length (Gilbert et al. 2021). Spacing among camera traps must be large enough so that 

the effective sampling areas do not overlap. This issue can be particularly challenging in 

situations where sites are randomly selected on private lands and camera densities are high. 

Studies targeting rare animals may also benefit from maximum camera densities, provided that 

model assumptions are met. This sampling approach may increase animal detections, which is 

particularly pertinent as N-mixture models can perform poorly with small sample sizes and low 

detection probabilities (Royle 2004, Couturier et al. 2013, Veech et al. 2016, Barker et al. 2018). 

Further, reducing the distribution of cameras could affect the abundance estimates of sex-and-

age classes due to variations in home range size and susceptibility to photographic capture 

(Jacobson et al. 1997, Weckel et al. 2011). 

Using the best performing sampling strategies (daily-sampling frequency = 1 per day; 

sampling duration = 63 days; camera distribution = 18 sites per township) I estimated a 3.26% 

50 

 
CV, highlighting the N-mixture model’s ability to produce relative abundance estimates with 

high precision. A CV <25% is often considered sufficient for rough wildlife management 

decisions and <12.8% for precise management (Skalski et al. 2005). Compared with other 

similar studies, my results included an estimated precision that was higher than previously 

recorded in the literature. For example, Haus et al. (2019) estimated a CV as low as 12.3% for a 

14-day survey of a free-ranging deer population using camera traps and an N-mixture model; 

and Keever et al. (2017) estimated a CV consistently around 20% for a 7-day survey of a semi-

captive deer population. It is worth noting that both studies utilized bait to improve 

detectability. Haus et al. (2019) did not evaluate accuracy of their abundance estimates 

whereas Keever et al. (2017) used number of known, marked individuals to validate the 

accuracy of their results. The more precise abundance estimates in my study were likely the 

result of a larger sample size associated with a longer sampling period (63 days). Further, my 

simulation results validated the abundance estimator’s ability to produce relatively accurate 

and unbiased estimates. Although longer surveys may improve precision, large sample sizes 

may not be feasible for some studies due to budget or logistical constraints. A potential 

alternative approach to improving precision of parameter estimates is implementing a multi-

species model to leverage shared information (Yamura et al. 2012, Gomez et al. 2017, Moral et 

al. 2018). Similarly, if multiple years of data are available, a year-stratified approach may also 

leverage shared information (Kéry and Royle 2021). Although promising, these frameworks may 

require more data and can be more complex and computationally intensive than single-species 

or single-season models.  

51 

As confirmed in this study, the human effort required to manage and process camera-

trap data can be substantial (Price Tack et al. 2016) and even exceeded that of the fieldwork 

involved (Table 1.3). Altogether, the collection, management, and processing of image data 

required an estimated 4,700 person-hours of work in a single season (Table 1.3). This is a 

conservative measure and pertains to the work conducted after the study design phase and 

before the analysis phase of the study, otherwise considered the photo collection and 

processing phase. This high level of effort is concerning and may not be sustainable for other 

camera-trap studies, which should consider novel ways to reduce such labor requirements (e.g., 

artificial-intelligence approaches for image processing; see Vélez et al. 2023 for review of 

platforms). A large portion of photo-processing time was spent reviewing irrelevant images, 

including images without animals (i.e., empty images). Excluding time periods when target 

species are least active would reduce irrelevant or empty images. Interestingly, I found a bulk of 

non-deer photos (comprised of mostly empty images) occurring midday and peaking at solar 

noon (Figure 1.13). Field records indicated a pattern of vegetation movement or the interaction 

of solar radiation and shadow movement triggering cameras midday (Wilton 2021), although it 

is worth noting that these phenomena would be dependent on the local conditions of a site 

(Welbourne et al. 2016). For example, more false-trigger events may occur when vegetation is 

growing or when there is a lack of canopy cover and an interaction between isolation and 

shadow movement (Iannarilli et al. 2021). Excluding the midday period when deer are least 

active (an hour past sunrise to an hour before sunset) from data collection would translate to 

an estimated 61% reduction in images (~490,000 images) and an associated 57% reduction in 

data management and processing labor (~1,500 person-hours). Although this approach has 

52 

 
promise for labor reduction, the sensitivity of parameter estimates still need to be critically 

evaluated before application. Alternatively, while computationally intensive, all images could be 

initially reviewed by machine-learning applications designed to remove empty images (e.g., 

MegaDetector; Beery et al. 2019).  

My findings also highlighted the importance of sampling relevant to animal activity and 

its potential for photo processing reduction. Given knowledge of white-tailed deer diel activity 

patterns (Beier and McCullough 1990, Rouleau et al. 2002, Webb et al. 2010), it was not 

surprising that deer detections peaked during crepuscular hours (Figure 1.3). My intentions of 

the crepuscular-sampling frequency were to capture peak activity (i.e., maximize detection 

probability), minimize the possibility of double counting individuals, and reduce the amount of 

photo data. It was surprising to find that the crepuscular-sampling frequency produced similar 

detection probabilities to most scenarios (2, 3, and 4 per day) but significantly lower relative 

abundance estimates (Figure 1.4). The later result was likely due to missed counts occurring 

outside of the crepuscular sampling windows (Appendix 1C). Although deer were most active at 

crepuscular hours, larger aggregations of deer may be detected during other periods. This 

notion is further supported by the abundance estimator’s lowest error (RMSE) with crepuscular 

sampling (RMSE is sensitive to outliers; Figure 1.6). One suggestion to capture these higher 

counts would be to increase the length of the crepuscular periods subsampled. For example, 

increasing the crepuscular period to sunrise ± 2 hrs and sunset ± 2 hours. Keever et al. (2017) 

found that using only nighttime data resulted in accurate estimates of a known population size. 

However, studies seeking to characterize animals by distinctive features (e.g., sex, age, antler 

53 

points) should consider potential limitations of using photo data from low-light periods 

(Newbolt and Ditchkoff 2019).  

This study aimed to disentangle strengths and weaknesses of alternative camera-trap 

sampling strategies, and low detectability was recognized as a common limitation among 

scenarios evaluated. Specifically, mean detection probability was <0.10 among all scenarios for 

all 3 sampling strategies. As demonstrated by my results (Figure 1.4; Figure 1.5), lower 

detection probabilities can inflate abundance estimates when using N-mixture models (Dénes 

et al 2015, Dennis et al. 2015). Low detection probabilities were likely driven by a high 

occurrence of zero counts, with datasets becoming more saturated with zeros at higher 

sampling frequencies and longer sampling durations. Many studies estimate detection 

probabilities <0.5 (Kellner and Swihart 2014), but Duarte et al. (2018) found that their Poisson 

N-mixture model performed best when detection probability was ≥0.30 (and statistical 

assumptions were met). My observed increase in detectability when decreasing daily-sampling 

frequency from 2 to 1 per day supports a coarser sampling frequency as a viable option for 

increasing detection probability. However, the empirical data raises some concern regarding 

the detectability of deer when using unbaited, randomly placed camera traps, even when the 

target species is considered highly visible and relatively abundant (MDNR 2016). Adequate 

detection probabilities are important as they increase the chances of capturing all individuals in 

the population, providing a more representative sample and a stronger foundation for 

inference. Further, relatively high detection probabilities may allow for decreased sampling 

intensity and resource savings. For example, higher detectability may reduce the number of 

camera sites required to produce reliable estimates (MacKenzie and Royle 2005, Maffei et al. 

54 

 
2011, Guillera-Arroita and Lahoz-Monfort 2012). To achieve higher detection probabilities, 

future work should consider the application of a weekly or monthly sampling frequency. For 

example, Zou et al. (2019) addressed the issue of low detectability of pheasants by using month 

as a replicate (i.e., monthly sampling frequency). An alternative and common approach to 

increasing detection probability in camera-trap surveys is the use of bait or non-random camera 

placement (e.g., on trails). However, behavioral responses to baiting (Koerth and Kroll 2000, 

McCoy et al. 2011, Newbolt et al. 2017) and potential differences of animal activity on trails 

(Kayes et al. 2009) may violate the N-mixture model’s assumption of equal detectability. 

Another potential limitation of this study was the possible violation of the N-mixture 

model’s assumption of equal detectability. Past camera-trap studies have shown that detection 

probability can vary among sex-and-age classes of deer (Jacobson et al. 1997, Koerth and Kroll 

2000, McCoy et al. 2011, Weckel et al. 2011, Keever et al. 2017). By modeling abundance with 

counts aggregated by sex-and-age class, it was likely that I masked variations in detectability 

among classes. Failure to meet the equal-detectability assumption can result in biased 

parameter estimates. In such cases, it is advisable to interpret the estimates as relative 

abundance measures (Barker et al. 2018, Gilbert et al. 2021), however this aligns with the 

original intent of my abundance modeling efforts. 

To conclude, this study demonstrates that N-mixture models can perform well for the 

precise relative abundance estimation of white-tailed deer in the south-central Lower Peninsula 

of Michigan, based on the modeling of camera-trap count data. However, N-mixture models 

should be paired with careful consideration of assumptions and sampling strategies as large 

uncertainty in parameter estimates can obscure signals of change in abundance over time. 

55 

 
Although this study focused on white-tailed deer, the general approach could be applied to 

many terrestrial wildlife species, providing an explicit method to test for the required sampling 

frequency, camera duration, and camera distribution for N-mixture modeling. More specifically, 

I encourage study-specific sensitivity analyses to identify efficient and effective sampling 

strategies for long-term monitoring projects from pilot or initial datasets. Shorter sampling 

durations and lower camera distributions can facilitate resource savings, but they can also 

compromise the precision of relative abundance estimates, with the latter being most sensitive 

to manipulation. Precise and reliable abundance estimates may require a high amount of 

financial and human resources, but there are viable ways to improve efficiency. For example, 

surveys could exclude time periods when animals are least active (e.g., midday for deer) or 

machine-learning platforms could be used to accelerate processing of photo data (e.g., 

MegaDetector; Beery et al. 2019). For studies seeking to improve detection probability, coarser 

sampling frequencies (e.g., weeks, months) are recommended. Lastly, simulations are integral 

to understanding a hierarchical model’s ability to produce accurate and unbiased parameter 

estimates (Kéry and Schaub 2012, Kéry and Royle 2016, 2021). My diagnostic results were 

encouraging as they highlighted the N-mixture model’s ability to generate reasonably reliable 

estimates, irrespective of data modifications. Despite the value of diagnostic tests, many 

studies fail to report any validation of their hierarchical models, thus potentially undermining 

their statistical inference, reliability, and compatibility with open science practices (DiRenzo et 

al. 2023). Therefore, practitioners are strongly encouraged to implement simulation-based 

validation of their models before results are used to inform management and conservation 

decision making.

56 

Table 1.3. A breakdown of estimated person-hours required to collect, manage, and process a 
single season of white-tailed deer (Odocoileus virginianus) camera-trap data. Camera-trapping 
included 144 cameras that collected 797,407 images over a 63-day sampling period in the 
south-central Lower Peninsula of Michigan, USA, 2019. Estimates do not include person-hours 
associated with study-design labor or analyses.  

Employees 
4 
2 
14 

Labor 
Fieldworka 
Data managementb 
Photo processingc 
aFieldwork includes obtaining landowner permission, deploying cameras, biweekly camera 
checks, and camera retrieval. 
bData management includes uploading images from SD cards, transferring files, reformatting 
files, backing up data, and deleting data files. 
cPhoto processing includes classifying images (each image reviewed by 2 employees) and 
verifying discrepancies between classifications. Photo reviewers spent approximately 1 hour 
to review 1,000 photos and 1 hour to judge 300 discrepancies. 

Person-hours 
2,000 
800 
1,900 

57 

 
Figure 1.13. Distribution of images that included white-tailed deer (Odocoileus virginianus; 
Deer) in and images that did not (Not Deer) by time of day. Standard time was rescaled to local 
solar time (0–1). Images were collected during 15 July–15 September 2019 camera-trap surveys 
in the south-central Lower Peninsula, Michigan. Brown bins correspond to images with deer 
and tan bins to images without deer; and distributions overlay one another with transparency. 
Dashed boxes indicate defined crepuscular periods (sunrise ± 1 hr and sunset ± 1 hr). 

58 

 
 
 
LITERATURE CITED 

Albert, Dennis A. 1995. Regional landscape ecosystems of Michigan, Minnesota, and Wisconsin: 

a working map and classification. Gen. Tech. Rep. NC-178. St. Paul, MN:  U.S. Department 
of Agriculture, Forest Service, North Central Forest Experiment Station. Northern Prairie 
Wildlife Research Center Home Page. 
http://www.npwrc.usgs.gov/resource/1998/rlandscp/rlandscp.htm (Version 03JUN98). 

Barão-Nóbrega, J. A. L., M. González-Jaurégui, and R. Jehle. 2022. N-mixture models provide 

informative crocodile (Crocodylus moreletii) abundance estimates in dynamic 
environments. PeerJ 10:e12906. 

Barker, R. J., M. R. Schofield, W. A. Link, and J. R. Sauer. 2018. On the reliability of N-mixture 

models for count data. Biometrics 74:369–377. Wiley-Blackwell. 

Barnes, B.V. and W.H. Wagner. 2004. Michigan trees: a guide to the trees of the Great Lakes 

Region. University of Michigan Press. Ann Arbor, Michigan, USA. 

Beery, S., D. Morris, and S. Siyu. 2019. Efficient pipeline for camera trap image review. arXiv 

  preprint arXiv:1907.06772. beery2019efficient. 

Beier, P., and D. R. McCullough. 1990. Factors influencing white-tailed deer activity patterns 

and habitat use. Wildlife Monographs 3–51. 

Belant, J. L., F. Bled, C. M. Wilton, R. Fyumagwa, S. B. Mwampeta, and D. E. Beyer. 2016. 

Estimating lion abundance using N-mixture models for social species. Scientific Reports 
6:35920. 

Brack, I. V., A. Kindel, L. F. B. de Oliveira, and J. J. Lahoz-Monfort. 2023. Optimally designing 

drone-based surveys for wildlife abundance estimation with N-mixture models. Methods 
in Ecology and Evolution 00:1–13. DOI: 10.1111/2041-210X.14054. 

Burton, A. C., E. Neilson, D. Moreira, A. Ladle, R. Steenweg, J. T. Fisher, E. Bayne, and S. Boutin. 
2015. Wildlife camera trapping: a review and recommendations for linking surveys to 
ecological processes. Journal of Applied Ecology 52:675–685. 

Christensen, S. A., M. T. Farr, and D. M. Williams. 2021. Assessment and novel application of N-

mixture models for aerial surveys of wildlife. Ecosphere 12:e03725. 

Costa, A., A. Romano, and S. Salvidio. 2020. Reliability of multinomial N-mixture models for 

estimating abundance of small terrestrial vertebrates. Biodiversity and Conservation 
29:2951–2965. 

Couturier, T., M. Cheylan, A. Bertolero, G. Astruc, and A. Besnard. 2013. Estimating abundance 

and population trends when detection is low and highly variable: a comparison of three 
methods for the Hermann’s tortoise. The Journal of Wildlife Management 77:454–462. 

59 

Dail, D., and L. Madsen. 2011. Models for estimating abundance from repeated counts of an 

open metapopulation. Biometrics 67:577–587. 

Dénes, F. V., L. F. Silveira, and S. R. Beissinger. 2015. Estimating abundance of unmarked animal 
populations: accounting for imperfect detection and other sources of zero inflation. 
Methods in Ecology and Evolution 6:543–556. 

Dennis, E. B., B. J. Morgan, and M. S. Ridout. 2015. Computational aspects of N-mixture models. 

Biometrics 71:237–246. 

Dewitz, J., and U.S. Geological Survey. 2021. National Land Cover Database (NLCD) 2019 

Products (ver. 2.0, June 2021): U.S. Geological Survey data release, 
https://doi.org/10.5066/P9KZCM54. 

DeYoung, C.A., 2011. Population dynamics. Pages 160–193 in D. G. Hewitt, editor. Biology and 

Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

Diefenbach, D. R., W. M. Know, and C. S. Rosenberry. 2021. The future of managing ungulate 
species: white-tailed deer as a case study. Pages 327–339 in K. L. Pope and L. A. Powell, 
editors. Harvest of Fish and Wildlife: New Paradigms for Sustainable Management. CRC 
Press, Boca Raton, Florida, USA. 

DiRenzo, G. V., E. Hanks, and D. A. W. Miller. 2023. A practical guide to understanding and 
validating complex models using data simulations. Methods in Ecology and Evolution 
14:203–217. 

Doser, J. W., W. Leuenberger, T. S. Sillett, M. T. Hallworth, and E. F. Zipkin. 2022. Integrated 
community occupancy models: a framework to assess occurrence and biodiversity 
dynamics using multiple data sources. Methods in Ecology and Evolution 13:919–932. 

Duarte, A., M. J. Adams, and J. T. Peterson. 2018. Fitting N-mixture models to count data with 
unmodeled heterogeneity: bias, diagnostics, and alternative approaches. Ecological 
Modelling 374:51–59. 

Elliott, J. R., Newbolt, C. H., Dunning, K. H., Gulsby, W. D., and S. S. Ditchkoff. 2022. Training and 
experience increase classification accuracy in white-tailed deer camera surveys. Wildlife 
Research. 

Environmental Protection Agency [EPA]. 2010. Level III and IV ecoregions of Michigan. 

<https://gaftp.epa.gov/EPADataCommons/ORD/Ecoregions/mi/mi_eco.pdf>. Accessed 
October 2023. 

Environmental Systems Research Institute [ESRI] 2020. ArcGIS Pro: 2.7.1. Redlands, California, 

USA. 

60 

Felix, A. B., H. Campa III, K. F. Millenbah, S. Panken, S.R. Winterstein, and W.E. Moritz. 2002. 
Applications of using a landscape scale model to quantify white-tailed deer habitat 
potential in Michigan. Pages 107-114 in Eleftherios Hadjisterkotis, editor. Proceedings of 
the XXV International Congress of the International Union of Game Biologists and the IX 
International Symposium Perdix. Cyprus. 

Ficetola, G. F., B. Barzaghi, A. Melotto, M. Muraro, E. Lunghi, C. Canedoli, E. Lo Parrino, V. 
Nanni, I. Silva-Rocha, A. Urso, M. A. Carretero, D. Salvi, S. Scali, G. Scarì, R. Pennati, F. 
Andreone, and R. Manenti. 2018. N -mixture models reliably estimate the abundance of 
small vertebrates. Scientific Reports 8:10357. 

Frawley, B. J. 2020. Michigan deer harvest survey report 2019 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3691, Lansing, USA.  

Frawley, B. J. 2021. Michigan deer harvest survey report 2020 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3697, Lansing, USA. 

Frawley, B. J. 2022. Michigan deer harvest survey report 2021 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3704, Lansing, USA. 

Furnas, B. J., R. H. Landers, R. G. Paiste, and B. N. Sacks. 2020. Overabundance of black-tailed 

deer in urbanized coastal California. The Journal of Wildlife Management 84:979–988. 

Gelman, A. 2006. Prior distributions for variance parameters in hierarchical models. Bayesian 

Analysis 1:515–534. 

Gelman, A., and D. B. Rubin. 1992. Inference from iterative simulation using multiple 

sequences. Statistical Science 7: 457–472. 

Gilbert, N. A., J. D. J. Clare, J. L. Stenglein, and B. Zuckerberg. 2021. Abundance estimation of 
unmarked animals based on camera-trap data. Conservation Biology 35:88–100. 

Gomez, J. P., S. K. Robinson, J. K. Blackburn, and J. M. Ponciano. 2018. An efficient extension of 
N-mixture models for multi-species abundance estimation. Methods in Ecology and 
Evolution 9(2):340–353. 

Green, R. H. 1979. Sampling design and statistical methods for environmental biologists. Wiley 

Interscience, Chichester, England. 

Guillera-Arroita, G., and J. J. Lahoz-Monfort. 2012. Designing studies to detect differences in 
species occupancy: power analysis under imperfect detection. Methods in Ecology and 
Evolution 3:860–869. 

Hansen, L. P., E. B. Flinn, J. A. Sumners, X. Gao, and J. J. Millspaugh. 2017. Effects of an antler 
point restriction on harvest of white-tailed deer in Missouri. Wildlife Society Bulletin 
41:516–522. 

61 

Haus, J. M., T. B. Eyler, and J. L. Bowman. 2019. A spatially and temporally concurrent 
comparison of popular abundance estimators for white-tailed deer. Northeastern 
Naturalist 26:305–324.  

Hiller, T. L., H. Campa iii, and S. R. Winterstein. 2009. Estimation and Implications of Space Use 

for White-Tailed Deer Management in Southern Michigan. The Journal of Wildlife 
Management 73:201–209. 

Iannarilli, F., J. Erb, T. W. Arnold, and J. R. Fieberg. 2021. Evaluating species-specific responses 

to camera-trap survey designs. Wildlife Biology 2021:wlb.00726. 

Jacobson, H. A., J. C. Kroll, R. W. Browning, B. H. Koerth, and M. H. Conway. 1997. Infrared-

triggered cameras for censusing white-tailed deer. Wildlife Society Bulletin 25:547–556. 

Jakob, C., F. Ponce-Boutin, and A. Besnard. 2014. Coping with heterogeneity to detect species 
on a large scale: N-mixture modeling applied to red-legged partridge abundance. The 
Journal of Wildlife Management 78:540–549. 

Joseph, L. N., C. Elkin, T. G. Martin, and H. P. Possingham. 2009. Modeling abundance using N-
mixture models: the importance of considering ecological mechanisms. Ecological 
Applications 19:631–642. 

Kays, R., B. S. Arbogast, M. Baker-Whatton, C. Beirne, H. M. Boone, M. Bowler, S. F. Burneo, M. 
V. Cove, P. Ding, S. Espinosa, A. L. S. Gonçalves, C. P. Hansen, P. A. Jansen, J. M. Kolowski, 
T. W. Knowles, M. G. M. Lima, J. Millspaugh, W. J. McShea, K. Pacifici, A. W. Parsons, B. S. 
Pease, F. Rovero, F. Santos, S. G. Schuttler, D. Sheil, X. Si, M. Snider, and W. R. Spironello. 
2020. An empirical evaluation of camera trap study design: How many, how long and 
when? Methods in Ecology and Evolution 11:700–713. 

Kays, R., B. Kranstauber, P. Jansen, C. Carbone, M. Rowcliffe, T. Fountain, and S. Tilak. 2009. 

Camera traps as sensor networks for monitoring animal communities. Pages 811–818 in 
2009 IEEE 34th Conference on Local Computer Networks. 

Keever, A. C., C. P. McGowan, S. S. Ditchkoff, P. K. Acker, J. B. Grand, and C. H. Newbolt. 2017. 
Efficacy of N-mixture models for surveying and monitoring white-tailed deer populations. 
Mammal Research 62:413–422. 

Kellner, K. F. 2015. jagsUI: A wrapper around rjags to streamline JAGS analyses. R package 

version 1.5.2. https://cran.r-project.org/web/packages/jagsUI/index.html.  

Kellner, K. F., and R. K. Swihart. 2014. Accounting for imperfect detection in ecology: a 

quantitative review. PLoS ONE 9:e111436. 

Kéry M., and J. A. Royle. 2015. Applied hierarchical modeling in ecology. First edition. Elsevier, 

Amsterdam, Netherlands. 

62 

Kéry, M., and J. A. Royle. 2016. Applied hierarchical modeling in ecology: analysis of 

distribution, abundance and species richness in R and BUGS: Volume 1: Prelude and static 
models. Academic Press, Cambridge, Massachusetts, USA. 

Kéry, M., and J. A. Royle. 2021. Applied hierarchical modeling in ecology analysis of distribution, 
abundance and species richness in R and BUGS: Volume 2: Dynamic and advanced models. 
Academic Press, Cambridge, Massachusetts, USA. 

Kéry M., and M. Schaub. 2012. Bayesian population analysis using WinBUGS: a hierarchical 

perspective. First edition. Elsevier, Amsterdam, Netherlands. 

Kidwai, Z., J. Jimenez, C. J. Louw, H. P. Nel, and J. P. Marshal. 2019. Using N-mixture models to 

estimate abundance and temporal trends of black rhinoceros (Diceros bicornis L.) 
populations from aerial counts. Global Ecology and Conservation 19:e00687. 

Koerth, B. H., and J. C. Kroll. 2000. Bait type and timing for deer counts using cameras triggered 

by infrared monitors. Wildlife Society Bulletin 28:630–635. 

Link, W. A., M. R. Schofield, R. J. Barker, and J. R. Sauer. 2018. On the robustness of N-mixture 

models. Ecology 99:1547–1551. 

Long, E. S., D. R. Diefenbach, C. S. Rosenberry, and B. D. Wallingford. 2008. Multiple proximate 

and ultimate causes of natal dispersal in white-tailed deer. Behavioral Ecology 19:1235–
1242. 

Lyons, J. E., J. A. Royle, S. M. Thomas, E. Elliott-smith, J. R. Evenson, E. G. Kelly, R. L. Milner, D. R. 
Nysewander, and B. A. Andres. 2012. Large-scale monitoring of shorebird populations 
using count data and N-mixture models: black oystercatcher (Haematopus bachmani) 
surveys by land and sea. The Auk 129:645–652.  

MacKenzie, D. I., and J. A. Royle. 2005. Designing occupancy studies: general advice and 

allocating survey effort. Journal of Applied Ecology 42:1105–1114. 

Michigan Department of Natural Resources [MDNR]. 2016. Michigan Deer Management Plan. 

<https://www.michigan.gov/-
/media/Project/Websites/dnr/Documents/WLD/Deer/mi_deer_management_plan.pdf?re
v=19ecc9c9e4f046d2aa80bbf6d551f022>. Accessed 28 Jul 2023. 

Maffei, L., A. J. Noss, S. C. Silver, and M. J. Kelly. 2011. Abundance/density case study: jaguars in 
the Americas. Pages 119–144 in A. F. O’Connell, J. D. Nichols, and K. U. Karanth, editors. 
Camera traps in animal ecology: methods and analyses. Springer, New York, New York, 
USA. 

Marcon, A., D. Battocchio, M. Apollonio, and S. Grignolio. 2019. Assessing precision and 

requirements of three methods to estimate roe deer density. PLOS ONE 14:e0222349.  

63 

McCaffery, R., J. J. Nowak, and P. M. Lukacs. 2016. Improved analysis of lek count data using N-

mixture models. The Journal of Wildlife Management 80:1011–1021. 

McCoy, J. C., S. S. Ditchkoff, and T. D. Steury. 2011. Bias associated with baited camera sites for 
assessing population characteristics of deer. The Journal of Wildlife Management 75:472–
477. 

Moll, R. J., J. D. Cepek, P. D. Lorch, P. M. Dennis, T. Robison, J. J. Millspaugh, and R. A. 

Montgomery. 2018. Humans and urban development mediate the sympatry of 
  competing carnivores. Urban Ecosystems 21:765–778. 

Moral, R. A., J. Hinde, C. G. B. Demétrio, C. Reigada, and W. A. C. Godoy. 2018. Models for 
jointly estimating abundances of two unmarked site-associated species subject to 
imperfect detection. Journal of Agricultural, Biological and Environmental Statistics 23:20–
38. 

Newbolt, C. H., S. Rankin, and S. S. Ditchkoff. 2017. Temporal and Sex-related Differences in use 
of Baited Sites by White-tailed Deer. Journal of the Southeastern Association of Fish and 
Wildlife Agencies 4:109–114.  

Newbolt, C. H., and S. S. Ditchkoff. 2019. Misidentification error associated with classifications 

of white-tailed deer images. Wildlife Society Bulletin 43:527–536. 

Newkirk, E. S. 2016. CPW Photo Warehouse. Colorado Parks and Wildlife, Fort Collins, Colorado, 

USA. http://cpw.state.co.us/learn/Pages/ResearchMammalsSoftware.aspx. 

Nixon, C. M., L. P. Hansen, P. A. Brewer, and J. E. Chelsvig. 1991. Ecology of white-tailed deer in 

an intensively farmed region of Illinois. Wildlife Monographs 118:3-77. 

Nixon, CM., L.P. Hansen, P.A. Brewer, J. E. Chelsvig, J.B. Sullivan, R. Koerkenmeier, D.R. Etter, J. 

Cline, and J. A. Thomas. 1994. Behavior, dispersal, and survival of male white-tailed deer in 
Illinois. Illinois Natural History Survey Biological Notes 139. 

Nixon, C. M., L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, D. Etter, J. B. Sullivan, R. G. 

Koerkenmeier, and P. C. Mankin. 2001. Survival of white-tailed deer in intensively farmed 
areas of Illinois. Canadian Journal of Zoology 79:581–588. 

Nixon, C. M., P. C. Mankin, D. R. Etter, L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, and J. 
B. Sullivan. 2007. White-tailed deer dispersal behavior in an agricultural environment. The 
American Midland Naturalist 157:212–220. 

O’Connell A., J. D. Nichols, and K. U. Karanth, editors. 2011. Camera traps in animal ecology: 

methods and analyses. Springer Science & Business Media, Tokyo, Japan.  

64 

Parsons, A. W., T. Forrester, W. J. McShea, M. C. Baker-Whatton, J. J. Millspaugh, and R. Kays. 
2017. Do occupancy or detection rates from camera traps reflect deer density? Journal of 
Mammalogy 98:1547–1557. 

Pierce, B.L., R. R. Lopez, and N. J. Silvy. 2012. Estimating animal abundance. Pages 284–310 in N. 

J. Silvy, editor. The Wildlife Techniques Manual: Research. Volume 1. Seventh edition. The 
Johns Hopkins University Press, Baltimore, Maryland, USA. 

Plummer, M. 2003. JAGS: a program for analysis of Bayesian graphical models using Gibbs 

sampling. Pages 124–125 in K. Hornik, F. Leisch, and A. Zeileis, editors. Proceedings of the 
3rd International Workshop on Distributed Statistical Computing, March 20-23, 2003. 
Technische Universität Wien, Vienna, Austria. 

Price Tack, J. L., B. S. West, C. P. McGowan, S. S. Ditchkoff, S. J. Reeves, A. C. Keever, and J. B. 
Grand. 2016. AnimalFinder: a semi-automated system for animal detection in time-lapse 
camera trap images. Ecological Informatics 36:145–151. 

R Core Team. 2021. R: a language and environment for statistical computing. R Foundation for 

Statistical Computing, Vienna, Austria. 

Rosenberry, C. S., R. A. Lancia, and M. C. Conner. 1999. Population effects of white-tailed deer 

dispersal. Wildlife Society Bulletin (1973-2006) 27:858–864. 

Rouleau, I., M. Crête, and J. Ouellet. 2002. Contrasting the summer ecology of white-tailed deer 

inhabiting a forested and an agricultural landscape. Écoscience 9:459–469. 

Royle, J. A. 2004. N-Mixture models for estimating population size from spatially replicated 

counts. Biometrics 60:108–115.  

Schlichting, P. E., J. C. Beasley, R. K. Boughton, A. J. Davis, K. M. Pepin, M. P. Glow, N. P. Snow, 
R. S. Miller, K. C. VerCauteren, and J. S. Lewis. 2020. A rapid population assessment 
method for wild pigs using baited cameras at 3 study sites. Wildlife Society Bulletin 
44:372–382. 

Si, X., R. Kays, and P. Ding. 2014. How long is enough to detect terrestrial animals? Estimating 

the minimum trapping effort on camera traps. PeerJ 2:e374.  

Skalski, J. R., K. E. Ryding, and J. J. Millspaugh. 2005. Wildlife demography: analysis of sex, age, 

and count data. Elsevier Academic Press, San Diego, CA. 656 pp. 

Skuldt, L. H., N. E. Mathews, and A. M. Oyer. 2008. White-tailed deer movements in a chronic 
wasting disease area in south-central Wisconsin. The Journal of Wildlife Management 
72:1156–1160. 

Stevens, D. L., and A. R. Olsen. 2004. Spatially balanced sampling of natural resources. Journal 

of the American Statistical Association 99:262–278. 

65 

Strickland, B. K., and S. Demarais. 2008. Influence of landscape composition and structure on 

antler size of white-tailed deer. Journal of Wildlife Management 75:1101–1108. 

Suwanrat, S., D. Ngoprasert, C. Sutherland, P. Suwanwaree, and T. Savini. 2015. Estimating 
density of secretive terrestrial birds (Siamese Fireback) in pristine and degraded forest 
using camera traps and distance sampling. Global Ecology and Conservation 3:596–606. 

Veech, J. A., J. R. Ott, and J. R. Troy. 2016. Intrinsic heterogeneity in detection probability and its 

effect on N-mixture models. Methods in Ecology and Evolution 7:1019–1028. 

Vélez, J., W. McShea, H. Shamon, P. J. Castiblanco-Camacho, M. A. Tabak, C. Chalmers, P. 

Fergus, and J. Fieberg. 2023. An evaluation of platforms for processing camera-trap data 
using artificial intelligence. Methods in Ecology and Evolution 14:459–477. 

Ward, R. J., R. A. Griffiths, J. W. Wilkinson, and N. Cornish. 2017. Optimising monitoring efforts 
for secretive snakes: a comparison of occupancy and N-mixture models for assessment of 
population status. Scientific Reports 7:18074. 

Webb, S. L., K. L. Gee, B. K. Strickland, S. Demarais, and R. W. DeYoung. 2010. Measuring fine-
scale white-tailed deer movements and environmental influences using GPS collars. 
International Journal of Ecology 2010:e459610. 

Weckel, M., R. F. Rockwell, and F. Secret. 2011. A modification of Jacobson et al.’s (1997) 

individual branch-antlered male method for censusing white-tailed deer. Wildlife Society 
Bulletin 35:445–451. 

Welbourne, D. J., A. W. Claridge, D. J. Paull, and A. Lambert. 2016. How do passive infrared 
triggered camera traps operate and why does it matter? Breaking down common 
misconceptions. Remote Sensing in Ecology and Conservation 2:77–83. 

Wilton, C.M. 2021. White-tailed Deer (Odocoileus virginianus) Density and habitat use on the 

Beaver Island Archipelago using a camera trap array. Michigan Natural Features Inventory 
Report Number 2021-05, Lansing, MI, USA. 

Woolf, A., and J. L. Roseberry. 1998. Deer Management: Our Profession’s Symbol of Success or 

Failure? Wildlife Society Bulletin (1973-2006) 26:515–521. 

Yamaura, Y., J. A. Royle, N. Shimada, S. Asanuma, T. Sato, H. Taki, and S. Makino. 2012. 

Biodiversity of man-made open habitats in an underused country: a class of multispecies 
abundance models for count data. Biodiversity and Conservation 21:1365–1380. 

Zou, F., Q. Zhang, M. Zhang, M.-B. Lee, X. Wang, Y. Gong, and C. Yang. 2019. Temporal patterns 
of three sympatric pheasant species in the Nanling Mountains: N-mixture modeling 
applied to detect abundance. Avian Research 10:1–10. 

66 

CHAPTER 2: ASSESSING THE EFFECT OF A DEER HARVEST REGULATION CHANGE ON RELATIVE 
ABUNDANCE: AN EXPERIMENTAL APPROACH 

INTRODUCTION 

Assessing changes in population abundance is important when evaluating the 

effectiveness of conservation and management for wildlife. However, evaluating a single 

regulation change on a free-ranging population is considerably challenging. Given partial 

controllability limitations (Fackler and Pacifici 2014), robust evaluations generally require 

coupling the regulation change with before and after population monitoring within treatment 

and control areas (Green 1979, Christie et al. 2019). For game species, many agencies (i.e., 

federal, state, or provincial wildlife management organizations) instead rely on estimated or 

enumerated harvest for population monitoring efforts (Roseberry and Woolf 1991, Skalski et al. 

2005, Hansen 2011, Ryder 2018). Although useful, sex and age data of the harvested population 

may be nonrepresentative of the true state of the population (Carpenter 2000, Demarais et al. 

2005, Collier and Krementz 2007). For example, changes in harvest trends may reflect changes 

in harvest regulations and hunter effort rather than population-level changes. Ultimately, 

wildlife management actions cannot be thoroughly assessed without reliable data on 

population parameters (Lubow et al. 1996, Lancia et al. 2000). 

Selective-harvest regulations involve the differential protection or harvest of animals 

based on specific criteria like phenotypic traits, sex, and age. Agencies generally implement 

selective-harvest regulations because of 1) hunter preferences for sex, age, or size, and 2) the 

expectation that the regulation will exert a desired population effect (Carpenter 2000, Demarais 

et al. 2000). For species where hunter harvest is a large source of mortality, sex- and age-

specific harvest can affect population composition, structure, and demographic processes 

67 

 
 
(Ginsberg and Milner-Gulland 1994, Milner et al. 2007). For example, density reduction 

programs may focus on female harvest as a conventional means to reduce a population’s 

reproductive potential (Woolf and Rosenberry 1998, Brown et al. 2000). Further, male-biased 

harvest can lead to female-biased sex ratios in a population (Noyes et al. 1996, Nilsen and 

Solberg 2006) whereas disproportionate harvests of young animals can limit animals from 

advancing to older age classes and skew the age composition of a population (Milner et al. 

2007).  

Antler-based regulations are a common form of selective harvest applied to cervid 

(family Cervidae) management programs. In practice, antler-based regulations are designed to 

limit harvest of antlered animals, especially younger individuals, allowing these age classes a 

greater likelihood of survival and thus entering older age classes (Carpenter and Gill 1987, 

Frawley 2017, Hansen et al. 2017, Wallingford et al. 2017). These types of regulations are based 

on age-specific antler growth and vary by species, population attributes, and management 

objectives. Agencies have used various criteria to define antler-based regulations, including 

minimum main beam length, spread width, number of antler points (i.e., antler point 

restrictions), or some combination thereof (Demarais and Strickland 2011, Morina et al. 2021). 

Over time, antler-based regulations have been widely adapted for the management of elk 

(Cervus canadensis; Boyd and Lipscomb 1976, Bender and Miller 1999, Biederbeck 2001, 

Bender et al. 2002), moose (Alces alces; Schwartz et al. 1992, Young and Boertje 2008, Child et 

al. 2010), mule deer (Odocoileus hemionus; Erickson et al. 2003, Kuzyk et al. 2011), and more 

recently white-tailed deer (Odocoileus virginianus; Cohen et al. 2016, Wallingford et al. 2017, 

Kellner et al. 2021, Cain et al. 2022). Many U.S. states have, or currently use, some form of 

68 

 
antler-based regulation to achieve management goals, including increasing the number of older 

males in the population or harvest (Boyd and Lipscomb 1976, Bender et al. 2002, Frawley 2017, 

Wallingford et al. 2017, Hansen et al. 2017), managing sex ratios (Schwartz et al. 1992, Bender 

and Miller 1999, Young and Boertje 2008), influencing population size or increasing antlerless 

harvest (Schroeder et al. 2014, Hansen et al. 2017, Wallingford et al. 2017), and responding to 

stakeholder requests or increasing hunter satisfaction (Frawley 2017, Hansen et al. 2017). Antler 

point restrictions (APRs) are the most common form of antler-based regulations and are 

frequently applied to white-tailed deer (hereafter, deer) harvest programs—typically in 

response to the preference among some hunters for harvesting older male deer with larger 

antler growth (Adams and Hamilton 2011, Cohen et al. 2016, Frawley 2017, Hansen et al. 2017, 

Cain et al. 2022). 

It is hypothesized that APRs advance the age structure of male deer in a population 

(Wallingford et al. 2017). Given the direct relationship between antler growth, age-specific male 

survival and male age structure, this hypothesis has foundations in logic. In theory, 

implementing a mandatory APR that protects most yearling males from harvest will result in 

increased yearling-male survival and thus increased recruitment of yearling males into the adult 

age class (Carpenter and Gill 1987, Hansen et al. 2017, Wallingford et al. 2017). Further 

substantiating this hypothesis is the widely held consensus that APRs reduce the proportion of 

yearlings in the antlered harvest as yearlings are largely protected (Demarais et al. 2005, 

Hansen et al. 2017, Wallingford et al. 2017, Kellner et al. 2021, Cain et al. 2022). APRs have been 

implemented and evaluated under a diversity of conditions (e.g., motivations, type of APR, pre-

existing conditions) resulting in a diversity of outcomes among studies. For example, Kellner et 

69 

 
 
al. (2021) evaluated the effect of APR treatments in 2 study areas in New York and found that 

the proportion of yearlings in the antlered harvest declined from 51% and 58% to 13% and 19% 

after 5 years, respectively. In 2 study areas in Missouri, Hansen et al. (2017) found that the 

proportion of yearling males in the antlered harvest decreased from 58% and 60% to 26% and 

22% after 4 years of APR treatments, respectively. Numerous studies have also observed 

increased proportions of older male deer harvested following APR implementation (Strickland 

et al. 2001, Hansen et al. 2017, Wallingford et al. 2017, Kellner et al. 2021, Cain et al. 2022), but 

these increased proportions may be explained in part by lower proportions of yearling harvest 

(Demarais et al. 2005, Collier and Krementz 2007). Regardless, these studies lacked estimates of 

male abundance by age, thus it was not possible to evaluate the magnitude of effect APRs had 

on adult male abundance. 

Although APRs focus on age-structure management of antlered deer, an indirect 

outcome is also hypothesized. Specifically, APRs are hypothesized to reduce the overall 

abundance of deer in a population. The theory underlining this hypothesis is that hunters will 

voluntarily shift harvest pressure to antlerless deer when APRs reduce the availability of 

harvestable yearling males (Hamilton et al. 1995, Hansen et al. 2017, Wallingford et al. 2017, 

Hansen et al. 2018). The additional compensatory harvest pressure on antlerless deer can 

translate to increased female mortality and a subsequent reduction in a population’s 

reproductive potential (Woolf and Rosenberry 1998, Brown et al. 2000, Diefenbach et al. 2021). 

For example, Wallingford et al. (2017) concluded that the combination of APR-regulation 

changes and increased antlerless harvest were effective in reducing deer abundance in 

Pennsylvania over a 5-year period. Under APR regulations, Hansen et al. (2017) found different 

70 

 
antlerless harvest outcomes in different regions of Missouri. Antlerless harvest increased in a 

region with better-quality deer habitat (northern Missouri) but did not increase in a region with 

poorer-quality deer habitat and a relatively lower deer population density (central Missouri; 

Hansen et al. 2017). In contrast, APR studies in New York (Kellner et al. 2021) and northern 

Michigan (Cain et al. 2022) evaluated harvest data and failed to find definitive empirical support 

for any increases in antlerless harvest. To my knowledge, Wallingford et al. (2017) were the only 

authors to evaluate the effects of APRs on overall deer abundance. To better understand the 

relationship between APRs and deer abundance, there is a critical need for additional 

population-level assessments. 

Hunter harvest accounts for a significant proportion of deer mortality in the United 

States (Ditchkoff et al. 2001, Nixon et al. 2001). Therefore, selective harvest has the potential to 

influence population size and sex-age composition (Milner et al. 2007), which in turn can 

influence disease dynamics (Cross et al. 2009). These concepts are particularly relevant to 

emergence in wildlife health issues because changing the selectivity of harvest over sex and age 

classes has implications for disease spread and growth. Therefore, knowing the true 

demographic features (e.g., sex-age composition) of affected deer populations is more pertinent 

and useful to management than harvest data alone. 

Wildlife-management agencies need to also consider other biological ramifications 

associated with APRs, like potential influence on disease dynamics (Miller and Fischer 2016, 

Morina et al. 2021). For example, both bovine tuberculosis (Mycobacterium bovis) and chronic 

wasting disease affect sex-and-age classes disproportionately (O’Brien et al. 2002, Jennelle et al. 

2014). Chronic wasting disease (CWD) is a fatal prion disease that infects cervids (Williams 2005) 

71 

 
 
and is a major threat to the sustainability of free-ranging cervids and conservation (Gillin and 

Mawdsley 2018). Notably, the prevalence of CWD in deer is estimated to be about twice as high 

in adult males compared to females, with age-specific prevalence generally increasing with age 

(Grear et al. 2006, Osnas et al. 2009, Heisey et al. 2010, Rees et al. 2012, Samuel and Storm 

2016). The observed higher prevalence in males is likely attributed to differences in behavior. 

For example, yearling males tend to disperse at the greatest frequency within white-tailed deer 

populations (Nelson 1993, Long et al. 2005, Nixon et al. 2007, Skuldt et al. 2008) and mature 

males increase their movements and expand their home ranges seasonally (Beier and 

McCullough 1990). These life-history traits are important because they can facilitate increased 

contact rates and thus increased disease spread (Gross and Miller 2001, Skuldt et al. 2008, Cross 

et al. 2009). Further, the observed increase in disease prevalence with age can be a 

consequence of an increase in the length of potential cumulative infection risk (Wobeser 2006, 

Cross et al. 2009).  

Following the detection of CWD, agencies generally alter deer harvest regulations or 

initiate management practices in an attempt to reduce disease transmission (Thompson et al. 

2023). Some studies have shown that reducing deer densities has been successful at 

maintaining low prevalence of CWD (Manjerovic et al. 2014, Mateus-Pinilla et al. 2013). Harvest 

strategies that target specific, high-risk sex-and-age classes have also been considered useful for 

CWD management (Skuldt et al. 2008, Jennelle et al. 2014, Potapov et al. 2016, Gillin and 

Mawdsley 2018, Mysterud and Edmunds 2019, Belsare and Stewart 2020). For example, a 

simulation study by Belsare and Stewart (2020) found lower probabilities of CWD outbreak 

associated with higher harvest rates of yearling male deer (i.e., a non-APR harvest scenario). 

72 

 
Most APR studies to date have focused on evaluating harvest in response to APR 

regulation changes. Consequently, population-level effects of APRs remain unclear, particularly 

on sex-and-age distribution (Morina et al. 2021). Given the widespread application of and 

increasing interest in APRs (Adams and Hamilton 2011, Connelly et al. 2012, Frawley 2019), and 

the seemingly inexorable geographic spread of CWD (Miller and Fisher 2016, Uehlinger et al. 

2016, Belsare et al. 2021), empirical investigations are warranted. In 2019, Michigan’s Natural 

Resources Commission implemented an experimental APR in a portion of a 5-county study area 

that included a known CWD hotspot. This action was coupled with this research designed to 

evaluate the subsequent effects on white-tailed deer abundance by sex-and-age class. Pairing 

the regulation change with research provided me a unique opportunity to empirically evaluate 

two common, independent APR hypotheses: (H1) antler point restrictions increase the 

abundance of adult males, and (H2) antler point restrictions decrease overall deer abundance 

(Figure 2.1). I predicted that the abundance of adult males would only increase in APR-

treatment areas, given the pattern of decreased yearling- and increased adult-male harvest 

observed in other APR studies (Hansen et al. 2017, Wallingford et al. 2017, Kellner et al. 2021, 

Cain et al. 2022). I also predicted that, irrespective of harvest treatment, the abundance of 

other sex-and-age classes would not decline. This prediction was based on the absence of 

elevated antlerless harvest in a recent APR study in northern Michigan (Cain et al. 2022), as well 

as the historically low levels of antlerless harvests in the broader context of Michigan (Stewart 

2023). A camera-trap sampling design was used to survey deer populations 1 year prior to APR 

implementation and 3 consecutive years after APR implementation. Using these data, I 

estimated deer relative abundance by sex-and-age class over time and compared trends 

73 

 
between APR and non-APR areas. By linking field-based population estimates with a before-

after-control-impact design in response to APR regulation changes, I quantify and thoroughly 

evaluate subsequent population-level effects. My findings highlight potential limitations of APRs 

as a management tool and the importance of developing harvest regulations specific to the 

targeted deer population, area, and management goals.

74 

Figure 2.1. Conceptual diagrams of hypotheses regarding white-tailed deer (Odocoileus virginianus) population-level changes 
following the implementation of antler point restrictions (APRs). In (A), young males are protected from harvest in an area with APRs 
(APR Zone), resulting in Legal Antlered abundance increasing over time. In (B), the reduced availability of harvestable yearling males 
in the APR Zone translate to increased antlerless harvest and subsequent declines in the abundance of females (yearling and adult), 
yearling males, and fawns. No changes occur under the status quo harvest regime in the Non-APR Zone. 

75 

 
 
STUDY AREA 

The study took place in the south-central Lower Peninsula of Michigan in a 5-county 

area (Newaygo, Kent, Mecosta, Montcalm, and Ionia County; hereafter, 5-County Area) that 

included a known chronic-wasting-disease hotspot (Kent and Montcalm County; Figure 2.2). In 

2019, there was an APR change in the 5-County Area and a study was designed to evaluate its 

effect on the abundance and sex-and-age composition of deer populations in the area. A paired-

comparison study design was implemented to monitor deer populations in APR and non-APR 

areas (i.e., experimental and control areas, respectively). A robust before-after-control-impact 

(BACI) study design (Green 1979) was employed to monitor potential population-level changes, 

over 3 consecutive years (2020–2022), following the 2019 regulation change. This design was 

intended to allow researchers to identify potential changes in population abundance and 

composition in the treatment area (APR Zone) relative to the control area (Non-APR Zone) over 

the course of the study (Figure 2.2). 

Given north-south differences in land-use and land-cover types, the study area was 

longitudinally divided instead of latitudinally to minimize the effects, other than APRs, on deer 

populations (see Chapter 1 for detailed description of study area). The study implemented a 

camera-trap sampling design restricted to 8 townships within the 5-County Area, encompassing 

an area of approximately 749 km2 (Figure 2.2). Landscape analyses (e.g., land-cover 

composition, proportion of public hunting land) were completed for each township in the 5-

County Area to identify similar townships for pairing between APR and Non-APR Zones (Table 

2.1). Additional pairing considerations included geological features (e.g., rivers), human density, 

and apparent CWD prevalence. Eight townships were systematically selected and paired 

76 

between the APR Zone and Non-APR Zone to compare deer populations over time at a scale 

that was achievable with camera traps while also reflecting the variation within the 5-County 

Area. In the APR Zone (Mecosta, Montcalm, and Ionia County; 4,845-km2), antlered deer with at 

least four points on one antler could be taken with a valid license (a legal point was defined as ≥ 

2.54 cm [1 inch] long as measured from its tip to the nearest edge of antler beam). In the Non-

APR Zone (Newaygo and Kent County; 4,488-km2), any antlered deer with an antler ≥7.62 cm (3 

inches) in length could be taken. Deer hunting occurred annually every fall in Michigan. 

Since 1991, Michigan’s statewide hunting regulations have limited hunters to a 

maximum harvest of 2 antlered deer annually (Rudolph 2012, Cain et al. 2022). These antlered 

deer were defined as those with at least one antler measuring ≥7.62 cm (3 inches) in length 

(MDNR 2016). In 1997, Michigan enacted its first mandatory APR specific to the second antlered 

hunting license (Rudolph 2012, Cain et al. 2022). According to this regulation, if hunters 

harvested 2 antlered deer annually, at least one of the deer was required to have ≥4 antler 

points on a side (Rudolph 2012, Cain et al. 2022). In Michigan, a legal antler point was defined 

as ≥2.54 cm (1 inch) long as measured from its tip to the nearest edge of antler beam. Hunters 

who purchased a single antlered hunting license were permitted to harvest any legal antlered 

deer without limitations on antler-point count (Cain et al. 2022). Historically, there has never 

been a limit on the number of hunters pursuing antlered deer or quotas on antlered licenses 

(Rudolph 2012). In contrast, antlerless-deer harvests have been limited through license quotas 

specific to Michigan’s deer management units. However, in more recent years Michigan began 

increasing the allocation of antlerless licenses and increasing opportunity to harvest antlerless 

deer to manage population sizes (Rudolph 2012, MDNR 2016). Antlerless deer are defined as 

77 

 
deer without antlers and deer with antlers <7.62 cm (3 inches) in length. Today, Michigan’s deer-

harvest regulations vary by management unit, select federal lands (e.g., wildlife refuges), and 

disease management zone (Frawley 2023, MDNR 2023). 

In Michigan, CWD was first identified in free-ranging deer in 2015 (Stewart et al. 2016). 

Following CWD detection, Michigan’s regulatory responses to CWD included increased harvest 

opportunities by increasing quotas or licenses, extending preexisting hunting seasons, and 

adding additional hunting seasons (Thompson et al. 2023). In addition to changes in state and 

peninsula-wide deer harvest regulations designed to mediate potential CWD transmission, the 

Natural Resource Commission implemented a 4-point APR in a portion of the 5-County Area in 

2019 as part of experimental management. The APR prohibited hunters from harvesting 

antlered deer that did not have at least 4 antler points on one side. This action was expected to 

protect approximately 70% of yearling males from harvest (B. Rudolph, Michigan Department of 

Natural Resources, unpublished data). Youth hunters (<17 years of age) and disabled hunters 

were exempt from the APR during select seasons. 

The APRs in the 5-County Area (APRs in 2 counties) were based on a request by the 

Natural Resource Commission for the Michigan Department of Natural Resources to evaluate 

the effects of APRs on deer abundance and sex-and-age composition, with the anticipation that 

the data would better inform management and regulation decisions in CWD management areas 

(Frawley 2019). It is important to note that Michigan’s guidelines for evaluating APR proposals 

(QDMWG 2013) did not apply in this situation because the APRs were not requested by a local 

group, but instead directly by the Natural Resource Commission (Frawley 2019). The Natural 

Resources Commission maintained consistent APR regulations in the study area for a full 3-year 

78 

 
 
harvest regulation cycle (2019–2021). Apart from the APR regulation, all other deer hunting 

regulations were comparable between the APR and Non-APR Zones throughout the duration of 

the study (Frawley 2020, 2021, 2022) and in the years preceding it. 

79 

Table 2.1. Land-cover composition and total public land for each township pairing (A–D) in areas without antler point restrictions 
(the control area or Non-APR Zone) and areas with antler point restrictions (the experimental area or APR Zone). Land-cover 
composition and percent public land were the main criteria used for pairing townships with a before-after-control-impact study 
design. Land composition was calculated using the National Land Cover Database (Dewitz 2019) land-cover classification layer (30-m2 
resolution) in ArcPro (ESRI 2020). Landcover reclassifications included Agriculture (Cultivated crop, Hay-pasture, Grassland-
herbaceous), Forested (Deciduous forest, Coniferous forest, Mixed forest), Wetland (Palustrine forested wetland, Palustrine scrub-
shrub wetland, Palustrine emergent wetland, unconsolidated shore, Palustrine aquatic bed), and Developed (Highly developed, 
Moderately developed, Low development, Developed open space). Total public land included public lands open to hunting and was 
calculated using in the Protected Areas Database of the United States (USGS 2022) in ArcPro (ESRI 2020). 

Township 
by zone 

Non-APR 

A 

B 

C 

D 

APR 

A 

B 

C 

D 

% Agriculture 

% Forested 

% Wetland 

% Scrub-
shrub 

% Open 
water 

% Developed 

% Barren 
land 

Total 
public 
land (%) 

32.56 

49.77 

67.61 

48.13 

37.71 

63.73 

66.44 

58.46 

34.60 

24.45 

11.46 

21.28 

31.72 

16.65 

6.68 

10.91 

22.47 

17.16 

15.28 

20.40 

20.60 

14.08 

22.72 

23.33 

4.14 

2.68 

1.22 

2.83 

5.90 

1.83 

1.81 

1.94 

3.39 

0.51 

0.66 

1.14 

2.00 

0.37 

0.84 

2.59 

2.67 

4.84 

3.61 

5.98 

2.03 

3.23 

1.44 

2.73 

0.18 

0.59 

0.17 

0.24 

0.04 

0.11 

0.07 

0.05 

19.38 

19.61 

0.00 

0.00 

3.74 

10.23 

0.00 

0.00 

80 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.2. Study area in the south-central Lower Peninsula of Michigan, USA, in a designated 5-
county area. Mandatory antler point restrictions (APRs) were implemented in 2019 in the 
experimental area (APR Zone) and not in the control area (Non-APR Zone). Townships were 
paired (A–D) between zones, and remote cameras were placed in each township to monitor 
white-tailed deer (Odocoileus virginianus) populations over a duration of four years (2019–
2022). Maps created in ArcGIS Pro (version 2.7.1; ESRI 2020). 

81 

 
 
 
METHODS 

Field sampling and site selection 

A stratified-random design (at the township-section scale) was used to select 144 

camera sites evenly distributed across the 8 townships using generalized random-tessellation 

stratification (GRTS; Stevens and Olsen 2004). The GRTS sampling design is advantageous 

because it maintains statistical qualities of a random draw when removing intractable samples 

(i.e., no land access), while yielding a spatially balanced set of points (Stevens and Olson 2004). 

Random camera placement was selected with the intent of providing the least biased 

approximation of population structure. Sample sites were located on both public and private 

land, the latter necessitating annual landowner permission. Note that only half of the township 

pairs (C and B; Figure 2.2) were surveyed in 2020 due to COVID-19 pandemic-related 

constraints. 

Camera-trap setup and data collection 

Eighteen infrared cameras (Strike Force HD Pro X®, Browning Trail Cameras, Birmingham, 

AL) were deployed in each of the 8 selected townships. To minimize potential bias, camera sites 

were nonbaited (Koerth and Kroll 2000, McCoy et al. 2011, Newbolt et al. 2017) and placed as 

close to the generated GRTS sample locations as possible (Kays et al. 2009). In exceptional 

circumstances cameras were placed within 100 m of the point. In such situations, exact camera 

location was selected to avoid locations with a high risk of theft, open water, road rights-of-way, 

and to maintain a clear field of view. Cameras were oriented north to minimize direct sunlight 

exposure, false triggers caused by exposure to the sun’s rays (Wilton 2021), and observer bias in 

placement. Cameras were placed on a straight tree and secured with a security box, cable, and 

82 

lock. If no suitable trees were available, a steel T-post was used to mount the camera. Cameras 

were mounted so that the center of the lens was 36–41 cm (14–16 inches) above the ground 

and the horizon was centered in the field of view (guidance provided by Moll et al. 2018). The 

selected camera height was intended to detect all age groups of deer and allow overhanging 

vegetation (e.g., branches) to be reached and removed from the field of view. Ground 

vegetation and debris were cleared 5 m in front of the camera to minimize false triggering and 

allow for an unobstructed field of view.  

Cameras were active for 63 days on 24-hour capture mode with a 5-sec delay, taking a 

burst of 3 photographs per motion-triggered event. Since camera sites were not baited, cameras 

were programed to rapid fire (0.3 sec between each image within a burst) and fast-motion 

infrared flash to maximize clear images of mobile deer. Photo data were collected during what 

was considered a 9-week closure period (i.e., no immigration or emigration) from 15 July to 15 

September for four consecutive years (2019–2022). Each camera site was visited for 

maintenance (e.g., check batteries, change memory cards, clear vegetation) approximately 

every two weeks over the duration of the data-collection period. Camera surveys were used to 

create detection histories for each site. If a camera was not functional for some time, these 

occurrences were treated as missing data in the detection history (Furnas et al. 2020). 

All photos were entered into Colorado Parks and Wildlife Photo Warehouse, a custom 

Microsoft Access application designed to facilitate archiving, managing, and processing camera-

trap data (Newkirk 2016). Deer were counted in each image and classified as Legal Antlered 

(antlered deer that met the APR criteria), Female (yearling and adult females, i.e., does), Sub-

legal Antlered (antlered deer that did not meet the APR criteria), Fawn, or Unknown Deer. Legal 

83 

Antlered are assumed to be adult males and Sub-legal Antlered are assumed to be yearling 

males. Deer were classified as Unknown when it was impossible to determine the sex and age 

of an individual (e.g., unable to see head). To minimize misidentifications, all photos were 

processed by two observers that received species-specific image training (Newbolt and 

Ditchkoff 2019, Elliot et al. 2022). If there was a discrepancy on the identification of a deer in an 

image, then a third observer served as a referee. Discrepancies were judged by trained referees 

(with years of professional experience reviewing deer images) to maintain consistent and 

accurate classification of photographs (Newbolt and Ditchkoff 2019, Elliot et al. 2022). See 

Chapter 1 appendices for detailed camera-trap and photo-review protocols (Appendix 1A, 

Appendix 1B).  

Image processing 

Images were downloaded from memory cards after each camera check and organized 

into a folder hierarchy by zone, township, camera-check number, and unique site ID (e.g., 

NonAPR/Sherman/Check1/11001). This folder structure facilitated a multi-step method for 

filtering and manually classifying images. Given the concerningly high level of human effort 

required to process the 2019 camera-trap data and the surplus of false positive images (i.e., 

empty images with no animals in frame; see Chapter 1 Discussion), it was critical to improve 

efficiency in subsequent years of the study. This need motivated change in the existing workflow 

to integrate machine learning for animal detection while continuing manual classification of 

species. I implemented MegaDetector, an open-source, generalizable, object-detection model 

designed to expedite camera-trap image processing (version 3; Beery et al. 2019, Microsoft 

2020). I used this automated model to determine whether animals (not species) were present in 

84 

 
images—thus it was implicitly used as a coarse filter to screen out empty images. Before 

implementing it into the workflow, it was important to first evaluate the platform’s performance 

with a test dataset (Christin et al. 2021). A total of 52,232 validated photos from 2019 were 

leveraged to evaluate MegaDetector’s accuracy for detecting deer and determine a desired 

confidence threshold (see Appendix 2E for more details).  

All images from 2020–2022 seasons were initially reviewed by MegaDetector to remove 

empty images and improve efficiency of the manual species-classification process. To produce 

image-recognition data in real-time during sampling periods, a set of local modern computers 

(e.g., in-office agency laptops) executed MegaDetector in tandem. Timelapse software (version 

2.2.2.4; Greenburg 2019) was used to inspect MegaDetector’s image-recognition data and 

organize detections based on a desired confidence threshold. An intermediary database was 

used to transfer data from Timelapse to CPW Photo Warehouse. CPW Photo Warehouse was 

used to manually classify species within images containing animals (i.e., animals detected by 

MegaDetector). A detailed description of the MegaDetector workflow is provided in Appendix 

2A. 

General abundance-modeling approach  

In this study, I used relative abundance of deer as an index, assuming it was functionally 

related to population size. When modeling abundance, I assumed site-level abundance 

reflected the number of deer within the effective sampling area surrounding a camera site (see 

Chapter 1 for details on effective sampling area). I used these site-level abundances to derive 

estimated abundance by township, where abundance related to the number of deer within the 

total area of all effective sampling areas in a specified township (18 sites per township = 22 km2 

85 

 
[9 mi2]). Hence, my abundance estimates reflect relative abundance, not absolute, as I did not 

infer site-level abundances for areas beyond the total surveyed area (i.e., total effective 

sampling area). Given the incorporation of baseline data and the study’s focus on examining 

changes over time, the use of relative abundance as an index was considered adequate. To 

interpret the potential effects of harvest treatment on deer abundance, I compared 2019 

baseline abundance estimates (i.e., the system before the APR implementation) to estimates 

from subsequent years (i.e., the system after the APR implementation). 

I investigated changes in deer abundance over 3 consecutive years using two separate 

hierarchical modeling approaches. Model development is an iterative undertaking, exemplified 

by my use of two distinct frameworks. I modeled relative abundance first using a static binomial 

N-mixture model (Royle 2004) and then extended it to develop a year-stratified N-mixture 

model (Kéry and Royle 2021). The static model is described in detail in the Appendix (Appendix 

2B). For both the static and year-stratified N-mixture approaches, I modeled the abundance of 

sex-and-age classes individually (Legal Antlered, Female, Sub-legal Antlered, Fawn). I followed 

recommendations from Chapter 1 and used data associated with a weekly sampling frequency 

(i.e., weekly counts), a 63-day sampling duration (15 July–15 September), and a camera 

distribution of 18 sites per township. Both N-mixture models included similar covariates, in 

which agriculture cover (% of land cover) affected abundance and landscape cover (open or 

closed) affected detection probability (see Chapter 1 for details on deriving covariates). Prior to 

building my models, I standardized all covariates (mean = 0) to improve interpretation and 

reduce potential multicollinearity. With regards to the Bayesian implementation, Markov chain 

Monte Carlo (MCMC) settings and model-convergence assessments were similar between 

86 

modeling approaches (described in detail in Chapter 1). I assumed vague prior distributions for 

all analyses.  

N-mixture models are subject to critical assumptions, including population closure (i.e., 

no individuals leave or enter the population via birth, immigration, death, or emigration), 

detection probability is equal for all individuals, absence of false-positive detections (i.e., no 

misidentifications or double counting of individuals), and detections of individuals are 

independent of one another (Royle 2004). Deviations from these assumptions can affect the 

validity of the estimates produced by these models (Barker et al. 2018, Link et al. 2018). 

Consequently, if the underlying assumptions are not satisfied, it is advisable to interpret 

estimates as measures of relative abundance indices instead of absolute values (Barker et al. 

2018, Gilbert et al. 2021).  

I considered a minimum of 3 years post-harvest regulation change was needed to 

observe and evaluate potential population-level changes. Multiple years of data are important 

to recognizing natural, annual variation in deer abundance. Delayed population-level effects 

from the APR regulation change were also expected. For example, the males (including fawns) 

that remain after harvest need time to mature and advance to older age classes (Figure 2.3). 

Further, any change in antlerless hunting pressure needs time to affect the female population, 

fawn production, and maturing of males (Figure 2.3). Therefore, I considered comparisons 

between 2019 and 2022 abundance estimates within townships important and comparisons 

among paired townships as most meaningful. A significant change in one of the paired 

townships, but not the other, implied that different harvest treatment may influence 

abundance.

87 

 
 
Figure 2.3. Conceptual diagram of the timeframe needed to evaluate potential population-level changes of white-tailed deer 
(Odocoileus virginianus) populations following the implementation of antler point restrictions (APRs). Pink circles indicate annual, 
summer population surveys. Deer hunting occurred every fall following the summer surveys. Black vertical dashed line indicates that 
the APR was implemented and effective following the 2019 survey. Delayed population-level effects from the APR regulation change 
were expected. The males (including fawns) that remain after harvest need time to mature and advance to older age classes. Further, 
any change in antlerless hunting pressure needs time to affect the female population, fawn production, and maturing of antlered 
males (pink horizontal dashed line). Three years of data post-harvest regulation change was needed to observe and evaluate 
potential population-level changes (4 years of data total, including 2019 baseline data). 

88 

 
 
 
Year-stratified N-mixture model 

To accommodate the open-population structure that arose from sampling across 

multiple years, I fit all the 𝑇 years (4) jointly using a year-stratified framework (Kéry and Royle 

2021). The year-stratified N-mixture model is a class of hierarchical models for open populations 

(i.e., populations subject to change over time via addition or subtraction of individuals) that can 

be used to estimate trends or covariate effects, when dynamics are not of interest (Kéry and 

Royle 2021). By analyzing the entire data set in a model where every parameter is year-specific, 

it allows the user to impose explicit constraints on the parameters and to share parameters 

among the datasets (Kéry and Royle 2021). This approach is like fitting T separate static models 

(e.g., Appendix 2B), except with the data pooled into a single dataset (also referred to as 

stacking the data) and analyzed jointly (Kéry and Royle 2021). Stacking successive years of data 

yields distinct site-year combinations, enabling the estimation of abundance based on these 

combinations. This approach also satisfies the model’s closure assumption, which denotes 

closure during survey periods and openness between them. 

To account for imperfect detection and spatiotemporal differences in the data (Kellner 

and Swihart 2014), I fit a year-stratified N-mixture model as described by Kéry and Royle (2021). 

For this modeling approach, I converted from JAGS to NIMBLE (Nimble Development Team 

2023a) for increased modeling flexibility (Kéry and Royle 2021) and efficiency (Ponisio et al. 

2020). I fit the model using NIMBLE (de Valpine et al. 2017) in program R (version 4.1.2; R Core 

Team 2021) with the nimble package (version 0.13.1; NIMBLE Development Team 2023b). My 

year-stratified model was much like my static model (Appendix 2B), but with an additional index 

𝑡 for year (i.e., an additional loop). To accommodate this new looping structure, I reformatted 

89 

 
  
the count data from wide to long format (i.e., stacked) and stored data in a 3-dimensional array 

by site (𝑖), replicate count (𝑗), and year (𝑡).  

Using a year-stratified N-mixture modeling approach, I modeled sex-and-age classes 

independently to estimate township-level abundances. My township-abundance model was as 

follows, for each site 𝑖 = 1, 2, …, 𝑀: 

𝑁𝑖,𝑡 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 (𝜆𝑖,𝑡) 

𝑙𝑜𝑔(𝜆𝑖,𝑡) = 𝛽1(𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑖,𝑡) + 𝛽2(𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑖,𝑡) ∗ 𝑌𝑒𝑎𝑟𝑖,𝑡 

+ 𝛽3 ∗ (%𝐴𝑔𝑟𝑖𝑐𝑢𝑙𝑡𝑢𝑟𝑒𝑖,𝑡)

2

+ 𝜀(𝑇𝑜𝑤𝑛𝑠ℎ𝑖𝑝𝑖,𝑡) 

In addition to the extra level of hierarchy (𝑡), my year-stratified model differed from my static 

model in other ways. Harvest treatment and year were hypothesized to influence abundance, 

therefore I incorporated both into the year-stratified model. To account for changes across years 

(i.e., the openness of the system), I included a year effect in the abundance model’s log-link 

function as a set of 𝑇 year-specific intercepts by harvest treatment (𝛽1) and as a set of 𝑇 year-

specific interactions between year and harvest treatment (𝛽2). Note that harvest treatment 

(APR or Non-APR) was not included as a binary covariate via categorical indicator variables, but 

instead as categorical index variables (analogous to ID numbers). Simply put, I had 2 values for 

the intercept (𝛽1) and 2 values for the interaction term (𝛽2) which the model accessed by 

referencing the specified index variable (APR or Non-APR). This mechanism was advantageous 

over common indicator variables (e.g., using 1s and 0s as on-off switches) which can introduce 

unwanted asymmetric uncertainty between treatment groups. I used a similar indexing 

structure to introduce a township random effect in the abundance model. More specifically, I 

gave the model latitude to account for variation in lambda (𝜆) among township and year 

90 

 
combinations by adding the residual-error term epsilon (𝜀) to the model’s log-link function. I 

assigned epsilon an exponential prior to ensure positive values (i.e., drawn from a mean-zero 

normal distribution). 

The year-stratified observational model differed from my static model (Appendix 2B), 

with the additional index 𝑡 for year and the addition of a random effect. My year-stratified 

observation model specified in algebra, was as follows, for sites 𝑖 = 1, 2, …, 𝑀: 

𝑦𝑖,𝑗,𝑡 ~ 𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙(𝑁𝑖,𝑡,  𝑝𝑖,𝑡) 

𝑙𝑜𝑔𝑖𝑡(𝑝𝑖,𝑡) =  𝛼0 +  𝛼1(𝐶𝑜𝑣𝑒𝑟𝑖,𝑡) +  𝜀𝑖,𝑡 

Here, I included a site-by-year random effect in the observation model’s logit-link function, with 

the standard deviation among site and year combinations modeled as the residual-error epsilon 

(𝜀). This approach gave the model latitude to account for heterogeneity in detection probability 

among sites and years, which if not addressed, could confound trend estimates. I assigned 

epsilon an exponential prior to ensure positive values. Parameters monitored included 𝛼, 𝛽, and 

𝜀 values. The R code for the year-stratified N-mixture model is available in the Appendix 

(Appendix 2C). 

Change in site-abundance 

As models grow in complexity, it can be increasingly difficult to interpret coefficients. 

This is particularly relevant when models include quadratic or interaction terms. In such cases, 

visualizing marginal effects can help interpret the relationship between predictors and outcome. 

To interpret the effects of harvest treatment, year, and interaction of the two on deer 

abundance, I plotted the marginal effects derived from the year-stratified N-mixture model. I 

used the estimated model to interpret these effects by township and sex-and-age class, 

91 

 
 
enabling a more intuitive interpretation expressed in terms of mean site-abundance. Put 

differently, I used model predictions for interpretation. This analysis was informed by the N-

mixture model’s intercept, error, and coefficient estimates, with the agriculture covariate 

excluded as it was held constant at the standardized mean (i.e., 0). To preserve uncertainty, I 

used full posterior distributions (28,200 datapoints) for summarizing means and 95% BCIs of 

parameter estimates. I visually inspected marginal-effects plots to interpret relationships 

between the predictors and abundance. Marginal-effect visualization in this context helped 

determine whether the implementation of an APR would produce a negative or positive impact 

on deer abundance in the years following. Note that for township pairs A and D, marginal 

effects were visualized without 2020 data (missing data due to COVID-19 pandemic-related 

constraints). 

Using the year-stratified model, I quantified mean change in site-abundance (𝑥̅) by 

summing differences between 2019 abundance estimates (i.e., the system before the APR 

implementation; 𝑁𝐵̂ ) and 2022 abundance estimates (i.e., the system 3 years after the APR 

implementation; 𝑁𝐴̂ ), for each MCMC iteration (𝑖), divided by the total number of datapoints (𝑛 

= 28,200): 

𝑥̅ =  

𝑛
𝑖=1

∑ (𝑁𝐴̂ 𝑖 − 𝑁𝐵̂ 𝑖)
𝑛

I calculated mean change and determined the magnitude of change to differ between APR and 

Non-APR townships if 95% BCIs did not overlap. Further, I concluded there was a significant 

change in site-abundance if 95% BCIs did not overlap zero. Code for quantifying change in 

abundance and evaluating marginal effects is provided in the Appendix (Appendix 2D). 

92 

 
 
RESULTS 

Field sampling  

From 2019–2022, 144 or 72 camera traps were deployed annually for 63 days, which 

resulted in a total survey effort of 31,227 trap days (Table 2.2). Including camera operation 

failures, the mean camera deployment period was 62 days (SD = 4.2; range = 27–63 days; Table 

2.2). Across years, an average of 11 cameras (SD = 8.8; range = 5–24) experienced partial 

operation issues throughout the deployment period (e.g., full memory cards, camera 

malfunctions, vandalism; Table 2.2). Camera density was approximately 1 per 5.2 km2 (1 per 2.0 

mi2) within each township and cameras averaged 1.3 km (SD = 0.7) between nearest neighbor 

camera sites. Approximately 83% of camera sites were on private lands, an outcome of the 

random site-selection process and partnership with 160 landowners. Under rare circumstances 

(e.g., land-use changes, change in landownership, landowner ceasing to participate in study), 

alternative camera sites had to be secured in later years of the study. In total, 185 distinct 

camera sites were used during this study, resulting in a site similarity of 72% between 2019 and 

2022. 

93 

 
Table 2.2. Annual summaries of the total number of camera traps deployed, the number of 
cameras not fully operational during the deployment period, the mean, SD, and range of camera 
deployment period (days), and total survey effort (trap days). Camera traps were deployed 
during summer months (15 July–15 September) in the south-central Lower Peninsula of 
Michigan, USA, 2019–2022. 

Camera 
traps 

Cameras not 
fully 
operational 

Average 
camera 
deployment 

SD of camera 
deployment  

Range of 
camera 
deployment  

144 

72 

144 

144 

24 

6 

5 

10 

60.9 

61.9 

62.5 

62.5 

5.9 

4.1 

3.2 

2.4 

27–63 

42–63 

32–63 

43–63 

Year 

2019 

2020 

2021 

2022 

Survey 
effort 

8,772 

4,457 

9,002 

8,996 

94 

 
 
Image processing 

Camera traps collected 2,644,590 images during the 4 years of the study, with the APR 

Zone accounting for 1,489,730 images and the Non-APR Zone 1,154,860 (Table 2.3). To expedite 

photo processing after year one of the study (2019), 1,847,183 images from 2020–2022 were 

processed using the MegaDetector object-detection model. A 90+ confidence threshold setting 

was selected for MegaDetector for its ability to minimize the number of irrelevant images 

needing manual review while having little effect on the number of false-negative deer images 

(Appendix 2E). MegaDetector classified 56% of images (1,039,972) as “Animal” and 44% as 

“Empty” (807,211; Figure 2.4).   

All Animal images were manually reviewed to classify species in the field of view. 

Altogether, ≥1 deer were detected in 906,792 photos (Table 2.4). Cameras detected deer at 97% 

of site-year combinations (496/509) throughout the sampling periods (2019–2022), resulting in 

a total of 1,118,757 verified deer detections. Most deer photos included Females in the field of 

view (510,486 detections; Table 2.5). Apart from Unknown Deer (45,606 detections), Legal 

Antlered were detected the least (83,407 detections; Table 2.5).

95 

 
 
 
Table 2.3. Summary of total images collected by year, zone, and study area total (zones 
combined). Images were collected during summer months (15 July–15 September) using a 
camera-trap study design in the south-central Lower Peninsula of Michigan, USA. 

Year 

2019 

2020 

2021 

2022 

APR Zone 

NonAPR Zone 

Study area total 

414,626 

249,972 

390,693 

434,439 

382,781 

198,014 

271,439 

302,626 

797,407 

447,986 

662,132 

737,065 

Table 2.4. Summary of total deer images by year, zone, and study area total. Deer images 
included ≥1 deer detected in the field of view, verified by dual observers. Images were collected 
during summer months (15 July–15 September) using a camera-trap study design in the south-
central Lower Peninsula of Michigan, USA. 

Year 

2019 

2020 

2021 

2022 

APR Zone 

NonAPR Zone 

Study area total 

155,111 

72,184 

140,816 

185,383 

120,683 

46,441 

85,463 

100,711 

275,794 

118,625 

226,279 

286,094 

96 

 
 
 
 
 
Table 2.5. Summary of yearly white-tailed deer (Odocoileus virginianus) image classifications by 
sex-and-age class, zone, and total study area. Deer classifications included ≥1 deer detected in 
the field of view, verified by dual observers. Images were collected during summer months (15 
July–15 September) using a camera-trap study design in the south-central Lower Peninsula of 
Michigan, USA.  

APR Zone 

Non-APR Zone 

Study area total 

61,940 
54,456 
15,392 
5,635 
6,534 

84,205 
57,416 
24,649 
14,404 
9,627 

28,248 
21,824 
4,004 
3,839 
2,587 

43,518 
22,805 
10,830 
5,559 
3,694 

71,766 
44,629 
14,834 
9,398 
6,281 

146,145 
111,872 
40,041 
20,039 
16,161 

Photo classification 
by year 
2019 
Femalea 
Fawnb 
Sub-legal Malec 
Legal Maled 
Unknown Deere 
2020 
Femalea 
Fawnb 
Sub-legal Malec 
Legal Maled 
Unknown Deere 
2021 
Femalea 
Fawnb 
Sub-legal Malec 
Legal Maled 
Unknown Deere 
2022 
Femalea 
61,051 
Fawnb 
39,573 
Sub-legal Malec 
13,657 
Legal Maled 
8,393 
Unknown Deere 
3,608 
aFemale classifications include yearling and adult female deer. 
bFawn classifications include male and female fawns. 
cSub-legal Male classifications include antlered deer that did not meet the antler point 
restriction criteria. 
dLegal Male classifications include antlered deer that met the antler point restriction criteria. 
eDeer were classified as Unknown Deer when it was impossible to determine the sex or age of 
the deer (e.g., unable to see head). 

168,726 
113,053 
43,970 
20,977 
10,619 

123,849 
77,104 
33,980 
32,993 
12,545 

107,675 
73,480 
30,313 
12,584 
7,011 

75,854 
42,700 
20,480 
25,805 
7,111 

47,995 
34,404 
13,500 
7,188 
5,434 

97 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.4. Classification results produced by MegaDetector, a machine-learning model designed to detect and classify objects 
in images. Images analyzed were collected using a camera-trap study design in the south-central Lower Peninsula of Michigan, 
USA, 2020–2022.

98 

 
 
Static binomial N-mixture model 

I used the static binomial N-mixture model to estimate deer abundance one-year-at-a-

time. Although there are applications for this closed-population model, I did not consider it 

appropriate for this study—based on model limitations and the objectives of the state wildlife 

agency. Outcomes from this modeling effort are described in detail in the Appendix (Appendix 

2B). 

Year-stratified N-mixture model 

Using my year-stratified N-mixture model, I fit all 4 years of data jointly to estimate 

annual deer abundance. I did not detect any significant changes in Legal Antlered abundance in 

APR or Non-APR townships (Figure 2.5). Relative to its corresponding baseline estimate in 2019, 

I detected a single increase in Female abundance in the Non-APR Zone’s B Township (2019: x̅ = 

29.4 [95% BCI = 26–35]; 2021: x̅ = 42.1 [95% BCI = 37–48]; Figure 2.6). Relative to 2019 baseline 

estimates, I detected significant increases in Sub-legal Antlered abundance in the Non-APR 

Zone’s Township A (2019: x̅ = 21.2 [95% BCI = 17–27]; 2022: x̅ = 37.7 [95% BCI = 31–47]) and 

Township D (2019: x̅ = 21.6 [95% BCI = 17–28]; 2022: x̅ = 41.4 [95% BCI = 34–51]; Figure 2.7). I 

failed to detect any significant changes in Fawn abundance in APR or Non-APR townships 

(Figure 2.8).

99 

 
 
Figure 2.5. Pre-harvest mean abundance of legal antlered white-tailed deer (Odocoileus 
virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Relative 
abundance was used as an index and assumed to be functionally related to population size. 
Beginning in 2019, antlered deer harvest was limited by a 4-point antler point restriction (APR) 
in the APR Zone, but not in the Non-APR Zone. Legal-antlered deer are defined by the APR 
criteria in the APR Zone. Zones are displayed in the grid columns and township pairs (A–D) in 
the grid rows. Abundance relates to the number of deer within the effective sampling area (i.e., 
area surveyed) of a specified township. Error bars indicate 95% Bayesian credible intervals. Only 
half of the townships were surveyed in 2020 due to pandemic-related constraints. Relative to 
2019 baseline estimates (i.e., the system before APR implementation), no significant changes 
were detected.

100 

 
Figure 2.6. Pre-harvest mean abundance estimates of female (subadult and adult, i.e., does) 
white-tailed deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, 
USA, 2019–2022. Relative abundance was used as an index and assumed to be functionally 
related to population size. Beginning in 2019, antlered deer harvest was limited by a 4-point 
antler point restriction (APR) in the APR Zone, but not in the Non-APR Zone. Zones are 
displayed in the grid columns and township pairs (A–D) in the grid rows. Abundance relates to 
the number of deer within the effective sampling area (i.e., area surveyed) of a specified 
township. Error bars indicate 95% Bayesian credible intervals. Only half of the townships were 
surveyed in 2020 due to pandemic-related constraints. Relative to baseline estimates in 2019 
(i.e., the system before APR implementation), a significant increase was detected in the Non-
APR Zone (Township B 2021). 

101 

 
Figure 2.7. Pre-harvest relative abundance estimates of sub-legal antlered white-tailed deer 
(Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. 
Relative abundance was used as an index and assumed to be functionally related to population 
size. Beginning in 2019, antlered deer harvest was limited by a 4-point antler point restriction 
(APR) in the APR Zone, but not in the Non-APR Zone. Sub-legal antlered deer are defined by not 
meeting the APR criteria in the APR Zone. Zones are displayed in the grid columns and township 
pairs (A–D) in the grid rows. Abundance relates to the number of deer within the effective 
sampling area (i.e., area surveyed) of a specified township. Error bars indicate 95% Bayesian 
credible intervals. Only half of the townships were surveyed in 2020 due to pandemic-related 
constraints. Relative to baseline estimates in 2019 (i.e., the system before APR implementation), 
a significant increase was detected in the Non-APR Zone (Township A 2022; Township D 2022).

102 

 
Figure 2.8. Pre-harvest relative abundance estimates of fawn white-tailed deer (Odocoileus 
virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Relative 
abundance was used as an index and assumed to be functionally related to population size. 
Beginning in 2019, antlered deer harvest was limited by a 4-point antler point restriction (APR) 
in the APR Zone, but not in the Non-APR Zone. Zones are displayed in the grid columns and 
township pairs (A–D) in the grid rows. Abundance relates to the number of deer within the 
effective sampling area (i.e., area surveyed) of a specified township. Error bars indicate 95% 
Bayesian credible intervals. Only half of the townships were surveyed in 2020 due to pandemic-
related constraints. Relative to 2019 baseline estimates (i.e., the system before APR 
implementation), no significant changes were detected.

103 

 
Change in site-abundance 

To better interpret the year-stratified N-mixture model’s predictions, I plotted the 

marginal effect of explanatory variables (harvest treatment, year, and interaction of the two) on 

site-abundance by sex-and-age class. These visualizations revealed a pattern of positive trends 

in marginal effects for all sex-and-age classes across all townships (Figure 2.9, Figure 2.10, Figure 

2.11, Figure 2.12). I calculated the difference between 2019 and 2022 site-abundance and 

determined the magnitude of change to be similar between paired townships for all sex-and-

age classes (Figure 2.13, Figure 2.14, Figure 2.15, Figure 2.16). I detected significant changes 

(i.e., 95% BCIs did not include zero) in site-abundance with Legal Antlered and Sub-legal 

Antlered increasing in all townships (Figure 2.13, Figure 2.15). I failed to detect significant 

changes in site-abundance for Females and Fawns (Figure 2.14, Figure 2.16). The largest mean 

change in site-abundance was estimated with Legal Antlered in the APR Zone’s Township B (x̅ = 

1.35; 95% BCI = 0.39–2.54; Figure 2.13) and smallest with Fawns in the APR Zone’s Township D 

(x̅ = 0.18; 95% BCI = -0.42–0.79; Figure 2.16).  

104 

 
Figure 2.9. Marginal effect of harvest treatment, year, and the interaction of the two on mean site-abundance of legal-antlered 
white-tailed deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Beginning in 2019, 
antlered deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in the Non-APR Zone. Legal-
antlered deer are defined by the APR criteria in the APR Zone. Zones are differentiated by color and individual township pairs (A–D) 
are displayed in each panel. Site-abundance relates to the mean number of deer within the effective sampling area at survey sites. 
Error bars indicate 95% Bayesian credible intervals. Only half of the township pairs were surveyed in 2020 (due to COVID-19 
pandemic-related constraints), and consequently, marginal effects were visualized in the absence of 2020 data for township pairs A 
and D.

105 

 
Figure 2.10. Marginal effect of harvest treatment, year, and the interaction of the two on mean site-abundance of female (subadult 
and adult, i.e., does) white-tailed deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. 
Beginning in 2019, antlered deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in the Non-
APR Zone. Zones are differentiated by color and individual township pairs (A–D) are displayed in each panel. Site-abundance relates 
to the mean number of deer within the effective sampling area at survey sites. Error bars indicate 95% Bayesian credible intervals. 
Only half of the township pairs were surveyed in 2020 (due to COVID-19 pandemic-related constraints), and consequently, marginal 
effects were visualized in the absence of 2020 data for township pairs A and D.

106 

 
Figure 2.11. Marginal effect of harvest treatment, year, and the interaction of the two on mean site-abundance of sub-legal antlered 
white-tailed deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Beginning in 2019, 
antlered deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in the Non-APR Zone. Sub-legal 
antlered deer are defined by not meeting the APR criteria in the APR Zone. Zones are differentiated by color and individual township 
pairs (A–D) are displayed in each panel. Site-abundance relates to the mean number of deer within the effective sampling area at 
survey sites. Error bars indicate 95% Bayesian credible intervals. Only half of the township pairs were surveyed in 2020 (due to 
COVID-19 pandemic-related constraints), and consequently, marginal effects were visualized in the absence of 2020 data for 
township pairs A and D.

107 

 
Figure 2.12. Marginal effect of harvest treatment, year, and the interaction of the two on mean site-abundance of fawn white-tailed 
deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Beginning in 2019, antlered deer 
harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in the Non-APR Zone. Zones are differentiated 
by color and individual township pairs (A–D) are displayed in each panel. Site-abundance relates to the mean number of deer within 
the effective sampling area at survey sites. Error bars indicate 95% Bayesian credible intervals. Only half of the township pairs were 
surveyed in 2020 (due to COVID-19 pandemic-related constraints), and consequently, marginal effects were visualized in the absence 
of 2020 data for township pairs A and D. 

108 

 
Figure 2.13. Mean change in site-abundance of legal antlered white-tailed deer (Odocoileus 
virginianus) between 2019 and 2022 in the south-central Lower Peninsula of Michigan, USA. 
Estimates were derived from pre-harvest abundance estimates. Beginning in 2019, antlered 
deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in 
the Non-APR Zone. Legal-antlered deer are defined by the APR criteria in the APR Zone. Zones 
are differentiated by color, the horizontal dashed line indicates zero change in site abundance, 
and error bars indicate 95% Bayesian credible intervals. Similar increases were detected across 
APR and Non-APR townships.

109 

 
Figure 2.14. Mean change in site-abundance of female (subadult and adult, i.e., does) white-
tailed deer (Odocoileus virginianus) between 2019 and 2022 in the south-central Lower 
Peninsula of Michigan, USA. Estimates were derived from pre-harvest abundance estimates. 
Beginning in 2019, antlered deer harvest was limited by a 4-point antler point restriction (APR) 
in the APR Zone, but not in the Non-APR Zone. Zones are differentiated by color, the horizontal 
dashed line indicates zero change in site abundance, and error bars indicate 95% Bayesian 
credible intervals. Estimates were similar among townships and no changes were detected.

110 

 
Figure 2.15. Mean change in site-abundance of sub-legal antlered white-tailed deer (Odocoileus 
virginianus) between 2019 and 2022 in the south-central Lower Peninsula of Michigan, USA. 
Estimates were derived from pre-harvest abundance estimates. Beginning in 2019, antlered 
deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone, but not in 
the Non-APR Zone. Sub-legal antlered deer are defined by not meeting the APR criteria in the 
APR Zone. Zones are differentiated by color, the horizontal dashed line indicates zero change in 
site abundance, and error bars indicate 95% Bayesian credible intervals. Similar increases were 
detected across APR and Non-APR townships.

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Figure 2.16. Mean change in site-abundance of fawn white-tailed deer (Odocoileus virginianus) 
between 2019 and 2022 in the south-central Lower Peninsula of Michigan, USA. Estimates were 
derived from pre-harvest abundance estimates. Beginning in 2019, antlered deer harvest was 
limited by a 4-point antler point restriction (APR) in the APR Zone, but not in the Non-APR Zone. 
Zones are differentiated by color, the horizontal dashed line indicates zero change in site 
abundance, and error bars indicate 95% Bayesian credible intervals. Estimates were similar 
among townships and no changes were detected.

112 

 
DISCUSSION 

In this study, I assessed population-level changes over time and space following a deer 

harvest regulation implementation in a before-after-control-impact design. I used several 

analytical approaches to evaluate if APRs affect deer relative abundance by sex-and-age class. To 

my knowledge, this is the first study paired with an APR regulation change specifically designed 

to evaluate this question. I found weak evidence for APRs affecting the relative abundance by 

sex-and-age classes. In both APR and Non-APR areas, I consistently observed increasing trends 

in the relative abundance of Legal- and Sub-legal Antlered deer. In comparison, there was a lack 

of evidence supporting change in Female and Fawn relative abundance in APR or Non-APR 

areas. 

My results suggest that the implementation of APRs had an insignificant impact on the 

Legal-Antlered deer populations in the experimental zone of the 5-County Area. In contrast to 

my prediction, I found increases in the relative abundance of Legal-Antlered deer in both APR 

and Non-APR treatment areas. It is important to note that when evaluating results, I considered 

comparisons between 2019 and 2022 relative abundance estimates within townships important 

and comparisons among paired townships as most meaningful due to partial controllability in a 

natural system (i.e., I relied on the BACI study design). Relative to 2019 baseline abundance 

estimates, I did not detect any significant township-level changes in APR or Non-APR areas, but 

I did observe a general trend of increasing mean estimates over time (Figure 2.5). Further, I 

detected similar increases in site-abundance of Legal Antlered deer from 2019–2022 among 

paired townships. This finding was reinforced by my evaluation of the year-stratified N-mixture 

model, where I observed similar effects of harvest treatment, year, and the interaction of the 

113 

two on Legal-Antlered deer abundance among paired townships (Figure 2.9). It is worth noting 

that the increases in Legal-Antlered deer were considerably small at the site level 

(approximately 1 deer for APR and Non-APR areas; Figure 2.13). These small magnitudes of 

change were likely the reason why I was unable to detect annual changes in abundance at the 

township scale (Figure 2.5). The APR may have helped with advancing Sub-legal Antlered deer 

to the next age class, as I observed higher mean estimates of site-level changes in APR areas 

compared to Non-APR areas. 

Despite the increased protection of Sub-legal Antlered deer in APR-treatment areas, my 

results indicated similar trends in relative abundance of Legal-Antlered deer between APR and 

Non-APR areas. These results were surprising, as I expected the additional antlered-harvest 

opportunities in the Non-APR Zone would limit the number of Sub-legal Antlered deer 

advancing to the Legal-Antlered class. Kellner et al. (2021) evaluated the effects of an APR on 

deer harvest in New York and observed a decline in the proportion of yearlings in the antlered 

harvest in Non-APR areas adjacent to APR-treatment areas. However, this phenomenon may 

have been explained in part by New York’s outreach strategies to encourage hunters to 

voluntarily restrain from harvesting young antlered deer (New York State Department of 

Environmental Conservation 2011, 2023; Robinson et al. 2016). Michigan’s state agency did not 

encourage hunters to harvest any specific age class of antlered deer. It is possible that there was 

some sort of linkage effect, where hunter behavior changed in the Non-APR Zone because of 

the study or implementation of APRs in adjacent counties. Alternatively, the similar increases in 

Legal-Antlered deer in APR and Non-APR treatment areas may indicate a generalized shift 

towards yearling male protection among Michigan deer hunters.  

114 

It is possible that voluntary (i.e., non-mandatory) APRs played an important role in the 

results of this study. Partial controllability of hunter harvest (also referred to as implementation 

uncertainty) can limit the influence of management decisions on realized harvest (Williams 

1997, Moa et al. 2017, Dahlgren et al. 2021). My results showed similar trends in relative 

abundance of Legal-Antlered deer between APR and Non-APR areas, at both the township and 

site level (Figure 2.5, Figure 2.13). It is important to emphasize that the hypothesis that 

mandatory APRs increase adult male abundance was dependent on hunters not practicing 

voluntary APRs. Given it was not feasible to prevent hunters from practicing voluntary APRs 

before or during this study, it is possible that this accounts for similar trends in the Non-APR 

Zone. Similarly, it is possible that hunters in the APR Zone were already practicing APRs prior to 

them becoming mandatory. One of these scenarios on its own could affect the results of this 

study. Combined, voluntary APRs in these contexts could explain the similar population-level 

trends for Legal-Antlered deer in APR and Non-APR areas.  

Over the past few decades, there has been a growing interest in APRs across the United 

States (Adams and Hamilton 2011), and the MDNR has received numerous requests to 

implement mandatory APRs (Frawley 2019). Concurrently, there has been an increasing 

percentage of Michigan hunters who indicate they voluntarily restrict themselves from 

harvesting young antlered deer (Frawley and Rudolph 2008, 2014). Further, this hunter behavior 

has been reflected in trends from MDNR deer check station data. These data have shown a 

steady decline in the proportion of yearling males harvested in the 5-County Area, declining by 

approximately 10% in the years leading up to this study (Appendix 2F). Prior to the APR 

regulation change in this study, opinion surveys indicated that 63% of hunters in the 5-County 

115 

Area supported the implementation of mandatory APRs (Frawley 2019). Later, in 2022, Michigan 

began a mandatory harvest reporting program and found that approximately two-thirds of all 

antlered deer harvested in the state of Michigan met the 4-point APR described in this study 

(Stewart 2023). Although this program occurred outside of our study period and included areas 

with and without mandatory APRs, it does suggest a statewide trend of hunter selection for 

larger-antlered deer and self-imposed restrictions on yearling male harvest (Appendix 2F).  

Hunter selectivity for older deer with larger antler growth has implications for CWD 

spread and growth. With regards to hunter selectivity, increasing deer populations can translate 

to more, larger-antlered deer on the landscape, which may facilitate hunters being more 

selective for these deer (i.e., not harvesting females or younger males). This type of selective 

behavior may influence the size of the adult-male population on the landscape (Milner et al. 

2007), as suggested by this study. From a CWD-management perspective, this is concerning, 

given that CWD prevalence generally increases with age and is estimated to be higher in adult 

males than females (Grear et al. 2006, Osnas et al. 2009, Heisey et al. 2010, Rees et al. 2012, 

Samuel and Storm 2016). Further, APRs (mandatory or voluntary) leave more yearling males on 

the landscape with larger movement patterns than adults (Nelson 1993, Long et al. 2005, Nixon 

et al. 2007, Skuldt et al. 2008), which can further contribute to disease spread. Several model-

based studies have concluded that harvesting males, without distinguishing among age classes, 

or intensifying harvest of yearling males, is a viable strategy to mitigate CWD prevalence or 

lower the likelihood of CWD outbreaks (Potapov et al. 2016, Belsare and Stewart 2020). Further, 

Michigan-specific agent-based models (Belsare and Stewart 2020) informed and adapted with 

116 

empirical data from this study show harvest plays an important role in CWD dynamics, with 

higher outbreak severity in populations with higher compositions of adult males (Appendix 2G). 

My results suggest that deer densities are likely increasing throughout the study area. I 

found clear support for my prediction that the abundance of Females, Sub-legal Antlered deer, 

and Fawns would not decline under APR or Non-APR harvest treatments. Survival rates of 

female deer are important to the extent that they influence population growth (Gaillard et al. 

1998). Relative to 2019 baseline abundance estimates, I did not detect any significant declines 

in township-level relative abundance of Female deer in APR or Non-APR areas. However, I did 

detect a significant increase in a Non-APR township and observed a general increasing trend in 

mean abundance estimates over time (Figure 2.6). I did not detect significant changes in Female 

relative abundance from 2019–2022 at the site level, but most posterior estimates included 

values greater than zero, suggesting overall increasing trends (Figure 2.14). Model predictions 

further reinforce these claims, highlighting increasing trends in relative abundance for all sex-

and-age classes in APR and Non-APR areas (Figure 2.9, Figure 2.10, Figure 2.11, Figure 2.12).  

Harvest data from the MDNR indicated that both antlered and antlerless deer harvest 

were similar between APR and Non-APR counties in the 5-County Area during the study period 

(2019–2021 harvest seasons) and in the preceding year (2018 harvest season; Appendix F). 

While the evaluation of harvest data was not an objective of this study, it is important to 

consider harvest when interpreting the pre-harvest relative abundance estimates here. This is 

particularly relevant to the hypothesis that APRs reduce deer abundance, as it depends on 

augmented antlerless harvest. This effect did not materialize, as the trends in antlerless harvest 

were comparable between APR and Non-APR counties throughout the 2018–2021 deer harvest 

117 

seasons. Although not significant, the highest antlerless harvests were observed in 2020 for 

both APR and Non-APR counties. 

While the scope of this study was limited to measuring deer ecology and abundance in 

relation to a harvest regulation, I recognize that the human dimensions and social landscape are 

important to consider. This is especially relevant given that my study sites were predominantly 

on private land (83%) and the southern Lower Peninsula of Michigan has the highest density of 

private-land, deer-hunting cooperatives in the state (Kramer et al. 2016). There are several 

important factors that affect whether hunters on private land support or disapprove of APRs 

(voluntary or mandatory). One may be the participation in a hunter cooperative, as there were 

at least 15 deer-hunting cooperatives within the study area (MUCC 2023). These cooperatives 

voluntarily collaborate to meet common harvest and population management goals, and 

provide opportunities for hunters to influence deer management across private lands 

(Mitterling et al. 2021). Close-knit families or social groups that do not belong to cooperatives, 

but own large or adjacent parcels, may have had a similar influence. For either group, support 

may be high among hunters pursuing adult males if the APR is intended to increase the 

abundance of adult male deer. In contrast, deer hunters interested in harvesting any sex-and-

age class may feel a loss of opportunity under APR scenarios. In this study, hunters were not 

required to harvest antlerless deer in Michigan, and antlerless harvest was dependent on 

hunter willingness. As seen in other regions, hunter willingness to harvest antlerless deer is 

often limited (Brown et al. 2000, Riley et al. 2003, Giles and Findlay 2004, Van Deelen et al. 

2010), and may be a limiting factor in Michigan (Stewart 2023). 

118 

It is unlikely that recreational harvest will have the capacity to control deer populations 

in Michigan. Although undetected in my data, there were statewide increases in hunter 

participation and antlerless harvest in the 2020 season. From 2019–2020, there was a 5% 

significant increase in hunters afield and a 26% significant increase in the number of antlerless 

deer harvested (Frawley 2020). These increases likely reflected the effect of COVID-19 

restrictions allowing more individuals more time to hunt (Danks et al. 2022), and that hunters in 

the Lower Peninsula could harvest an antlerless deer with a combination license beginning in 

2020 (Frawley 2020). Further, most counties in the study area accounted for some of the 

highest antlerless harvest densities in the state (Frawley 2020). Despite the increased mortality 

of antlerless deer, I failed to detect any significant declines in Female relative abundance in 

2021. At the township level, most pre-harvest Female mean abundance estimates were actually 

higher in 2021 than 2020, including a significant increase in a Non-APR township (Figure 2.6). 

Together, these findings suggest that deer populations continued to grow despite higher hunter 

participation and antlerless harvest. 

The increasing deer populations may, in part, be attributed to a decline in overall hunter 

participation or willingness to harvest antlerless deer (Brown et al. 2000, Riley et al. 2003, Giles 

and Findlay 2004). For example, the number of deer hunting license buyers in Michigan has 

declined 33% from 1995–2019 and has been projected to decline an additional 26% by 2030 

(50% total decline from 1995; B. Frawley, MDNR, unpublished data). Today, approximately 50% 

of Michigan deer hunters harvest deer, most of which are antlered, and most hunters only 

harvest a single deer (Frawley 2020, 2021, 2022). To highlight the extent to which hunters favor 

antlered deer, MDNR data shows that 75% of Michigan hunters do not harvest an antlerless 

119 

deer (Stewart 2023). To stabilize or reduce current deer densities, more females would need to 

be harvested—and my results suggest that APR and Non-APR harvest regimes were not 

sufficient in achieving these goals. To achieve these goals, it may require the adoption of 

hunting regulations that incentivize hunters to harvest antlerless deer voluntarily or require 

them to do so (Brown et al. 2000). 

It is possible that other uncontrollable factors influenced deer populations in this study, 

including natural and anthropogenically driven landscape changes. Resulting deer habitat 

alterations can impact populations at different spatial scales, depending on the size, shape, 

frequency, and intensity of the manipulation or disturbance (Hiller et al. 2009). For example, 

agricultural practices, including annual crop rotations, were a common occurrence at study 

sites. Evidence of timber harvest was also observed, although these occurrences were 

infrequent at sites and did not occur at annual intervals. Changes in deer habitat such as these 

are particularly relevant because deer distribution and abundance is influenced by the amount 

of forested cover and agricultural food available (VerCauteren and Hygnstorm 1994, Walter et 

al. 2009). Further, during non-breeding seasons (e.g., the summer survey period), sexual 

segregation occurs within deer populations (McCullough 1979), defined as the differential use 

of space or other resources by the sexes (Bowyer 2004). For example, in agro-forested 

ecosystems, adult males commonly associate with row crops and females with early 

successional upland forests (Nixon et al. 1991, 1994). Therefore, any deer habitat alterations 

during this study may have influenced the distribution and abundance of sex-and-age classes 

across the landscape. 

120 

This study highlights the challenge of evaluating regulation changes on free-ranging 

wildlife populations given inherent structural and observational uncertainty. I found that the 

APR regulation change in this study had little effect on deer populations and the magnitude of 

change was unimportant at the deer-management scale (e.g., county, multi-county). Similar 

studies seeking to improve the ability to identify temporal or spatial differences in abundance 

could pair the camera-trap study design with marked animals (e.g., ear-tagged or collared deer) 

to help correct for imperfect detection and address assumptions of closure and independence. 

A potential alternative approach to improving precision of parameter estimates is 

implementing a multi-species model to leverage shared information (Yamura et al. 2012, 

Gomez et al. 2017, Moral et al. 2018). Although promising, these frameworks may require more 

data and can be more complex and computationally intensive than single-species models. 

Further, the high level of effort in this study (see Chapter 1 single-season labor estimates) may 

not be sustainable for other camera-trap studies and additional efforts may challenge the 

feasibility of such studies altogether. 

Here, I assessed potential population-level changes following the implementation of a 

mandatory APR and examined two prevalent APR hypotheses: (H1) implementing APRs 

increases adult male abundance, and (H2) implementing APRs decreases overall deer 

abundance. Taking a comprehensive view of my findings, I found little and no support for these 

two hypotheses, respectively. In areas where deer populations exceed management objectives, 

declining hunter participation, increased selectivity, and increasing deer populations will likely 

decrease the effectiveness of recreational harvest as a population-control mechanism under 

current regulatory systems (Brown et al. 2000, Riley et al. 2003, Giles and Findlay 2004). 

121 

 
Specifically, my results highlight potential limitations of APRs achieving desired effects for 

population reduction goals and the importance of developing harvest regulations specific to the 

targeted deer population, area, and management goals, and I recommend careful consideration 

of the partial controllability of harvest regulations.  

122 

LITERATURE CITED 

Adams, K. P. and R. J. Hamilton. 2011. Management history. Pages 355–377 in D.G. Hewitt, 

editor. Biology and management of white-tailed deer, CRC Press, Boca Raton, Florida, USA. 

Barker, R. J., M. R. Schofield, W. A. Link, and J. R. Sauer. 2018. On the reliability of N-mixture 

models for count data. Biometrics 74:369–377. Wiley-Blackwell. 

Beery, S., D. Morris, and S. Siyu. 2019. Efficient pipeline for camera trap image review. arXiv 

preprint arXiv:1907.06772. beery2019efficient. 

Beier, P., and D. R. McCullough. 1990. Factors influencing white-tailed deer activity patterns 

and habitat use. Wildlife Monographs 3–51.  

Belsare, A. V., J.  J. Millspaugh, J. R. Mason, J. Sumners, H. Viljugrein, and A. Mysterud. 2021. 
Getting in front of chronic wasting disease: model-informed proactive approach for 
managing an emerging wildlife disease. Frontiers in Veterinary Science, 7, 608235. 
doi.org/10.3389/fvets. 2020.608235. 

Belsare, A. V., and C. M. Stewart. 2020. OvCWD: An agent-based modeling framework for 
informing chronic wasting disease management in white-tailed deer populations. 
Ecological Solutions and Evidence 1:e12017. 

Bender, L. C., P. E. Fowler, J. A. Bernatowicz, J. L. Musser, and L. E. Stream. 2002. Effects of 

open-entry spike-bull, limited-entry branched bull harvesting on elk composition in 
Washington. Wildlife Society Bulletin 30:1078–1084. 

Bender, L. C., and P. J. Miller. 1999. Effects of elk harvest strategy on bull demographics and 

herd composition. Wildlife Society Bulletin 27:1032–1037. 

Biederbeck, H. H., M. C. Boulay, and D. H. Jackson. 2001. Effects of hunting regulations on bull 

elk survival and age structure. Wildlife Society Bulletin 29:1271–1277. 

Boyd, R. J., and J. F. Lipscomb. 1976. An evaluation of yearling bull elk hunting restrictions in 

Colorado. Wildlife Society Bulletin 4:3–10. 

Bowyer, R. T. 2004. Sexual segregation in ruminants: definitions, hypotheses, and implications 

for conservation and management. Journal of Mammalogy 85:1039–1052. 

Brown, T., S. Riley, J. Enck, T. Lauber, P. Curtis, and G. Mattfeld. 2000. The future of hunting as a 
mechanism to control white-tailed deer populations. Wildlife Society Bulletin 28:797–807. 

Cain, R. L., D. M. Williams, and W. F. Porter. 2022. The effectiveness of antler point restrictions 

to achieve management goals. Wildlife Society Bulletin 46:e1359. 

123 

Carpenter, L. H., 2000. Harvest management goals. Pages 192–213 in S. Demarais and P. R. 
Krausman, editors. Ecology and management of large mammals in North America. 
Prentice-Hall, Upper Saddle River, New Jersey, USA. 

Carpenter, L. H., and R. B. Gill. 1987. Antler point regulations the good, the bad, and the ugly. 

Transactions of the Western Association of Game and Fish Commissioners 67:94–107. 

Child, K., D. A. Aitken, R. V. Rea, and R. A. Demarchi. 2010. Potential vulnerability of bull moose 
in central British Columbia to three antler-based hunting regulations. Alces: A Journal 
Devoted to the Biology and Management of Moose 46:113–121. 

Christie, A. P., T. Amano, P. A. Martin, G. E. Shackelford, B. I. Simmons, and W. J. Sutherland. 
2019. Simple study designs in ecology produce inaccurate estimates of biodiversity 
responses. Journal of Applied Ecology 56:2742–2754. 

Christin, S., É. Hervet, and N. Lecomte. 2021. Going further with model verification and deep 

learning. Methods in Ecology and Evolution 12:130–134. 

Cohen, B., E. Leone, E. Garrison, C. Morea, S. Shea, K. Miller, M. Cherry, J. Stickles, and J. Kelly. 
2016. Evaluation of antler-based selective harvest criteria on harvest and antler size of 
male white-tailed deer in Florida. Journal of Southeastern Association of Fish and Wildlife 
Agencies 3:203–209. 

Collier, B. A., and D. G. Krementz. 2007. Uncertainty in age-specific harvest estimates and 
consequences for white-tailed deer management. Ecological Modeling 201:194–204. 

Connelly, J. W., J. H. Gammonley, and T. W. Keegan. 2012. Harvest management. Pages 202–231 
in N. J. Silvy, editor. The Wildlife Techniques Manual: Management. Volume 2. Seventh 
edition. The Johns Hopkins University Press, Baltimore, Maryland, USA.  

Cross, P. C., J. Drewe, V. Patrek, G. Pearce. M. D. Samuel, and R. J. Delahay. 2009. Wildlife 

population structure and parasite transmission: implications for disease management. 
Pages 9–29 in R. J. Delahay, G. C. Smith, and M. R. Hitchings, editors. Management of 
disease in wild mammals. Springer, Tokyo, Japan. 

Dahlgren, D. K., E. J. Blomberg, C. A. Hagen, and R. D. Elmore. 2021. Upland game bird harvest 

management. Pages 307–325 in K. L. Pope and L. A. Powell, editors. Harvest of fish and 
wildlife: new paradigms for sustainable management. CRC Press, Boca Raton, Florida, USA. 

Danks, Z. D., M. V. Schiavone, A. B. Butler, K. Fricke, A. Davis, and D. T. Cobb. 2022. Effects of the 
COVID-19 pandemic on 2020 spring turkey hunting across the United States. Wildlife 
Society Bulletin 46:e1294. 

Demarais, S., K. V. Miller, and H. A. Jacobson. 2000. White-tailed deer. Pages 601–628 in S. 
Demarais and P.R. Krausman, editors. Ecology and Management of Large Mammals in 
North America. Prentice Hall, Upper Saddle River, New Jersey, USA. 

124 

Demarais, S. and B. K Strickland. 2011. Antlers. Pages 107–145 in D.G. Hewitt, editor. Biology 

and Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

Demarais, S., B. Strickland, and L. Castle. 2005. Antler regulation effects on white-tailed deer on 

Mississippi public hunting areas. Proceedings of the Annual Conference of the 
Southeastern Association of Fish and Wildlife Agencies 59:1–9. 

de Valpine, P., D. Turek, C.J. Paciorek, C. Anderson-Bergman, D. Temple Lang, and R. Bodik. 2017. 

Programming with models: writing statistical algorithms for general model structures 
with NIMBLE. Journal of Computational and Graphical Statistics 26:403–
413. https://doi.org/10.1080/10618600.2016.1172487. 

Dewitz, J. 2019. National Land Cover Database (NLCD) 2016 Products (ver. 3.0, November 2023): 

U.S. Geological Survey data release, https://doi.org/10.5066/P96HHBIE. 

Diefenbach, D. R., W. M. Know, and C. S. Rosenberry. 2021. The future of managing ungulate 
species: white-tailed deer as a case study. Pages 327–339 in K. L. Pope and L. A. Powell, 
editors. Harvest of Fish and Wildlife: New Paradigms for Sustainable Management. CRC 
Press, Boca Raton, Florida, USA. 

Ditchkoff, S. S., E. R. Welch, R. L. Lochmiller, R. E. Masters, and W. R. Starry. 2001. Age-specific 
causes of mortality among male white-tailed deer support mate-competition theory. The 
Journal of Wildlife Management 65:552–559. 

Elliott, J. R., Newbolt, C. H., Dunning, K. H., Gulsby, W. D., and S. S. Ditchkoff. 2022. Training and 
experience increase classification accuracy in white-tailed deer camera surveys. Wildlife 
Research. 

Erickson, G. L., J. R. Heffelfinger, and J. H. Ellenberger. 2003. Potential effects of hunting and 

hunt structure on mule deer abundance and demographics. Pages 119–138 in J. C. de Vos, 
Jr., M. R. Conover, and N. E. Headrick, editors. Mule deer conservation: issues and 
management strategies. Berryman Institute Press, Utah State University, Logan, USA. 

Environmental Systems Research Institute [ESRI] 2020. ArcGIS Pro: 2.7.1. Redlands, California, 

USA. 

Fackler, P., and K. Pacifici. 2014. Addressing structural and observational uncertainty in resource 

management. Journal of Environmental Management 133:27–36. 

Frawley, B. J. 2017. Evaluation of antler point restrictions in deer management units in the 

northwest Lower Peninsula. Michigan Department of Natural Resources Wildlife Division 
Report 3638, Lansing, USA. 

Frawley, B. J. 2019. Antler point restrictions study survey in the core CWD area. Michigan 

Department of Natural Resources Wildlife Division Report No. 3672, Lansing, USA. 

125 

 
 
 
Frawley, B. J. 2020. Michigan deer harvest survey report 2019 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3691, Lansing, USA.  

Frawley, B. J. 2021. Michigan deer harvest survey report 2020 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3697, Lansing, USA. 

Frawley, B. J. 2022. Michigan deer harvest survey report 2021 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3704, Lansing, USA. 

Frawley, B. J. 2023. Michigan deer harvest survey report 2022 seasons. Michigan Department of 

Natural Resources Wildlife Division Report No. 3713, Lansing, USA. 

Frawley, B. J., and B. A. Rudolph. 2008. 2006 deer hunter opinion survey. Wildlife Division 

Report 3482. Michigan Department of Natural Resources, Lansing, Michigan, USA. 

Frawley, B. J., and B. A. Rudolph. 2014. 2012 deer hunter opinion survey. Wildlife Division 

Report 3580. Michigan Department of Natural Resources, Lansing, Michigan, USA. 

Furnas, B. J., R. H. Landers, R. G. Paiste, and B. N. Sacks. 2020. Overabundance of black-tailed 

deer in urbanized coastal California. The Journal of Wildlife Management 84:979–988. 

Gaillard, J.-M., M. Festa-Bianchet, and N. G. Yoccoz. 1998. Population dynamics of large 

herbivores: variable recruitment with constant adult survival. Trends in Ecology & Evolution 
13:58–63. 

Gilbert, N. A., J. D. J. Clare, J. L. Stenglein, and B. Zuckerberg. 2021. Abundance estimation of 
unmarked animals based on camera-trap data. Conservation Biology 35:88–100. 

Giles, B. G., and C. S. Findlay. 2004. Effectiveness of a selective harvest system in regulating deer 

populations in Ontario. Journal of Wildlife Management 68:266–277. 

Gillin, C. M., and J. R. Mawdsley, editors. 2018. AFWA technical report on best management 

practices for surveillance, management and control of chronic wasting disease. Association 
of Fish and Wildlife Agencies, Washington, D. C., USA. 

Ginsberg, J. R., and E. J. Milner-Gulland. 1994. Sex-biased harvesting and population dynamics 
in ungulates: implications for conservation and sustainable use. Conservation Biology 
8:157–166. 

Gomez, J. P., S. K. Robinson, J. K. Blackburn, and J. M. Ponciano. 2018. An efficient extension of 
N-mixture models for multi-species abundance estimation. Methods in Ecology and 
Evolution 9(2):340–353. 

Grear, D. A., M. D. Samuel, J. A. Langenberg, and D. Keane. 2006. Demographic patterns and 
harvest vulnerability of chronic wasting disease infected white-tailed deer in Wisconsin. 
Journal of Wildlife Management 70:546–553.  

126 

Green, R. H. 1979. Sampling design and statistical methods for environmental biologists. Wiley 

Interscience, Chichester, England.FRESULTS 

Greenberg, S. 2019. Timelapse: an image analyser for camera traps. Version 2.2.2.4. 

http://saul.cpsc.ucalgary.ca/timelapse/. 

Gross, J. E., and M. W. Miller. 2001. Chronic wasting disease in mule deer: disease dynamics and 

control. The Journal of Wildlife Management 65:205–215.  

Hamilton, J., W. M. Knox, and D. C. Guynn. 1995. How quality deer management works. Pages 
7–18 in K. V. Miller and R. L. Marchinton, editors. Quality whitetails: the why and how of 
quality deer management. Stackpole Books, Mechanicsburg, Pennsylvania, USA. 

Hansen, L., 2011. Extensive management. Pages 409–451 in D. G. Hewitt, editor. Biology and 

Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

Hansen, L. P., E. B. Flinn, J. A. Sumners, X. Gao, and J. J. Millspaugh. 2017. Effects of an antler 
point restriction on harvest of white-tailed deer in Missouri. Wildlife Society Bulletin 
41:516–522. 

Hansen, L. P., J. A. Sumners, R. Reitz, Y. Bian, X. Gao, and J. J. Millspaugh. 2018. Effects of an 
antler point restriction on deer hunter perceptions and satisfaction in Missouri. Wildlife 
Society Bulletin 42:607–615. 

Heisey, D. M., E. E. Osnas, P. C. Cross, D. O. Joly, J. A. Langenberg, and M. W. Miller. 2010. Linking 

process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross-
sectional data. Ecological Monographs 80:221–240. 

Hiller, T. L., H. Campa III, and S. R. Winterstein. 2009. Estimation and implications of space use 

for white-tailed deer management in southern Michigan. The Journal of Wildlife 
Management 73:201–209. 

Jennelle, C. S., V. Henaux, G. Wasserberg, B. Thiagarajan, R. E. Rolley, and M. D. Samuel. 2014. 
Transmission of chronic wasting disease in Wisconsin white-tailed deer: implications for 
disease spread and management. PLoS ONE 9:e91043. 

Kellner, K. F., J. E. Hurst, D. W. Kramer, and J. L. Belant. 2021. Effects of antler point restrictions 

on deer harvest in New York. Wildlife Society Bulletin 45:581–588. 

Kellner, K. F., and R. K. Swihart. 2014. Accounting for imperfect detection in ecology: a 

quantitative review. J. Buckel, editor. PLoS ONE 9:e111436. 

Kays, R., B. Kranstauber, P. Jansen, C. Carbone, M. Rowcliffe, T. Fountain, and S. Tilak. 2009. 

Camera traps as sensor networks for monitoring animal communities. Pages 811–818 in 
2009 IEEE 34th Conference on Local Computer Networks. 

127 

Kéry, M., and J. A. Royle. 2021. Applied hierarchical modeling in ecology analysis of distribution, 
abundance and species richness in R and BUGS. Volume 2: dynamic and advanced models. 
Academic Press, Cambridge, Massachusetts, USA. 

Koerth, B. H., and J. C. Kroll. 2000. Bait type and timing for deer counts using cameras triggered 

by infrared monitors. Wildlife Society Bulletin 28:630–635. 

Kramer, D. B., A. Mitterling, and K. A. Frank. 2016. Understanding peer influence in hunter 

harvest decisions using social network theory and analysis. Human Dimensions of Wildlife 
21:414–426. 

Kuzyk, G., C. Procter, I. Hatter, and D. Jury. 2011. Utilizing antler point restrictions for mule deer 
to maximize hunter opportunity in southern British Columbia. Pages 37–45 in Proceedings 
of the 9th western states and provinces deer and elk workshop. New Mexico Department 
of Game and Fish, Santa Fe, USA.  

Lancia, R. A., C. S. Rosenberry, and M. C. Conner. 2000. Population parameters and their 
estimation. Pages 64–83 in S. Demarais and P. R. Krausman, editors. Ecology and 
Management of Large Mammals in North America. Prentice-Hall, Upper Saddle River, New 
Jersey, USA. 

Link, W. A., M. R. Schofield, R. J. Barker, and J. R. Sauer. 2018. On the robustness of N-mixture 

models. Ecology 99:1547–1551. 

Long, E. S., D. R. Diefenbach, C. S. Rosenberry, B. D. Wallingford, and M. D. Grund. 2005. Forest 

cover influences dispersal distance of white-tailed deer. Journal of Mammalogy 86:623–
629. 

Lubow, B. C., G. C. White, and D. R. Anderson. 1996. Evaluation of a linked sex harvest strategy 

for cervid populations. The Journal of Wildlife Management 60:787–796. 

Manjerovic, M. B., M. L. Green, N. Mateus-Pinilla, and J. Novakofski. 2014. The importance of 
localized culling in stabilizing chronic wasting disease prevalence in white-tailed deer 
populations. Preventive Veterinary Medicine 113:139–145. 

Mateus-Pinilla, N., H.-Y. Weng, M. O. Ruiz, P. Shelton, and J. Novakofski. 2013. Evaluation of a 
wild white-tailed deer population management program for controlling chronic wasting 
disease in Illinois, 2003–2008. Preventive Veterinary Medicine 110:541–548. 

McCoy, J. C., S. S. Ditchkoff, and T. D. Steury. 2011. Bias associated with baited camera sites for 
assessing population characteristics of deer. The Journal of Wildlife Management 75:472–
477. 

McCullough, D. R. 1979. The George Reserve deer herd: population ecology of a K-selected 

species. University of Michigan Press, Ann Arbor, USA. 

128 

Michigan Department of Natural Resources [MDNR]. 2016. Michigan Deer Management Plan. 

<https://www.michigan.gov/-
/media/Project/Websites/dnr/Documents/WLD/Deer/mi_deer_management_plan.pdf?re
v=19ecc9c9e4f046d2aa80bbf6d551f022>. Accessed 28 Jul 2023. 

Michigan Department of Natural Resources [MDNR]. 2023. Wildlife Conservation Order. 

<https://www.michigan.gov/dnr/managing-resources/laws/orders/wildlife-conservation-
order>. Accessed 20 Nov 2023. 

Michigan United Conservation Clubs [MUCC]. 2023. Michigan wildlife cooperatives. 

<https://mucc.org/cooperatives/>. Accessed 07 Dec 2023. 

Microsoft, 2020. AI for Earth camera trap image processing API. Version 3. 

https://github.com/microsoft/CameraTraps/blob/master/megadetector.md. 

Miller, M. W., and J. R. Fischer. 2016. The first five (or more) decades of chronic wasting disease: 
lessons for the five decades to come. Transactions of the North American Wildlife and 
Natural Resources Conference 81:1–12.  

Milner, J. M., E. B. Nilsen, and H. P. Andreassen. 2007. Demographic side effects of selective 

hunting in ungulates and carnivores. Conservation Biology 21:36–47. 

Mitterling, A. M., B. A. Rudolph, and D. B. Kramer. 2021. The influence of private land deer 

management cooperatives on harvest outcomes and hunter satisfaction. Wildlife Society 
Bulletin 45:456–464. 

Moa, P. F., L. F. Eriksen, and E. B. Nilsen. 2017. Harvest regulations and implementation 

uncertainty in small game harvest management. Frontiers in Ecology and Evolution 5:118. 

Moll, R. J., J. D. Cepek, P. D. Lorch, P. M. Dennis, T. Robison, J. J. Millspaugh, and R. A. 
  Montgomery. 2018. Humans and urban development mediate the sympatry of 
  competing carnivores. Urban Ecosystems 21:765–778. 

Moral, R. A., J. Hinde, C. G. B. Demétrio, C. Reigada, and W. A. C. Godoy. 2018. Models for 
jointly estimating abundances of two unmarked site-associated species subject to 
imperfect detection. Journal of Agricultural, Biological and Environmental Statistics 23:20–
38. 

Morina, D. L., C. P. Hansen, L. P. Hansen, and J. J. Millspaugh. 2021. The efficacy of antler harvest 
regulations in meeting management objectives. Pages 263–282 in K. L. Pope and L. A. 
Powell, editors. Harvest of fish and wildlife: new paradigms for sustainable management. 
CRC Press, Boca Raton, Florida, USA. 

Mysterud, A., and D. R. Edmunds. 2019. A review of chronic wasting disease in North America 

with implications for Europe. European Journal of Wildlife Research 65:26. 

129 

Nelson, M. E. 1993. Natal dispersal and gene flow in white-tailed deer in northeastern 

Minnesota. Journal of Mammalogy 74:316–322. 

Newbolt, C. H., and S. S. Ditchkoff. 2019. Misidentification error associated with classifications 

of white-tailed deer images. Wildlife Society Bulletin 43:527–536. 

Newbolt, C. H., S. Rankin, and S. S. Ditchkoff. 2017. Temporal and Sex-related Differences in use 
of Baited Sites by White-tailed Deer. Journal of the Southeastern Association of Fish and 
Wildlife Agencies 4:109–114.  

Newkirk, E. S. 2016. CPW Photo Warehouse. Colorado Parks and Wildlife, Fort Collins, Colorado, 

USA. http://cpw.state.co.us/learn/Pages/ResearchMammalsSoftware.aspx. 

New York State Department of Environmental Conservation. 2011. Management plan for white-

tailed deer in New York State 2012−2016. Division of Fish, Wildlife and Marin Resources, 
Bureau of Wildlife, Albany, NY, USA. 

New York State Department of Environmental Conservation. 2023. Buck hunting. 
<www.dec.ny.gov/outdoor/27663.html>. Accessed September 2023. 

Nilsen, E. B., and E. J. Solberg. 2006. Patterns of hunting mortality in Norwegian moose (Alces 

alces) populations. European Journal of Wildlife Research 52:153–163. 

NIMBLE Development Team. 2023a. Converting to NIMBLE from JAGS, OpenBUGS or WinBUGS. 
<https://r-<nimble.org/nimbleExamples/converting_to_nimble.html>. Accessed 03 Aug 
2023. 

NIMBLE Development Team. 2023b. NIMBLE: MCMC, particle filtering, and programmable 

hierarchical modeling. doi: 10.5281/zenodo.1211190. R package version 
1.0.1, https://cran.r-project.org/package=nimble.  

Nixon, C. M., L. P. Hansen, P. A. Brewer, and J. E. Chelsvig. 1991. Ecology of white-tailed deer in 

an intensively farmed region of Illinois. Wildlife Monographs 118:3-77. 

Nixon, CM., L.P. Hansen, P.A. Brewer, J. E. Chelsvig, J.B. Sullivan, R. Koerkenmeier, D.R. Etter, J. 

Cline, and J. A. Thomas. 1994. Behavior, dispersal, and survival of male white-tailed deer in 
Illinois. Illinois Natural History Survey Biological Notes 139. 

Nixon, C. M., L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, D. Etter, J. B. Sullivan, R. G. 

Koerkenmeier, and P. C. Mankin. 2001. Survival of white-tailed deer in intensively farmed 
areas of Illinois. Canadian Journal of Zoology 79:581–588. 

Nixon, C. M., P. C. Mankin, D. R. Etter, L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, and J. B. 
Sullivan. 2007. White-tailed deer dispersal behavior in an agricultural environment. The 
American Midland Naturalist 157:212–220.  

130 

Noyes, J. H., B. K. Johnson, L. D. Bryant, S. L. Findholt, and J. W. Thomas. 1996. Effects of bull 

age on conception dates and pregnancy rates of cow elk. The Journal of Wildlife 
Management 60:508–517. 

O’Brien, D. J., S. M. Schmitt, J. S. Fierke, S. A. Hogle, S. R. Winterstein, T. M. Cooley, W. E. 

Moritz, K. L. Diegel, S. D. Fitzgerald, D. E. Berry, and J. B. Kaneene. 2002. Epidemiology of 
Mycobacterium bovis in free-ranging white-tailed deer, Michigan, USA, 1995–2000. 
Preventive Veterinary Medicine 54:47–63. 

Osnas, E. E., D. M. Heisey, R. E. Rolley, and M. D. Samuel. 2009. Spatial and temporal patterns of 
chronic wasting disease: fine-scale mapping of a wildlife epidemic in Wisconsin. Ecological 
Applications 19:1311–1322. 

Plummer, M. 2003. JAGS: a program for analysis of Bayesian graphical models using Gibbs 

sampling. Pages 124–125 in K. Hornik, F. Leisch, and A. Zeileis, editors. Proceedings of the 
3rd international Workshop on Distributed Statistical Computing (DSC 2003), March 20–23, 
2003. Technische Universität Wien, Vienna, Austria. 

Ponisio, L. C., P. de Valpine, N. Michaud, and D. Turek. 2020. One size does not fit all: 

customizing MCMC methods for hierarchical models using NIMBLE. Ecology and Evolution 
10:2385–2416. 

Potapov, A., E. Merrill, M. Pybus, and M. A. Lewis. 2016. Chronic wasting disease: transmission 

mechanisms and the possibility of harvest management. PLOS ONE 11:e0151039. 

Quality Deer Management Working Group [QDMWG]. 2013. Guidelines for initiation, 

evaluation, and review of mandatory antler point restrictions. Michigan Department of 
Natural Resources Wildlife Division, Lansing, USA. 

R Core Team. 2021. R: a language and environment for statistical computing. R Foundation for 

Statistical Computing, Vienna, Austria. 

Rees, E. E., E. H. Merrill, T. K. Bollinger, Y. T. Hwang, M. J. Pybus, and D. W. Coltman. 2012. 

Targeting the detection of chronic wasting disease using the hunter harvest during early 
phases of an outbreak in Saskatchewan, Canada. Preventive Veterinary Medicine 104:149–
159. 

Riley, S. J., D. J. Decker, J. W. Enck, P. D. Curtis, T. B. Lauber, and T. L. Brown. 2003. Deer 

populations up, hunter populations down: Implications of interdependence of deer and 
hunter population dynamics on management. Écoscience 10:455–461. 

Robinson, K. F., A. K. Fuller, J. E. Hurst, B. L. Swift, A. Kirsch, J. Farquhar, D. J. Decker, and W. F. 
Siemer. 2016. Structured decision making as a framework for large-scale wildlife harvest 
management decisions. Ecosphere 7:e01613. 

131 

Roseberry, J. L., and A. Woolf. 1991. A comparative evaluation of techniques for analyzing white-

tailed deer harvest data. Wildlife Monographs 117:3–59. 

Royle, J. A. 2004. N-Mixture models for estimating population size from spatially replicated 

counts. Biometrics 60:108–115.  

Rudolph, A. B. 2012. History and management perspective on Michigan buck hunting 

regulations background document. Michigan Department of Natural Resources Wildlife 
Division, East Lansing, USA. 

Ryder, T., editor. 2018. State Wildlife Management and Conservation. Johns Hopkins University 

Press, Baltimore, Maryland, USA. 

Samuel, M. D. and D. J. Storm. 2016. Chronic wasting disease in white-tailed deer: infection, 
mortality, and implications for heterogeneous transmission. Ecology 97:3195–3205. 

Schroeder, S. A., L. Cornicelli, D. C. Fulton, and M. D. Grund. 2014. What predicts support for 

antler point restrictions? Human Dimensions of Wildlife 19:301–318. 

Schwartz, C. C., K. J. Hundertmark, and T. H. Spraker. 1992. An evaluation of selective bull moose 

harvest on the Kenai Peninsula, Alaska. Alces: A Journal Devoted to the Biology and 
Management of Moose 28:1–13. 

Skalski, J. R., K. E. Ryding, and J. J. Millspaugh. 2005. Wildlife demography: analysis of sex, age, 

and count data. Elsevier Academic Press, San Diego, CA. 656 pp. 

Skuldt, L. H., N. E. Mathews, and A. M. Oyer. 2008. White-tailed deer movements in a chronic 
wasting disease area in south-central Wisconsin. The Journal of Wildlife Management 
72:1156–1160. 

Stevens, D. L., and A. R. Olsen. 2004. Spatially balanced sampling of natural resources. Journal 

of the American Statistical Association 99:262–278. 

Stewart, C. 2023. Showcasing the DNR: an open letter to Michigan’s deer hunters. Michigan 

Department of Natural Resources. 
<https://content.govdelivery.com/accounts/MIDNR/bulletins/3716e4f>. Accessed 
September 2023. 

Stewart, C., M. Cosgrove, and J. Melotti. 2016. 2015-2016 Michigan chronic wasting disease 
management and surveillance report. Unpublished report. Michigan Department of 
Natural Resources, Lansing, USA. 

Strickland, B. K., S. Demarais, L. E. Castle, J. W. Lipe, W. H. Lunceford, H. A. Jacobson, D. Frels, 
and K. V. Miller. 2001. Effects of selective-harvest strategies on white-tailed deer antler 
size. Wildlife Society Bulletin 29:509–520. 

132 

Thompson, N. E., M. H. J. Huang, S. A. Christensen, and S. Demarais. 2023. Wildlife agency 
responses to chronic wasting disease in free-ranging cervids. Wildlife Society Bulletin 
47:e1435. 

Uehlinger, F. D., A. C. Johnston, T. K. Bollinger, and C. L. Waldner. 2016. Systematic review of 

management strategies to control chronic wasting disease in wild deer populations in 
North America. BMC Veterinary Research 12:173. 

U.S. Geological Survey Gap Analysis Project [USGS]. 2020. Protected Areas Database of the 

United States (PAD-US) 2.1: U.S. Geological Survey data release, 
https://doi.org/10.5066/P92QM3NT. 

Van Deelen, T. R., B. J. Dhuey, C. N. Jacques, K. R. Mccaffery, R. E. Rolley, and K. Warnke. 2010. 

Effects of earn-a-buck and special antlerless-only seasons on Wisconsin’s deer harvests. 
The Journal of Wildlife Management 74:1693–1700. 

VerCauteren, K. C., and S. E. Hygnstrom. 1994. A review of white-tailed deer movements in the 
Great Plains relative to environmental conditions. Great Plains Research: A Journal of 
Natural and Social Sciences. 158:117-132. 

Wallingford, B. D., D. R. Diefenbach, E. S. Long, C. S. Rosenberry, and G. L. Alt. 2017. Biological 
and social outcomes of antler point restriction harvest regulations for white-tailed deer: 
antler point restrictions. Wildlife Monographs 196:1–26. 

Walter, W. D., K. C. VerCauteren, H. Campa III, W. R. Clark, J. W. Fischer, S. E. Hygnstrom, N. E. 
Mathews, C. K. Nielsen, E. M. Schauber, T. R. Van Deelen, and S. R. Winterstein. 2009. 
Regional assessment on influence of landscape configuration and connectivity on range 
size of white-tailed deer. Landscape Ecology 24:1405–1420. 
https://doi.org/10.1007/s10980-009-9374-4. 

Williams, B. K. 1997. Approaches to the management of waterfowl under uncertainty. Wildlife 

Society Bulletin (1973-2006) 25:714–720. 

Williams, E. S. 2005. Chronic wasting disease. Veterinary Pathology 42(5): 530-549. 

Wilton, C.M. 2021. White-tailed Deer (Odocoileus virginianus) Density and habitat use on the 

Beaver Island Archipelago using a camera trap array. Michigan Natural Features Inventory 
Report Number 2021-05, Lansing, MI, USA. 

Wobeser, G. A. 2006. Essentials of disease in wild animals. Blackwell Publishing Professional, 

Ames, Iowa, USA. 

Woolf, A., and J. L. Roseberry. 1998. Deer management: our profession’s symbol of success or 

failure? Wildlife Society Bulletin 26:515–521. 

133 

Yamaura, Y., J. A. Royle, N. Shimada, S. Asanuma, T. Sato, H. Taki, and S. Makino. 2012. 

Biodiversity of man-made open habitats in an underused country: a class of multispecies 
abundance models for count data. Biodiversity and Conservation 21:1365–1380. 

Young, D. D., and R. D. Boertje. 2008. Recovery of low bull:cow ratios of moose in interior 

Alaska. Alces: A Journal Devoted to the Biology and Management of Moose 44:65–71. 

134 

CONCLUSIONS AND MANAGEMENT IMPLICATIONS 

By investigating camera-trap sampling strategies that attain precise and reliable 

estimates of white-tailed deer relative abundance using N-mixture models and applying 

population-estimation techniques appropriate for population-change assessment, I was able to 

address uncertainties on population impacts of antler point restrictions (APRs) for white-tailed 

deer by sex-and-age class. In this final section, I briefly review the findings and contributions 

from each chapter. 

Chapter 1 sought to disentangle strengths and weaknesses of alternative camera-trap 

sampling strategies. This post hoc methodological assessment included a subset of camera-trap 

data and data-simulation approaches. My results demonstrate that N-mixture models can 

perform well for the precise relative abundance estimation of white-tailed deer in in the south-

central Lower Peninsula of Michigan, based on the modeling of camera-trap count data. 

However, N-mixture models should be paired with careful consideration of assumptions and 

sampling strategies as large uncertainty in parameter estimates can obscure signals of change in 

abundance over time. I found that the precision of abundance estimates was relatively 

insensitive to modifications in sampling frequency, but detection probability was highly sensitive 

to these manipulations. Shorter sampling durations and lower camera distributions can facilitate 

resource savings, but my results showed reductions compromised the precision of relative 

abundance estimates, with the latter being most sensitive to manipulation. My results also 

highlighted the importance of designing sampling efforts relevant to animal activity and its 

potential application in improving sampling efficiency. The findings from this chapter can be 

used to provide general recommendations to researchers and practitioners seeking to identify 

135 

sampling strategies that minimize financial and human resources to attain precise and reliable 

estimations of relative abundance when using N-mixture models with count data from camera-

trap surveys. 

Chapter 2 sought to assess potential population-level changes over time and space 

following a deer harvest regulation change in a before-after-control-impact design. More 

specifically, this chapter aimed to fill knowledge gaps regarding effects of antler point 

restrictions (APRs) on relative abundance by sex-and-age class. Using sampling 

recommendations from Chapter 1 and data associated with approximately 3 million camera-

trap images, I used several analytical approaches to evaluate if antler point restrictions affect 

deer relative abundance by sex-and-age class. Looking at all my results holistically, I found weak 

evidence for APRs affecting the relative abundance by sex-and-age classes. My results suggest 

that the implementation of APRs had an insignificant impact on the relative abundance of Legal-

Antlered deer. Although trends may have suggested increases in the abundance of Legal-

Antlered deer, they do not represent significant statistical change in either the APR or Non-APR 

areas. There was a lack of evidence supporting change in Female and Fawn relative abundance 

in APR or Non-APR treatment areas. Harvest data from the Michigan Department of Natural 

Resources further substantiates these outcomes as antlerless deer harvest was similar between 

APR and Non-APR counties during the study period. Collectively, my results suggested that 

overall deer densities were increasing in the 5-County Area. My results from Chapter 2 highlight 

potential limitations of APRs achieving desired effects for population reduction goals and the 

importance of developing harvest regulations specific to the targeted deer population, area, 

and management goals. I recommend careful consideration of the partial controllability of 

136 

harvest regulations. For example, hunters in a Non-APR area may participate in voluntary APRs, 

and thus a desired outcome of a regulation change may not be realized. This issue is particularly 

relevant to emergence of wildlife health issues because selectivity of harvest over sex-and-age 

classes has implications for disease spread and growth. The finding from this chapter can be 

used to help managers and hunters alike set reasonable expectations for changes in deer 

abundance by sex-and-age class under antler point restrictions.

137 

APPENDIX 1A: CAMERA-TRAPPING PROTOCOL 

Protocol for Camera-Trap Set Up and 
Maintenance 

Supplemental research to:  
Influence of deer harvest regulations on antlerless harvest, abundance, and sex and age 
composition: implications for managing deer in the face of chronic wasting disease 

October 2023 

Prepared by: 
Melissa J. Nichols – Wildlife Research Technician, Michigan Department of Natural Resources, 
Wildlife Division 

Revised by: 
Steven M. Gurney – Graduate Research Assistant, The Christensen Lab for Wildlife Population 
Health, Michigan State University 

Principle Investigators: 
Sonja A. Christensen – The Christensen Lab for Wildlife Population Health, Michigan State 
University 
Dwayne R. Etter – Michigan Department of Natural Resources, Wildlife Division 
Sarah L. Mayhew – Michigan Department of Natural Resources, Wildlife Division 

The Christensen Lab for Wildlife Population Health 
Michigan State University 
Natural Resources Building 
480 Wilson Road, Room 13  
East Lansing, MI 48824 

138 

 
 
 
 
 
 
 
 
 
 
 
Site Selection and Camera Setup 

1.  You have an ordered list of 108 randomly selected locations for the cameras within each 

of the 8 townships. Use OnX app (with GRTS sites uploaded) for navigating and 
identifying landowners. Note that our electronic devices do not have cell service, so 
consider saving offline OnX maps, or installing OnX on your personal cell phone, or both. 
Work your way through the list in sequential order and attempt to gain permission from 
landowners to access 18 points per township (this process may have been started in 
previous seasons). Leave door hangers when you visit a residence, and nobody is home. 
Leave contact information on the back of door hangers (do not use personal contact 
information, use GoogleVoice accounts). If landowners grant permission after all sites 
are already secured, request to use their property as a back up option (you will likely 
need it). For new camera sites only, you will have latitude to set the camera within 50 m 
or 100 m of the randomly selected point (see details below), which may place the 
camera location on the land of a different landowner. A landowner grants permission 
for you to access their land by signing the “Landowner Agreement” document annually. 
For camera sites from previous seasons, given you have permission again, try to place 
cameras in the exact locations as previous seasons (refer to GPS-coordinate records).  

2.  Before you go into the field to set up cameras, make sure you have an iPad (or CAT 

device) with the Survey123 survey Deer Cameras downloaded (and updated). You must 
also have one hard copy of the “Camera Location Datasheet” for each camera. 

3.  Once you have permission to access the appropriate land, set up the camera. Remember that 
some landowners may want a phone call or text before you visit their property. Use 
your GoogleVoice account for this. Aim to start setting up cameras by mid-June. All cameras 
must be set up before July 14 (data collection starts on July 15). Ideally, cameras will be set up 
about 2 weeks before the official data collection period starts. This approach will allow time for 
an initial camera check and time to address any problematic cameras (e.g., poor field of view, 
vegetation setting off camera) prior to the start of the data collection period. If site ends up 
being a poor location altogether, consider any backup points or finding new locations. Place 
camera within 50 m of the randomly selected point to maintain a clear field of view, but 
prioritize staying as close to the random point as possible. Be cognizant of property lines, as 
points may fall near property boundaries. Make sure you are not trespassing. In exceptional 
circumstances you may select a location within 100 m. Exceptional circumstances include high 
risk of theft, open water, road right-of-ways, agricultural fields.  

4.  Record basic site information in Survey123. 

a.  Season Year  
b.  Study Area (APR or Non-APR) 
c.  Township 
d.  Point ID 

i.  1st digit = 1 for Non-APR Zone; 2 for APR Zone 

139 

 
 
 
 
 
ii.  2nd digit = 1-4 corresponding to the paired townships 
iii.  3rd - 5th digit = 3 digit number based on GRTS sample selection order 

5.  Record specific location information on a “Camera Location Datasheet” (datasheet 

included at end of document). Note that location data (e.g., coordinates, landowner 
names) are private to Michigan State University. Save established camera site as a 
waypoint on the GPS.  

6.  Always check that camera settings, date, and time are correct. Record camera ID, card 

ID, and SD card set date in Survey 123. Camera settings: 

a.  Mode = Trail 
b.  Capture Delay = 5s 
c.  PicSize – LOW 
d.  MultiShot = RPF-3 SHOT 
e.  Smart IR = On 
f.  Night Exp = Fast Motion  
g.  Temp Units = F 
h.  Info Strip = On 
i.  SD Management = Off 

i.  If this is accidentally turned on, and the SD card becomes full, the camera will 

start to delete photos to make room for the new ones. This must be set to “off”. 

7.  Camera Placement Protocol: 

a.  Remember that some landowners may want a phone call or text before you visit 

their property. Use your GoogleVoice account for this. 

b.  Cameras will be placed in a northerly direction to minimize direct sunlight exposure 
to the camera trap. Sunlight can trigger cameras and UV exposure can reduce the 
sensitivity of the camera’s heat sensor. South-facing bearings between 91 and 269 
should be avoided. Record camera direction, in degrees, in Survey123. 

c.  Find the closest straight tree that is not so thin that it will blow in the wind (or so 

thin that people can easily cut through the tree to remove the camera). Do not place 
cameras on snags or dead trees. 

d.  If no suitable trees are available, use a steel T-post to mount the camera. 
e.  Mount the camera to the tree (or T-post) using the fabric strap with the center of 
lens 14 – 16” above ground, but use personal judgement if terrain is uneven. For 
example, if your camera tree is located on a hill, you should adjust the height of the 
lens to maximize the detection window and so the horizon is approximately 
centered in the field of view. Small sticks can be lodged behind the camera to get 
desired angle, but make sure the sticks are secured tightly because animals can 
bump the camera and alter the angle (strap slack can be used to secure wedged 
sticks). Record camera height in inches from ground to center of lens in Survey123. 

140 

 
 
 
 
 
f.  Clear all vegetation and debris (e.g., branches, logs, large rocks) five meters in front 

of the camera. Keep in mind that debris, tree trunks, boulders, human-made objects, 
etc., can trigger cameras due to differences in temperature. Our cameras have an 
approximate 44-degree horizontal detection angle (22 degrees to the left and 22 
degrees to the right). Using a compass, determine the area to be cleared and 
remove all ground and shrubby vegetation. Overhanging vegetation (e.g., branches) 
that greatly obstruct the field of view or may trigger the camera on a windy day 
should be removed from the target viewing area. Ground vegetation and debris 
(e.g., tall grass, shrubs, large rocks, man-made objects, etc.) should be cleared from 
the target viewing area to minimize false triggering and allow for an unobstructed 
field of view. The camera is set very low to the ground so clear all vegetation to a 
maximum height of 2–3 inches. Cameras a low so they can detect fawns (and 
mesocarnivores like bobcats). Also, consider how much the vegetation will grow 
between maintenance visits (e.g., ferns grow very fast). Try to remove branches 
immediately around and behind the camera to further limit vegetation issues. Any 
large shrubs or branches cleared should also be removed from the camera’s field of 
view and away from the camera site. 

g.  Turn on the camera and use the display screen to check your camera placement. In 
Survey123, hold the phone directly in front of the camera lens and take a picture of 
the camera field of view. Note that the camera’s field of view is similar to that of a 
camera phone. Review photo and make sure: 
i.  No vegetation that will easily be moved by wind was in camera view. 
ii.  Horizon is close to the center of the image. 
iii.  Ensure the camera is level (i.e., not crooked) and take a test image to verify 

orientation and that the intended target area is viewed. 

h.  In Survey 123, enter SD card number and the SD card set date and time. 
i. 
j.  Legibly record the site name, set date, and set time on the whiteboard. Using the 

In Survey 123, enter the names of staff that set up the camera. 

viewing screen on the camera, center the whiteboard in the camera frame so that all 
information is visible and push “OK” to take a photo of the whiteboard. These 
photos will be saved on the SD card and provide additional reference. 
k.  Check camera to see if photos were taken and recorded on the SD card. 

i.  If you are unable to record photos on the card, switch out the card with one of 

the extras provided and try again. Sometimes SD cards fail, or their tiny lock gets 
flipped on. 

ii.  Do not delete whiteboard photos as they will be used to double check that 

photos are assigned to the correct site. 

l.  Check that camera is set to “ON” and close camera. If you are with a partner, both of 
you are responsible for making sure the camera is on. You can do this by using a 
double-verbal confirmation (e.g., one of you says “camera is on” and the other 
person responds with “camera is on”). 

141 

m.  Wrap cable around tree and secure it to camera with lock. Tuck away camera strap 

and lock cable. 

n.  Take a photo of the camera in Survey123. Stand 10 ft in front of the camera and take 

a picture of the camera set-up. Center the camera in the image. 

8.  Complete the “Land-cover” fields in Survey123. 

a.  Near Cover – Select the majority cover in a 1-m radius from the camera (“Open” or 

“Closed”) 

b.  Landscape Cover – Select the majority cover in a 100-m radius from the camera. 

(“Open” or “Closed”) 

c.  Landscape Land-cover Type – Select the majority land cover in a 100-m radius from 

the camera. 

d.  Open Water – Stand next to the camera and look around. Is there open water within 

sight? (“Yes” or “No”) 

e.  Deer Sign – Meander around within a few meters of the camera. Is there deer sign 

(scat, tracks, bedding, etc.) within sight? (“Yes” or “No”) 

f.  Wildlife Trail – Stand next to the camera. Is the camera on or within sight of a 

wildlife trail? (“Yes” or “No”) 

9.  If there is additional information you would like to capture about the site, use the 
“Comments” section in Survey123 if it does not relate to the specific location or 
landowner. Note that location data (e.g., coordinates, landowner names) are private to 
Michigan State University. 

10. If a site is difficult to navigate to, or if it might be difficult for a teammate to navigate to, 
consider putting some flagging up. However, do not draw to much attention to the 
actual camera site. 

142 

 
 
CWD APR Deer Study 
CAMERA LOCATION DATASHEET 

Point ID: ____________________________ 
Record the 5-digit unique ID assigned to point. 

Staff Name 1:  
____________________________________ 

Staff Name 2:  
____________________________________ 

Landowner Name: 
____________________________________ 

Landowner Agreement Signed:        

YES            NO 

Landowner Phone: 
____________________________________ 

Landowner Email:_____________________ 

Date Location Recorded: _______________

Latitude: ____________________________         Longitude: _____________________________ 
Hold the GPS receiver directly over the camera.  Record the location in decimal degrees to as many 
decimal places as possible. 

Street Address: _________________________________________________________________ 
Record street address of property, if available. 

Directions: 
Describe how to access the camera location. 

Notes: 

CHECKLIST ON BACK 

143 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Field Setup Checklist: 

 Marked in GPS 

 SD card checked for recording 

 Camera batteries >80% 

 Camera date checked 

 Camera settings checked 

 Field of view clear of vegetation 

 Photo of whiteboard with Point ID and date taken and saved to  

the trail camera’s SD card 

 Survey123 form completed 

144 

 
 
 
 
 
 
 
 
 
 
 
 
 
Survey123 And Camera Checking 

1.  Getting started with Survey123 

a.  Connect a CAT phone (or iPad) to a WIFI network. Go to the Play Store and install 

the “Survey123 for ArcGIS” app (if Survey123 is already installed, update if 
necessary). 

b.  Open the “Survey123” app. In the “My Surveys” screen, tap the menu icon and 

sign in using your assigned ArcGIS username and password. 

i.  If the Deer Cameras survey (created by S. Mayhew) is already 
installed, tap the Updates Available header. Then tap Deer 
Cameras to download the updated version. 

ii.  If the Deer Cameras survey is not already installed, tap your 

initials in the upper right corner and select Download Surveys. 
Find the survey called Deer Cameras and tap to download. 

c.  Tap the left-pointing arrow in the upper left corner to return to “My Surveys” 

screen. 

2.  Collecting data with Survey123 during camera setup 

a.  Note, your CAT phone (or iPad) should be offline at the time of data collection. 
b.  When at each camera location, tap “Collect” in Survey 123. 
c.  Complete the entire Survey 123 form (as described in the Site Selection and 

Camera Setup protocol). Note that you should only enter 1 SD card per camera 
at the time of set up.   

d.  When the survey form is completed, tap the check mark at the bottom of the 

screen. Your survey will be saved in the outbox. 

3.  Submitting Survey123 data 

a.  Whenever possible, preferably at the end of each field day, connect the CAT 

phone to a WIFI network.   

b.  On the “Deer Cameras” screen in Survey123, open the Outbox and tap the 

“Send” button at the bottom of the screen. If you do not see the “Send” button, 
you may need to force close the Survey123 app and restart. 

4.  Survey123 data collection and SD-card replacement 

a.  Before heading out into the field for camera maintenance (i.e., camera checks), 
open the Survey123 app on your CAT phone. Open the “Deer Cameras” survey. 

b.  Tap “Inbox.” At the bottom of the “Deer Cameras Inbox” screen, tap the 
“Refresh” button so you can see all of the available camera locations. 

c.  Once you are at a camera location, tap on the appropriate camera location in the 

“Deer Cameras Inbox” screen.   

d.  Do not change any of the setup data. Scroll down to the “SD Cards” section. Tap 

the + button to add another SD card. 

e.  Enter the new SD card ID and the date and time of SD card change. 

145 

 
 
 
 
f.  Tap the check mark at the bottom of the survey screen. Your survey will be saved 

in the outbox.   

g.  Make sure to follow the “Submitting Data” instructions when possible. 

5.  Camera maintenance during camera checks 

a.  Remember that some landowners may want a phone call or text before you visit 

their property. Use your GoogleVoice account for this. 

b.  Verify camera is still set up appropriately. 

i. 

ii. 

Confirm field of view and fix any issues or deviations from setup 
protocol.  
If cameras record a high volume of images, flip through photos 
using the camera, and try to diagnose and address problems if 
they exist (e.g., a branch triggering the camera). 

c.  Change SD cards during every camera check. 

i. 

ii. 

iii. 

iv. 

To remove the SD card, push it in so it clicks and unlocks, then 
remove (to replace it, push it in and make sure it clicks and 
locks).  
Sometimes the new SD card (the one brought into the field to 
replace the SD card in the camera) will still have photos on it. To 
check, press the D-pad arrows to scroll through any old photos. 
To delete, press “M” and scroll up or down to the “Delete All” 
function.  
To prevent mixing up new and old SD cards, always make sure 
the camera is off and the old SD card has been removed and put 
away before inserting a new card and deleting photos. SD card 
wallets help with this process. 
SD cards can accidentally become locked if a tiny tab is switched 
on the actual SD card.  

d.  Take photo of whiteboard with site ID, date and time during every camera check. 

i.  Write legibly. 
ii.  Make sure SD card is recording photos. 

e.  Clear vegetation at every camera check. 

i. 

Clear all vegetation to a maximum height of 2 – 3 inches. 

f.  Complete Survey123 form during every camera check (SD card portion). 
g.  Double check camera settings every camera check.  
h.  Replace batteries if <80% battery life. 

If you change batteries, you may have to reset all the settings 
(including time and date).  

i.  Make sure the battery pack is locked into place properly 

because it may back out over time and eventually fail to take 
pictures. 

146 

 
 
 
APPENDIX 1B: PHOTO-REVIEW PROTOCOL 

Protocol for Identifying Wildlife in 
Camera-Trap Photos 

Supplemental research to:  
Influence of deer harvest regulations on antlerless harvest, abundance, and sex and age 
composition: implications for managing deer in the face of chronic wasting disease 

October 2023 

Prepared by: 
Melissa J. Nichols – Wildlife Research Technician, Michigan Department of Natural Resources, 
Wildlife Division 

Revised by: 
Steven M. Gurney – Graduate Research Assistant, The Christensen Lab for Wildlife Population 
Health, Michigan State University 

Principle Investigators: 
Sonja A. Christensen – The Christensen Lab for Wildlife Population Health, Michigan State 
University 
Dwayne R. Etter – Michigan Department of Natural Resources, Wildlife Division 
Sarah L. Mayhew – Michigan Department of Natural Resources, Wildlife Division 

The Christensen Lab for Wildlife Population Health 
Michigan State University 
Natural Resources Building 
480 Wilson Road, Room 13  
East Lansing, MI 48824

147 

 
 
 
 
 
 
 
 
 
 
 
Please review this document before beginning to review (i.e., tag) photos, even if you have 
tagged photos for this project in the past. To improve your understanding and accuracy of photo 
IDing, you will be provided with comprehensive, species-specific training prior to reviewing 
photos. We use CPW Photo Warehouse for storing, managing, and reviewing photos (more info 
here: https://cpw.state.co.us/learn/Pages/ResearchMammalsSoftware.aspx). 

Getting Started 
A designated data-manager (e.g., data-management technician, MDNR staff) will provide you 
with a flash drive. The main folder on the flash drive will contain subfolders labeled with things 
like “21003_Check2.” Within this folder will be another folder titled “Photos” and a database 
file called “PhotoID.accdr.” This database file is a standalone file that is not truly connected to 
our main photo database (i.e., if something happens to this file while you have access to it will 
not harm the main database). Each of these folders and databases contains the info for a single 
camera during a single two-week period. Depending on the site, the folder could contain 5 to 
over 5000 photos—and our big goal is to identify the deer in each of these photos. Also worth 
noting, the database you will be working with is a Microsoft Access application and uses an 
auto-save feature (so you don’t have to worry about hitting a save button before you close the 
application). 

When you open the PhotoID.accdr file you will be asked to select your name. If your name does 
not appear in the list, just type it in and the database will add your info (we just need your 
name and initials in the dialog box that pops up). Sometimes it is much quicker to flip through 
the photos outside of the database (where they will be larger and you can zoom in), and 
sometimes you will want to look at a series of photos before deciding on an ID. 

To assign a species to a photo, select the appropriate species in the drop-down box at the 
bottom left. You can assign multiple species to the same photo by adding additional rows in the 
subform. For this project, we have divided deer into multiple “species” – Doe, Fawn, Legal Buck, 
Sub-legal Buck, and Unknown Deer, then those species are broken down even farther based on 
the number of antler points on bucks and details (e.g., cannot see head) on Unknown deer. The 
only other species we are interested in are bear, bobcat, fox, and coyote (fox and coyote new 
to 2022). Once you have created a row in the subform for each species present in an image, use 
the “Next” button to move on. Do not just skip photos with nothing or non-focus species in 
them – specify “None” as the ID otherwise you will not be able to differentiate between photos 
that have not been looked at yet and those that have been reviewed but do not contain any 
focal species. We are only identifying deer, bear, bobcat, fox, and coyote. Please do not add 
other species to the table (e.g., if a photo contains a raccoon, it is still tagged as “None”). Also, 
do not worry about the number of individuals in a photo tagged as “None”—leave it as the 
default 1 individual for photos tagged as “None”. For example, if a photo contains 5 raccoons it 
would be tagged as “None” with the default 1 number of individuals, which basically means we 
have a single record for an image labeled “None”. 

148 

 
 
 
If you spot an interesting photo, a photo that would be good for presentations, a photo of a 
feral hog, or a photo of an animal that appears ill, please use the “Highlight” checkbox on the 
right side – tick this box to flag photos to be reviewed by project PIs. If you identify an animal 
that looks ill, or if you identify a feral hog in any images, share that information with the project 
PIs immediately. You can also add comments to these photos in the comments column for 
future reference. 

Using Keyboard Shortcuts 
Using the mouse to identify species can be unwieldy and time-consuming, so there are 
keyboard shortcuts available when using the PhotoID form. To see a list of keyboard shortcuts 
available, click the link below the “Next” and “Previous” buttons. These shortcuts will only work 
when the “focus” is on the main form, not within the subform where species are listed. This can 
be tricky to figure out, but if the keyboard shortcuts are not working, try clicking the “Next” 
button, and then click the “Previous” to return to the record you were on – this ensures that 
the main form has the focus. In addition to the shortcuts specific to a species or detail, you can 
use the “Z” key to repeat all of the data recorded from the previous photo.  

You can also use the up, down, left, and right arrows to move between records, and pressing 
the space bar will move to a new line in the subform so you can add an additional ID. Getting 
this system down can take some practice, but once you learn how to use it you will be able to 
work through hundreds of photos in no time. There are a couple of situations to note when 
using the shortcut keys – first, detail shortcuts will only work if the appropriate species has 
already been assigned. Otherwise, the species shortcut will take precedence if it exists. For 
example, if “f” is the shortcut for fawn, “b” is the shortcut for bear (both in the Species table), 
and “b” is also assigned for the detail “Buttonbuck” associated with the species fawn (in the 
Detection Details table). Pressing “f” then “b” will set the species to Fawn and the detail to 
“Buttonbuck,” but pressing “b” first will set the species to Bear.  

149 

  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
How To ID Photos 
Almost all deer should be assigned a species and detail tag. Keyboard shortcuts for all possible 
combinations are below. See Figure 1B.1 for data-input and keystroke example. See Figure 1B.2 
for a photo with data-input example.

Species shortcut table:  

Shortcut 

Species 

Detection Details List: 

Shortcut  Species 

Detail 

B 

C 

Y 

V 

P 

D 

F 

L 

S 

U 

X 

r 

Bear 

Bobcat 

Coyote 

Fox 

Camera Problem 

Doe 

Fawn 

Legal Buck (at least 4 points 
on one side) 

Sub-legal buck (does not 
have 4 points on a side) 

Unknown Deer 

Camera Setup/Takedown 

Remove (photos of humans) 

b 

f 

q 

f 

s 

v 

e 

n 

t 

t 

q 

f 

s 

p 

a 

l 

u 

Fawn 

Fawn 

Buttonbuck 

Female 

Legal Buck 

Four Point 

Legal Buck 

Five Point 

Legal Buck 

Six Point 

Legal Buck 

Seven Point 

Legal Buck 

Eight Point 

Legal Buck 

Nine Point 

Legal Buck 

≥ Ten Point 

Sub-Legal Buck 

Three Point 

Sub-Legal Buck 

Four Point 

Sub-Legal Buck 

Five Point 

Sub-Legal Buck 

Six Point 

Sub-Legal Buck 

Spike 

Unknown Deer 

Antlered 

Unknown Deer 

Antlerless 

Unknown Deer 

Cannot see 
head 

150 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1B.1. Data input example for an image that includes a doe, two fawns, and a buck with 
three points on one side and two points on the other. This example has three rows of data. If 
you were using keyboard shortcuts you would have typed out: “d”, “space bar”, “f”, “2”, “space 
bar”, “s”, “f” → these keystrokes would indicate “Doe”, next row, “Fawn”, “2 individuals”, next 
row, “Sublegal buck”, “Five Points”, next photo. 

Figure 1B.2. Photo example and data-input example that includes one doe and two fawns. Note 
that there are only two rows of data. 

Note that the spacebar will allow you to jump to the next row for data entry without having to 
point and click. Also, there is an option to add comments in the table where you input species. 
However, you should only add comments when deemed absolutely necessary because adding 
comments can really slow down the photo-review process for you. 

151 

 
 
 
 
 
Legal Bucks must have 4 or more points on at least one antler beam. Sub-legal Bucks must have 
less than 4 points on both antler beams. First determine if the buck is Legal or Sub-legal then 
move on to the detail category. Count every single point that looks like it would be an inch or 
greater by November—this can be tricky when antlers are still covered in velvet so use your 
best judgement. We are recording total points in the detail category, not just the points from 
one side. Sometimes it is not possible to see every single point. If you can see that a deer has at 
least four points on one main antler beam but cannot see the other main antler beam, ID the 
deer as “Legal Buck” with no point description (i.e., provide no detail). If you can only see one 
main antler beam and there are three or fewer points on that side, ID the deer as “Unknown 
Deer” with an “Antlered” detail since you cannot be sure the other antler beam does not have 
four or more points. Sometimes it is obvious that a deer is not a legal buck, but you cannot 
count all points, in this case it would be okay to ID the deer as “sublegal buck” with no detail, 
but only use this if you are extremely confident there’s no way the other side has four points. A 
similar approach can be applied for legal bucks. 

Every deer tagged as “Unknown Deer” must also be assigned a detail (antlered, antlerless, 
cannot see head). It can be very difficult to differentiate between sexes of fawns, so it is okay if 
you do not assign a detail to fawn photos. However, later in the season many male fawns will 
start to have antler growth and small buttons will become visible on their heads—so keep an 
eye out for that and assign the “Buttonbuck” detail to these fawn images. 

If a deer walks completely out of the frame, you should no longer tag it. If, however, one deer 
walks in front of another deer, but you know both deer are still present you should ID both 
deer. If a deer walks out of the frame and then a deer walks back in the frame, be conservative 
and do not assume it was the same deer unless you identify similar characteristics (e.g., number 
of antler points). 

Eyeshine without deer confirmation is not enough to ID a deer, photos that contain eyeshine 
that does not later reveal itself to be a deer should be labeled as “None”. If you see eyeshine in 
the distance, and a deer slowly reveals itself, then it would be appropriate to tag the early 
eyeshine photos as that deer. Don’t be afraid to go back and change your IDs if more 
information presents itself. For example, you did not notice a fawn in some tall grass until it 
pops out later, but then you go back in the image series and can see movement behind the 
grass. In this situation, those earlier photos should likely be tagged as fawn. It is a common 
occurrence to have to go back and change IDs, so make sure to address these issues as they 
arise because if you do not, they will likely be flagged in the database and result in additional 
work for the photo judge (i.e., the 3rd observer or referee that resolves discrepancies between 
IDs). 

If you find a photo of a human who is not one of our technicians (i.e., the photo is not a camera 
maintenance photo at the very beginning or end of the series), please ID it as “Remove” so we 

152 

 
 
 
 
can delete them from our master photo storage. We do not want to keep any photos of 
humans—we are required by the university to remove all photos of humans (tag as “Remove” 
and so we can delete in bulk later). If a photo is a white-out due to flash overexposure, and you 
cannot be sure what is in the photo frame, label the photo as “camera problem.” If there is a 
white-out photo but you can identify deer, then do not label the photo as “camera problem”, 
instead provide deer IDs. A similar approach should be applied for our other species of interest 
defined above. 

The “Batch ID” button is a wonderful resource, especially when you are looking at a thousand 
photos of a bedded deer (or photos of a fawn dawdling in front of the camera also happens 
often). Flip through the photos outside of the database to find the last photo in the series. 
Starting with the first photo in the series, click “Batch ID” and navigate to the final photo of the 
series. Notice you can only add one ID per “Batch ID,” so if you have a doe and a fawn in 100 
photos you will have to add them separately using the Batch ID function (i.e., do 2 separate 
batch ID functions, one for the doe and one for the fawn). 

Sometimes you will have a group of deer hang out in front of a camera for a long series of 
photos and it can be difficult to know what deer are in each photo. In these instances, it can be 
helpful to copy the photos into a PowerPoint and label each deer; then track one deer through 
the series of photographs to better tell A) what the deer is (i.e., sometimes you only get one 
clear shot of antlers out of a series of 100 photographs) and B) to tell when each deer leaves 
the frame. Once you have tracked each deer throughout the photo series and have triple 
checked that each deer has been marked, go back to the database and enter all of the 
information for each photograph. 

Adding Boxes to Photos 
In some cases, even after photos have been identified it can be difficult to spot the animal in 
question or figure out exactly what’s going on. These cases can be frustrating when the IDs are 
reconciled, since the referee needs to repeat the effort of trying to find the animal all over 
again to determine which ID is correct. To alleviate these issues, you can add “boxes” to photos 
to highlight specific regions, thereby helping the referee spot the important content. A box is 
just an orange box that draws attention to a specific part of a photo. They are stored in the 
database and not added to the image files themselves, so they will not appear if you open the 
image file externally. They only appear within the database in the PhotoID form, and they are 
only visible to the observer who created them or when comparing IDs. To add boxes in the 
PhotoID form, single-click or click and drag on the region you want to highlight. You can add up 
to 5 boxes per photo. To delete an existing box, click within it. Also, there is an option to add 
comments in the table where you input species. However, you should only add comments 
when deemed absolutely necessary because adding comments can really slow down the photo-
review process for you. 

153 

 
 
 
 
APPENDIX 1C: EXPLORATORY DATA ANALYSIS REPORT 

Exploring Alternative Mixing Distributions, Sampling 
Frequencies, and Covariates: An N-Mixture Modeling 
Approach with Empirical Data 

Steven M. Gurney, David M. Williams, and Sonja A. Christensen 

Supplemental research to Michigan’s antler-point-restriction study in the south-central Lower 
Peninsula, October 2023. 

SUMMARY 

Exploratory data analyses with an N-mixture model show that a Poisson mixing 
distribution best fit data from an unmarked camera-trap survey of white-tailed deer (Odocoileus 
virginianus; hereafter, deer). Results varied by sampling frequency and further evaluation is 
recommended to determine its effect on accuracy and bias of the abundance estimator. Of the 
covariates explored, Far Cover (landscape cover open or closed within 100 m of camera) and 
Percent Agriculture were identified as important to detection and ecological processes, 
respectively. When modeling the abundance of deer in the south-central Lower Peninsula of 
Michigan, it is recommended to carefully consider these findings as they may help produce an 
appropriate and meaningful model. 

INTRODUCTION 

White-tailed deer are an important game species, and reliable abundance estimation is 

essential for the evaluation of management actions. This need is especially relevant in areas 
where population-management actions are aimed to mediate the spread of chronic wasting 
disease (CWD) in free-ranging deer. Camera trapping has become an increasingly common 
method for monitoring deer populations, but poorly designed analytical methods may 
compromise abundance estimation and lead to flawed management decisions. Using a camera-
trap study design, we plan to evaluate the effect of an antler point regulation (APR) change in an 
area with CWD on a deer population over three consecutive years. Here, we use a subset of 
data from that study to conduct an exploratory data analysis with an N-mixture model (Royal 
2004). The purpose of the exploratory data analysis was threefold and included explorations of 
mixing distributions, sampling frequencies, and potential covariates. 

STUDY GOAL 

Use an N-mixture model with empirical data to estimate parameters, explore 

characteristics of data, and provide recommendations for appropriate and meaningful 
abundance modeling. 

154 

 
 
 
 
 
 
 
 
 
 
OBJECTIVES  

1.  Identify a mixing distribution that best fits the underlying data. 
2.  Explore the use of alternative daily sampling frequencies. 
3.  Evaluate potential covariates to include in the ecological- and observational-process 

models. 

STUDY AREA 

My exploratory data analysis included a subset of camera-trap data from a 5-county area 
(Newaygo, Kent, Mecosta, Montcalm, and Ionia County) in the south-central Lower Peninsula of 
Michigan that included a known chronic-wasting-disease hotspot (Kent and Montcalm County; 
Figure 1C.1). The study area had an experimental and control area (APR Zone and Non-APR 
Zone, respectively) with townships paired (A–D) between zones.  

METHODS 
General modeling approach 

During the summer of 2019 (15 July to 15 September), randomly placed, unbaited 

camera traps collected 797,407 photos, including 275,794 photos of deer. We leveraged this 
high volume of camera images of a highly visible and relatively abundant species (MDNR 2016) 
to conduct an exploratory data analysis. To account for imperfect detection in the camera 
survey of unmarked deer, we used a hierarchical modeling approach. Specifically, we used a 
Bayesian framework to estimate parameters with an N-mixture model (Royal 2004). We used 
software program JAGS (Plummer et al. 2003) in program R (version 4.1.2; R Core Team 2021) 
and used the R package jagsUI (version 1.5.2; Kellner 2021) to streamline analyses.  

We first started modeling abundance with a Poisson model that produced abundance 
estimates one township at a time (Appendix 1C.1). After some experimentation, it was clear 
that this approach was inefficient and made poor use of the data. We decided to revise the 
model so that it would share information across townships and produce estimates for all 
townships in a single model run (Appendix 1C.2). We used this general modeling framework for 
all analyses. For Markov chain Monte Carlo (MCMC) settings, we ran 3 parallel chains for 
100,000 iterations, discarded the first 5,000 iterations as a burn-in period, and thinned the 
remaining iterations by 1 in 5, resulting in 57,000 draws of the posterior distribution for 
inference. We assumed vague prior distributions for all analyses to express the absence of prior 
information about model parameters. We monitored model convergence via visual inspection of 
MCMC trace plots and using the Gelman-Rubin convergence diagnostic (Rhat or 𝑅̂; Gelman 
2006). To further assess model performance, we evaluated precision of abundance estimates 
(coefficient of variation [CV]) and effective sampling size. If a model exhibited evidence of 
autocorrelation (e.g., relatively short effective samples), we increased all MCMC settings (Kéry 
and Royle 2015) by a multiple of 4, resulting in a comparable 57,000 draws of the posterior 
distribution. We summarized posterior distributions of abundance and detection probability 
using means and 95% Bayesian credible intervals (95% BCIs).  

We used a multi-step approach to evaluate the ecological realism of abundance 
estimates (Joesph et al. 2009). First, we calculated a 1.24-km2 (0.48 mi2) effective sampling area 
per camera site based on average home range size (Suwanrat et al. 2015, Wilton 2021) using 
data from GPS-collared deer in the area (𝑛 = 22 rural female deer; Trudeau et al., unpublished 

155 

 
 
 
 
data). We summed site-level abundances to derive estimated abundance by township, where 
abundance related to the number of deer within the total area of all effective sampling areas in 
a specified township (18 sites per township = 22 km2 [9 mi2]). We used mean abundance 
estimates to calculate deer density within the total area of effective sampling areas per 
township. Lastly, we compared deer density estimates to historical density estimates for the 
areas of interest (Michigan Department of Natural Resources; Appendix 1C.3). 

Alternative mixing distributions and sampling frequencies  

We tested four variants of the simplistic N-mixture model, including Poisson (Appendix 

1C.2), zero-inflated Poisson (Appendix 1C.4), negative binomial (Appendix 1C.5), and Poisson 
lognormal (Appendix 1C.6) to estimate both total abundance and township abundance. Note 
that these were simplistic models without explanatory variables on model parameters (i.e., no 
covariates on the ecological or observational process). The Poisson distribution is one of the 
most common distributions used when analyzing count data, when the probability of a given 
number of independent events occur in a fixed interval of time and space. Royal (2004) used the 
Poisson mixing distribution for the development of the N-mixture model, thus was our a priori 
selection when building our base models (Appendix 1C.1, Appendix 1C.2). 

In the 2019 dataset, we noticed many zero-counts and at least one camera failing to 
detect deer altogether (i.e., all zero counts). These observations motivated us to test a zero-
inflated Poisson mixing distribution. Zeros are common in count data and often cannot be 
accompanied properly by a Poisson or negative binomial model, as these count distributions 
generally under-predict zeros. Excessive zeros can cause overdispersion and ignoring these zeros 
can lead to biased estimated parameters and standard errors.  

Overdispersed data (i.e., variance > mean) are also common for individuals that form 
groups. White-tailed deer are a gregarious species that can form small groups (DeYoung and 
Miller 2011), thus overdispersion was a potential concern with the data. In such situations, the 
negative binomial distribution can be advantageous over the Poisson because it has a 
parameter (𝜃) that accounts for overdispersion. The Poisson-lognormal mixing distribution is 
also used to account for overdispersion in count data. Specifically, the lognormal component of 
the Poisson-lognormal distribution describes the overdispersion in the Poisson rate parameter 
due to clustering of some factors and describes how the average of these factors varies across 
the population. This approach is a common alternative to a negative binomial because the 
Poisson-lognormal can be more straightforward while producing similar inferences. For these 
reasons, we tested both the negative binomial and Poisson-lognormal mixing distributions. 

Given that sampling frequency was undetermined (i.e., how often to count deer), we 

tested each of the mixing distributions (i.e., model variants) with alternative daily sampling 
frequencies. Early data explorations suggested that sampling frequency affected parameter 
estimation and that sampling efforts needed to be relative to animal activity. To better 
understand deer activity, we plotted the density of deer photos by time of day (Figure 1C.2) and 
sex-age-class counts by time of day (Figure 1C.3). We rescaled standard time to local solar time 
and decided to systematically sample within 1, 2, 3, and 4 even time intervals throughout the 
day and at crepuscular hours. For example, a daily frequency of 2 generated 2 samples (counts) 
per day, one for the first half of the day and another for the second half of the day. Crepuscular 
sampling occurred within 2-hr time intervals, at a frequency of twice per day, 1 hour before and 

156 

  
 
 
 
after sunrise and sunset. The crepuscular-style sampling was intended to minimize the 
possibility of double counting individuals with repeated visits while still capturing peak activity 
(Figure 1C.2, Figure 1C.3). Counts were restricted to the maximum number of individuals 
observed in a single image within a selected time interval (Haus et al. 2019, Zou et al. 2019). 

Covariates on detection probability and abundance 

We evaluated the effect of covariates on detection probability using the Poisson N-

mixture model with a crepuscular sampling strategy. This analysis was conducted independent 
of our other efforts here. The Poisson mixing distribution and crepuscular sampling frequency 
were an a priori selection. It is important to note that detection probability (𝑝) consists of three 
components: 1) the probability of presence during survey, 2) the probability of availability given 
presence, and 3) the probability of detection given availability and presence. To select potential 
detection covariates for inclusion in the model, we used data collected during camera-trap 
setup and during sampling occasions. Most potential covariates were selected and defined prior 
to camera setup (Table 1C.1). After reviewing images, we decided to evaluate Camera Field of 
View (relative size: low, medium, large) because it was believed to potentially limit ability to 
identify individuals and limit the maximum number of individuals that can be captured in a 
single image (Table 1C.1, Figure 1C.4). Other data explorations suggested temporal variation of 
detectability (Figure 1C.5), so we also explored the importance of time on the detection 
process. Specifically, we explored the effect of time on detection probability using sampling 
occasion (𝑗) as an index of time (Appendix 1C.7). It is important to note that modeling the time 
covariate occurred later in the exploratory data analysis phase and included Far Cover as a 
predictor in the observational-process model. 

Aside from the time covariate, each covariate was modeled independent of one another. 
Covariates were determined to be important to the detection process if categories differed from 
one another (i.e., at least one category had BCIs that did not overlap the others) and 95% BCIs 
did not include a value of zero. We tested correlations among landscape metrics to identify any 
potential correlations. Using the psych package (Revelle 2023) in program R (version 4.1.2; R 
Core Team 2021), we used a tetrachoric correlation coefficient to measure the correlation (0–1) 
between two binary variables in a 2-by-2 contingency table, Near Cover and Far Cover (Table 
1C.2). Using the package rcompanion (Mangiafico 2023) in program R, we used Cramer’s V 
correlation to examine the association (0–1) between two nominal variables with a contingency 
table larger than a 2-by-2, Far Cover and Cover Type (Table 1C.3). Note that due to small sample 
sizes, Cover Type was collapsed from eight categories to four: 1) Crops, 2) Open Vegetation 
(Mowed Grass, Shrub), 3) Upland Forest, and 4) Wetland (Forested Wetland, Open Wetland). 
The Other Cover Type had a sample size of zero thus was excluded. 

We tested covariates on abundance using an alternative Poisson model that included 
township random effects on abundance and the Far Cover covariate on detection probability 
(Appendix 1C.8). This analysis was conducted independent of our other efforts here and 
included a much coarser sampling frequency (week). The study area’s two dominant land-cover 
classes, forest and agriculture, were hypothesized to be important predictors of deer 
abundance (e.g., forest for cover and agriculture for food). We used a multi-step process to 
evaluate Percent Forest cover and Percent Agriculture cover as potential covariates on 
abundance. First, we calculated the proportion of cover (forest or agriculture) for each camera 

157 

 
 
site using effective sampling areas (1.24-km2 circular buffers around camera sites [0.48 mi2]) and 
the National Land Cover Database land-cover classification layer (30-m2 resolution; Dewitz and 
USGS 2021) in ArcPro (ESRI 2020). This approach allowed us to collapse 3 land-cover types into 
a single ‘agriculture’ classification (herbaceous, hay/pasture, cultivated crops), collapse 4 cover 
types into a single ‘forest’ classification (deciduous forest, evergreen forest, mixed forest, woody 
wetland), and extract associated values. We incorporated these site-specific covariates 
independently into the ecological model, associated with abundance through a log-link 
function, and described by a nonlinear relationship with specified cover (forest or agriculture). 
Therefore, percent agriculture and percent forest were each modeled as quadratic because the 
two were considered to be in direct competition with another. We plotted relationships using 
parameters estimated by the models and compared results. 

RESULTS 

We compared the relative performance of 4 simplistic variants of an N-mixture model 

(Poisson, zero-inflated Poisson, negative binomial, Poisson lognormal) with 5 alternative 
sampling frequencies (1, 2, 3, and 4 times per day and at crepuscular times [2 per day]) to 
identify a suitable mixing distribution. Results varied by sampling frequency for all model 
variants (Table 1C.4). Most model variants demonstrated successful convergence (𝑅̂ values 
below 1.1; Gelman and Rubin 1992; Table 1C.4). However, the zero-inflated Poisson model failed 
to converge in every sampling-frequency scenario and the Poisson lognormal failed with 
crepuscular sampling (Table 1C.4). We observed the lowest 𝑅̂ values with the Poisson model (𝑅̂ 
= 1 for all parameters). The original negative-binomial model failed to successfully run as it 
produced infinite abundance estimates, but a zero-truncated version of the model successfully 
ran after increasing MCMC settings. The best mixing was observed with the Poisson model and 
the worst with Poisson lognormal (see Figure 1C.6 for examples of mixing). We estimated 
abundance with the highest precision using the Poisson model (CV range = 2.75–3.14%) and 
with the least using the Poisson lognormal (CV range = 11.22–17.51%; Table 1C.4). The most 
precise abundance estimates were produced with the Poisson model and a 4-per-day sampling 
frequency. The Poisson produced the most ecologically realistic abundance and density 
estimates (total abundance range = 1,195–1,927; township abundance range = 69–349; 
township density range = 8–39 deer per mi2) and the negative binomial variants produced the 
most unrealistic (total abundance range = 8,666–13,071; township abundance range = 407–
2,467; township density range = 45–274 deer per mi2; Table 1C.4, Table 1C.5, Table 1C.6). 

We explored potential covariates on detection probability and determined if landscape 

metrics were correlated. Results indicated that mean detection probability was similar (i.e., 95% 
BCIs overlapped) for categories within Open Water (water: 𝑥̅ = 0.027, 95% BCIs = 0.024–0.031; 
no water: 𝑥̅ = 0.033, 95% BCIs = 0.031–0.035), Wildlife Trails (trail: 𝑥̅ = 0.034, 95% BCIs = 0.031–
0.038; no trail: 𝑥̅ = 0.030, 95% BCIs = 0.028–0.033), and Camera Field of View (small: 𝑥̅ = 0.029, 
95% BCIs = 0.024–0.034; medium: 𝑥̅ = 0.023, 95% BCIs = 0.020–0.026; large: 𝑥̅ = 0.029, 95% BCIs 
= 0.023–0.036; Table 1C.7). Far Cover was correlated with Near Cover (0.8; Table 1C.2) and 
highly correlated with Cover Type (0.96; Table 1C.3). Models failed to run properly (e.g., failed to 
converge, poor mixing, very low precision, high autocorrelation, extreme parameter estimates) 
when including time as a covariate on detection probability, thus no results are presented here. 
We explored potential covariates on abundance and found Percent Forest and Percent 

158 

 
 
 
Agriculture produced similar parameter estimates (Table 1C.8). Further, expected abundance 
was estimated high when Percent Agriculture values were just above average and high when 
Percent Forest values were just below average (Figure 1C.7). 

DISCUSSION 

The Poisson mixing distribution was identified as the best performing of the four N-
mixture model variants tested. The Poisson model produced the most precise abundance 
estimates (CV range =2.75–3.14%; Table 1C.4). The Poisson was also the only converging model 
to produce ecologically realistic estimates of population size (Table 1C.2, Table 1C.3, Table 1C.4). 
These ecologically realistic estimates were likely a result of the Poisson’s higher detection 
probabilities (𝑝 range = 0.02–0.08) compared to the other model variants (𝑝 ≤ 0.02). At 
convergence, 𝑅̂ equals 1 (Gelman and Rubin 1992), but values below 1.1 are usually taken as 
indicating convergence. However, 𝑅̂ values closer to 1 (e.g., < 1.01) can be better for producing 
posterior summaries with lower Monte Carlo error (Kéry and Royle 2015). The Poisson was the 
only model to produce perfect convergence for all parameters monitored (𝑅̂ = 1). Further, 
MCMC trace plots showed that the Poisson model had exceptional mixing (Figure 1C.6).  

The results from the zero-inflated Poisson variant were not reliable because the model 

failed to converge. Specifically, the model failed to converge on the zero-inflation parameter (𝑧), 
indicating that the chains failed to agree on camera sites (𝑖) with abundance estimates of zero 
(driven by a Bernoulli process for zero and non-zero values). The negative binomial model 
produced very low mean detection probabilities (𝑝 ≤ 0.02), which was likely the driver of 
ecologically unrealistic estimates (e.g., township densities 45–274 deer per mi2). Ficetola et al. 
(2018) did not consider evaluating a negative binomial error distribution in their N-mixture 
model because of its potential to produce infinite abundance estimates, especially when 
detection probability is limited (Joseph et al. 2009). We considered the negative binomial mixing 
distribution and ran into this issue, causing our negative-binomial model to fail during most 
simulations. The slice sampler (used by JAGS) does not work properly when the probability 
density of the sampled variable is infinite at a point. Specifically, distributions with a Gamma 
shape parameter (a component of 𝜆) can cause trouble when the shape parameter is less than 1 
(i.e., close to zero) and the probability mass gets concentrated into a single point. The cause of 
the error can be from sampling extremely small values for the shape parameter of a dataset 
with a particularly large variance and small mean. In these situations, the density function is not 
bounded but goes to infinity at the boundary of support (0 for the Gamma distribution). We 
successfully worked around this issue by truncating the Gamma distribution away from its 
problematic endpoint using the JAGS truncation construct on the stochastic relation. However, 
the zero-truncated negative binomial variant showed evidence of high autocorrelation in the 
chains (i.e., it produced low effective sample size values in the hundreds). We increased MCMC 
settings by a multiple of 4 and successfully reduced autocorrelation (i.e., produced effective 
sample size values in the thousands). Despite these efforts, this model was the most 
computationally expensive of the variants and was deemed computationally prohibitive for our 
future modeling efforts.  

  Of the model variants that converged, all models but the Poisson-lognormal successfully 

converged under all sampling frequencies. The Poisson-lognormal failed to converge with a 
crepuscular sampling frequency (Table 1C.4). After plotting deer activity, we considered 

159 

 
 
crepuscular sampling important because deer activity and counts were high during these times 
(Figure 1C.2, Figure 1C.3). We found it concerning that the Poisson-lognormal model failed to 
converge with data from this important time interval. A visual inspection of trace plots 
suggested marginal mixing with the Poisson-lognormal model variant. Further, the Poisson-
lognormal produced abundance estimates with the lowest precision (CV range = 11.22–17.51%; 
Table 1C.4). In comparison, the precision was over four times worse than that of the Poisson 
variant (CV range = 2.75–3.14%; Table 1C.4). Like our results from the negative binomial model, 
we observed low effective sample sizes with the Poisson-lognormal model variant, which 
suggested high levels of autocorrelation (Table 1C.4). We considered increasing the MCMC 
settings to reduce autocorrelation like we did with the negative binomial but decided it too 
would be computationally prohibitive to our future modeling efforts. 

Our results indicated that Open Water, Wildlife Trails, and Camera Field of View were not 

important to the detection process, thus are not recommended for future modeling efforts of 
the system. Many important covariates were correlated with one another, including Near Cover 
and Far Cover (0.8; Table 1C.2). We recommend using Far Cover over Near Cover because Far 
Cover was considered a more limiting factor on the landscape and a 100-m scale (Far Cover) was 
likely more important to the detection process than a 1-m scale (Near Cover). There was an 
even stronger correlation between Far Cover and Cover Type (0.96; Table 1C.3). Further, we 
found similar detection probabilities between Crops and Open Vegetation Cover Types (Crops: 𝑥̅ 
= 0.039, 95% BCIs = 0.036–0.043; Open vegetation: 𝑥̅ = 0.034, 95% BCIs = 0.030–0.038) and 
similar detection probabilities between Upland Forest and Wetland Cover Types (Upland Forest: 
𝑥̅ = 0.025, 95% BCIs = 0.022–0.028; Wetland: 𝑥̅ = 0.024, 95% BCIs = 0.020–0.028). These 
similarities highlighted a noticeable break point in detection probability between the Crops-
Open Vegetation group (95% BCI ranges = 0.030–0.043) and the Upland-Wetland group (95% 
BCI ranges = 0.020–0.028; Table 1C.7). Notably, the range of estimates for these groups closely 
reflected that of Far Cover estimates (Open: 95% BCIs = 0.034–0.040; Closed: 95% BCIs = 0.023–
0.028; Table 1C.7). Given these results, and the value of simplicity in modeling, we recommend 
selecting for the more parsimonious Far Cover covariate over Cover Type.  

We attempted to model time as a covariate on detection probability, but models failed 
to run properly (e.g., failed to converge, poor mixing, very low precision, high autocorrelation, 
extreme parameter estimates). We used sampling occasion (𝑗) as an index for time and as a 
covariate on detection probability (Appendix 1C.8). After our first failed modeling attempt, we 
found that sites with all zero counts (i.e., no deer detected) were associated with poor mixing 
and extreme parameter estimates. We suspected that these zeros were causing problems, so 
we revised the structure of the model to include a Bernoulli variable (𝑧) on the 𝑗 parameter in 
the logit function (Appendix 1C.9). This new revision treated the Bernoulli variable like an on-off 
switch and allowed the time covariate to be modeled or not depending on patterns (i.e., zero 
counts at sites). Despite our efforts, however, we found that the model still failed to converge. 
These results suggested that including 𝑗 as a covariate overparameterized the model. We 
suspected that data limitations prevented the model from estimating two parameters for each 
site, so we tried modeling with other sampling frequencies to increase the amount of data 
informing the model. The model still failed to converge with the additional data. My final 
attempt introduced an additional hierarchical level to the model, incorporating weeks (𝑘) into 
the structure (Appendix 1C.10). However, the model still performed poorly. After many failed 

160 

 
attempts, we abandoned time as a covariate and considered it as unimportant to the detection 
process.   

We explored the effects of Percent Forest and Percent Agriculture as covariates on deer 

abundance and found similar results (Table 1C.8). It is worth noting that we also explored a 
week sampling frequency during these analyses and found that the model produced detection 
probabilities higher than the alternative daily sampling frequencies (e.g., values in the tenths 
compared to hundredths). Expected site abundance peaked just below average Percent Forest 
cover and just above average Percent Agriculture cover (Figure 1C.8), which suggested a 
potential correlation. Further investigation showed the two were highly correlated with one 
another (0.96; Table 1C.3). This result was not surprising given the agro-forested landscape of 
the study area. Given the high correlation, we did not consider modeling Percent Forest and 
Percent Agriculture simultaneously or modeling an interaction between the two. Most 
parameter estimates were comparable between the two classes, but the Percent Agriculture 
covariate estimated abundance with slightly more precision (agriculture: CV = 4.6%; forest: CV = 
4.7%). Further, past studies in the Midwest have considered agriculture to be an important 
driver of demographic variation in deer abundance (Nixon et al. 1991, Nixon et al. 1994, Nixon 
et al. 2001). For these reasons, we recommend using the Percent Agriculture covariate over 
Percent Forest.  

Collectively, our results suggest that the Poisson mixing distribution best fits the 

underlying count data. All other model variants tested failed to perform well (e.g., lack of 
convergence, unrealistic abundance estimates). Results varied by sampling frequency, with the 
Poisson model and a 4-per-day sampling frequency producing the highest precision (CV = 
2.75%). However, we found that this sampling frequency also produced the lowest detection 
probability with the Poisson model (𝑝 = 0.02), thus coarser sampling frequencies may be a 
viable option for increasing detection probability. Although explored here, we recommend 
further evaluation of alternative sampling frequencies to determine levels of accuracy and bias 
associated with each of the alternatives. Most covariates tested were found to be unimportant 
to the detection process. However, we recommend the inclusion of Far Cover as a covariate on 
detection probability. We also recommend including Percent Agriculture as a covariate on 
abundance. When using an N-mixture model to estimate the abundance of deer in the south-
central Lower Peninsula of Michigan, we recommend careful consideration of these findings as 
they may help produce an appropriate and meaningful model. 

161 

 
TABLES 
Table 1C.1. Table listing potential covariates on detection probability of white-tailed deer (Odocoileus virginianus), how they were 
defined, and logic as why they were considered for inclusion in the observational-process model of an N-mixture model.  

Potential covariate 

Near cover 

Far cover  

Cover type 

Open water 

Wildlife trail 

Definition 

Why consider? 

The majority cover in a 1-m radius from 
the camera (“Open” or “Closed”) 

The majority cover in a 100-m radius from 
the camera (“Open” or “Closed”) 

The majority land cover in a 100-m radius 
from the camera (Crops, Forested 
Wetland, Grassland, Mowed Grass, Open 
Wetland, Other, Shrub, Upland Forest) 
Was there open water within sight of the 
camera (“Yes” or “No”) 

Deer need cover, cover requirements may 
vary by sex-age class, and vegetation can 
limit detection 

Deer need cover, cover requirements may 
vary by sex-age class, and vegetation can 
limit detection 

Deer use a variety of habitat types, 
certain sex-age classes may favor certain 
habitat types, and different vegetation 
can affect detection differently 
Deer frequent water sources 

Stand next to the camera. Is the camera 
on or within sight of a wildlife trail? (“Yes” 
or “No”) 

Deer may favor the path of least 
resistance 

Camera field of view 

The relative field of view for a camera 
(Small, Medium, Large) 

Can limit ability to identify an individual 
deer, limits the maximum number of deer 
that can be captured in a single image  

162 

 
Table 1C.2. The 2-by-2 contingency table used to measure the tetrachoric correlation coefficient between two binary variables, Near 
Cover and Far Cover (open or closed). Near cover was defined as the majority cover in a 1-m radius from the camera. Far cover was 
defined as the majority cover in a 100-m radius from the camera. Both landscape metrics were considered for inclusion in an N-
mixture model as covariates on detection probability. 

Open near cover 

Closed near cover 

35 

37 

3 

70 

Open far cover 

Closed far cover 

163 

 
 
Table 1C.3. The 2-by-4 contingency table used to measure Cramer’s V correlation between two categorical variables, Far Cover and 
Cover Type. Far cover was binary and defined as the majority cover in a 100-m radius from the camera (open or closed). Cover type 
was defined as the majority of land cover in a 100-m radius from the camera. Both landscape metrics were considered for inclusion 
in an N-mixture model as covariates on detection probability. 

Crop cover type 

Open vegetation cover 
type 

Upland forest cover type  Wetland cover type 

Open far cover 

Closed far cover 

43 

0 

25 

0 

0 

58 

4 

15 

164 

 
 
 
Table 1C.4. Estimates from an N-mixture model with different combinations of daily sampling frequencies and mixing distributions. 
Estimates include convergence results (𝑅̂ <1.1 = convergence), degree of mixing observed in Markov chain Monte Carlo (MCMC) 
trace plots, effective sampling size for abundance (𝑁 n.eff), total abundance (𝑁), standard deviation of abundance (𝑁 SD), and the 
coefficient of variation for abundance (𝑁 CV%). All sampling frequencies with the zero-inflated Poisson and the crepuscular sampling 
frequency with the Poisson-lognormal failed to converge, thus these estimates were not reliable. NA values indicate that the model 
failed to run. 

Mixing 
distribution 

Sampling 
frequency 

Did it 
converge? 

Degree of 
mixing 

𝑵 n.eff 

𝑵 

𝑵 SD 

𝑵 CV (%) 

Poisson 

Zero-inflated 
Poisson 

Negative 
binomial 

Negative 
binomial, 
zero-
truncated 

1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

Yes 
Yes 
Yes 
Yes 
Yes 
No 
No 
No 
No 
No 
Yes 
Yes 
NA 
NA 
NA 
Yes 
Yes 
Yes 
Yes 
Yes 

1,759 
1,845 
1,908 
1,927 
1,195 
1,870 
1,949 
2,019 
2,036 
1,355 
9,818 
11,684 
NA 
NA 
NA 
9,901 
11,772 
12,483 
13,071 
8,666 

53 
52 
53 
53 
37 
60 
58 
60 
59 
49 
956 
1,059 
NA 
NA 
NA 
969 
1,084 
1,092 
1,119 
917 

3.02 
2.81 
2.78 
2.75 
3.14 
3.23 
2.99 
2.96 
2.91 
3.61 
9.74 
9.06 
NA 
NA 
NA 
9.79 
9.21 
8.75 
8.56 
10.59 

11,129 
57,000 
8,785 
28,663 
23,196 
9,015 
57,000 
24,914 
4,451 
25,747 
1,001 
1,610 
NA 
NA 
NA 
997 
674 
8,178 
870 
2528 

Good 
Good 
Good 
Good 
Good 
Good 
Good 
Good 
Good 
Good 
Marginal 
Marginal 
NA 
NA 
NA 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 

165 

 
 
 
 
 
 
 
 
 
Table 1C.4. (cont’d) 

Negative 
binomial, 
zero-
truncated, 
high MCMC  
Poisson-
lognormal 

1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
No 

Marginal 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 
Marginal 

25391 
2,974 
5,223 
12,670 
3,418 
1,051 
778 
832 
123 
349 

9,904 
11,715 
12,539 
13,029 
8,693 
4,473 
6,480 
8,162 
9,066 
4,667 

967 
1,065 
1,127 
1,127 
931 
502 
790 
1,188 
1,287 
817 

9.76 
9.09 
8.99 
8.65 
10.71 
11.22 
12.18 
14.55 
14.20 
17.51 

166 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1C.5. Mean abundance estimates by township (e.g., APR-Zone A) by alternative combinations of daily sampling frequencies and 
mixing distributions. All sampling frequencies with the zero-inflated Poisson and the crepuscular sampling frequency with the 
Poisson-lognormal failed to converge, thus these estimates were not reliable. NA values indicate that the model failed to run. Note 
that estimates of error are not included because mean values were used as the key metric for evaluating ecological realism of 
estimates. 

Mixing 
distribution 

Poisson 

Zero-
inflated 
Poisson 

Negative 
binomial 

Negative 
binomial, 
zero-
truncated 

Sampling 
frequency 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

Non-APR 
Zone A 
175 
182 
184 
187 
122 
186 
192 
195 
198 
139 
915 
1,080 
NA 
NA 
NA 
922 
1,088 
1,120 
1,192 
828 

Non-APR 
Zone B 
119 
119 
122 
121 
69 
127 
126 
130 
128 
79 
593 
666 
NA 
NA 
NA 
598 
672 
710 
718 
407 

Non-APR 
Zone C 
230 
237 
244 
248 
147 
244 
251 
259 
262 
166 
1,266 
1,477 
NA 
NA 
NA 
1,277 
1,488 
1,570 
1,655 
1,004 

Non-APR 
Zone D 
166 
170 
175 
177 
117 
176 
180 
185 
188 
133 
846 
981 
NA 
NA 
NA 
854 
988 
1,039 
1,100 
761 

APR Zone 
A 
224 
233 
244 
244 
148 
239 
246 
259 
258 
168 
1,244 
1,460 
NA 
NA 
NA 
1,254 
1,471 
1,589 
1,635 
1,031 

APR Zone 
B 
260 
277 
289 
288 
173 
276 
292 
306 
304 
196 
1,477 
1,784 
NA 
NA 
NA 
1,489 
1,797 
1,931 
1,982 
1,295 

APR Zone 
C 
318 
334 
345 
349 
217 
337 
352 
364 
368 
246 
1,867 
2,213 
NA 
NA 
NA 
1,883 
2,229 
2,355 
2,467 
1,666 

APR Zone 
C 
268 
294 
305 
313 
202 
284 
309 
322 
330 
226 
1,609 
2,022 
NA 
NA 
NA 
1,623 
2,038 
2,169 
2,323 
1,673 

167 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1C.5. (cont’d) 

Negative 
binomial, 
zero-
truncated, 
high MCMC  

Poisson-
lognormal 

1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

923 
1,083 
1,125 
1,188 
831 
487 
674 
854 
867 
450 

599 
668 
714 
716 
409 
413 
526 
582 
639 
239 

1,277 
1,481 
1,577 
1,649 
1,007 
659 
916 
1,133 
1,288 
595 

854 
984 
1,043 
1,096 
763 
488 
671 
834 
882 
466 

1,255 
1464 
1,596 
1,630 
1,035 
541 
793 
983 
1,089 
538 

1,490 
1,789 
1,940 
1,975 
1,299 
542 
811 
1,003 
1,189 
558 

1,884 
2,219 
2,365 
2,459 
1,671 
697 
1,096 
1,406 
1,554 
876 

1,623 
2,027 
2,179 
2,315 
1,679 
646 
993 
1,366 
1,558 
943 

168 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1C.6. Density estimates by township (e.g., APR-Zone A) by alternative combinations of daily sampling frequencies and mixing 
distributions. All sampling frequencies with the zero-inflated Poisson and the crepuscular sampling frequency with the Poisson-
lognormal failed to converge, thus these estimates were not reliable. NA values indicate that the model failed to run. Note that 
estimates of error are not included because mean values were used as the key metric for evaluating ecological realism of estimates. 
Of the models that converged, only the Poisson variant produced ecologically realistic density estimates. 

Mixing 
distribution 
Poisson 

Zero-inflated 
Poisson 

Negative 
binomial 

Negative 
binomial, 
zero-
truncated) 

Sampling 
frequency 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

Non-APR 
Zone A 
19 
20 
20 
21 
14 
21 
21 
22 
22 
15 
102 
120 
NA 
NA 
NA 
102 
121 
124 
132 
92 

Non-APR 
Zone B 
13 
13 
14 
13 
8 
14 
9 
14 
14 
9 
66 
74 
NA 
NA 
NA 
66 
75 
79 
80 
45 

Non-APR 
Zone C 
26 
26 
27 
28 
16 
27 
28 
29 
29 
18 
141 
164 
NA 
NA 
NA 
142 
165 
174 
184 
112 

Non-APR 
Zone D 
18 
19 
19 
20 
13 
20 
20 
21 
21 
15 
94 
109 
NA 
NA 
NA 
95 
110 
115 
122 
85 

APR Zone 
A 
25 
26 
27 
27 
16 
27 
27 
29 
29 
19 
138 
162 
NA 
NA 
NA 
139 
163 
177 
182 
115 

APR Zone 
B 
29 
31 
32 
32 
19 
31 
32 
34 
34 
22 
164 
198 
NA 
NA 
NA 
165 
200 
215 
220 
144 

APR Zone 
C 
35 
37 
38 
39 
24 
37 
39 
40 
41 
27 
207 
246 
NA 
NA 
NA 
209 
248 
262 
274 
185 

APR Zone 
C 
30 
33 
34 
35 
22 
32 
34 
36 
37 
25 
179 
225 
NA 
NA 
NA 
180 
226 
241 
258 
186 

169 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1C.6. (cont’d) 

Negative 
binomial, 
zero-
truncated, 
high MCMC 
Poisson-
lognormal 

1 
2 
3 
4 
Crepuscular 
1 
2 
3 
4 
Crepuscular 

103 
120 
125 
132 
92 
54 
75 
95 
96 
50 

67 
74 
79 
80 
45 
46 
58 
65 
71 
27 

142 
165 
175 
183 
112 
73 
102 
126 
143 
66 

95 
109 
116 
122 
85 
54 
75 
93 
98 
52 

139 
163 
177 
181 
115 
60 
88 
109 
121 
60 

166 
199 
216 
219 
144 
60 
90 
111 
132 
62 

209 
247 
263 
273 
186 
77 
122 
156 
173 
97 

180 
225 
242 
257 
187 
72 
110 
152 
173 
105 

170 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1C.7. Mean estimates for the effect of potential covariates on detection probability. The 2.5% and 97.5% represent the lower 
and upper limits of 95% Bayesian credible intervals, respectively.  

2.5% 
0..034 
0.023 
0.036 
0.030 
0.022 
0.020 
0.024 
0.031 
0.031 
0.028 
0.024 
0.020 
0.023 

97.5% 
0.040 
0.028 
0.043 
0.038 
0.028 
0.028 
0.031 
0.035 
0.038 
0.033 
0.034 
0.026 
0.036 

Potential covariate 
Far cover  

Cover type 

Open water  

Wildlife trail  

Camera field of view 

Category 
Open 
Closed 
Crops 
Open vegetation 
Upland forest 
Wetland 
Open water nearby 
No open water nearby 
Trail nearby 
No trail nearby 
Small 
Medium 
Large 

Mean 
0.037 
0.025 
0.039 
0.034 
0.025 
0.024 
0.027 
0.033 
0.034 
0.030 
0.029 
0.023 
0.029 

171 

 
 
Table 1C.8. Parameter estimates for the effect of potential covariates on abundance, including detection probability in areas with 
open (𝑝1) and closed far cover (𝑝2), and total abundance (𝑁). The 2.5% and 97.5% represent the lower and upper limits of 95% 
Bayesian credible intervals, respectively. Estimates were comparable between covariates. 

Potential covariate 
Percent forest 

Percent agriculture 

Parameter 
𝑝1 
𝑝2 
𝑁 
𝑝1 
𝑝2 
𝑁 

Mean 
0.323 
0.313 
1,206 
0.328 
0.310 
1,200 

SD 
0.018 
0.019 
56.3 
0.018 
0.019 
55.2 

2.5% 
0.289 
0.277 
1,102 
0.294 
0.274 
1,100 

97.5% 
0.358 
0.351 
1,324 
0.364 
0.348 
1,317 

172 

 
 
 
 
FIGURES 

Figure 1C.1. Study area in the south-central Lower Peninsula of Michigan, USA, in a designated 
5-county area. Mandatory antler point restrictions (APRs) were implemented in 2019 in the 
experimental area (APR Zone) and not in the control area (Non-APR Zone). Townships were 
paired (A–D) between zones, and remote cameras were placed in each township to monitor 
white-tailed deer (Odocoileus virginianus) populations over a duration of four years (2019 – 
2022). Maps created in ArcGIS Pro (version 2.7.1; www.esri.com). 

173 

 
 
 
 
Figure 1C.2. Density of white-tailed deer (Odocoileus virginianus) photos by time of day (rescaled 0–1). Using density of photos as an 
index, peak activity was observed during crepuscular hours. Grey-shaded boxes represent defined crepuscular sampling windows (2 
separate 2-hour windows around sunrise and sunset). Photos were collected during a 2019 camera-trap survey in the south-central 
Lower Peninsula, Michigan, USA.

174 

 
 
Figure 1C.3. Maximum number of individual white-tailed deer (Odocoileus virginianus) detected by time of day (rescaled 0–1) and 
sex-age class, including A) doe, B) fawn, C) sub-legal male, and D) legal male. Legal males had ≥4 antler points on at least one antler 
and sub-legal males did not. Does included yearling and adult females. Peak deer activity was observed during crepuscular hours for 
all sex-age classes. Grey-shaded boxes represent defined crepuscular sampling windows (2 separate 2-hour windows around sunrise 
and sunset). Photos were collected during a 2019 camera-trap survey in the south-central Lower Peninsula, Michigan, USA.

175 

 
A) 

B) 

C) 

Figure 1C.4. Examples of different classifications of camera-trap field of view. Field of view was 
classified based on the relative frame size, including A) small, B), medium, or C) large. Field of 
view was considered as a covariate on detection probability because of its potential to affect 
ability to identify individuals and could limit the maximum number of individuals captured in a 
single image. 

176 

 
 
 
Figure 1C.5. Results from early data explorations with an N-mixture model highlighting monthly variation of detectability among sex-
age classes of white-tailed deer (Odocoileus virginianus) by land-cover type. Month 1 survey was July 15th–August 14th and Month 2 
survey was August 15th–September 14th. Error bars indicate 95% credible intervals. Detection probability of Legal Bucks differed from 
Does in Month 1 Upland Forest, from both Does and Fawns in Month 2 Upland Forest, and differed from all sex-age classes in Month 
2 Crops.  

177 

 
 
 
A
) 

B) 

Figure 1C.6. Markov chain Monte Carlo trace plot examples of A) exceptional mixing with the Poisson model and B) marginal mixing 
with the Poisson lognormal model for total abundance. These examples highlight the best and worse mixing observed in this study. 
For both scenarios, a simplistic N-mixture model was used for data explorations with white-tailed deer (Odocoileus virginianus) count 
data from a camera-trap study design. 

178 

 
 
A) 

B) 

e
c
n
a
d
n
u
b
a
d
e
t
c
e
p
x
E

e
c
n
a
d
n
u
b
a
d
e
t
c
e
p
x
E

Agriculture cover 

Forest cover 

Figure 1C.7. Change in expected deer site abundance as a function of site covariates, including A) percent of agriculture cover and B) 
percent of forest cover within each camera site’s a 1.24-km2 [0.48 mi2] effective sampling area. X-axis values are standardized with a 
mean zero and gray bands represent 95% confidence limits. Expected abundance was high when percent agriculture was slightly 
higher than average and when percent forest cover was slightly below average. 

179 

 
 
 
 
 
 
 
APPENDIX 1C.1: CODE FOR MODELING ABUNDANCE BY TOWNSHIP WITH A POISSON 
DISTRIBUTION 

nmix <- function(twn.final){ 

  #Data 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  p ~ dunif(0, 1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda) 

    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p, N[i]) 
      } #j 
    } #i 

  # Derived quantities 
  totalN <- sum(N[])   
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 

180 

 
 
 
 
   
 
 
   
   
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("lambda", "p", "totalN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

181 

 
 
 
 
APPENDIX 1C.2: CODE FOR MODELING ABUNDANCE FOR ALL TOWNSHIPS WITH A POISSON 
DISTRIBUTION 

nmix <- function(twn.final){ 

  #Data 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  p ~ dunif(0, 1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda) 

    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p, N[i]) 
      } #j 
    } #i 

  # Derived quantities 
  totalN <- sum(N[]) 

  #Relies on input data (rows) being sorted by      site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144]) 

182 

 
 
 
 
   
 
 
 
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("lambda", "p", "totalN", "shermanN", "tyronN", "bowneN", 
"nelsonN", "sheridanN", "eastonN", "bushnellN", "douglasN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

183 

   
   
 
 
 
 
APPENDIX 1C.3: SUPPLEMENTARY DEER DENSITY MAP PRODUCED BY THE MICHIGAN 
DEPARTMENT OF NATURAL RESOURCES 

Figure 1C.8. White-tailed deer (Odocoileus virginanus) density estimates by deer management 
unit (DMU) in Michigan, USA, 2009. Estimates and map produced by the Michigan Department 
of Natural Resources. 

184 

 
 
APPENDIX 1C.4: CODE FOR MODELING ABUNDANCE FOR ALL TOWNSHIPS WITH A ZERO-
INFLATED POISSON DISTRIBUTION 

zipmix <- function(twn.final){ 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  p ~ dunif(0, 1) 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  psi ~ dunif(0,1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(mu[i]) 
    mu[i] <- lambda * z[i] + 0.000001 
    z[i] ~ dbern(psi) 

    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p, N[i]) 
      } #j 
    } #i 

  # Derived quantities 
  totalN <- sum(N[])  

  #Relies on input data (rows) being sorted by      site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 

185 

 
 
 
 
 
 
  
  douglasN <- sum(N[127:144]) 
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("lambda", "p", "totalN", "shermanN", "tyronN", "bowneN", 
"nelsonN", "sheridanN", "eastonN", "bushnellN", "douglasN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

186 

   
   
 
 
 
 
APPENDIX 1C.5: CODE FOR MODELING ABUNDANCE FOR ALL TOWNSHIPS WITH A NEGATIVE 
BINOMIAL DISTRIBUTION 

nmix.negbin <- function(twn.final){ 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  for (i in 1:R){ 
  lambda[i] ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  } 
  th ~ dunif(0, 50) 
  p ~ dunif(0, 1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) {   #sites 
    N[i] ~ dnegbin(prob[i], th) 
    prob[i] <- th / (th + lambda[i])  

    # Observation model for replicated counts 
    for (j in 1:T) {   #sample occasions 
      y[i,j] ~ dbin(p, N[i]) 
      } #j 
    } #i 

  # Derived quantities 
  totalN <- sum(N[]) 

  #relies on input data (rows) being sorted by site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 

187 

 
 
 
 
 
 
   
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144]) 
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y))  

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("p", "totalN", "shermanN", "tyronN", "bowneN", 
"nelsonN", "sheridanN", "eastonN", "bushnellN", "douglasN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 10 
  nb <- 100000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

188 

   
   
 
 
 
 
APPENDIX 1C.6: CODE FOR MODELING ABUNDANCE FOR ALL TOWNSHIPS WITH A POISSON-
LOGNORMAL DISTRIBUTION 
nmix.poslognorm <- function(twn.final){ 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 
  # Priors 
  for (i in 1:R) { 
    p[i] ~ dunif(0, 1) 
  } 
  mean.lambda ~ dunif(0, 200) 
  beta0 <- log(mean.lambda) 
  tau ~ dgamma(0.1, 0.1) # Excess-Poisson variation (precision) 
  sigma <- sqrt(1 / tau) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda[i]) 
    eta[i] ~ dnorm(0, tau) 
    log(lambda[i]) <- beta0 + eta[i] 

    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p[i], N[i]) 
      } #j 
    } #i 

  # Derived quantities 
  totalN <- sum(N[]) 

  #relies on input data (rows) being sorted by site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 

189 

 
   
 
 
  
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144]) 
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("p", "totalN", "shermanN", "tyronN", "bowneN", 
"nelsonN", "sheridanN", "eastonN", "bushnellN", "douglasN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

190 

   
   
 
 
 
 
APPENDIX 1C.7: CODE FOR MODELING SAMPLING OCCASION AS A COVARIATE ON DETECTION 

nmix.det.newtime <- function(twn.final, cov.table){ 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  NewCover <- cov.table$LandCoverNew 
  max.cov <- 2 # Hardcoding solution  
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  #Landscape cover (far cover) covariate has 2 levels, going to 
estimate p for each level 
  alpha ~ dunif(-20,20) 
  beta1 ~ dunif(-20,20) 

  for (i in 1:R) { 
    beta3[i] ~ dunif(-20,20) 
  } 

  #for(i in 1:2){ 
  #  p[i] ~ dunif(0, 1) 
  #} 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda) 

    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p[i,j], N[i]) 
      logit(p[i,j]) <- alpha + beta1 * NewCover[i] + beta3[i] *j 
      } #j 
    } #i 

  # Derived quantities 

191 

 
 
 
   
 
 
 
 
  totalN <- sum(N[]) 

  #relies on input data (rows) being sorted by site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144]) # SG look to see if there's >144 sites 
  } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y), NewCover = 
as.integer(NewCover)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored, SG included p 09JUL22 
  params <- c("alpha", "beta1", "beta3", "totalN", "shermanN", 
"tyronN", "bowneN", "nelsonN", "sheridanN", "eastonN", "bushnellN", 
"douglasN") 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

192 

   
   
   
 
 
 
 
APPENDIX 1C.8: CODE FOR MODELING COVARIATES ON ABUNDANCE 

nmix <- function(twn.final, cov.table){ 
  #Cover (open or closed) covariate on detection process 
  #Percent agriculture covariate on abundance process 
  #Week counts 
  #Township as random effect on abundance process 

  #Data 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  NewCover <- cov.table$LandCoverNew #Open or closed cover covriate on 
detection 
  AgCover <- cov.table$AgCover #%agriculture covariate on abundance 

  #Create group ID for townships; requires all 18 sites in 4 townships 
(8 in other years) 
  twn <- sort(rep(1:8, 18))  

  #Load JAGS package 
  library("jagsUI") 

  #Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 
  # Priors 
  alpha ~ dnorm(0,0.25) 
  beta1 ~ dnorm(0,0.25) 
  beta4 ~ dnorm(0,0.25) 
  beta5 ~ dnorm(0,0.25) 
  mu.kappa ~ dnorm(0,0.25) 
  sigma.kappa ~ dexp(1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { # Sites 
    N[i] ~ dpois(mu.lambda[i]) 
    log(mu.lambda[i]) <- kappa[twn[i]] + (beta4 * AgCover[i]) + (beta5 
* pow(AgCover[i],2)) 

    # Observation model for replicated counts 

193 

 
 
 
     
     
   
     
         
    for (j in 1:T) { #count reps 
      y[i,j] ~ dbin(p[i], N[i]) 
    } #j 
    logit(p[i]) <- alpha + (beta1 * NewCover[i]) 
  } #i 

  for (k in 1:8) { # Townships for random effect on lambda, hard coded 
for 8 townships 
    kappa[k] ~ dnorm(mu.kappa, tau.kappa) 
  } 

  # Derived quantities 
  tau.kappa <- pow(sigma.kappa,-2) 

  totalN <- sum(N[]) 

  # Relies on input data (rows) being sorted by site (LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144])  # 144 camera sites 

  } 
  ",fill = TRUE) 
  sink() 

  #Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y[,,1]), NewCover = 
as.integer(NewCover), AgCover = as.numeric(scale(AgCover)), twn = twn) 

  #Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  #Parameters monitored 

194 

     
     
 
 
     
   
     
     
     
  params <- c("alpha", "beta1", "beta4", "beta5", "mu.kappa", 
"sigma.kappa", "kappa", "p", "totalN", "shermanN", "tyronN", "bowneN", 
"nelsonN", "sheridanN", "eastonN", "bushnellN", "douglasN") 

  # MCMC settings 
  ni <- 50000 
  nt <- 5 
  nb <- 3000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
}} 

195 

     
     
 
APPENDIX 1C.9: CODE FOR MODELING SAMPLING OCCASION AS A COVARIATE ON DETECTION 
WHILE ACCOUNTING FOR ZEROS 

nmix.det.newtime <- function(twn.final, cov.table){ 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  NewCover <- cov.table$LandCoverNew 
  max.cov <- 2 # Hardcoding solution  
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  #Landscape cover (far cover) covariate has 2 levels, going to 
estimate p for each level 
  alpha ~ dunif(-20,20) 
  beta1 ~ dunif(-20,20) 
  psi ~ dunif(0,1) 

  for (i in 1:R) { 
    beta3[i] ~ dunif(-20,20) 
  } 
  #for(i in 1:2){ 
  #  p[i] ~ dunif(0, 1) 
  #} 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda) 
    z[i] ~ dbern(psi) 
    # Observation model for replicated counts 
    for (j in 1:T) { 
      y[i,j] ~ dbin(p[i,j], N[i]) 
      logit(p[i,j]) <- alpha + (beta1 * NewCover[i]) + (z[i] * 
beta3[i] * j) 
      } #j 
    } #i 

196 

 
 
 
 
 
  # Derived quantities 
  totalN <- sum(N[]) 

  #relies on input data (rows) being sorted by site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144])  
  sumZ <- sum(z[1:144]) 
  } 

  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y), NewCover = 
as.integer(NewCover)) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored, SG included p 09JUL22 
  params <- c("alpha", "beta1", "beta3", "totalN", "shermanN", 
"tyronN", "bowneN", "nelsonN", "sheridanN", "eastonN", "bushnellN", 
"douglasN", “sumZ”) 

  # MCMC settings 
  ni <- 100000 
  nt <- 5 
  nb <- 5000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

197 

 
   
 
   
   
 
 
 
 
APPENDIX 1C.10: CODE FOR MODELING WEEK AS A COVARIATE ON DETECTION  

nmix.det.newtime2 <- function(twn.final, cov.table){ 

  max <- ncol(twn.final) 
  y1 <- twn.final[,2:max] 
  y <- array(unlist(y1), dim=c(144,14,9))  #restructuring data into 3 
dimensions (144 sites, 14 counts per week, 9 weeks) 

  NewCover <- cov.table$LandCoverNew 
  max.cov <- 2 # Hardcoding 
  library("jagsUI") 

  # Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 

  # Priors 
  lambda ~ dgamma(0.005, 0.005) # Standard vague prior for lambda 
  #Landscape cover (far cover) covariate has 2 levels, going to 
estimate p for each level 
  alpha ~ dunif(-20,20) 
  beta1 ~ dunif(-20,20) 
  beta4 ~ dunif(-20,20) 

  for (i in 1:R) { 
    beta3[i] ~ dunif(-20,20) 
  } 
  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { 
    N[i] ~ dpois(lambda) 
    #z[i] ~ dbern(psi) 
    # Observation model for replicated counts 
    for (k in 1:9) { 
      for (j in 1:T) { 
        y[i,j,k] ~ dbin(p[i,k], N[i]) 
        } #j 
      logit(p[i,k]) <- alpha + (beta1 * NewCover[i]) + (beta3[i] * k) 
      #logit(p[i,k]) <- alpha + (beta1 * NewCover[i]) + (beta3[i] * k) 
+ ((beta4 * NewCover[i] * k)) 

198 

 
   
 
 
 
 
    } #k 
  } #i 

  # Derived quantities 
  totalN <- sum(N[]) 

  #relies on input data (rows) being sorted by site(LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144])  
    } 
  ",fill = TRUE) 
  sink() 

  # Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y[,,1]), NewCover = 
as.integer(NewCover), sherman.rows=sherman.rows) 

  # Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 
  inits <- function() list(N = Nst) 

  # Parameters monitored 
  params <- c("alpha", "beta1", "beta3", "beta4", "p", "totalN", 
"shermanN", "tyronN", "bowneN", "nelsonN", "sheridanN", "eastonN", 
"bushnellN", "douglasN") 
  # MCMC settings 
  ni <- 10000 
  nt <- 5 
  nb <- 1000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 
n.thin = nt, n.iter = ni, n.burnin = nb) 
} 

199 

 
 
   
   
   
 
 
 
REFERENCES 

Dewitz, J., and U.S. Geological Survey. 2021. National Land Cover Database (NLCD) 2019 

Products (ver. 2.0, June 2021): U.S. Geological Survey data release, 
https://doi.org/10.5066/P9KZCM54. 

DeYoung, C.A., and K. V. Miller. 2011. White-tailed deer behavior. Pages 311–351 in D. G. Hewitt, 
editor. Biology and Management of White-tailed Deer. CRC Press, Boca Raton, Florida, USA. 

ESRI 2020. ArcGIS Pro: 2.7.1. Environmental Systems Research Institute. Redlands, California, 

USA. 

Ficetola, G. F., B. Barzaghi, A. Melotto, M. Muraro, E. Lunghi, C. Canedoli, E. Lo Parrino, V. Nanni, 
I. Silva-Rocha, A. Urso, M. A. Carretero, D. Salvi, S. Scali, G. Scarì, R. Pennati, F. Andreone, 
and R. Manenti. 2018. N -mixture models reliably estimate the abundance of small 
vertebrates. Scientific Reports 8:10357. 

Gelman, A. 2006. Prior distributions for variance parameters in hierarchical models. Bayesian 

Analysis 1:515–534. 

Gelman, A., and D. B. Rubin. 1992. Inference from iterative simulation using multiple sequences. 

Statistical Science 7: 457–472. 

Haus, J. M., T. B. Eyler, and J. L. Bowman. 2019. A spatially and temporally concurrent 

comparison of popular abundance estimators for white-tailed deer. Northeastern 
Naturalist 26:305–324.  

Joseph, L. N., C. Elkin, T. G. Martin, and H. P. Possingham. 2009. Modeling abundance using N-
mixture models: the importance of considering ecological mechanisms. Ecological 
Applications 19:631–642. 

Kellner, K. F. 2015. jagsUI: a wrapper around rjags to streamline JAGS analyses. R package 

version 1.5.2. https://cran.r-project.org/web/packages/jagsUI/index.html.  

Kéry M., and J. A. Royle. 2015. Applied hierarchical modeling in ecology. First edition. Elsevier, 

Amsterdam, Netherlands. 

Mangiafico, S. 2023. rcompanion: functions to support extension education program evaluation. 

Version 2.4.3. https://cran.r-project.org/web/packages/rcompanion/index.html. 

Michigan Department of Natural Resources [MDNR]. 2016. Michigan Deer Management Plan. 

<https://www.michigan.gov/-
/media/Project/Websites/dnr/Documents/WLD/Deer/mi_deer_management_plan.pdf?rev
=19ecc9c9e4f046d2aa80bbf6d551f022>. Accessed 28 Jul 2023. 

200 

Nixon, C. M., L. P. Hansen, P. A. Brewer, and J. E. Chelsvig. 1991. Ecology of white-tailed deer in 

an intensively farmed region of Illinois. Wildlife Monographs 118:3-77. 

Nixon, CM., L.P. Hansen, P.A. Brewer, J. E. Chelsvig, J.B. Sullivan, R. Koerkenmeier, D.R. Etter, J. 

Cline, and J. A. Thomas. 1994. Behavior, dispersal, and survival of male white-tailed deer in 
Illinois. Illinois Natural History Survey Biological Notes 139. 

Nixon, C. M., L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, D. Etter, J. B. Sullivan, R. G. 

Koerkenmeier, and P. C. Mankin. 2001. Survival of white-tailed deer in intensively farmed 
areas of Illinois. Canadian Journal of Zoology 79:581–588. 

Plummer, M. 2003. JAGS: a program for analysis of Bayesian graphical models using Gibbs 

sampling. Pages 124–125 in K. Hornik, F. Leisch, and A. Zeileis, editors. Proceedings of the 
3rd International Workshop on Distributed Statistical Computing, March 20-23, 2003. 
Technische Universität Wien, Vienna, Austria. 

R Core Team. 2021. R: a language and environment for statistical computing. R Foundation for 

Statistical Computing, Vienna, Austria. 

Revelle, W. 2023. psych: Procedures for Psychological, Psychometric, and Personality Research. 

Version 2.3.5. https://personality-project.org/r/psych-manual.pdf. 

Royle, J. A. 2004. N-Mixture models for estimating population size from spatially replicated 

counts. Biometrics 60:108–115.  

Suwanrat, S., D. Ngoprasert, C. Sutherland, P. Suwanwaree, and T. Savini. 2015. Estimating 

density of secretive terrestrial birds (Siamese Fireback) in pristine and degraded forest 
using camera traps and distance sampling. Global Ecology and Conservation 3:596–606. 

Wilton, C.M. 2021. White-tailed deer (Odocoileus virginianus) density and habitat use on the 

Beaver Island Archipelago using a camera trap array. Michigan Natural Features Inventory 
Report Number 2021-05, Lansing, MI, USA. 

Zou, F., Q. Zhang, M. Zhang, M.-B. Lee, X. Wang, Y. Gong, and C. Yang. 2019. Temporal patterns 

of three sympatric pheasant species in the Nanling Mountains: N-mixture modeling applied 
to detect abundance. Avian Research 10:1–10. 

201 

APPENDIX 2A: MEGADETECTOR DATA-PROCESSING PROTOCOL 

Protocol for Managing and Processing 
Camera-Trap Data 

Supplemental research to:  
Influence of deer harvest regulations on antlerless harvest, abundance, and sex and age 
composition: implications for managing deer in the face of chronic wasting disease 

May 2019 
Last revised September 2023 

Prepared by: 
Melissa J. Nichols – Wildlife Research Technician, Michigan Department of Natural Resources, 
Wildlife Division 
Sarah L. Mayhew – Research Specialist, Michigan Department of Natural Resources, Wildlife 
Division 

Revised by: 
Steven M. Gurney – Graduate Research Assistant, The Christensen Lab for Wildlife Population 
Health, Michigan State University 

Principle Investigators: 
Sonja A. Christensen – The Christensen Lab for Wildlife Population Health, Michigan State 
University 
Dwayne R. Etter – Michigan Department of Natural Resources, Wildlife Division 
Sarah L. Mayhew – Michigan Department of Natural Resources, Wildlife Division 

The Christensen Lab for Wildlife Population Health 
Michigan State University 
Natural Resources Building 
480 Wilson Road, Room 13  
East Lansing, MI 48824

202 

 
 
 
 
 
 
 
 
 
MegaDetector Installation and Setup 

1.  Go to https://docs.anaconda.com/anaconda/install/windows/ and follow instructions to 

install Anaconda. You can skip step 2 (verify data integrity) and step 12 (installing 
PyCharm). The rest of the instructions will assume you have installed to 
C:\Workspace\Anaconda but you can choose a different location, if necessary. It 
is recommended you choose a location where you know you have write authority and 
whose address does not contain any spaces (so don’t choose C:\Program Files or 
something similar). 

2.  From your Start menu, Open Anaconda Navigator. Update to latest version, if prompted. 

3.  In Anaconda Navigator, go to Environments and then Create cameratraps-detector. 

Make sure to select the Python package and select 3.7 from the dropdown (Figure 2A.1).  

You may not see an option for 3.7 initially because Anaconda needs time to think, or you 
need to “update index” first, this might prompt an update too. If 3.7 is not an option try 
typing it in, otherwise you may need to download a more current version and 
troubleshoot to downgrade to get the 3.7 version used here. 

Figure 2A.1 Screenshots from the Anaconda Navigator workflow for installing and setting 
up MegaDetector. Workflow includes creating a new environment with cameratraps-
detector and Python version 3.7. 

203 

 
 
 
 
 
 
 
 
 
4.   Go to Environments, select cameratraps-detector, change dropdown to All (Figure 2A.2). 

Figure 2A.2. Screenshot from the Anaconda Navigator workflow for installing and setting 
up MegaDetector. Once the cameratraps-detector environment is created, the workflow 
includes selecting the all-packages option in the index. 

a.  Make sure all items listed in 

https://github.com/microsoft/CameraTraps/blob/master/environment-
detector.yml as dependencies are selected except tensorflow. After selecting 
each necessary package, click Apply. Dependencies may also need to be installed. 

i.  You may need to Update index to find all the packages (Figure 2A.3). 

Figure 2A.3. Screenshot from the Anaconda Navigator workflow for installing and setting 
up MegaDetector. The workflow may require updating the index to find all the required 
pacages for MegaDetector. 

ii.  While you are installing packages, if Anaconda seems to get stuck on the 
fetching step, cancel the process, close and restart Anaconda. Then you 
can start installing the rest of the packages.   

iii.  MegaDetector may require additional downloads, specifications include: 

name: cameratraps-detector,   
channels:  

204 

 
 
   
 
 
 
 
- conda-forge  
- pytorch  
dependencies:  
- python=3.8  
- Pillow=9.1.0  
- nb_conda_kernels  
- ipykernel  
- tqdm  
- jsonpickle  
- humanfriendly  
- numpy  
- matplotlib  
- nb_conda_kernels  
- ipykernel  
- opencv  
- requests  
# for running MegaDetector v4  
# - tensorflow>=2.0   
# for running MegaDetector v5  
- pandas  
- seaborn>=0.11.0  
- PyYAML>=5.3.1  
- pytorch::pytorch=1.10.1  
- pytorch::torchvision=0.11.2  
- conda-forge::cudatoolkit=11.3  
- conda-forge::cudnn=8.1  
# the `nb_conda_kernels` and `ipykernel` packages are installed so 
that we can use Jupyter Notebooks with this environment as a 
kernel 

5.  Download MegaDetector 

fromhttps://lilablobssc.blob.core.windows.net/models/camera_traps/megadetector/me
gadetector_v3.pb. The rest of the instructions assume you have installed to 
C:\Workspace\MegaDetector but you can choose a different location, if 
necessary. It is recommended that you choose a location where you know you have 
write authority and whose address does not contain any spaces (so don’t choose 
C:\Program Files or something similar). Other than that, you should not need to 
do any special setup with this step. 

6.  Go to https://git-scm.com/download/winand follow the instructions to download and 
install Git. Install the version called 64-bit Git for Windows Setup. The rest of the 
instructions assume you have installed to C:\Workspace\Git but you can choose a 
different location, if necessary. Again, no spaces in the address.  Accept all defaults while 
installing (make sure to open and use all pre-selected options for setup). 

205 

 
 
a.  I renamed my file pathway and workspace to match what I thought would be 

easier to run on S. Gurney’s laptop, “c:\Users\gurneyst\Git” 

7.  Go to Start menu and open Anaconda prompt. 

a.  In the prompt enter: conda activate cameratraps-detector 

b.  At the next prompt, enter: cd c:\workspace\git 

i.  Instead of c:\workspace\git you should enter the location where 

you installed Git. I had c:\Users\gurneyst\Git. You can move the 
MegaDetector files to your liking, just make sure that the code matches 
the pathway where the files are. 

c.  At the next prompt, enter: git clone 

https://github.com/microsoft/CameraTraps 

d.  At the next prompt, enter: git clone 

https://github.com/microsoft/ai4eutils/ 

e.  At the next prompt, enter:  

set 
PYTHONPATH=c:\workspace\git\cameratraps;c:\workspace\g
it\ai4eutils 

i.  Instead of c:\workspace\git you should enter the location where 

you installed Git. 

f.  At the next prompt, enter: pip install tensorflow==1.13.1 

g.  At the next prompt, enter: pip install humanfriendly Pillow 

pandas tqdm 

8.  Close all open windows. 

9.  If the software does not operate, it may require additional troubleshooting. New 

software updates might require this troubleshooting.

206 

 
 
 
 
 
 
 
 
 
 
Data Management and Processing with CPW Photo Warehouse and MegaDetector 

A.  Create 2 separate CPW Photo Warehouse databases—one for the APR Zone and one for 
the NonAPR Zone. Dividing the databases this way will prevent the databases from 
getting too bogged down (and makes it easier when dividing database tasks among 
technicians). Using CPW Photo Warehouse, you (the data manager) will need to begin by 
entering all the camera sites using the “Add or Edit Locations” button in the switchboard 
(the main menu). Do not enter location information here (e.g., coordinates; this 
information is private to MSU). Once all camera sites for the appropriate study area are 
listed in the locations table, you can begin adding camera visits. Click on “Add or Edit 
Visits” in the switchboard then select a location from the dropdown in the visits form. 
Once you have selected a location click “Add New Visit” (Figure 2A.4). 

Figure 2A.4. Screenshot from the CPW Photo Warehouse workflow for managing 
camera-trap data. The workflow includes adding new visits and associated data for each 
camera location. 

B.  For each camera you will need to first add the set date. Because we are only collecting 

data starting July 15 you should make the set date 07/15/YYYY for all cameras.  

C.  Pick up SD card from field technicians 

207 

 
 
 
 
 
a.  Use pocket organizer (i.e., SD wallet) to keep cards organized and to help keep 

track of when the cameras were checked. A mailbox-type system works well for 
delivering and returning SD cards (e.g., one mailbox for SD cards that need to be 
uploaded and one mailbox for SD cards ready to go back into the field). 

D.  For the first camera check (which should occur shortly after July 15), start by moving all 
photos from the SD cards to the correct 1-TB external hard drive (individual 1-TB hard 
drives should be assigned to individual townships). Next, separate photos into “pre-July 
15” and “post-July 15” locations. So, create a folder called “Pre-Post-Jul15” in the Check 
1 folder, include a subfolder for each site, like “11001” and then give it subfolders “pre-
Jul15” and “post-Jul15” to store photos before renaming them (e.g., 
“APR_Easton\Check1\Pre-Post-Jul15\Post-Jul15”). We only want to import post July 15 
photos into the Photo Warehouse database, and it will be easier to have them 
presorted. See Figure 2A.4 for an example of a file pathway. None of the folder or file 
names can have spaces in them. So, you will need to create: 

a.  Subfolder for pre-July 15 photos 

b.  Subfolder for first access post-July 15 photos (this is a subfolder needed before 

manual file renaming happens in CPW Photo Warehouse).  

i.  Subfolder for each township 

1.  Subfolder for each site 

c.  Subfolder for each Access (i.e., camera check) 

i.  Subfolder for each township 

1.  Subfolder for each site 

Figure 2A.4. Screenshot from the CPW Photo Warehouse workflow for managing camera-trap 
data. The workflow includes saving data using a folder hierarchy. This example displays the file 
pathway for site 22001, Check2, in Easton Township (APR Zone) as “APR_Easton\Check2\22001”. 
Note that there are individual subfolders for each camera site. 

208 

 
 
 
 
 
 
 
 
 
 
It is very important to have file pathways good from the start; and maintain 
organizational structure of hard drives throughout seasons). 

Since the sampling period ends on September 15th, we will use a similar approach 
(like D-a and D-b) for separating Pre- and Post-Sep15 photos in the Check 5 folder. 
Do not forget to separate Pre- and Post-Sep15 photos after the last camera check 
or it will cause many problems. 

E.  Once you have a set date in the database you can add check dates and pull dates using 
the “Add or Edit Visits” option from Photo Warehouses switchboard (main menu) and 
clicking the “Add New Visit” button. When you choose “Check” in the Visit Type field, a 
subform will pop up allowing you to load photos. Do not forget to list the final camera 
check as “pull.” 

F.  Enter the path for the folder containing the photos just for that camera site (for first 

access, you would choose the path from the “post-July 15 Access 1” subfolder (or at the 
end of the season “pre-Sep 15 Access 5”), then click the “copy image files”. I know it 
seems redundant to re-copy the images when they are already stored on the hard drive, 
but this will allow us to rename all the images in a consistent way. Copy the images into 
the appropriate subfolder and click the “Rename image files” box. Use the Location ID as 
the “Prefix option” and Image Number + Date as the “Rename files using” option. 

a.  After the first camera check (except for the final camera check), photos can be 

imported directly from the SD cards rather than saving them to the external hard 
drive first, then importing them. Continue uploading photos through the “Visits” 
subform in the database and copying and renaming the files in the same way as 
above.  

b.  It is easy to mix up what SD cards have and have not been uploaded, so keep 

track of what you upload in a notebook (e.g., write Sherman Township Check 3 
and list bullet points for each successful upload like, “Card 16/Site 11045, Card 
18/Site 11018” and so on). Keeping notes like this allows you to double check 
that you have uploaded all 18 SD cards per township—and that is important to 
prevent missing data. You may need to refer to the first few images on the SD 
card (which show a whiteboard) to identify what the site ID is. 

c.  Make sure that Check 1 and set date are not the same. Camera set = July 15th, 

Check 1 = any date other than July 15th. When check and set date are the same it 
creates duplicates of photos that are labeled incorrectly when adding into the 
database—and this cause serious database problems. Make sure technicians do 
not check the cameras on July 15th. 

209 

 
 
 
 
 
 
 
G.  The 1-TB hard drives (containing township photos) should be backed up to a 5-TB hard 
drive weekly (the 5TB hard drive will be stored at the MDNR warehouse). It is good 
practice to regularly backup the 5-TB hard drive with a separate 5-TB hard drive that is 
housed at a location off site (e.g., MSU). The 1-TB hard drives must be backed up after 
each camera check before the SD cards go out in the field again (because photos will be 
deleted from SD cards in the field). External hard drives can get damaged or ruined 
during the MegaDetector process (it has happened), so it is critical to back everything up 
before each round of MegaDetector. For example, after Sherman Check 3 photos have 
been uploaded to the Sherman external hard drive from the Sherman SD cards, the 
Sherman hard drive must be backed up before MegaDetector scans the Check 3 photos 
on Sherman’s hard drive.  

H.  You will run MegaDetector to screen out the images that do not have any wildlife (i.e., 

empty or blank images). You will need separate computers, best case scenario is to have 
one computer designated for each 1-TB hard drive (i.e., township). Repeat the steps 
below for each computer-hard drive pair. MegaDetector may run for several hours or 
days (most likely over a week), so the computers you use for MegaDetector should be 
dedicated to that sole process alone. It is important to change each computer’s settings 
to prevent it from automatically shutting down, going into sleep mode, or doing 
automatic updates—all of which will disrupt MegaDetector from running continuously. 
When running MegaDetector, keep computers and drives well ventilated (e.g., create 
additional space between hardware and surfaces) because days of use and heat can 
damage hardware (use additional fans if possible).  

a.  Connect 1-TB hard drive to the computer. Make sure the hard drive is listed as 

the “D” drive on your computer, if not it will cause many issues down the road. If 
the hard drive is listed on the computer as something else, like “E” drive, you will 
need to change the setting in your computers Disk Management (this issue is 
very common). You can fix the issue with the computer’s “Create and format 
hard disk partitions” option in the Control Panel. Once you open the Disk 
Management page, right click the hard drive and select “Change drive letters and 
paths…” and change the letter to “D.” If something else is currently listed as “D” 
you will need to change it so the hard drive can be labeled “D”. 

b.  Go to the Start menu, open Anaconda prompt. These instructions assume you 
have installed all software to locations recommended in the MegaDetector 
Installation and Setup instructions (above). You will need to modify the code 
below according to site, camera check, and zone. The easiest way to do this is by 
copying and pasting prompts into Anaconda (but remember you need to revise 
the code first). It can be helpful to save different versions of code below for each 
township—that way all you need to do is update camera check number. It also 

210 

 
 
 
can be helpful to keep the original code below intact. The comment section is a 
good place to revise the code accordingly—comment on this document by 
clicking on the “Review” tab and add a “New comment.”  

i.  In the prompt, enter: 

conda activate cameratraps-detector 

ii.  At the next prompt, enter: 

cd c:\workspace\git 

a. Here is an example pathway for setting the workspace 
on S. Gurney’s laptop: 

cd c:\Users\gurneyst\Git 

b.  In the example above, all program downloads for 

MegaDetector were in the folder “Git” 

iii.  At the next prompt, enter:  

set PYTHONPATH=c:\workspace\git\CameraTraps; 
c:\workspace\git\ai4eutils 

iv.  At the next prompt, enter:  

python 
CameraTraps/detection/run_tf_detector_batch.
py 
c:/workspace/megadetector/megadetector_v3.pb 
d:/Access1 d:/Access1/Access1_APR.json --
recursive -–output_relative_filenames --
checkpoint_frequency=50 

a.  In the command above, instead of d:/Access1, use the 
appropriate path for the access number you are trying to 
scan (i.e., run MegaDetector on). 

b.  In the command above, instead of 

d:/Access1/Access1_APR.json, use the 
appropriate path and file name to indicate both the 

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township, access number, and whether the results are for 
APR or NON. 

c.  Here is example code from S. Gurney’s laptop 

(MegaDetector will run this code to analyze each photo in 
the Easton Check2 folder): 

python 
CameraTraps/detection/run_tf_detector_b
atch.py 
c:/Users/gurneyst/Git/megadetector_V3.p
b d:/APR_Easton/Check2 
d:/APR_Easton/Check2/Check2_APR_Easton.
json --recursive --
output_relative_filesnames --
checkpoint_frequency=50  

v.  If the scan is interrupted for whatever reason, use the following code to 

restart from the last checkpoint:  

python 
CameraTraps/detection/run_tf_detector_batch.
py c:/workspace/megadetector_v3.pb 
d:/Access1 d:/Access1/Access1_APR.json --
recursive -–output_relative_filenames --
checkpoint_frequency=50 --
resume_from_checkpoint=d:/Access1/checkpoint
_20200601145050.json 

a.  In the command above, instead of 

checkpoint_20200601145050 you should enter 
the name of the checkpoint file created during the 
interrupted run (it will be a .json file automatically saved 
on the external hard drive; MegaDetector saves output at 
regular user-defined intervals [50]). 

I.  Backup MegaDetector data immediately after it finishes running. You can do this by 

backing up MegaDetector’s .json and .csv output files to our cloud storage (SharePoint). 
Also, make sure to include MegaDetector output files when backing up data on the 5-TB 
hard drives. For example, MegaDetector just finished processing Douglass Check 4, now 
immediately backup the .json and .csv files to the SharePoint cloud storage—then when 
you go and backup Douglass Check 5 photos on the 5-TB hard drive at the warehouse, 

212 

 
 
 
 
 
 
make sure to also backup Douglass Check 4 MegaDetector data at that time. 

J.  After MegaDetector has finished running, disconnect the hard drive from the designated 

MegaDetector computer—do not just unplug drive as it can cause issues—use the 
computer’s function to safely eject drive (e.g., right click on the drive icon at bottom 
right of the desktop screen [next to the clock] and select eject). Next, connect the hard 
drive to a computer not designated for MegaDetector tasks. Make sure the hard drive is 
listed as the “D” drive on your computer, if not it will cause many issues down the road 
(refer to section H-a for directions on how to change the drive settings). Copy the file 
called Mayhew_Test_Template.tbd (custom template for photo and MegaDetector data 
created by S. Mayhew) from wherever you have installed it and paste into the 
appropriate Access folder on the 1-TB external hard drive. Open Timelapse2.exe 
(Timelapse software) from C:\Mayhew on the computer (folder created by S. Mayhew 
designated to everything Timelapse). 

a.  Go to File -> Load template, images, and video files... 

b.  Select the template file from the Access folder and open. 

c.  When the image set has opened, go to File -> Import image recognition data for 

this image set. 

This option above might be hidden at first. Look at the Timelapse user manual for 
instructions on how to make it unhidden. Also, if the file path was written wrong 
in the code, then it will not transfer recognition data—to troubleshoot this, you 
can save copy of the .json as a .txt and inspect it—to fix issues you can use the 
“replace” feature to fix the pathway code. 

d.  Select the .json file you created above and open it. 

e.  Go to Select -> Custom selection... 

f. 

In the Image Recognition box, select the Use Detections check box. Make sure 
the Detected entity says “animal.” Adjust the Confidence to 0.90 to 1.00. Click OK 
(Figure 2A.5). 

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Figure 2A.5. Timelapse screenshot from the MegaDetector workflow. In this step, the 
detection confidence is adjusted for the image recognition data. 

g.  Back on the image screen, make sure you are at the first image in the set and 
select the check box next to Animal (Figure 2A.6). Right-click on the check box 
next to Animal and select Copy forward to end. Click Yes in the message box that 
appears. 

Figure 2A.6. Timelapse screenshot from the MegaDetector workflow. In this step, the 
“Animal” data is selected and confirmed. 

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h.  Go to Select -> All Files.    

Do not skip this step above, it selects all files that are labeled with and without 
wildlife. You want to make sure that all files get exported. 

i.  Go to File -> Export data for this image set as a .csv file...   

The data file will be exported and automatically saved to the Access (i.e., camera 
check) folder where the images are stored. 

j.  Close Timelapse. 

k.  Go to the Access folder where Timelapse sent the .csv file (it will still be named 
“Mayhew_Test_Template”). Rename the .csv file to indicate the appropriate 
study area, site ID, and camera check number (e.g., “APR_Bushnell_Check2”). 

i.  Open the CSV file in notepad or excel to make sure in the last column 
there are “false” and “true” labels, these are MegaDetector’s assigned 
labels for the photos (i.e., animal/no animal). 

l.  Copy the .csv and paste it at the root of the hard drive (D:\), and make sure to 
first delete any previous .csv file you had copied there.  Rename the .csv 
Timelapse.csv. The name of the file must be exactly Timelapse.csv and stored 
exactly at the root of the hard drive (so the file address is D:\Timelapse.csv) or 
the next steps will not work.   

i.  Make sure to rename that file at the root of the hard drive when you are 
done with it (e.g., Timelapse_Check3) because you will be putting the .csv 
file for each camera check here at the root drive and you do not want 
duplicates, or it will cause issues. 

K.  Make sure Photo Warehouse is closed. Open the database called MD_to_CPW.accdb 

(this is an intermediary database used to move MegaDetector data to Photo 
Warehouse). Follow the instructions that are displayed on the screen.   

a.  When you follow the instructions, know that MegaDetector1 = “1” and 

MegaDetector2 = “2”. These will be the observer IDs (ObsID) Photo Warehouse 
assigns to MegaDetector 1 and 2 (there are 2 MegaDetectors because 
MegaDetector uses a dual scan like a dual observer process).  

215 

 
 
 
 
 
 
 
 
 
 
 
b.  When you import timelapse, there will not be a pop up to indicate a successful 

import. 

c.  You might need to manually input detection data when you upload data for the 

first time (it is programmed to remove any previous data but since there is none, 
the program may not work appropriately). If this is the case, follow this 
workflow: MD_to_CPW > External Data Source > New Data Source > From File > 
Text File > Select the Timelapse.csv from external drive’s root and keep defaults > 
select delimited option > Specs (and keep default) > OK > Finish and close. Hit 
F11 to make sure that it was named Timelapse, if not right click and rename. This 
whole step can be tricky and may require some expert assistance.  

L.  Close the MD_to_CPW database.   

M.  To check to see if MegaDetector data successfully imported to Photo Warehouse, open 

Photo Warehouse, select the “View or Print a Report”, and create a “Photo ID Summary” 
from the dropdown menu. Once the report is produced, check to see if MD1 and MD2 
observers are listed as observers at the site(s) of interest for the date(s) of interest.  

N.  Once you have successfully imported all photos and MegaDetector information you can 
create a photo module for photo ID. Go to “View Photos” from the main switchboard 
then use the filters on the right to determine which photos you would like to ID. You will 
first select “Photos that haven’t been ID’d” in the “Species” section of filters to remove 
all the photos that MegaDetector determined there were no animals in. When you have 
selected the appropriate filters, click the “Copy Photos” button. Make sure to click the 
“Include Runtime Database” option and copy the photos to the appropriate external 
hard drive (you will probably get a security warning, but just hit “Open” numerous times 
and it will eventually work). It is important to keep a good organizational structure when 
saving modules and mirror structure across seasons (e.g., 
APR_Easton/Check1/Modules/22001_Check1). It is easiest to create and save modules 
first—then you can drag and drop modules to technician flash drives later. Use 
spreadsheet journal to stay organized and keep track of what modules have been 
created (example at bottom of document). See Figure 2A.7 for example screenshots of 
module file path for Easton Check1 modules and content example for the Easton Check1 
Module for site 22001. 

216 

 
 
 
 
Figure 2A.7. Screenshots from the CPW Photo Warehouse workflow displaying the 
photo-module file path for Easton Check1 and the post-module creation content for the 
Easton Check1 module folder for site 22001. 

O.  Distribute modules to technicians by copying entire module folders (e.g., 22001_Check1) 
to a flash drive (via drag and drop from external hard drives). Keep track of who has 
what modules in the designated spreadsheet journal (example at bottom of document) 
and keep it updated in real time (e.g., once you load 22001_Check1 on a flash drive for 
Technician A, immediately record it in the Excel document). 

P.  Once technicians have finished their assigned modules, have them give you (the data 
manager) the flash drive back with many completed modules (.accdr files). Import the 
technician’s modules when they are finished—this will allow you to import data slowly 
and steadily—and it can prevent both flash drives and work from being lost in the mix. 

Q.  To import the IDs, choose the “Import Photo ID Module” option from Photo 

Warehouse’s main switchboard, then search for the .accdr file you would like to import. 
Once imported, Photo Warehouse will tell you how many IDs it imported and how many 
are pending (i.e., not verified with a second observer) and how many were verified (i.e., 
they match an observation already in the database). Again, keep track of who has sent 
you what modules and when you have imported them in the spreadsheet journal 
(example at bottom of document)—and make sure to update it in real time to prevent 
mistakes (e.g., once you import 22001_Check1 from Technician A’s flash drive, 
immediately record it in the Excel document).  

217 

 
 
 
 
 
R.  Often the two photo observers will disagree on an ID. These instances get flagged in 

Photo Warehouse and someone will need to be the referee (the photo referee should be 
consistent and should be someone with years of photo-tagging experience). Do this by 
choosing the “Compare IDs” box from the main switchboard. Choose your name from 
the dropdown menu and any photos that need to be compared will pop up. If you have 
many flagged photos, you can filter by location to break them into easier-to-handle 
chunks.  

a.  View the photo and decide which species, detail and individual count is correct 
and click the “X” next to IDs that are incorrect. Sometimes all IDs will be correct 
(i.e., one observer saw a doe and one saw a doe and fawn, the fawn will display 
in red as it was only marked by one observer), in this case you would click the 
“Verify All Species” button. If you make a mistake and click the “X” on the wrong 
line you can click the “Reset” button and all IDs will pop back up. 

b.  You can use context clues to help you with refereeing by opening the original 

photo series and looking through surrounding photos. This can help when one 
observer notices a nose or piece of a leg in a photo that is easy to miss without 
the context of the deer popping into frame in the previous or next photo. 

S.  Once your spreadsheet journal (see Figure 2A.8 for example) indicates all modules have 
been completed by 2 observers and uploaded, you will need to double check that 
everything is completed. It is likely that a few (or thousands) of photos will slip through 
the cracks and go untagged. To check, go to Photo Warehouse’s main switchboard and 
select “View Photos”. Next, use the species filter options to identify any photos that still 
need one or multiple observers. If photos still need to be reviewed, take note of the 
zone, township, date, and site. Next, you will need to share the entire module associated 
with the unreviewed photos, so the technician has all photos for reference. Repeat steps 
above to complete the process. 

Figure 2A.8. Example of spreadsheet journal for tracking the creation and completion of 
modules by camera site (Point) and camera check number (Access), including the distribution 
(Sent) and successful upload of completed modules (Received) and record of technicians 
involved.

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A Candid Assessment of the MegaDetector Workflow by S. Gurney 

•  MegaDetector is a free application and there is value in that. However, MegaDetector required a 
significant amount of time, energy, and resources to get up and running and to maintain over the 
years. It first required a test with a validated set of data to confirm MegaDetector’s accuracy. It 
also required an experienced individual to be the main contact point for annual training and 
regular troubleshooting. Further, every season the technicians needed to set up multiple 
accounts and download various software packages, which can be a bit cumbersome. However, 
the MegaDetector approach did provide an educational opportunity for many individuals, 
including students.  

•  Once the data managers (i.e., MegaDetector operators) got up to speed, MegaDetector basically 
worked on its own and required little attention. However, problems would occasionally arise and 
require additional efforts and intervention (e.g., user mistakes, like using an improper naming 
convention for files or skipping steps).  

•  MegaDetector can take a considerably long time to review photos on a basic laptop. For 

example, it took approximately 30 seconds to review a single image. To put this in perspective, it 
would take about 35 days to run through 100,000 images. Note that we used up to four laptops 
at a time to speed up the process and to divide the workload among multiple employees. Given 
these long runtimes, it was often challenging to review photos throughout the field season 
(when we had a full team of technicians). More often than not, technicians were reviewing 
photos from weeks prior, and some camera issues went unnoticed for a while (e.g., poor field of 
view).  
A better use of MegaDetector would probably be to run all photos at the end of a field season on 
a supercomputer (e.g., using university supercomputing resources), and then have a team of 
technicians manually review animal photos after the initial MegaDetector review. However, this 
approach would not allow technicians to review photos during the existing field season. On a 
side note, the technicians really enjoyed seeing images from the cameras they deployed and 
took much pride in the data they collected (rightfully so because it required a lot of hard work).  
•  We did not use MegaDetector during the first field season. It was nice having fewer moving parts 
on and having fewer technical issues. For some, it was brain-numbing work to review thousands 
of blank images manually, but technicians were able to do it faster than MegaDetector. For 
example, if there were 10,000 images of a weeping willow blowing in the wind it would take 
MegaDetector 3.5 days to review but it would only take a technician maybe an hour or two (as 
they were able to review blank image sets at a much higher rate than animal photos). However, 
it is likely that MegaDetector was more accurate when reviewing large blocks of these types of 
image sets because there is a possibility an animal was present at one point; and it would be 
easy for a technician to flip past it if they were losing their focus while reviewing images quickly.  

•  Field records indicated a pattern of vegetation movement or the interaction of solar radiation 

and shadow movement triggering cameras and resulting in excessive ‘blank’ photos. Although, it 
is worth noting that these phenomena would be dependent on the local conditions of a site. For 
example, more false-trigger events may occur when vegetation is growing or when there is a 
lack of canopy cover and an interaction between isolation and shadow movement. Also, many 
cameras were facing agricultural fields and crops (e.g., corn, beans) would trigger cameras.  
In this study, it may have been a better use of time and resources to not use MegaDetector.  

• 

219 

 
APPENDIX 2B: STATIC BINOMIAL N-MIXTURE MODEL STUDY 

Population Snapshots: Estimating Deer Relative 
Abundance with a Static Binomial N-Mixture Model 

Steven M. Gurney 

Supplemental research the antler-point-restriction study that took place in the Lower Peninsula 
of Michigan in an that included a known chronic-wasting-disease hotspot. This study includes 
preliminary results that were provided to Michigan Department of Natural Resources staff for 
presentation at the May 2023 meeting of the Natural Resources Commission 
(https://www.michigan.gov/dnr/-
/media/Project/Websites/dnr/Documents/Boards/NRC/2023/May-2023/APRs.pdf). 

SUMMARY 

A static binomial N-mixture model informed by empirical count data produced deer 

abundance estimates that were highly variable among years. By modeling abundance one-year-
at-a-time, the model was considered to make poor use of the available data. Further, the model 
was considered less than ideal for evaluating population-level changes over time. If a wildlife 
agency’s goal is to compare snapshots among populations within a given year, then the static 
model is considered suitable. If an agency’s goal is to evaluate population trends over time, I 
recommend using an alternative modeling approach better equipped to test linear 
relationships, like the year-stratified N-mixture model. 

INTRODUCTION  

Managing potential spread and localized prevalence of chronic wasting disease (CWD) 
has proven challenging for wildlife managers nationwide. Whereas some studies have shown 
that localized intensive harvest of deer has been successful at maintaining low prevalence of 
CWD (Manjerovic et al. 2014, Mateus-Pinilla et al. 2013), other research has established that 
different sex-and-age classes of free-ranging deer have different prevalence rates of disease 
(Grear et al. 2006, Miller and Conner 2005). Consequently, harvest strategies to reduce deer 
abundance may be more effective if specific demographic segments of the deer population are 
targeted as well. Unfortunately, detecting change in prevalence of CWD and determining 
causation for such a change is not feasible given sampling limitations and the multiple factors 
that can impact wild deer populations. However, it is possible to determine if antler point 
restrictions (APRs) in an area with CWD result in changes to those demographic segments that 
contribute the most to the spread and growth of CWD (Grear et al. 2006, Osnas et al. 2009, 
Heisey et al. 2010, Rees et al. 2012, Samuel and Storm 2016).  

220 

 
 
 
 
 
 
 
 
 
 
STUDY GOAL 

The overall goal of this research is to evaluate the effect of an antler point regulation 

change in an area with chronic wasting disease on a white-tailed deer (Odocoileus virginianus) 
population. 

OBJECTIVES 

1.  Estimate annual deer relative abundance from 2019–2022 for adult males, does, yearling 

males, and fawns under APR and Non-APR harvest treatments. 

2.  Evaluate and compare trends in relative abundance by sex-and-age-class for APR and 

Non-APR harvest-treatment areas. 

STUDY AREA 

This study uses data collected in the south-central Lower Peninsula of Michigan in a 5-

county area (Newaygo, Kent, Mecosta, Montcalm, and Ionia County) that included a known 
chronic-wasting-disease hotspot (Kent and Montcalm County). That study included a robust 
before-after-control-impact study design paired with camera-trap surveys to monitor potential 
population-level changes, over 3 consecutive years (2020–2022), following the 2019 regulation 
change. This design was intended to make it possible to identify changes in abundance in the 
treatment area (APR Zone) relative to the control area (Non-APR Zone). 

METHODS 
Empirical data 

This study used a high-volume of camera-trap images collected on public and private 

lands. A random camera-site-selection process resulted in a partnership with 160 landowners. 
Data included 2,644,590 verified images collected during the 4 field seasons (2019 to 2022). Of 
the photos reviewed by artificial intelligence software, 44% were characterized as “Empty” and 
did not require any further review by personnel. The dataset included a total of 1,118,757 
verified images of deer. Count data associated with these images informed my abundance-
estimation model here. 

Abundance modeling 

In this study, I used relative abundance of deer as an index, assuming it was functionally 

related to population size. When modeling abundance, I assumed site-level abundance 
reflected the number of deer within the effective sampling area surrounding a camera site (see 
Chapter 1 for details on effective sampling area). I used these site-level abundances to derive 
estimated abundance by township, where abundance related to the number of deer within the 
total area of all effective sampling areas in a specified township (18 sites per township = 22 km2 
[9 mi2]). Hence, my abundance estimates reflect relative abundance, not absolute, as I did not 
infer site-level abundances for areas beyond the total surveyed area (i.e., total effective 
sampling area). Given the incorporation of baseline data and the study’s focus on examining 
changes over time, the use of relative abundance as an index was considered adequate. To 
interpret the potential effects of harvest treatment on deer abundance, I compared 2019 
baseline abundance estimates (i.e., the system before the APR implementation) to estimates 
from subsequent years (i.e., the system after the APR implementation). 

221 

 
 
 
 
 
 
To account for imperfect detection, I estimated population parameters with a closed N-
mixture model (Royle 2004) applied to camera surveys of unmarked deer. As described by Kéry 
and Schaub (2012), I implemented a Bayesian hierarchical framework using software program 
JAGS (Plummer 2003) in program R (version 4.1.2; R Core Team 2021) with the jagsUI package 
(Kellner 2015). Essentially, the N-mixture model consists of two linked generalized linear 
models. The first generalized linear model is the ecological process. The ecological process 
yields the latent state and the spatial variation of abundance at site 𝑖, 𝑁𝑖, for a group of sites 
with a mean 𝜆 (Kéry and Schaub 2012). Since properly modeling error maximizes the utility of 
N-mixture models (Joseph et al. 2009), it was important to select a mixing distribution that best 
fit the underlying data. An exploratory data analysis was conducted using data from this study 
and included an evaluation of N-mixture models with alternative mixing distributions, including 
Poisson, zero-inflated Poisson, negative binomial, and Poisson lognormal. Results from those 
explorations indicated that the Poisson mixing distribution best fit the data. Using these results 
as guidance, I opted to use the Poisson distribution in my ecological-process model. To extract 
more information from the data and better allocate variance, I built on the ecological model to 
include township as a random effect on abundance, thus 𝜆 was described as 𝜇𝜆 (i.e., a 
distribution of distributions): 

𝑁𝑖 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 (𝜇𝜆𝑖) 

Agriculture was the most dominant land-cover class in the study area and is considered 

an important driver of demographic variation in abundance (Nixon et al. 1991, Nixon et al. 1994, 
Nixon et al. 2001) and antler growth (Felix et al. 2002). Further, exploratory data analyses 
identified agricultural cover as a valuable predictor of abundance. For these reasons, I included 
agriculture cover as a covariate in the ecological-process model. I calculated the proportion of 
agricultural cover using effective sampling areas and the National Land Cover Database (Dewitz 
and USGS 2021) land-cover classification layer (30-m2 resolution) in ArcPro (ESRI 2020). This 
approach allowed me to extract values and collapse 3 NLCD land-cover types (herbaceous, 
hay/pasture, cultivated crops) into a single agriculture classification. I incorporated the effects of 
the agriculture covariate into the ecological model, associated with abundance through a log-
link function, and described by a nonlinear relationship with percent agricultural cover as a site-
specific covariate. Additionally, I included a random intercept 𝜅 into the log-link function, which 
allowed township to act as a random effect on abundance: 

𝑙𝑜𝑔(𝜇𝜆𝑖) =  𝜅(𝑇𝑜𝑤𝑛𝑠ℎ𝑖𝑝𝑖) +  𝛽2(%𝐴𝑔𝑟𝑖𝑐𝑢𝑙𝑡𝑢𝑟𝑒)2 

The second generalized linear model of the N-mixture framework is the observational 

process. The observational process yields the observed counts 𝑦𝑖,𝑗 (given 𝑁𝑖) at site 𝑖 and during 
replicate survey 𝑗, and are described by a binomial distribution with sample size 𝑁𝑖 and 
detection probability 𝑝 (Kéry and Schaub 2012): 

𝑦𝑖,𝑗 | 𝑁𝑖 ~ 𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙 (𝑁𝑖,  𝑝[𝐶𝑜𝑣𝑒𝑟𝑖]) 

Cover data were collected during camera-trap setup and was defined as far cover or the 
majority of cover in a 100-m radius of the camera (open or closed). Note that I included cover in 
the observational-process model as it may be important to both the presence and detectability 
components of detection probability. Further, an exploratory data analysis evaluated the value 
of alternative covariates and identified cover (far cover) as important to the detection process. 
To incorporate this covariate on detection probability, I used a logit-link function, described by a 
linear relationship with site-specific cover: 

222 

𝑙𝑜𝑔𝑖𝑡(𝑝𝑖) =  𝛼 +  𝛽1(𝐶𝑜𝑣𝑒𝑟𝑖) 
With regards to the Bayesian framework, I assumed vague prior distributions for all 
analyses to express the absence of prior information about estimated parameters. For my 
Markov Chain – Monte Carlo (MCMC) approach, I ran 3 parallel chains for 50,000 iterations, 
discarded the first 3,000 iterations as burn-in, and thinned the remaining iterations by 1 in 5, 
resulting in 28,200 draws of the posterior distribution for inference. Parameters monitored 
included total 𝑁, 𝑝, 𝛼, 𝛽 values, and 𝜅 values. I monitored model convergence by evaluating 
posterior distributions, visual inspection of MCMC trace plots, and using the Gelman-Rubin 
convergence diagnostic (R-hat or 𝑅̂; Gelman 2006). I summed site-level abundances to derive an 
estimated total study-area abundance, where total abundance relates to the number of deer 
within the total area of all 1.24-km2 effective sampling areas in the study area (e.g., 144 camera 
sites = 179 km2 [69 mi2]). It is important to note that my total abundance estimates reflect 
relative abundance, not absolute. Since the larger study included baseline data, and intended to 
look at change over time, relative abundance was deemed sufficient.  

I used the static N-mixture model to estimate relative abundance one-year-at-a-time and 

compare the number of significant changes detected in the APR and Non-APR townships. I 
modeled the abundance of sex-and-age classes individually (Legal Males, Does, Sub-legal Males, 
Fawns). I followed recommendations from an earlier data exploration and used data associated 
with a weekly sampling frequency (i.e., weekly counts), a 63-day sampling duration (15 July–15 
September), and a camera distribution of 18 sites per township. I considered that non-
overlapping credible intervals indicated significant differences in abundance between years. I 
counted and compared the number of significant differences observed in APR and Non-APR 
townships. When evaluating results, I considered comparisons of abundance estimates within 
townships from 2019 and subsequent years important, and comparisons among paired 
townships as most meaningful. Code for the static binomial N-mixture model is provided in the 
Appendix (APPENDIX 2B.1). 

RESULTS 

I used a static binomial N-mixture model to estimate relative abundance one-year-at-a-

time and compare the number of significant changes detected in the APR and Non-APR 
townships. Relative to 2019 baseline estimates, I detected increases in Adult Male relative 
abundance in both APR and Non-APR zones (Figure 2B.1). Most increases in Adult Male 
abundance were detected in the APR Zone and included Township A (2019: x̅ = 22.3 [95% BCI = 
17–30]; 2021: x̅ = 44.0 [95% BCI = 34–57]), Township B (2019: x̅ = 28.0 [95% BCI = 21–37]; 2021: 
x̅ = 53.7 [95% BCI = 41–70]), and Township D (2019: x̅ = 28.4 [95% BCI = 22–37]; 2021: x̅ = 61.7 
[95% BCI = 47–81]; Figure 2B.1). In comparison, I detected a single increase in Adult Male 
abundance in the Non-APR Zone’s A Township (2019: x̅ = 11.4 [95% BCI = 8–16]; 2021: x̅ = 25.1 
[95% BCI = 19–34]; Figure 2B.1).  

I detected significant increases in Doe abundance in both the APR and Non-APR zones 

(Figure 2B.2). Relative to 2019 baseline estimates, most increases in Doe abundance were 
detected in the Non-APR Zone and included Township B (2019: x̅ = 29.4 [95% BCI = 26–34]; 
2021: x̅ = 43.8 [95% BCI = 39–51]; 2022: x̅ = 39.3 [95% BCI = 35–45]) and Township C (2019: x̅ = 
46.5 [95% BCI = 42–53]; 2021: x̅ = 67.0 [95% BCI = 59–78]; Figure 2B.2). Relative to its 
corresponding baseline estimate in 2019, I detected a single increase in Doe abundance in the 

223 

 
 
APR Zone’s D Township (2019: x̅ = 48.6 [95% BCI = 44–55]; 2021: x̅ = 68.5 [95% BCI = 59–80]; 
Figure 2B.2).  

I also detected significant increases in Yearling Male abundance in both the APR and 
Non-APR zones (Figure 2B.3). Relative to 2019 baseline estimates, most increases in Yearling 
Male abundance were detected in the Non-APR Zone and included Township A (2019: x̅ = 19.5 
[95% BCI = 16–24]; 2021: x̅ = 32.5 [95% BCI = 26–41]; 2022: x̅ = 38.2 [95% BCI = 31–47]), 
Township B (2019: x̅ = 15.2 [95% BCI = 12–19]; 2022: x̅ = 25.1 [95% BCI = 20–31]), and Township 
D (2019: x̅ = 20.4 [95% BCI = 17–25]; 2022: x̅ = 43.1 [95% BCI = 36–52]; Figure 2B.3). In contrast, 
I detected increases in Yearling Male abundance in 2 of the APR townships, including Township 
A (2019: x̅ = 21.7 [95% BCI = 17–27]; 2022: x̅ = 37.7 [95% BCI = 31–46]) and Township D (2019: x̅ 
= 31.9 [95% BCI = 26–39]; 2021: x̅ = 54.2 [95% BCI = 44–69]; 2022: x̅ = 48.3 [95% BCI = 40–58]; 
Figure 2B.3). I failed to detect any significant changes in Fawn abundance in APR or Non-APR 
zones (Figure 2B.4). 

DISCUSSION 

It is important to note that the inferences drawn from these results are weak, as the 

static N-mixture model was considered poorly equipped to address the objectives of this study. 
I investigated changes in deer abundance over 3 consecutive years and found relative 
abundance of Adult Males increased in most areas with the APR treatment. In control and 
treatment areas, I detected no decreases in the relative abundance of Does. Further, I found no 
evidence that APRs facilitated reductions in overall deer abundance. Most significant increases 
in Doe abundance were detected in Non-APR Zone townships. Most increases in Yearling Male 
abundance were detected in the Non-APR Zone. I failed to detect any significant changes in 
Fawn abundance in APR or Non-APR townships.   

Fitting a static N-mixture model to data from each year separately was a simple way to 

accommodate the open population structure that arose from sampling multiple years in this 
study (Kéry and Royle 2021). The static N-mixture model provided me with valuable insights 
(and provided a foundation for future modeling efforts), but there was a lot of noise around the 
relative abundance estimates. In other words, there was a notable degree of inconsistency in 
estimates across years. These variable fluctuations were likely the result of unaccounted for 
spatiotemporal differences in the data (e.g., heterogeneity in detection probability). The noise 
around estimates made it difficult to identify trends and interpret results. The simplistic static-
model approach led to highly parameterized models (e.g., 𝑇 of each parameter in the model), 
resulting in statistical inefficiencies (Kéry and Royle 2021). Model development is an iterative 
undertaking, exemplified by my initial use of this framework here. 

A more suitable approach for handling the multiple-year data structure would be to fit 

all the 𝑇 years jointly using a year-stratified framework (Kéry and Royle 2021). The year-
stratified N-mixture model is a class of hierarchical models for open populations (i.e., 
populations subject to change over time via addition or subtraction of individuals) that can be 
used to estimate trends or covariate effects, when dynamics are not of interest (Kéry and Royle 
2021). For example, the effect of harvest treatment, year, and the interaction of the two. By 
analyzing the entire dataset in a model where every parameter is year-specific, it allows the 
user to impose explicit constraints on the parameters and to share parameters among the 
datasets (Kéry and Royle 2021). This approach is like fitting 𝑇 separate static models, except 

224 

 
 
with the data pooled into a single dataset (also referred to as stacking the data) and analyzed 
jointly (Kéry and Royle 2021). Stacking successive years of data yields distinct site-year 
combinations, enabling the estimation of abundance based on these combinations. This 
approach also satisfies the model’s closure assumption, which denotes closure during survey 
periods and openness between them. 

By modeling abundance one-year-at-a-time, the static binomial N-mixture model was 

considered to make poor use of the available data. Further, the model was considered less than 
ideal for evaluating population-level changes over time. Although there are applications for this 
closed-population model, I did not consider it appropriate for this study—based on model 
limitations and the objectives of the state wildlife agency. If a wildlife agency’s goal is to 
compare snapshots among populations within a given year, then the static model is considered 
suitable. If an agency’s goal is to evaluate population trends over time, I recommend using an 
alternative modeling approach better equipped to test linear relationships, like the year-
stratified N-mixture model.

225 

FIGURES 

Figure 2B.1. Pre-harvest relative abundance estimates of adult male white-tailed deer 
(Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. 
Estimates were produced using a static binomial N-mixture model. Beginning in 2019, antlered 
deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone and not in 
the Non-APR Zone (experimental area and control area, respectively). Zones are displayed in the 
grid columns and township pairs (Twp A, B, C, and D) in the grid rows. Error bars indicate 95% 
Bayesian credible intervals. Only half of the townships were surveyed in 2020 due to pandemic-
related constraints. Relative to baseline estimates in 2019, we detected significant increases in 
abundance in both the APR Zone (Twp A, B, and D 2021) and Non-APR Zone (Twp A 2021).

226 

Figure 2B.2. Pre-harvest relative abundance estimates of female (yearlings and adults, i.e., does) 
white-tailed deer (Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, 
USA, 2019–2022. Estimates were produced using a static binomial N-mixture model. Beginning 
in 2019, antlered deer harvest was limited by a 4-point antler point restriction (APR) in the APR 
Zone and not in the Non-APR Zone (experimental area and control area, respectively). Zones are 
displayed in the grid columns and township pairs (Twp A, B, C, and D) in the grid rows. Error bars 
indicate 95% Bayesian credible intervals. Only half of the townships were surveyed in 2020 due 
to pandemic-related constraints. Relative to baseline estimates in 2019, we detected significant 
increases in abundance in both the APR Zone (Twp D 2021) and Non-APR Zone (Twp B 2021 and 
2022, Twp C 2021).

227 

Figure 2B.3. Pre-harvest relative abundance estimates of yearling male white-tailed deer 
(Odocoileus virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. 
Estimates were produced using a static binomial N-mixture model. Beginning in 2019, antlered 
deer harvest was limited by a 4-point antler point restriction (APR) in the APR Zone and not in 
the Non-APR Zone (experimental area and control area, respectively). Zones are displayed in the 
grid columns and township pairs (Twp A, B, C, and D) in the grid rows. Error bars indicate 95% 
Bayesian credible intervals. Only half of the townships were surveyed in 2020 due to pandemic-
related constraints. Relative to baseline estimates in 2019, we detected significant increases in 
abundance in both the APR Zone (Twp A 2022, Twp D 2021 and 2022) and Non-APR Zone (Twp 
A 2021 and 2022, Twp B 2022, Twp D 2022).

228 

Figure 2B.4. Pre-harvest relative abundance estimates of fawn white-tailed deer (Odocoileus 
virginianus) in the south-central Lower Peninsula of Michigan, USA, 2019–2022. Estimates were 
produced using a static binomial N-mixture model. Beginning in 2019, antlered deer harvest 
was limited by a 4-point antler point restriction (APR) in the APR Zone and not in the Non-APR 
Zone (experimental area and control area, respectively). Zones are displayed in the grid columns 
and township pairs (Twp A, B, C, and D) in the grid rows. Error bars indicate 95% Bayesian 
credible intervals. Only half of the townships were surveyed in 2020 due to pandemic-related 
constraints. Relative to baseline estimates in 2019, we failed to detect any significant changes in 
abundance.

229 

REFERENCES 

Dewitz, J., and U.S. Geological Survey. 2021. National Land Cover Database (NLCD) 2019 

Products (ver. 2.0, June 2021): U.S. Geological Survey data release, 
https://doi.org/10.5066/P9KZCM54. 

Felix, A. B., H. Campa III, K. F. Millenbah, S. Panken, S.R. Winterstein, and W.E. Moritz. 2002. 
Applications of using a landscape scale model to quantify white-tailed deer habitat 
potential in Michigan. Pages 107-114 in Eleftherios Hadjisterkotis, editor. Proceedings of 
the XXV International Congress of the International Union of Game Biologists and the IX 
International Symposium Perdix. Cyprus. 

Grear, D. A., M. D. Samuel, J. A. Langenberg, and D. Keane. 2006. Demographic patterns and 
harvest vulnerability of chronic wasting disease infected white-tailed deer in Wisconsin. 
Journal of Wildlife Management 70:546–553. 

Heisey, D. M., E. E. Osnas, P. C. Cross, D. O. Joly, J. A. Langenberg, and M. W. Miller. 2010. 

Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from 
cross-sectional data. Ecological Monographs 80:221–240. 

Joseph, L. N., C. Elkin, T. G. Martin, and H. P. Possingham. 2009. Modeling abundance using N-
mixture models: the importance of considering ecological mechanisms. Ecological 
Applications 19:631–642. 

Kellner, K. F. 2015. jagsUI: A wrapper around rjags to streamline JAGS analyses. R package 

version 1.5.2. https://cran.r-project.org/web/packages/jagsUI/index.html.  

Kéry M., and M. Schaub. 2012. Bayesian population analysis using WinBUGS: a hierarchical 

perspective. First edition. Elsevier, Amsterdam, Netherlands. 

Kéry, M., and J. A. Royle. 2021. Applied hierarchical modeling in ecology analysis of distribution, 
abundance and species richness in R and BUGS. Volume 2: dynamic and advanced models. 
Academic Press, Cambridge, Massachusetts, USA. 

Manjerovic, M. B., M. L. Green, N. Mateus-Pinilla, and J. Novakofski. 2014. The importance of 
localized culling in stabilizing chronic wasting disease prevalence in white-tailed deer 
populations. Preventive Veterinary Medicine 113:139–145. 

Mateus-Pinilla, N., H.-Y. Weng, M. O. Ruiz, P. Shelton, and J. Novakofski. 2013. Evaluation of a 
wild white-tailed deer population management program for controlling chronic wasting 
disease in Illinois, 2003–2008. Preventive Veterinary Medicine 110:541–548. 

Miller, M.W., and M.M. Conner. 2005. Epidemiology of chronic wasting disease in free-ranging 
mule deer: spatial, temporal, and demographic influences on observed prevalence 
patterns. Journal of Wildlife Disease 41(2): 275-290. 

230 

Nixon, C. M., L. P. Hansen, P. A. Brewer, and J. E. Chelsvig. 1991. Ecology of white-tailed deer in 

an intensively farmed region of Illinois. Wildlife Monographs 118:3-77. 

Nixon, CM., L.P. Hansen, P.A. Brewer, J. E. Chelsvig, J.B. Sullivan, R. Koerkenmeier, D.R. Etter, J. 

Cline, and J. A. Thomas. 1994. Behavior, dispersal, and survival of male white-tailed deer in 
Illinois. Illinois Natural History Survey Biological Notes 139. 

Nixon, C. M., L. P. Hansen, P. A. Brewer, J. E. Chelsvig, T. L. Esker, D. Etter, J. B. Sullivan, R. G. 

Koerkenmeier, and P. C. Mankin. 2001. Survival of white-tailed deer in intensively farmed 
areas of Illinois. Canadian Journal of Zoology 79:581–588. 

Osnas, E. E., D. M. Heisey, R. E. Rolley, and M. D. Samuel. 2009. Spatial and temporal patterns of 
chronic wasting disease: fine-scale mapping of a wildlife epidemic in Wisconsin. Ecological 
Applications 19:1311–1322. 

Plummer, M. 2003. JAGS: a program for analysis of Bayesian graphical models using Gibbs 

sampling. Pages 124–125 in K. Hornik, F. Leisch, and A. Zeileis, editors. Proceedings of the 
3rd International Workshop on Distributed Statistical Computing, March 20-23, 2003. 
Technische Universität Wien, Vienna, Austria. 

R Core Team. 2021. R: a language and environment for statistical computing. R Foundation for 

Statistical Computing, Vienna, Austria. 

Rees, E. E., E. H. Merrill, T. K. Bollinger, Y. T. Hwang, M. J. Pybus, and D. W. Coltman. 2012. 

Targeting the detection of chronic wasting disease using the hunter harvest during early 
phases of an outbreak in Saskatchewan, Canada. Preventive Veterinary Medicine 104:149–
159. 

Royle, J. A. 2004. N-Mixture models for estimating population size from spatially replicated 

counts. Biometrics 60:108–115.  

Samuel, M. D. and D. J. Storm. 2016. Chronic wasting disease in white-tailed deer: infection, 
mortality, and implications for heterogeneous transmission. Ecology 97:3195–3205.

231 

APPENDIX 2B.1: CODE FOR MODELING ABUNDANCE WITH A STATIC BINOMIAL N-MIXTURE 
MODEL 

nmix <- function(twn.final, cov.table){ 
  #Cover (open or closed) covariate on detection process 
  #Percent agriculture covariate on abundance process 
  #Township as random effect on abundance process 

  #Data 
  max <- ncol(twn.final) 
  y <- twn.final[,2:max] 
  NewCover <- cov.table$LandCoverNew #Open or closed cover covariate 

on detection 

  AgCover <- cov.table$AgCover #%agriculture covariate on abundance 

  #Create group ID for townships; requires all 18 sites in 4 townships 

(8 in other years) 

  twn <- sort(rep(1:8, 18))  

  #Load JAGS package 
  library("jagsUI") 

  #Specify model in JAGS language 
  sink("model.txt") 
  cat(" 
  model { 
  # Priors 
  alpha ~ dnorm(0,0.25) 
  beta1 ~ dnorm(0,0.25) 
  beta4 ~ dnorm(0,0.25) 
  beta5 ~ dnorm(0,0.25) 
  mu.kappa ~ dnorm(0,0.25) 
  sigma.kappa ~ dexp(1) 

  # Likelihood 
  # Biological model for true abundance 
  for (i in 1:R) { # Sites 
    N[i] ~ dpois(mu.lambda[i]) 
    log(mu.lambda[i]) <- kappa[twn[i]] + (beta4 * AgCover[i]) + (beta5 

* pow(AgCover[i],2)) 

232 

 
 
   
   
   
   
   
   
   
   
   
   
    # Observation model for replicated counts 
    for (j in 1:T) { #count reps 
      y[i,j] ~ dbin(p[i], N[i]) 
    } #j 
    logit(p[i]) <- alpha + (beta1 * NewCover[i]) 
  } #i 

  for (k in 1:8) { # Townships for random effect on lambda, hard coded 

for 8 townships 

    kappa[k] ~ dnorm(mu.kappa, tau.kappa) 
  } 

  # Derived quantities 
  tau.kappa <- pow(sigma.kappa,-2) 

  totalN <- sum(N[]) 

  # Relies on input data (rows) being sorted by site (LocationName) 
  shermanN <- sum(N[1:18]) 
  tyronN <- sum(N[19:36]) 
  bowneN <- sum(N[37:54]) 
  nelsonN <- sum(N[55:72]) 
  sheridanN <- sum(N[73:90]) 
  eastonN <- sum(N[91:108]) 
  bushnellN <- sum(N[109:126]) 
  douglasN <- sum(N[127:144])  # 144 camera sites 

  } 
  ",fill = TRUE) 
  sink() 

  #Bundle data 
  win.data <- list(y = y, R = nrow(y), T = ncol(y[,,1]), NewCover = 

as.integer(NewCover), AgCover = as.numeric(scale(AgCover)), twn = 
twn) 

  #Initial values 
  Nst <- apply(y, 1, max, na.rm = TRUE) + 1 # This line is important 

233 

     
     
   
   
   
   
 
 
   
   
   
   
   
   
   
  inits <- function() list(N = Nst) 

  #Parameters monitored 
  params <- c("alpha", "beta1", "beta4", "beta5", "mu.kappa", 

"sigma.kappa", "kappa", "p", "totalN", "shermanN", "tyronN", 
"bowneN", "nelsonN", "sheridanN", "eastonN", "bushnellN", 
"douglasN") 

  # MCMC settings 
  ni <- 50000 
  nt <- 5 
  nb <- 3000 
  nc <- 3 

  # Call JAGS from R (BRT 0.1 min) 
  out <<- jags(win.data, inits, params, "model.txt", n.chains = nc, 

n.thin = nt, n.iter = ni, n.burnin = nb) 

}

234 

   
   
   
   
   
   
APPENDIX 2C: CODE FOR YEAR-STRATIFIED N-MIXTURE MODEL 

# Load package 
library(nimble) 

# Create constants for model from array 
constants <- list( 
  nyear = dim(legal_all)[[3]], 
  nsite = nsite,  
  nreps = dim(legal_all)[[2]], 
  trt = trt,  
  twn = twn 
  ) 

# Bundle data (counts and covariates) 
data <- list( 
  y = legal_all, 
  #trt = trt,  
  year = yr, 
  ag = ag,  
  cover = cover 
) 

code <- nimbleCode({ 
  alpha0 ~ dnorm(0, sd = 2) 
  alpha1 ~ dnorm(0, sd = 2) 

# Standard deviation among site x year combos for the residual error 
epsilon, given an exponential prior since it must be positive. 
  sd_epsilon ~ dexp(1) 

  # Use similar approach for lambda. 
  sd_epsilon_lambda ~ dexp(1) 

  # Intercept and slope for year are vectors of length 2 (1 for each 
treatment). So, we have beta1, beta2, beta3, & beta4. 
  for( i in 1:2){ 
    beta1[i] ~ dnorm(0, sd = 2) 
    beta2[i] ~ dnorm(0, sd = 2) 
  } 

  for( i in 1:8) { 
    epsilon_lambda[i] ~ dnorm(0, sd = sd_epsilon_lambda) 
  } 

235 

 
 
 
 
 
 
   
   
 
   
  beta3 ~ dnorm(0, sd = 2) 
  beta4 ~ dnorm(0, sd = 2) 

  for( t in 1:nyear ) { 

    # loop through only the sites that are surveyed in a given year. 
    for( i in 1:nsite[t] ){ 

      N[i, t] ~ dpois( lambda[ i, t ] ) 

      # Indexing here 
      # We are still treating treatment as a fixed effect 
      # but instead of doing the multiply by 0 or 1 hack, we index the 
intercept and slope of year by trt 
      # this will "level the playing field" so the two treatments will 
have similar uncertainty. Basically, we extract the current value from 
the "trt" matrix to tell the model which of the two beta1 and beta2s 
to use.  

      log( lambda[i, t] ) <- beta1[trt[i,t]] + beta2[trt[i, t]] * 
year[i, t] + beta3 * ag[i,t] + beta4 * ag[i, t] * ag[i, t] + 
epsilon_lambda[twn[i, t]] 

      # adding site x year random effect (epsilon) for detection 
probability  
      logit( p[i, t] ) <- alpha0 + alpha1 * cover[i, t] + epsilon[i, 
t] 

      # epsilon is modeled as a residual - a draw from a zero-mean 
normal distribution 
      # we let the model estimate the standard deviation 
      epsilon[i, t] ~ dnorm(0, sd = sd_epsilon) 

      for( j in 1:nreps ){ 
        y[i, j, t] ~ dbin( p[i, t], N[i, t] ) 

      } 
    } 
  } 

236 

   
   
 
 
 
       
       
       
 
       
       
     
         
 
         
   
  })          

# Initial values 
Nst <- apply( data$y, c(1, 3), max, na.rm = TRUE) 

Nst[Nst == -Inf] <- 0 

Nst <- Nst + 1 # This line is important 

yst <- data$y 

yst[is.na(yst)] <- round( mean( data$y, na.rm = TRUE) ) 

inits <- function(){ 
  list( 
    alpha0 = rnorm(1, 0, 0.5),  
    alpha1 = rnorm(1, 0, 0.5),  
    # important  
    # beta1 and beta2 get 2 initial values (not 1) since we are 
indexing by treatment. Given the indexing structure, initial values 
are provided a little differently. 
    beta1 = rnorm(2, 0, 0.5),  
    beta2 = rnorm(2, 0, 0.5),  
    beta3 = rnorm(1, 0, 0.5),  
    beta4 = rnorm(1, 0, 0.5), 
    N = Nst, 
    y = yst, 

    # don't forget to provide initial values for epsilon and 
sd_epsilon 
    epsilon = array( rnorm( constants$nsite[1] * constants$nyear, 0, 
0.5),  
                     dim = c(constants$nsite[1], constants$nyear)), 
    sd_epsilon = rexp(1, 1), 
    sd_epsilon_lambda = rexp(1, 1), 
    epsilon_lambda = rnorm(8, 0, 0.25) 
  ) 
} 

# Good to track sd_epsilon  
# to ensure convergence and to get an idea of how much among-site 
variation in p there is 
params <- c("alpha0", "alpha1", "beta1", "beta2", "beta3", "beta4", 
"sd_epsilon", "sd_epsilon_lambda", "N")  

237 

   
 
 
 
 
 
 
 
 
 
out <- nimbleMCMC( 
  monitors = params, 
  code = code,  
  data = data,  
  constants = constants,  
  inits = inits(),  
  niter = 50000,  
  nburnin = 3000,  
  thin = 5,  
  nchains = 3 
)

238 

APPENDIX 2D: CODE FOR MARGINAL EFFECTS AND CHANGE IN ABUNDANCE 

# Load packages 
library(tidyverse) 
library(MCMCvis) 

#Wrangle betas from the posterior. 
legal.betas <- MCMCpstr( out, params = c("beta1"), type = 
"chains")[[1]] |>  
  as_tibble(rownames = "param") |>  
  #Here's a way to avoid hardcoding the number of columns, if you 
change the number of iterations. 
  pivot_longer(starts_with("V")) |>  
  mutate( param = str_remove(param, "beta1")) |>  
  mutate( trt = parse_number(param),  
          iter = parse_number(name)) |> 
  add_column(param_name = "beta1") |>  
  dplyr::select(param = param_name, trt, iter, value) |>  

  #That was all for the intercept, now join up the coefficient for 
year. 
  full_join( 
    MCMCpstr( out, params = c("beta2"), type = "chains")[[1]] |>  
      as_tibble(rownames = "param") |>  
      pivot_longer(starts_with("V")) |>  
      mutate( param = str_remove(param, "beta2")) |>  
      mutate( trt = parse_number(param),  
              iter = parse_number(name)) |> 
      add_column(param_name = "beta2") |>  
      dplyr::select(param = param_name, trt, iter, value) 
  ) 

#Create list of year names to replace standardized years used in 
model. 
yr_names <- c( 2019, 2020, 2021, 2022) 

#Create keys for easier interpretation. 
yr_key <- tibble(yr = unique(data$year)[1,], year = yr_names) 
trt_key <- tibble( trt_name = c("Non-APR", "APR"),  
                   trt = c(1, 2)) 

#Create dataframe listing the townships and which treatment category 
each is in 
twn <- tibble( 
  twn = 1:8, 

239 

 
 
 
   
 
 
 
  trt = c(rep(1, 4), rep(2, 4))) 

#Create dataframe with one column with the unique year values (scaled 
values) 
yr <- tibble(yr = unique(data$year)[1,]) 

#Merge them together so that you have twn x trt x year combinations 
legal.pred_df <- as_tibble( merge( twn, yr, by = NULL)) 

#Abundance table for treatment and years (i.e., zone estimates) 
legal.df <- full_join( legal.betas, legal.pred_df) |>  
  as_tibble() |> 
  pivot_wider(names_from = param, values_from = value) |>  
  mutate( lambda = exp( beta1 + beta2 * yr )) |>  
  group_by(twn, trt, yr) |>  
  summarise(  
    mean = mean(lambda), 
    l95 = quantile(lambda, c(0.025)),  
    u95 = quantile(lambda, c(0.975))) |>  
  full_join(yr_key) |>  
  full_join(trt_key) 

#Reformat beta data frame. 
legal.betas <- legal.betas |>  
  pivot_wider(names_from = param, values_from = value) 

#Create object for epsilon_lambda estimates (incorporating random 
effect by township). 
legal.epsilons <- MCMCpstr( out, params = c("epsilon_lambda"), type = 
"chains")[[1]] |>  
  as_tibble(rownames = "twn") |>  
  pivot_longer(starts_with("V")) |>  
  mutate( twn = parse_number(twn),  
          iter = parse_number(name)) |> 
  dplyr::select(-name) 

#Create table for plotting marginal effects. "Value" corresponds to 
epsilon_lambda estimates. 
legal.me <- full_join(legal.betas, legal.epsilons) |>  
  right_join(legal.pred_df) |>  
  mutate( lambda = exp( beta1 + beta2 * yr + value)) |>  
  full_join(yr_key) |>  
  dplyr::select( twn, trt, year, iter, lambda) |>  
  group_by(twn, trt, year) |>  
  summarise( mean = mean(lambda),  
             l95 = quantile(lambda, c(0.025)),  

240 

 
 
 
 
 
 
             u95 = quantile(lambda, c(0.975))) |>  
  full_join(yr_key) |>  
  full_join(trt_key) 

#Save for marginal effects plot. 
write.csv(legal.me, "legal.twn.me.csv",row.names = FALSE) 

#Create a new table for calculating difference (i.e., the 2019 - 2022 
change) 
legal.diff <- full_join(legal.betas, legal.epsilons) |>  
  right_join(legal.pred_df) |>  
  mutate( lambda = exp( beta1 + beta2 * yr + value)) |>  
  full_join(yr_key) |>  
  dplyr::select( twn, trt, year, iter, lambda) |>  
  pivot_wider(names_from = year, values_from = lambda) |>  
  mutate(diff = `2022` - `2019`) |> 
  group_by(twn, trt) |>  
  summarise( mean = mean(diff),  
             l95 = quantile(diff, c(0.025)),  
             u95 = quantile(diff, c(0.975))) |>  
  full_join(trt_key) 

#Save for plotting 
write.csv(legal.diff, "legal.twn.diff.csv", row.names = FALSE) 

241 

 
 
 
 
 
 
APPENDIX 2E: MEGADETECTOR ACCURACY 

Figure 2E.1. Pie charts showing MegaDetector, a machine-learning model, accuracy for detecting deer when using alternative 
confidence-threshold settings (10+ to 90+) for general classification of camera-trap images (presence or absence of animal). Analysis 
conducted by S. Mayhew of the Michigan Department of Natural Resources using a subset of 52,232 validated photos. A 90+ 
confidence threshold was selected for its ability to minimize the number of irrelevant images needing manual review while having 
little effect on false-negative deer images. Figures created by S. Mayhew and revised by S. Gurney. 

242 

 
 
 
APPENDIX 2F: MICHIGAN DEER-HARVEST TRENDS 

Figure 2F.1. 2009–2018 trends in yearling-male harvest in the south-central Lower Peninsula of 
Michigan in a 5-county study area (Newaygo, Kent, Mecosta, Montcalm, and Ionia County) that 
included a known chronic-wasting-disease hotspot (Kent and Montcalm County). Data provided 
by MDNR deer check station data. These data show a steady decline in the proportion of 
yearling males in the annual harvest, declining over 10% from 2009–2018. Figure and analysis 
done by the Michigan Department of Natural Resources. These data below were presented by 
C. Stewart of the Michigan Department of Natural Resources (MDNR) at the May 2019 meeting 
of the Natural Resources Commission (https://www.michigan.gov/dnr/-
/media/Project/Websites/dnr/Documents/WLD/Deer/apr_field_study_summary_and_presenta
tion.pdf). 

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Figure 2F.2. Michigan map showing the proportion of antlered deer harvested in 2022 that had 
at least 4 antler points on one side. Counties are displayed in different shades of gray 
depending on harvest results. The analysis and map were conducted and created by the 
Michigan Department of Natural Resources. These data were presented by C. Stewart of the 
Michigan Department of Natural Resources (MDNR) at the May 2023 meeting of the Natural 
Resources Commission (https://www.michigan.gov/dnr/-
/media/Project/Websites/dnr/Documents/Boards/NRC/2023/May-
2023/Deer_Regulations.pdf). 

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Figure 2F.3. Estimated antlerless deer harvest in counties with antler point restrictions (APRs) 
and counties without antler point restrictions (Non-APRs) in a 5-county study area, MI, 2018–
2021. APR counties included Mecosta, Montcalm, and Ionia County. Non-APR counties included 
Newaygo and Kent County. Antlerless deer were defined as deer without antlers and deer with 
antlers <7.62 cm (3 inches) in length. Error bars indicate 95% confidence intervals. Overlapping 
confidence intervals indicated that antlerless harvest was similar between APR and Non-APR 
counties during the 2018–2021 deer harvest seasons. Harvest analysis and graph conducted and 
provided by B. Frawley of the Michigan Department of Natural Resources. 

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Figure 2F.4. Estimated antlered deer harvest in counties with antler point restrictions (APRs) and 
counties without antler point restrictions (Non-APRs) in a 5-county study area, MI, 2018–2021. 
APR counties included Mecosta, Montcalm, and Ionia County. Non-APR counties included 
Newaygo and Kent County. Antlered deer were defined as deer with at least one antler 
measuring ≥7.62 cm (3 inches) in length. Error bars indicate 95% confidence intervals. 
Overlapping confidence intervals indicated antlered harvest was similar between APR and Non-
APR counties during the 2018–2021 deer harvest seasons. Harvest analysis and graph 
conducted and provided by B. Frawley of the Michigan Department of Natural Resources. 

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APPENDIX 2G: APR-CWD SIMULATION STUDY 

Linking Antler Point Restrictions to CWD Spread and 
Growth: An Agent-Based Modeling Approach with 
Empirical Data 

Steven Gurney, Sonja Christensen, Melissa Nichols, Chad Stewart, Sarah Mayhew, Marjorie 
Liberati, and Dwayne Etter. 

Presented at the 4th Annual International Chronic Wasting Disease Conference, June 2023. 

SUMMARY 

Agent-based models informed by empirical population estimates show harvest 
regulations play an important role in CWD dynamics, with higher outbreak severity observed 
under antler point restrictions than without. If a wildlife agency’s goal is to reduce the potential 
severity of an outbreak in a naive population, we recommend harvest strategies that include 
targeting all age classes of antlered deer. 

INTRODUCTION  

Wildlife management agencies have limited information on how deer harvest 
regulations affect deer populations. Chronic wasting disease (CWD) transmission rates are 
related to sex-and-age composition (Miller and Conner 2005, Grear et al. 2006), thus sex- and 
age-based harvest regulations could have implications for CWD dynamics. Antler point 
restrictions (APRs) have become an increasingly popular regulatory action to limit the harvest of 
younger male deer. However, there is limited information on the realized effect of APRs on sex-
age cohort abundance, and by extension, potential outcomes for CWD spread and growth. 
Agent-based models (ABMs) can simulate disease and population parameters and are useful for 
understanding emerging properties from complex systems (Belsare and Stewart 2020, Kjær and 
Schauber 2022). Though, these models may be improved with validated data from field studies 
of existing deer populations.  

STUDY GOAL 

Use empirical white-tailed deer (Odocoileus virginianus; hereafter, deer) population 

estimates with varying harvest-regulation treatment to simulate and investigate CWD spread 
and growth. 

OBJECTIVES  
1.  Modify an existing ABM to simulate deer populations that reflect empirical population 

estimates.  

2.  Evaluate potential CWD spread and growth under APR and Non-APR harvest study 

treatments.

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STUDY AREA 

Our ABM simulations were specific to Montcalm County, Michigan (a known CWD 

hotspot) and included empirical data from the south-central Lower Peninsula of Michigan. 
These empirical data were associated with a 5-county study area (Newaygo, Kent, Mecosta, 
Montcalm, and Ionia County; Figure 2G.1). 

METHODS 
Agent-based modeling framework 

We used a published, agent-based modeling framework (OvCWD; Belsare and Stewart 

2020) to simulate deer populations and CWD spread and growth under APR and NonAPR 
harvest treatments (Figure 2G.2). The main components of OvCWD included the landscape, the 
agents (individual deer), and the decision-making rules and procedures (e.g., deer behavior, 
CWD transmission; Figure 2G.2). Deer are added to the landscape based on forest-cover data 
and user-defined deer density. The rules and procedures are the core of the ABM and govern 
both population and disease dynamics. The OvCWD framework we used comprised of two 
ABMs adapted to simulate Michigan’s deer populations, MIOvPOP (Michigan Odocoileus 
virginianus POPulation simulation model; Belsare 2019b) and MIOvCWDdy (Michigan 
Odocoileus virginianus Chronic Wasting Disease dynamics model; Belsare 2019a). This two-part 
agent-based modeling framework (OvCWD) was coded in the high-level language NetLogo 
(version 6.2.2; Wilensky 1999). 

Informing model with empirical data 

To simulate deer populations, we informed the ABM with data from a Michigan study (S. 
Gurney, unpublished data) that estimated sex-and-age composition of deer populations in APR 
and NonAPR treatment areas (townships). In the APR area, antlered deer with at least four 
points on one antler beam could be harvested with a valid license (a legal point was defined as 
≥2.54 cm [1 inch] long as measured from its tip to the nearest edge of antler beam). In the Non-
APR area, any antlered deer with an antler measuring ≥7.62 cm (3 inches) in length could be 
taken. Given the ABM operated on a county scale, we used township-level data as a proxy for 
county-level simulations. We used estimated proportions of adults in the antlered class for APR 
and NonAPR treatment areas, which assumed adult males met the APR criteria and yearlings 
did not (S. Gurney, Michigan State University, unpublished data; Table 2G.1). From these data, 
we selected the highest and lowest estimated proportions of adults in the antlered class and 
then adjusted the ABM’s yearling-male harvest rates to produce these values.  

Simulations and output evaluated 

We simulated APR and NonAPR harvest scenarios independent of one another using the 

OvCWD modeling framework. We used a stabilized (lambda or population growth rate 
approximates 1) 10-year population snapshot produced by MIOvPOP, with desired adult-male 
proportions at year 10, to initialize MIOvCWDdy for CWD simulations. We set each CWD 
simulation to run for a duration of 25 years and replicated simulations 100 times with model 
stochasticity. For each simulation, we introduced CWD to a naive system (i.e., no prior disease) 
via a single dispersing yearling male. We used ABM output to first evaluate the 25-year 
outbreak probability for each harvest scenario. We characterized an outbreak as a simulation 

248 

 
 
 
 
 
 
 
that resulted in true CWD prevalence (total cases/total deer) ≥ 0.01 at the end of a 25-year 
simulation. We counted the total number of outbreaks per 100 simulations and divided it by 
100 to determine outbreak probability. We plotted outbreak probabilities to visualize results 
and compare between treatments. To quantify the severity of these outbreaks, we evaluated 
additional model output including the total number of CWD cases, total CWD area (mi2), and 
true CWD prevalence at the end of 25-year simulations. Note that total CWD area is reported in 
mi2 to reflect measurement units most used by U.S. wildlife agencies. We summarized outbreak-
severity metrics by calculating means from each set of 100 simulations and determined means 
differed between treatment groups if 95% confidence intervals did not overlap. 

RESULTS  

We found that estimated proportions of adults in the antlered class varied by APR and 

Non-APR treatment, with the highest proportion estimated in an APR area (0.49) and lowest in a 
Non-APR area (0.35; Table 2G.1). We adapted the ABM to reflect these extreme values and 
found that outbreak probability was comparable between the APR harvest scenario (0.25) and 
the Non-APR scenario (0.27; Figure 2G.3). Mean number of CWD cases was ~1.6 times higher in 
the APR scenario (𝑥̅ = 5,410; 95% CI: 4,535 – 6,284) than the NonAPR scenario (𝑥̅ = 3,480; 95% 
CI: 2,828 – 4,132; Figure 2G.4). Mean CWD area was ~1.5 times higher in the APR scenario (𝑥̅ = 
1,399 sq. mi; 95% CI: 1,196 – 1,602 sq. mi) than the NonAPR scenario (𝑥̅ = 930 sq. mi; 95% CI: 
762 – 1,097 sq. mi; Figure 2G.4). Mean CWD prevalence was ~1.6 times higher in the APR 
scenario (𝑥̅ = 0.11; 95% CI: 0.09 – 0.14) than the NonAPR scenario (𝑥̅ = 0.07; 95% CI: 0.05 – 0.08; 
Figure 2G.4).  

DISCUSSION 

We found composition of males played an important role in CWD dynamics, and 
consequently CWD dynamics varied by APR and Non-APR harvest treatments. We found that 
the proportion of adult males in the antlered class were consistently higher in APR areas 
compared to Non-APR areas (Table 2G.1). These results suggest that APRs successfully help 
advance the age structure of antlered deer by limiting harvest of yearling males. Interestingly, 
the highest proportion of adult males observed in the Non-APR areas was higher than the 
lowest proportion observed in the APR areas. This is simply an observation, but it does allude to 
APRs having a different magnitude of effect in different landscape types (e.g., township types) 
or for the potential for hunters to be practicing non-mandatory APRs in a Non-APR area.  
When adapting the ABM to reflect our selected proportions of adult males in the 
antlered class (highest and lowest proportions), it required us to substantially adjust OvCWD’s 
yearling-male harvest rates. These harvest rates (APR = 0.50; Non-APR = 0.72) were 
approximately 0.18 – 0.25 higher compared to the harvest rates used by Belsare and Stewart 
(2020; APR = 0.32; Non-APR = 0.47). These large increases suggest that it requires high levels of 
yearling harvest to affect population-level changes in the age composition of antlered deer. 
These results may also suggest potentially limited understanding of the population prior to our 
study.  

Our outbreak probabilities for APR and Non-APR scenarios (APR = 0.25; NonAPR = 0.27; 
Figure 2G.3) were both more similar to one another and overall lower compared to Belsare and 
Stewart’s (2020) findings (APR = 0.45; Non-APR = 0.37). Our lower outbreak probabilities were 

249 

 
 
 
 
 
 
likely driven by our higher harvest rates of yearling males. Replicating our 100-year stochastic 
simulations could help determine if outbreak probabilities are statistically similar or different 
between our APR and Non-APR scenarios. At the end of our 25-year simulations, we found that 
CWD outbreaks were more severe in the APR scenario than the Non-APR scenario. In our APR 
scenario, the mean number of CWD cases, mean CWD area, and mean CWD prevalence were all 
> 1.5 times higher than the Non-APR scenario (Figure 2G.4). These results suggest that 
protecting yearling males from harvest can be counterproductive to CWD-management efforts.  

If a wildlife agency’s goal is to reduce the potential severity of an outbreak in a naive 

population, we recommend harvest strategies that include targeting all age classes of antlered 
deer. Several other model-based studies have reached comparable conclusions, proposing 
strategies like targeting the harvest of antlered deer (without distinguishing among age classes) 
or intensifying the harvest of yearling males, to mitigate CWD prevalence or lower the likelihood 
of CWD outbreaks (Potapov et al. 2016, Belsare and Stewart 2020). The OvCWD framework is a 
unique adaptive management tool that allows users to customize and update the models 
(Belsare and Stewart 2020), as highlighted in this study. Models like OvCWD are invaluable 
because they can improve our ability to infer unobservable disease processes and improve 
understanding of disease transmission and our capacity to predict disease dynamics. Future 
studies should continue to integrate new data and update the ABM’s assumptions based on 
current best knowledge of the system. 

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TABLES 
Table 2G.1. Estimated proportions of adult males in the antlered class of white-tailed deer 
(Odocoileus virginianus) harvest treatment (APR, Non-APR) and township pairing (A–D) in the 
south-central Lower Peninsula of Michigan, USA, 2022 (S. Gurney, unpublished data). The antler 
point restriction (APR) harvest treatment limited antlered harvest to deer with ≥4 antler points 
on at least one antler beam. Under the Non-APR harvest treatment, deer with at least one 
antler measuring ≥7.62 cm (3 inches) in length could be taken with an antlered license. Antlered 
deer were assumed to be adults if they met the APR criteria, otherwise they were assumed to 
be yearlings.  

Township 
A 
B 
C 
D 

APR harvest treatment 
0.41 
0.47 
0.49 
0.44 

Non-APR harvest treatment 
0.35 
0.36 
0.43 
0.39 

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FIGURES 

Figure 2G.1. Study area in the south-central Lower Peninsula of Michigan, USA, in a designated 
5-county area. Mandatory antler point restrictions (APRs) were implemented in the eastern 3 
counties. Agent-based modeling was used to simulate chronic wasting disease spread and 
growth under alternative deer harvest scenarios in Montcalm County (a known CWD hotspot). 
Maps created in ArcGIS Pro (version 2.7.1; www.esri.com).

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Figure 2G.2. Conceptual diagram of the OvCWD agent-based modeling framework (Belsare and Stewart 2020) used to evaluate 
chronic wasting disease (CWD) spread and growth in a white-tailed deer (Odocoileus virginiaus) population under alternative deer 
haverst scenarios. The main components of the ABM include the landscape, the agents (i.e., individual deer), and the decision-
making rules and procedures (e.g., deer behavior, transmission of CWD). Deer are added to the landscape based on forest-cover data 
and user-defined deer density. The rules and procedures are the core of the model and govern both population and disease 
dynamics. This 2-part ABM (Belsare 2019a, 2019b) was coded in NetLogo (version 6.2.2; Wilensky 1999). 

253 

 
 
Figure 2G.3. Waffle plots illustrating model-derived CWD outbreak probabilities for two white-tailed deer (Odocoileus virginianus) 
harvest scenarios in Montcalm County, MI, USA. Harvest scenarios include (A) NonAPR and (B) antler point restrictions (APRs). Each 
square represents one model iteration and red squares indicate iterations that resulted in a chronic wasting disease outbreak at the 
end of a 25-year simulation. OvCWD, an agent-based modeling framework (Belsare and Stewart 2020), was used for all simulations. 
Modeling efforts incorporated data from field studies of existing deer populations with APR and NonAPR harvest treatments (S. 
Gurney, unpublished data). Outbreak probabilities were considered similar between APR and NonAPR harvest scenarios. 

254 

 
 
Figure 2G.4. Model-derived estimates for (A) total number of chronic wasting disease (CWD) cases, (B) total CWD area, and (C) true 
CWD prevalence for antler point restriction (APR) and NonAPR harvest scenarios in Montcalm County, Michigan, USA. Estimates were 
derived from 25-year simulations using the OvCWD agent-based modeling framework (Belsare and Stewart 2020). Modeling efforts 
incorporated data from field studies of existing deer populations with APR and NonAPR harvest treatments (S. Gurney, unpublished 
data). Plotted values are means and error bars indicate a ± 95% confidence interval. The APR scenario resulted in significantly more 
CWD cases, more CWD area, and higher CWD prevalence compared to the NonAPR scenario. 

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REFERENCES 

Belsare, A. V. 2019a. MIOvCWD. Version 1.0.0. CoMSES Computational Model Library. 

https://doi.org/10.25937/6qeq-1c13. 

Belsare, A. V. 2019b. MiOVPop. Version 1.1.0. CoMSES Computational Model Library. 

https://doi.org/10.25937/kv07-3e08. 

Belsare, A. V., and C. M. Stewart. 2020. OvCWD: An agent-based modeling framework for 
informing chronic wasting disease management in white-tailed deer populations. 
Ecological Solutions and Evidence 1:e12017. 

ESRI 2020. ArcGIS Pro: 2.7.1. Environmental Systems Research Institute. Redlands, California, 

USA. 

Grear, D. A., M. D. Samuel, J. A. Langenberg, and D. Keane. 2006. Demographic patterns and 
harvest vulnerability of chronic wasting disease infected white-tailed deer in Wisconsin. 
Journal of Wildlife Management 70(2): 546-553. 

Kjær, L. J., and E. M. Schauber. 2022. The effect of landscape, transmission mode and social 

behavior on disease transmission: Simulating the transmission of chronic wasting disease 
in white-tailed deer (Odocoileus virginianus) populations using a spatially explicit agent-
based model. Ecological Modelling 472:110114. 

Miller, M. W., and M. M. Conner. 2005. Epidemiology of chronic wasting disease in free-ranging 

mule deer: spatial, temporal, and demographic influences on observed prevalence 
patterns. Journal of Wildlife Diseases 41(2): 275-290. 

Potapov, A., E. Merrill, M. Pybus, and M. A. Lewis. 2016. Chronic wasting disease: transmission 

mechanisms and the possibility of harvest management. PLoS ONE 11:e0151039. 

Wilensky, U. 1999. NetLogo. Center for Connected Learning and Computer-Based Modeling, 
Northwestern University. Evanston, IL, USA. http://ccl.northwestern.edu/netlogo/. 

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