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THESIS
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thesis entitled

INTEGRATION OF ARCHERY WHITE-TAILED DEER
(Odocoileus virginianus) HARVEST DATA INTO A
SEX-AGE-KILL POPULATION MODEL

presented by

Kimberly Marie Mattson Hansen

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INTEGRATION OF ARCHERY WHITE-TAILED DEER
(Odocoileus virginianus) HARVEST DATA INTO A SEX-AGE-KILL
POPULATION MODEL
By

Kimberly Marie Mattson Hansen

A THESIS

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

MASTER or SCIENCE '
Department of Fisheries and Wildlife

1998 '

ABSTRACT

INTEGRATION OF ARCHERY WHITE-TAILED DEER HARVEST DATA
(Odocoileus virginianus) INTO A SEX-AGE-KILL POPULATION ESTIMATOR

By

Kimberly Marie Mattson Hansen

Archery hunting for white-tailed deer (Odocoileus virginianus) has gained
popularity in Michigan over the past thirty years. Historically, few hunters participated in
the archery hunting season, but Michigan has had a dramatic increase in archery license
sales, hunter-days, and harvest since the 19605. With an increasing proportion of the deer
harvest coming from archery hunting season, harvest statistics were studied to determine
if biological data from archery harvested deer should be included in a sex-age-kill (SAK)
population model. It was determined that there were significant differences between
firearm and archery harvest biological data. Firearm harvest biological data were
incorporated both independently and combined with archery harvest biological data into
the SAK model. Population estimates for years 1987-1996 for five geographic areas in
Michigan were determined. Population estimates from the SAK model were plotted with
annual deer-vehicle accident rates by year to detect trends. Results indicated that the
SAK model appeared to be a reliable index of the size of the deer herd at various
geographic scales. Variation among geographic areas appeared to be the result of density
independent factors and regulation processes in each area. Further studies are needed to

determine if the SAK model can be used as a reliable population estimator in Michigan.

DEDICATION

T 0 Lily and Thore Mattson

Who encouraged each of their grandchildren
to go to school and get an education

ACKNOWLEDGEMENTS

Financial support was provided by the Michigan Department of Natural Resources
(MDNR) through a contract (Federal Aid to Wildlife Restoration Project W-127-R) with
Michigan State University.

Appreciation is extended to all of the MDNR Wildlife Division biologists and
field staff who answered questions and provided feedback regarding this project. Special
thanks to Drs. Bill Moritz and Harry Hill, who were instrumental in providing insight to
both specific and broad implications of this project. The rest of the MDNR Wildlife
Biometrics group were also instrumental to the success of this project, especially MDNR
student assistants Dominique Clemente, Amanda Meredith, Davis Coye, and Todd F elke
for entering and verifying a lot of data. This project would have taken much longer if not
for their efforts.

I would like to extend a special appreciation to my major professor, Dr. Scott
Winterstein. It has been a joy to work with someone who is thoughtful and patient. The
rest of my committee, Drs. Bill Moritz, Henry Campa III, and Carl Ramm also deserve
special. acknowledgements. Their guidance and support throughout this project has been
greatly appreciated.

I would also like to thank the graduate students in the Department of Fisheries and
Wildlife for their support, assistance, advice and patience throughout this project.

My husband, Scott, deserves much appreciation for his unending support and
encouragement throughout this study. His tolerance was much appreciated, and his

humor kept my studies in perspective.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
INTRODUCTION .............................................................................................................. 1
Population Estimates ....................................................................................................... 1
Archery Hunting Season Data ......................................................................................... 3
Population Model Analysis ............................................................................................. 7
STUDY OBJECTIVES ..................................................................................................... 10
METHODS ....................................................................................................................... 11
Sample Size ................................................................................................................... 11
Seasonal Check Station Comparison ............................................................................ 14
SAK Model ................................................................................................................... l4
Bucks ......................................................................................................................... 16
Does and F awns ........................................................................................................ 18
SAK Model Assumptions ............................................................................................. 20
Testing SAK Model Assumptions ................................................................................ 20
Intrastate and Interstate Comparisons ........................................................................... 22
Mortality ....................................................................................................................... 23
SAK Model Analysis .................................................................................................... 24
RESULTS ......................................................................................................................... 26
Sample Sizes ................................................................................................................. 26
Seasonal Check Station Comparisons ........................................................................... 35
Stable Age Distribution ................................................................................................. 37
SAK Model Analysis .................................................................................................... 42
DISCUSSION ................................................................................................................... 62
Sample Size ................................................................................................................... 63
Seasonal Check Station Comparisons ........................................................................... 67
SAK Model Assumptions ............................................................................................. 71
SAK Model Analysis .................................................................................................... 74
MANAGEMENT IMPLICATIONS ................................................................................ 8]
LITERATURE CITED (Title page) ................................................................................. 86
LITERATURE CITED ..................................................................................................... 87
APPENDICES .................................................................................................................. 90
APPENDIX A. Derivation of a doezbuck ratio for the SAK population model. .............. 91

APPENDIX B. Deer-vehicle accident data and SAK model results for years
1987-1991 ................................................................................................ 93

LIST OF TABLES

Table 1. F irearrn and archery hunting season check station biological data for yearling
(1.5) and older (2.5+) white-tailed deer by sex, year, and geographic group. .......... 27

Table 2. F irearrn and archery hunting season check station biological data for fawn (buck

and doc) and adult doe (1.5+) white-tailed deer by sex, year, and geographic group.
................................................................................................................................... 32

Table 3. Combined season (firearm and archery) check station biological data for
yearling (1.5) and older (2.5+) white-tailed deer by sex, year, and geographic group.
................................................................................................................................... 38

Table 4. Results of regression analysis (n=10) of the slope of the percent yearling bucks
and does from 1987-1996 (see Figures 3 and 4). ...................................................... 41

Table 5. Deer-vehicle accident data and SAK model results for years 1987-1996. ........ 93

vi

LIST OF FIGURES

Figure 1. Statewide white-tailed deer harvest and hunter effort in Michigan
(1967-1996) ......................................................................................................... 5

Figure 2. Geographic group delineation of Michigan. Groups are based on ecological
similarities and 1996 MDNR Wildlife Division district boundaries. Numbers on the
map correspond to the descriptions of each area on the left. .................................... 13

Figure 3. Regression analysis (n=10) of yearling white-tailed bucks by year. Equation is
in the form y=mx+b. ................................................................................................. 42

Figure 4. Regression analysis (n=10) of yearling white-tailed does by year. Equation is
in the form y=mx+b. ................................................................................................. 46

Figure 5. Percent yearling bucks by year and mean percent yearling bucks for the period
1987-1996. ................................................................................................................ 49

Figure 6. Percent yearling does by year and mean percent yearling does for the period
1987-1996. ................................................................................................................ 52

Figure 7. SAK model results using firearm and combined seasons (CombSeas) data
(firearm and archery) and deer-vehicle accident (D-V Rate) trends plotted against
time. .......................................................................................................................... 56

vii

INTRODUCTION

Population Estimates

Managers have relied on various techniques, including nonharvest and harvest-
based population estimators, to monitor local and regional white-tailed deer (Odocoileus
virginianus) populations (McCullough 1979, Roseberry and Woolf 1991). Although data
for nonharvest-based population models can be collected and evaluated directly by
managers, harvest-based population models are dependent upon hunters for data
collection. Changes in hunter participation, hunting regulations, hunter success rates and
technology are only a few factors that would affect the quality of harvest-based data
collected from hunters. Unless these changes are accounted for in harvest-based models,
population estimates may be incorrectly determined. Therefore, reevaluation of harvest-
based population models may be required if data begin to vary due to regulation or
hunter-related changes.

There are a number of methods that can be employed to estimate the size of
white-tailed deer populations. Three broad categories can be used to describe these
methods: total population counts, population indices, and population estimators - which
measure certain attributes of a population. Although total counts have been used in
isolated areas, they are not reliable in large land areas and take many hours to perform
(Hawn and Ryel 1969, McCullough 1979). Population indices provide information on
relative abundance rather than absolute p0pulation numbers. Indices are important not
only for general information about deer in a particular area, but also to assist in the

validation of other population estimation techniques (Roseberry and Woolf 1991).

Validation generally comes from long-term monitoring of an index. Population
estimators, however, ordinarily give absolute numbers rather than the relative results of
indices. Furthermore, there are two general types of population indices and estimators,
nonharvest-based and harvest-based.

Nonharvest-based population indices may incorporate data from spotlight surveys,
track counts, summer deer observations, and deer—vehicle accidents. Relative densities of
deer can be determined from spotlight surveys (Progulske and Duerre 1964). Counting
the number of tracks on a known deer trail is an index of relative abundance (McCatfery
1976). This technique has been compared to other indices as well as to the sex-age-kill
population estimator (McCaffery 1976, Mooty and Karns 1984). Summer deer herd
observations are performed from July through September in Michigan (Langenau 1995).
This index provides information on the numbers of bucks, does and fawns seen
throughout Michigan. Deer population trends can also be determined by the number of
deer-vehicle accidents in an area (Case 1978, McCaffery 1973). A positive relationship
has been found between the number of deer-vehicle accidents and the estimated size of
the deer population in Michigan and other areas (Case 1978, McCaffery 1973, MDNR
unpublished data).

Nonharvest-based population estimators are also important. One of the primary
population estimators used in Michigan is the deer pellet survey. ‘Data are collected in the
spring in the northern Lower and Upper Peninsulas of Michigan, but cannot be collected
in southern Michigan due to habitat conditions (see Hill (1995) for a detailed study
description). Pellet surveys are used to estimate the size of the previous fall’s deer herd

(Hill 1995), but can also be an index, giving relative densities of deer in particular

habitats (Van Etten and Bennett 1965).

Most harvest-based population estimators have the same basic mechanism. There
are usually three major parameters: harvest mortality, nonharvest mortality, and age
structure data. These models estimate total population sizes, and some models may
provide age class population estimates as well (Roseberry and Woolf 1991). The
composition of the data collected depends on harvest regulations. For example, if the
management goal is to protect young bucks, regulations are going to be different than in
an area where a hunter may harvest any buck. Changes in regulations may affect the sex

and age of deer harvested, and, hence, the data collected from harvested deer.

Archery Hunting Season Data

The most comprehensive information collected about the deer herd in Michigan is
obtained from hunters through voluntary check stations and from mail surveys. Michigan
has three annual fall hunting seasons. The split archery season extends from October 1
through November 14 and from December 1 to January 1 (MDNR 1996a). Firearm
season is November 15-30, and muzzleloader season is held in December (MDNR
1996a). Biological data are obtained throughout the deer hunting seasons, with voluntary
check stations open for the duration of all the seasons. In addition, highway check
stations are open during a portion of the firearm hunting season. Information collected at
check stations includes the sex and age of deer harvested and the hunting season and deer
management unit in which each deer was harvested. Annual mail surveys are sent to a
sample of hunters to obtain information regarding the sex of the deer harvested as well as

the deer management unit and county in which hunting occurred (MDNR 1995).

Traditionally, the Michigan Department of Natural Resources (MDNR) has
employed a harvest-based population estimator for setting deer harvest quotas in the fall
hunting season. Models employing harvest-based population data have been developed
for this purpose (Roseberry and Woolf 1991). Most of these models are based on firearm
harvest data, as these data provide the most comprehensive historical base. In the early
and mid twentieth century, archery hunting was not popular, so the number of deer
harvested by this method was negligible. In recent years, however, archery hunting has
gained popularity. This is demonstrated in the increasing numbers of deer harvested
during the archery hunting season as shown in Figure 1 (Langenau et a1. 1994).

With an increasing proportion of the deer harvest coming from archery hunting
season, there is concern that data from these deer should be included in traditional
harvest-based population models (Langenau et al. 1994). This is especially important
when the types of data collected at check stations are considered. Biological data
(henceforth, biodata) retrieved from deer harvested during the firearm season in Michigan
have been used to determine sex ratios, fawnzdoe ratios and total populations of white-
tailed deer at various geographic scales (Moritz, MDNR, personal communication). It
has yet to be determined if the inclusion of archery data will alter results that had been
obtained exclusively from firearm harvest statistics in Michigan.

The MDNR has also been concerned in recent years about the effect of an increase
in both archery license sales and the archery harvest on harvest-based population model
estimates. Although firearm hunter numbers have remained relatively stable over the
years, there has been a marked increase in the number of archery licenses sold

(Winterstein et al. 1995). In 1981, less than 292,000 eligible bow hunting licenses

+ Firearm harvest _._ Archery harvest + Firearm hunter-days _._ Archery hunter-days

 

  

 

 

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Figure 1. Statewide white-tailed deer harvest and hunter effort in Michigan (1967-1996).

were sold with a harvest of 33,320 deer; in contrast, 488,774 eligible bow hunting
licenses were sold in 1995 with a harvest of 132,130 deer (Figure 1, MDNR 1980,
MDNR 1996b). In addition to the normal archery hunting season license, eligible bow
hunting licenses include those bow hunting licenses that are part of a package, such as the
senior hunt license, which entitles the holder to hunt deer, small game, furbearing
animals, and waterfowl. Because traditional harvest-based population estimates in
Michigan have not included archery biodata, population estimates may not be an accurate
representation of the size of the deer herd.

Further evidence that archery data may be an important component of estimating
the size of the deer population in Michigan is reflected in harvest counts and the number
of hunter-days during each deer hunting season. Harvest counts indicate that the
proportion of archery kills was 27% of the total statewide deer harvest in 1992 (Langenau
et a1. 1994). This is an increase from the archery harvest in 1970, which was 10% of the
combined (archery and firearm) statewide deer harvest (MDNR unpublished data).
Recently, as much as 50% of the harvest has occurred during archery season in some
areas (Langenau unpublished data). Hunterodays have shown a similar trend. Archery
hunter-days statewide have almost doubled since 1980, whereas the number of firearm
hunter-days have remained relatively stable (Figure 1, MDNR unpublished data).

All of these factors have contributed to a large increase in the number of deer
harvested during the archery season. There are several concerns associated with this
increase. First and foremost, managers need to determine how archery harvest data
should be evaluated in terms of harvest-based population models. Once these data are

evaluated, managers can determine if archery harvest is having a biological impact on the

deer herd. Such a scenario would occur if the archery harvest is directly altering age
and/or sex ratios. Biological impacts on the herd would then need to be considered
during the regulation process. Results from studying the impacts of changing harvest

statistics are also important when hunter relations and other sociological concerns are

considered.

Population Model Analysis

The MDNR is studying the use of the sex-age-kill (SAK) method of population
analysis as developed by Eberhardt (1960) and modified for use as a standard procedure
in Wisconsin (Creed et a1. 1984). The overall SAK method is actually a combination of
kill-curves, as introduced by Eberhardt (1960), and sex and age ratios as discussed by
Severinghaus and Maguire (1955). Creed et al. (1984) developed SAK further to assess
the Wisconsin deer herd, using annual expansion factors when sample sizes were
adequate and long-term averages when sample sizes were small. Since 1985, the
Wisconsin method has also incorporated archery data into SAK analysis in an attempt to
meet the assumptions of the model (WDNR unpublished data). This estimator is
currently also being used in several other states (Moritz pers. comm). Although the
MDNR has relied on a derivative of this population estimator for years, its use has not
been validated for the Michigan deer herd.

SAK is a retrospective population estimator, and does not consider over-winter
loss (Creed et a1. 1984). Being harvest-based, SAK relies on accurate biodata from the
hunting seasons. The numbers of bucks, does and fawns harvested are used to determine

the population size prior to the hunting seasons. This method works best when both

bucks and antlerless deer are harvested, but an alternate source of data for sex and age
compositions may be substituted in years or geographic areas with a bucks-only harvest
(Creed et a1. 1984). In Michigan, firearm harvest biodata are incorporated into the SAK
model to determine deer harvest and population numbers each year. It is still unknown
what effect the addition of archery harvest biodata may have on model results in
Michigan.

Regulation changes and fluctuations in management goals may influence proper
evaluation of the deer population. Any major change in regulations is reflected in the
number and types of hunting permits available, and, therefore, in the harvest data
collected at check stations. Although most regulation changes are minor, major changes
can take place. One such example of changing management goals would be to limit the
number of buck permits while allowing a very liberal number of antlerless permits, which
is defined by some as the practice of quality deer management. Quality deer management
(QDM) is defined as a strategy that promotes a healthy deer population through an
appropriate antlerless harvest and a limited yearling buck harvest (Miller and Marchinton
1995). To understand the implications of these types of changes in management
strategies, current archery harvest statistics must be evaluated to determine if sex and age
compositions within the deer herd have changed without such revisions. This study
attempted to aid in developing harvest regulations by giving the MDNR an evaluation of
the impacts that an increasing archery harvest is having on the Michigan deer herd.

Due to the increasing percentages of archery hunters and harvest, archery harvest
data may play a key role in obtaining accurate SAK population estimates. Considering

the increasing number of archery hunters and the rising percentages of deer harvested

during archery hunting season, data derived from the archery hunting season should be
given closer examination. This study attempted to demonstrate the validity of a harvest-
based population estimator by examining the importance of incorporating archery harvest

data into the SAK population model.

STUDY OBJECTIVES

The primary objective of this study was to determine the validity of the sex-age-

kill (SAK) model in estimating the size of the deer population of Michigan. The

secondary objective was to determine if archery biodata should be incorporated into the

SAK model. The assumptions of the SAK model were examined with respect to the

primary objective. Data were analyzed on a statewide basis as well as by various

geographic areas.

Objectives for this research were to:

l)

2)

3)

4)

5)

6)

Determine if current sample sizes of archery harvest data are large enough to permit
population analysis at the district level.

Determine if biodata collected from the archery deer harvest are significantly different
from biodata of firearm harvested deer.

Determine if voluntary check station sex and age composition data are comparable to
that of mandatory check stations.

Test the assumptions of the SAK model to determine if the SAK model is a valid
estimator for the population size of white-tailed deer in Michigan.

Determine if the inclusion of archery biodata into the SAK model significantly
changes any of the following estimates: total population estimates, sex ratios, and/or
fawnzdoe ratios already expressed in the model.

Recommend procedures and guidelines for the use of the SAK population model.

10

METHODS

Sample Size

This study utilized harvest statistics and check station biodata fumished by the
MDNR. More than forty years of firearm harvest data were available, compared to about
twenty years of archery harvest data. Although the MDNR has been collecting archery
hunting season data since the 1970s, sample sizes were small for antlerless deer until the
19805. Antlerless deer biodata were not routinely collected in the Lower Peninsula until
1975 and not in the Upper Peninsula until 1978 (MDNR 1976, 1979). There were many
areas closed to antlerless deer hunting within Michigan, and restricted permit availability
in other areas (MDNR 1976, 1979). These factors, coupled with a small sample of
archery biodata, prevented this study from utilizing the first several years of archery
check station biodata.

To evaluate the check station biodata, harvest data were segregated by year,
hunting season, sex of deer, and county of harvest. Buck and doe fawns were aggregated
as one age class. All unknown age deer, which are deer with a recorded age of “A” or
“AA” in the check station data, were removed from the study. These age categories are
used by the MDNR to denote a 1.5 year old and older or a 2.5 years old and older deer,
respectively, and are used when age cannot accurately be determined (MDNR
unpublished data). One problem in using deer aged as an “A” or “AA” is that it is
difficult to assess any discrepancies with their use. Since unknown age deer account for
roughly 3-5% of the statewide deer check station data each year (MDNR unpublished

data), deleting these age classes was not perceived to be a problem.

11

Adequate sample sizes (no) were determined for a 95% confidence level and a
0.10 degree of precision using the following equation:

= 22120-13)

1'10 d2

where z is the a/2 point of the normal distribution, p is the population proportion
observed, and d is the desired degree of precision of the estimate (Thompson 1992:31-
46). Adequate sample sizes could not be determined at county or district levels, so data
had to be grouped into larger units.

Once adequate sample sizes were determined, county level data were grouped to
obtain sample. sizes that were statistically adequate, ecologically sound, and which
provided study results that were useful to managers across the state. At the time this
study was started, Michigan had 13 wildlife management districts. In 1998, the MDNR
combined some of these districts to result in eight management units across the state
(MDNR unpublished data). Five geographic groups were made from the thirteen wildlife
management districts based on both district boundaries and ecological similarities (Figure
2). Ecological information was based on a hierarchical classification system as described
by Albert (1995). Section level classifications were utilized throughout Michigan (Albert
1995). The resulting geographic groups were used for seasonal check station

comparisons and for analyzing the SAK model.

12

 

 

Group 1: The Upper Peninsula

 

 

Group 2: The northeastern
region of the Lower Peninsula

 

 

Group 3: The western , .
portion of the middle of 3 t
the Lower Peninsula ‘ 4

 

 

 

Group 4: Thumb and .
southeastern portion of the " ”‘9
Lower Peninsula ' -

Group 5: Southwestern and south
central portion of the Lower
Peninsula

Figure 2. Geographic group delineation of Michigan. Groups are based on ecological
similarities and 1996 MDNR Wildlife Division district boundaries. Numbers on the map
correspond to the descriptions of each area on the lefi.

Seasonal Check Station Comparison

Voluntary check station biodata from 1987-1996 were utilized for this part of the
study. Adult bucks and adult does were grouped into the five geographic groups shown
in Figure 2. Data from firearm and archery harvested deer were aggregated by sex then
into two adult age classes: 1.5 year old and 2.5 years old and older. Chi-square tests were
performed to determine if there was a significant difference in harvest age structure
between the firearm and archery hunting seasons. Data from adult bucks and adult does
1.5 year old and 2.5 years old and older were used to determine if age distributions in the
harvest are independent of harvest methods. Similar Chi-square tests were done for
fawns. Buck and doe fawns were aggregated as one age class. All fawns were evaluated
against adult does 1.5 year old and older by hunting season. In effect, Chi-square
analyses for this part of the study determined any significant differences in fawnzdoe
ratios between the archery and firearm hunting seasons. All analyses were done as 2x2

Chi-square tests with 1 degree of freedom and at a-levels of 0.05 and 0.10.

SAK Model

The population model used for this study was the SAK population estimator
(Eberhardt 1960, 1969; Johnson 1994). This model uses biological data from harvested
deer to estimate the population size prior to all hunting seasons. Future populations can
be projected by following averages and trends. The data needed for the model are a
nonharvest mortality rate, check station biodata, and information from post-hunting

season mail surveys. Biodata used from the check stations include the numbers of bucks,

l4

does, and fawns brought to the stations as well as sex and age ratios from these deer.
Model results include estimates of buck mortality, doezbuck ratios, and fawnzdoe ratios
prior to the hunting seasons, and the total number of deer in the previous fall population
(Creed et al. 1984).

To use the SAK model as a population estimator, a major mortality source and a
measure of age structure are needed. These criteria are conveniently obtained from
harvest data. Each year, harvested deer are sexed and aged at voluntary check stations
throughout Michigan. These biodata are then used as a representative sample of the deer
harvested to estimate the population size prior to the hunting seasons. Only known age
deer are used in this estimate due to a lack of age ratios for unknown age deer. To obtain
a population estimate of the entire deer herd, bucks and antlerless deer need to be
harvested and counted. Otherwise, for a bucks-only season, there are insufficient data to
estimate doc and fawn numbers. In an area without an antlerless hunting season, summer
herd observations, spotlight counts, or another index of sex and age ratios may be used
(Creed et al. 1984).

In the SAK model, nonharvest mortality is used as a constant rate over the whole
year. Nonharvest mortality includes density dependent and density independent factors
such as scant summer food sources, illegal hunting and winter mortality. Winter severity
varies throughout the state each year and may differentially affect age classes. However,
a constant mortality rate is used for all sectors of the population in the SAK model, so
any differences in mortality for fawns versus adults throughout the year is not directly
reflected in this model (Creed et al. 1984). Nonharvest mortality, considered separate

from harvest mortality, is called the lifetime recovery rate, r, and is presented as the

15

percentage of deer living throughout the year (Creed et al. 1984). For example, if 15% of
the population (fawns and adults) died of nonharvest mortality throughout the year, the
lifetime recovery rate would be 85%.

The size of each sector of the population is extrapolated using the following
methods. Mail surveys are sent to a random sample of deer hunters shortly after the
hunting seasons have ended. Survey methods include a random or a systematic sample
with a random start drawn from hunting license holders, and reminders are sent to
nonrespondents (Research Triangle Institute 1966, MDNR 1995). This provides a
response rate of approximately 90% each year. The returned surveys provide a
representative sample of the total buck harvest across seasons (Hawn and Ryel 1969).
This estimate is then used in the SAK model to calculate the buck population from the
previous fall (before any harvesting had taken place). All other model variable data are

taken directly from check station biodata.

Bucks

 

Methods used to calculate the number of bucks that were alive prior to the hunting
seasons are shown below. The information needed for the first equation is collected at

check stations. Fawns are dealt with separately from adults.

#1.5 year old bucks
Total known age adult bucks

 

Percentageof yearling bucks =

For example, if there were 1,000 adult bucks of known age registered at the check

stations, and 750 of them were aged as yearlings, then there would be a percentage of

16

0.75 yearling bucks in the harvest.

Total buck mortality includes both yearling and adult bucks, but not fawn bucks.
To calculate the total adult buck mortality, the lifetime recovery rate, r, must be used to
account for any natural mortality that may have occurred throughout the year. The r
value is a total survival rate for the population; the product of r and the percentage of

yearling bucks in the harvest is the estimated total adult buck mortality:
Total adult buck mortality = percentage of yearling bucks x r

Therefore, if 90% of the deer population survives throughout the year, the r value
is 0.90. Multiply this value by the percentage of yearling bucks from the previous
example, 0.75. The estimated total adult buck mortality is, therefore, 0.675, which is the
percentage of adult bucks that died from both nonharvest and harvest-based mortality
factors.

Once the total buck mortality has been estimated, the adult buck population prior
to the hunting seasons can be determined. This population is the adult buck population
(1.5 year old and 2.5 years old and older) available on October 1 of the previous year,
since the archery deer hunting season starts October 1. Information from the mail survey

is used for this estimate:

Total buck harvest
Total buck mortality

Total available bucks =

 

To continue the example, assume the mail survey returned a sample of 14,000 1.5

17

year old and 2.5 years old and older bucks harvested across all hunting seasons. Divide
this number by the total buck mortality of 0.675, and the total adult buck population prior

to the hunting seasons would be 20,741 deer.

Docs and Fawns

In areas that have antlerless hunting seasons, check station biodata should be used
to determine doc and fawn populations. If harvest data are not available, other data
sources, such as summer deer observations or spotlight counts, can be utilized (Creed et
al. 1984). These data would be used in a similar manner as that listed below for harvest
data. Because some areas in Michigan have not continually been open to antlerless
harvest, not all years will have adequate harvest data samples.

The percentage of yearling does in the population is determined in a similar

manner to the percentage of yearling bucks:

#1.5 year old does
Total known age adult does

 

Percentage of yearling does =

Assume 1,000 known age does were obtained from the check stations. If 450 of
these were 1.5 year olds, the percentage of yearling does in the population is 0.45.

The percentage of does can be compared to the percentage of bucks to find the sex
ratio in the population. This ratio is not affected by the lifetime recovery rate because it
uses firearm check station data exclusively. Only yearling bucks and yearling docs are
used to find the sex ratio because it is assumed that harvest data reflects each age group

proportionally to abundance in the population (Severinghaus and MacGuire 1955). See

18

Appendix A for a detailed derivation of this equation.

Percentage of yearling bucks in firearm biodata

Doe:buck =
Percentage of yearling does in firearm biodata

The doezbuck ratio can be found using results from the previous calculations.
There are 0.75 yearling bucks and 0.45 yearling does obtained at the check stations,
yielding a doezbuck ratio of 1.67 adult does for each adult buck.

It is possible to estimate the numbers of does and fawns in the population for
management areas that have sex and age composition data available. Information
recorded at check stations is used to estimate the number of does and fawns, as well as
the fawnzdoe ratio. The number of adult does, including yearlings, is calculated using the

doezbuck ratio, which determines the total doe population on the previous October 1.

Total Available Does = Total available bucks "' Doe:buck ratio

In this example, the total available does is 20,741 total available bucks multiplied
by the doezbuck ratio (1.67). This results in an estimate of 34,638 does in the population
prior to the hunting seasons.

The fawnzdoe ratio includes all fawns as well as yearling and 2.5 years old and
older does. Data are collected at the check stations, and the calculation is the number of
fawns divided by the number of adult does. The number of available fawns is calculated

similarly to the numbers of available does and bucks.

l9

Total number of fawns = # of adult does "' fawn:doe ratio

The total fawn population would then be the 34,638 adult does multiplied by the
fawn:doe ratio from the check stations, say 1.01 , resulting in 34,984 fawns in the
population prior to the hunting seasons.

The estimated total deer population before the beginning of the hunting seasons
can now be calculated by summing the total numbers of bucks, does and fawns estimated
above. In this example, the estimated total population would be the sum of 20,741 bucks,

34,638 does, and 34,984 fawns for a grand total of 90,363 deer.

SAK Model Assumptions

For the SAK model to be accurate, there are a number of assumptions that must be
met (Eberhardt 1960, Creed et al. 1984). The assumptions are that: 1) the population is at
a stable age distribution; 2) the sample sexed and aged at check stations is representative
of the population; 3) fawn production is measured accurately; 4) nonharvest mortality is
known; and 5) buck harvest pressure is uniform from year to year. Wisconsin, which has
mandatory registration of harvested deer, also uses the assumption that 98% of the deer
harvested are registered in that state (WDNR unpublished data). Since Michigan has

voluntary check stations, the MDNR does not use this assumption.

Testing SAK Model Assumptions
Most of the SAK model assumptions were analyzed. First, a stable age

distribution was tested by utilizing firearm and archery harvest biodata. A stable age

20

distribution is defined as a distribution of constant pr0portions of individuals in each age
class. It occurs in a population when age-dependent survival and productivity rates
remain constant over a long period of time, resulting in a stabilization of each age class
(Johnson 1994). To test this assumption, firearm and archery check station biodata were
combined, then grouped by sex and separated into adult age classes for each of the five
geographic groups in Figure 2. Percent yearlings from the combined seasons were tested
for differences among years during a ten year period (1987-1996) to determine if a stable
age distribution existed over the years.

Contingency tables were constructed to determine absolute differences in percent
yearlings among the ten years. For individual geographic groups, the expected number of
yearling and 2.5 years old and older deer were determined each year. Additionally, the
percent yearlings from the combined seasons were plotted against each respective year
for individual geographic groups to determine long-term trends within age classes.
Regression analyses were done on these data to determine any significant deviations in
the percent yearlings from the long-term mean among years. The regression analyses
tested the assumption that the percent yearlings in the check station biodata each year
represent random fluctuations around a long-term mean with a slope of zero.

The other SAK model assumptions were handled as follows. For the purposes of
this study, estimates of fawn production in Michigan were considered accurate. No data
were available to assess this assumption further. In determining nonharvest mortality for
the SAK model, a constant value has traditionally been used over long periods of time
(Creed et al. 1984). A value of 0.9 has been used for the Michigan deer herd, so this

value was kept constant when determining model estimates. The assumption that buck

21

harvest pressure is uniform from year to year was tested. This assumption also relies on
the stability of year to year values for percent yearling bucks in the harvest data. The
validity of this assumption was determined by evaluating the percent yearling bucks in
the check station biodata, thus the results of the stable age distribution analyses were also

utilized to test this assumption.

Intrastate and Interstate Comparisons

One of the SAK model assumptions is that the biodata are representative of the
herd. It was determined that the best method of testing this assumption was to compare
voluntary and mandatory check station biodata, since mandatory check stations are
assumed to collect representative data about the herd. Check station biodata are collected
on a voluntary basis in Michigan, so data were requested from surrounding states that had
mandatory check stations. Data were requested from Wisconsin, Ohio, and Indiana. One
of the overlying assumptions of this analysis was that the herds in each of these states had
similar compositions. If this particular assumption was not met, then results may be
erroneous due to the fact that equivalent populations were not being tested. To mitigate
this, data from similar geographic areas in each state were requested.

The southern farmland region of Michigan has similar ecological features as
Wisconsin’s southern farmland region, Indiana and Ohio (Albert 1995). This made it
potentially possible to compare the deer herds among these areas to determine if
voluntary check station data are representative of the herd. Mandatory check station data
are assumed by definition to be representative of the deer herd. Voluntary registration, on

the other hand, checks a random, or assumed random, sample of deer from the

22

population. Since one of the assumptions of the SAK model is that the harvest is
representative of the herd, the initial intent was to compare voluntary check station
biodata from Michigan to mandatory check station biodata from nearby states to
determine if the voluntary check station biodata really do represent the herd.

There were too many assumptions and uncontrollable factors involved to be able
to correctly interpret any results. There could be two reasons for this. First, the herds
may have had different compositions. Each state’s data could accurately reflect the
composition of that state’s deer herd, but the herd composition could be different between
states. Secondly, data collection methods in Wisconsin may have been different from
those in Michigan. For example, the major assumption of this analysis was that Michigan
and the other states had herds with similar sex and age compositions. If this assumption
was false, then the trends seen within the check station biodata may not be interpreted
correctly. After examining the biodata from Michigan and Wisconsin, it was determined
that the results of such an analysis were invalid. Therefore, this analysis did not progress,

and no results are presented.

Mortality

The SAK model has three data sources that involve mortality: check station
biodata, mail surveys, and nonharvest mortality. The MDNR collects harvest data
annually from post-hunt mail surveys. These data include the hunting season in which a
deer was harvested and the sex of the harvested deer. Total buck harvest data across
hunting seasons from 1987-1996 were utilized for this study. Nonharvest mortality was

not determined empirically. The MDNR has consistently used an r value of 0.90 in the

23

SAK model, which corresponds to an overall annual nonharvest mortality of 10% for the

deer herd. This value was utilized and kept constant throughout the SAK model analysis.

SAK Model Analysis

All data for the SAK model variables were aggregated into the five geographic
groups shown in Figure 2. These variables included the total buck harvest from mail
surveys, as well as the percent yearling bucks, percent yearling does, and fawn:doe ratios
from check station biodata. There were two models generated for each geographic group.
One model used only firearm check station biodata, while the other model used combined
firearm and archery check station biodata. Both models included total buck harvest
estimates. SAK model results were calculated for each of the five geographic groups in
each year (1987-1996).

In previous analyses, SAK had been shown to consistently underestimate deer
populations, so comparison with a population index was intrinsic to this study (Mooty
and Karns 1984). Deer-vehicle accidents have been a consistent and reliable source of
population trends throughout Michigan and elsewhere (Case 1978, McCaffery 1973), and
were used to compare general trends in the SAK model results. Deer-vehicle accident
data were collected by the Michigan State Police and reported at a county level each year,
so these data were aggregated into the same five geographic groups as the hunting
seasons data (Figure 2). To account for any fluctuations in the number of miles traveled,
deer vehicle accidents were standardized by the total number of million miles traveled
within each geographic group. Total population estimates from the SAK model results

were plotted with annual deer-vehicle accident rates by year (1987-1996).

24

SAK population estimates from the study were also compared to statewide deer
population estimates. Deer herd population estimates were obtained from the MDNR
(MDNR unpublished data). By summing all of the geographic group estimates together
each year, it was possible to determine if the study results were reasonable absolute
estimates of the statewide deer population. Any large differences between the geographic
group sum and the statewide population estimates might indicate that the SAK model
estimates were incorrect. Statewide deer-vehicle accident rates were plotted with

seasonal SAK model results by year to compare trends.

25

RESULTS

Sample Sizes

Historical voluntary check station biodata were aggregated into the five
geographic groups shown in Figure 2. These geographic groups were delineated based on
ecological characteristics and management boundaries. Therefore, some geographic
groups have larger sample sizes than others. Sample sizes were generally larger in the
northeastern Lower Peninsula of Michigan (geographic group 2) than the rest of the state.
Minimal sample sizes were determined for varying confidence levels following
Thompson (1992). If 95% certainty is warranted with a 0.05 degree of precision, then
minimum sample sizes should be 385 deer, for 95% confidence with a 0.10 degree of
precision, minimum sample ’sizes should be 96 deer. All sample sizes within this study
were determined with 95% confidence and a'0.10 degree of precision.

Adequate sample sizes were determined based on total sample size of each sex
and age category (1.5 year old and 2.5 years old and older) by year within each
geographic group. This made it possible to have adequate sample sizes for almost all
geographic groups each year (Tables 1 and 2). Sample sizes dropped below the desired
standards when data were further broken down by age class. Sample sizes from firearm
hunting season were adequate, but archery biodata consistently had smaller sample sizes
than did frrearrn biodata For example, there were adequate sample sizes for firearm adult
buck biodata in all geographic groups and all years, whereas archery adult buck biodata
consistently had less than the desired sample sizes of bucks 2.5 years old and older (Table

1). The same trend was found in adult does, except that both age classes in the archery

26

 

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31

Table 2. Firearm and archery hunting season check station biological data for fawn (buck
and doc) and adult doe (1.5+) white-tailed deer by sex, year, and geographic group.

 

 

 

 

 

a) Group 1

Firearm Season Archery Season 2 1,
Year Fawns' Adult Does Fawn:Doe Fawns Adult Does F awn:Doe X
1987 1087 1326 0.82 43 61 0.70 0.552
1988 284 446 0.64 33 65 0.51 1.000
1989 393 358 1.10 45 89 0.51 15.989
1990 344 558 0.62 50 79 0.63 0.019
1991 405 544 0.74 93 128 0.73 0.026
1992 426 599 0.71 65 126 0.52 3.791 ’
1993 208 252 0.83 91 155 0.59 4.442 “
1994 389 550 0.71 194 318 0.61 1.724
1995 942 1322 0.71 104 264 0.39 23.547 “
1996 390 822 0.47 66 169 0.39 1.528

b) Group 2

Firearm Season Archery Season 2 a
Year Fawns' Adult Does Fawn:Doe Fawns Adult Does Fawn:Doe X
1987 876 1266 0.69 299 276 1.08 22.771 ”°
1988 1086 1483 0.73 241 294 0.82 1.392
1989 785 733 1.07 334 303 1.10 0.093
1990 1094 1621 0.67 317 323 0.98 18.132 ”
1991 976 1266 0.77 446 510 0.87 2.642
1992 789 1 148 0.69 300 396 0.76 1.186
1993 498 679 0.73 256 225 1.14 16.396 ”
1994 239 390 0.61 304 361 0.84 7.905 "
1995 361 682 0.53 271 319 0.85 20.356 “
1996 759 1681 0.45 203 400 0.51 1.464

 

32

Table 2 (cont’d).

 

 

 

 

 

c) Group 3

Firearm Season Archery Season 2 I,
Year Fawns' Adult Does Fawn:Doe Fawns Adult Does Fawnzboe X
1937 505 739 0.64 132 154 0.36 4.945
1933 776 1335 0.56 130 161 0.31 3.456 “
1939 993 1271 0.79 120 143 0.34 0.253
1990 943 1613 0.59 122 99 1.23 23.431 ”
1991 396 603 0.65 195 160 1.22 25.597 ”
1992 215 391 0.55 1 11 173 0.64 1.033
1993 134 236 0.57 103 103 1.05 12.333 "
1994 142 174 0.32 161 137 0.36 0.1 13
1995 353 756 0.47 130 329 0.55 1.642
1996 453 1067 0.43 115 166 0.69 12.997 "

d) Group 4

Firearm Season Archery Season 2 a
Year Fawns' Adult Does Fawnzboe Fawns Adult Does Fawnzboe X
1937 139 264 0.72 77 34 0.92 1.303
1933 396 523 0.75 100 91 1.10 5.733
1939 514 669 0.77 145 119 1.22 11.460 "
1990 364 523 0.69 109 105 1.04 7.232 "
1991 296 434 0.63 125 145 0.36 2.672
1992 264 331 0.30 163 160 1.02 3.126 ’
1993 233 239 0.32 1 17 135 0.37 0.1 10
1994 374 494 0.76 192 163 1.14 10.751 "
1995 322 454 0.71 165 175 0.94 4.757 “
1996 420 631 0.67 174 205 0.35 4.059 “

 

33

Table 2 (cont’d).

9)

 

 

Group 5

Firearm Season Archery Season 2 0
Year Fawns' Adult Does Fawn:Doe Fawns Adult Does Fawn:Doe X
1937 563 574 0.93 63 59 1.15 0.741
1933 567 609 0.93 54 43 1.26 1.994
1939 560 590 0.95 33 63 1.32 3.445 “
1990 493 522 0.94 73 57 1.23 2.651
1991 513 513 1.01 97 96 1.01 0.000
1992 406 41 1 0.99 1 17 92 127 2.632
1993 406 490 0.33 106 131 0.31 0.026
1994 530 649 0.32 132 163 0.79 0.033
1995 543 779 0.70 159 134 0.36 2.353 ‘
1996 323 1025 0.30 140 167 0.34 0.121

 

a: Only known agedeer from check station biodata were used in the analysis.

b: This is a test of the fawn:doe ratios in each harvest season being independent

of harvest methods. Degrees of freedom=l
c: ‘P<0.10, ” P<0.05

34

season frequently had small sample sizes. The exception is for geographic group 2, in
which all age classes for every year, except 1993, had adequate sample sizes. Fawn
sample sizes mirrored those for adult does. Fawn biodata for geographic groups 2 and 3
had robust sample sizes in both seasons every year, while geographic groups 1 and 5
lacked sample size for the archery season (Table 2). Geographic group 4 fawn biodata

had robust sample sizes every year for both seasons except 1987 and 1988.

Seasonal Check Station Comparisons

Biodata for each geographic group were tested for differences among age classes
and hunting seasons. Analyses were for each geographic group for each of 10 years
(1987-1996), and results were determined at a-levels of 0.05 and 0.10. Chi-square
analyses for adult bucks generally rejected the null hypothesis of no difference among age
classes between hunting seasons. Results were significant for all geographic groups for
all years (p50.05), with the exception of geographic group 4, in which 1989 was
significant only at an a-level of 0.10 (Table 1). In all significant tests, there were more
yearling bucks harvested during archery season than expected when compared to firearm
season. A nonsignificant result indicated that the same proportion of yearlings were
harvested in both the archery and firearm seasons.

Adult does were tested under the same null hypothesis as the adult bucks. It was
determined that there was a significant difference between firearm and archery check
station biodata for several of the years within each geographic group tested (Table I). In

all significant tests, there were more yearling does harvested during archery season than

35

expected when compared to firearm season. Chi-square results for geographic group 1
indicated significant differences in 1988 through 1991 and 1995, as well as 1992 (p=0.05
and 0.10, respectively). Geographic group 2 had significant Chi-square values (p=0.05)
for all years, indicating that archery hunters consistently harvested younger deer than
expected in this area when compared to firearm hunters. Results for geographic group 3
suggested significant differences in 1995 $0.05), and in both 1989 and 1996 (p=0.10).
In the southernmost parts of Michigan, only a few years had significant differences
between the firearm and archery biodata. Chi-square results indicated younger deer were
harvested in 1989 (p=0.05), 1990 and 1996 (p=0.10) for geographic group 4, while
geographic group 5 had significant results in 1987, 1991 (p=0.05 for both), and 1994
(p=0.10).

All buck and doe fawns were aggregated as a group against all adult does, and
fawn:doe harvest ratios were tested. The null hypothesis was that check station biodata
collected for the firearm and archery hunting seasons had the same fawn:doe ratios.
Geographic groups 1, 2, and 3 had significant results (p=0.05) for about half of the years
tested (Table 2). Results indicated that geographic group 4 had significantly different
fawn:doe ratios in all years except 1987, 1991, and 1993. The fawn:doe ratios for
geographic group 5 were significantly different in 1.989 and 1995 (p=0.05). In all
significant cases, there were more fawns harvested during archery hunting season than

expected when compared to the firearm hunting season.

36

Stable Age Distribution

Maintaining a stable age distribution in the deer herd is one of the assumptions of
the SAK model. This assumption was tested by combining firearm and archery check
station biodata for all of the adult bucks and does by year (1987-1996). These data were
then separated by sex and age class, and a bivariate distribution of yearlings versus all
deer 2.5 years old and older was created. The percent yearlings for each geographic
group (Figure 2) were then compared for differences over the ten year period (1987-
1996)

Table 3 shows results of the Chi-square analysis. All geographic groups for both
the yearling bucks and yearling does had different percent yearling age classes each year
of the ten year period. Therefore, Chi-square results suggested that a stable age
distribution did not exist throughout the ten year period for any geographic group of
bucks or does (p=0.05).

Regression analyses were also performed on the percent yearlings to determine
how the changes in percent yearlings deviated from a long-term mean over the ten year
period. The null hypothesis tested for the slope equaling zero. Regression results
indicated that geographic group 5 had a significant negative slope for both yearling bucks
and yearling does (Table 4). Geographic groups 2 and 4 had significantly negative slopes
for yearling does (Table 4). No other geographic groups were significant (0t=0.05) for
either sex. The regression analyses suggested that, although Chi-square results indicated
that the percent yearlings were different among all geographic groups and years, the

differences did not have large effects on the long-term mean for each geographic group.

37

Table 3. Combined seasons (firearm and archery) check station biological data for
yearling (1.5) and older (2.5+) white-tailed deer by sex, year, and geographic group.

 

 

 

 

 

a) Group 1
No. of Adult Bucks' 2 b No. of Adult Does 2

Year 1.5 2.5+ X, 1.5 2.5+ X
1987 2385 960 389 998

1988 2492 1 199 164 347

1989 185 1 907 157 290

1990 1971 1542 201 436

1991 2079 1335 213 459

1992 1642 1511 214 511

1993 1996 1742 127 280

1994 4302 221 l 273 595

1995 3094 1645 522 1064

1996 1 1 18 1629 225 766

1072.14 “° 43.29 "
b) Group 2
No. of Adult Bucks' 2 b No. of Adult Does 2

Year 1.5 2.5+ X 1.5 2.5+ x
1987 4230 1592 61 5 927

1988 4085 1827 678 1099

1989 2595 960 391 645

1990 3964 1964 694 1250

1991 3541 1749 588 1188

1992 2419 1299 538 1006

1993 2421 1628 274 630

1994 4188 2107 247 504

1995 4291 1482 362 639

1996 3848 2159 626 1455

403.54 “° 63.55 ”

 

38

Table 3 (cont’d).

9)

d)

 

 

 

 

 

 

 

Group 3
No. of Adult Bucks' 2 b No. of Adult Does 2
Year 1.5 2.5+ X, 1.5 2.5+ X
1987 3133 714 335 608
1988 3312 927 551 995
1989 2 196 632 532 882
1990 2748 1018 591 1121
1991 2659 729 272 496
1992 1981 502 228 336
1993 1824 682 1 l l 228
1994 3194 940 151 210
1995 3350 682 457 628
1996 2471 701 352 331
139.64 ”° 62.60 ”
Group 4
No. of Adult Bucks' 2 b No. of Adult Does 2
Year 1.5 2.5+ X, 1.5 2.5+ x
1987 1328 353 158 190
1988 1506 360 286 333
1989 1540 438 368 420
1990 1309 364 304 329
1991 1313 428 250 329
1992 1 193 429 232 259
1993 1218 500 201 223
1994 2096 605 298 364
1995 1883 550 254 375
1996 1957 533 313 523
74.51 30.15 ”

 

39

Table 3 (cont’d).

 

 

 

e) Group 5
No. of Adult Bucks' 2 b No. of Adult Does 2
Year 1.5 2.5+ X 1.5 2.5+ x
1987 1 142 352 322 31 1
1988 1235 296 342 310
1989 1330 390 340 313
1990 1351 366 295 284
1991 1289 383 279 330
1992 1218 388 231 272
1993 1 169 471 288 333
1994 1779 676 377 440
1995 1682 681 425 538
1996 1839 567 495 697
90.49 40.37 “

 

a: Only known age deer from check station biodata were used in the analysis.

b: Test of null hypothesis of no difference in percent yearlings among years.
Degrees of freedom=9

c: ‘P<0.10, " P<0.05

40

Table 4. Results of regression analysis (n=10) of the slope of the percent yearling bucks
and does from 1987-1996 (see Figures 3 and 4).

 

 

 

 

 

 

Adult Bucks
Geographic
Group Slope Y-intcrcept F‘ P
1 -0.0190 0.7049 4.788 0.060
2 -0.0058 0.7104 1.441 0.264
3 -0.0004 0.7790 0.001 0.980
4 -0.0032 0.7866 0.987 0.350
5 -0.0069 0.7955 6.308 0.036
Adult Does
Geographic
Group Slope Y-intercept F' P
1 -0.0039 0.3276 1.1 15 0.322
2 -0.0085 0.3958 12.938 0.007
3 0.0002 0.3633 0.002 0.969
4 -0.0072 0.4865 5.435 0.048
5 -0.0112 0.5381 42.557 < 0.001

 

41

a: Test of null hypothesis that slope=0, with degrees of freedom 1,8.

Figures 3 and 4 display regression plots of the percent yearlings versus year by
geographic group for bucks and does, respectively. As evidenced on these plots, the
slopes were all close to zero, suggesting that there were no major changes in the
proportion of yearlings over the ten year period. All of the slopes were slightly negative,
except one positive slope for the percent yearling does (geographic group 3). A slope
close to zero (p>0.05) suggested a stable age distribution in each respective geographic
group (Table 4). If there had been a significant positive or negative slope (p<0.05), this
would have indicated a growing or declining proportion of yearlings in the population
over the ten year period. A significantly negative slope was determined for the percent
yearling does in geographic group 5.

To determine the deviation of percent yearlings from the long-term mean within
each geographic group, the long-term percent yearling mean was plotted with individual
percent yearling values for each year (Figures 5 and 6). The largest deviation from a
long-term mean was for bucks in geographic group 1, which had a 19% lower value in
1996 than the long-term mean (Figure 5b). The percent yearling bucks deviated from the
mean by 11% in 1987 in geographic group 1, as well (Figure 5b). Deviations found in
the yearling does were not as extreme. Geographic groups 1 and 3 both had individual
percent yearling does that were 8% lower than each respective mean in 1996 (Figure 6a
and c). These results may suggest which individual years are having the most effect on

the rejection of a stable age distribution.

42

Figure 3. Regression analysis (n=10) of yearling white-tailed bucks by year. Equation is
in the form y=mx+b.

 

 

 

 

 

 

41) Adult bucks: geographic groupl y=-0.019x+ 0.7049
‘ %Yearlings R2=0.3744
Regression line
1 2
.. 0.3 __
50
€ 0.6
8
>1 0.4
.\°
0.2
0 2...-.. _ 2 f .3 _ _
S 3 S S 3 ES '5‘ S '3 3
co co 00 9 Va \0 \G \D \O VD
\l co \9 c r— N u A U! 05
Year
b) Adult bucks: geographic gmup 2 y = -0.0058x + 0.7104
A %Yearlipgs. R2=0.1526
Regressron km
1 f.“ .........................
0.3 1 ........ , ‘
:0 *- ‘fig A A
E 0. 1. f ‘ ‘ ‘ g ‘. fl
I- 4'
8 _.
>. 0.4 E ............
\° 1
° 0,2 ..........
0 ::_TT'T ‘T‘T—w’ * F‘ “7 ‘* "T“ ”T “T" __‘Tfi——*__* —‘
l-I I-I I-t I-i l-l I" 1" l— H l-I
\O \O \O \O \O \0 V9 so \0
co co cc \9 \D \O \D \b \O c
\I co 9 G r-t N 03 A U! ON
Year

43

c) Adult bucks: geographic group 3

A % Wading, y = 113-0451 + 0.779

 

 

_Regression line R2 = 813-05
1 _- , ,
1
0.8 i a . L A ,,,,,,,,
m A t — 1:
5° ‘ t ‘ ‘ 7
- 1
1.. 0.6 3.
3
>.. 0.4 j
\G 2
° 0.2 L .
0 ______2_-- - .. . - .. _24
hi hi l-i l-i l-4 H H H H H
9 9 9 9 9 9
co on as 9 9 9 9 9 9 9
\l co 9 c H N M A (It 65

Year

(1) Adult bucks: geographic group 4

‘ %Yearlings y= -0.0032x+ 0.7366

 

___Regression line R2 = 0 1098
l - ....... , ..... _ ............
., 0,3 3; AI. _.. _, . . ......... A
E 7. - - T A A i i
.h 0.6 -:~— ,. .......
3 1
> 004 _~ rrrrr
e
=\ 0.2 52
0 ‘L—‘——‘——T—_— ‘ V" - '1 '* fiW’— — *“-—5 —'¥ — W‘T—— —
h-I III. III‘ H H H l—i h‘ H H
9 9 9 9 9 9 9 9
co 00 fl 9 9 9 9 9 9 9
\l on 9 G I— N M :3 0| 0‘

44

0.0069x + 0.7955
R2

y=’

e) Adult bucks: geographic group 5

0.4409

% Yearlin gs
Regression line

 

A

A..

 

l

0.4 4.

6. 2
0 0

muéeao> .x.

8.
0

 

45

Figure 4. Regression analysis (n=10) of yearling white-tailed does by year. Equation is in
the form y=mx+b.

 

 

 

 

 

a) Adult does: geographic group 1 y = -0.0039x + 0.3276
%Y 1'
1 ‘ 11.85.1200“... R2 = 0.1223
n 0.8 4. ......
a L
'é 0.6 :2.
a L
9 J
>. 0.4 .3 .
e\° 7‘ ‘ - ‘ a a 9r A A A
0.2 ; A
01— an“. -___ . _ -_~.___—.
2 S G S 3 C3 {'5 {'3 C3 {'3
co co co 9 9 9 9 9 9 9
\1 on se a ~— N u a u- a
Year
b) Adult does: geographic group 2 y = -0.0085x + 0.3953
‘ %Yearlings R2=0.6179
_ Regression line
1 T .....................
0.3 ;
‘6”6 3
E 0.6 1
h _.
8 1
>1 0.4 v:— A_ A A ’A" A rrrrr - ‘ -------
° 7 ‘ _ A ; *-
°\ 0.21- ..... .....
S S E; S G 13‘ "‘ “" 3 1'5
co co co to to e x: 9 so 9
\I no 9 G H N 03 A U! 6‘

46'

c) Adult does: geographic group 3 y = 0.0002x + 0.3633

 

 

 

 

 

°/ Yearlin
A 0 85 2 _
1 _Regression line R ‘0-0002
1
.1. 0.3 11- .e
90 2‘
a 0.6 3L .
3 04 L
. “ . . . ....A A
>; { r 4‘ 'A— ‘ 1 ‘ A A
e\ 0.2 3‘ .................
0 :1“ "—1— " “‘ —“_‘— ‘ 1 —
H H H H H H H H H H
9 9 9 9 9 9 9 9 9 9
co co co 9 9 9 9 9 9 9
\I oo 9 9 n— N u a u: a
Year
(1) Adult does: geographic group 4 y = -0.0072x + 0. 4865
‘ %Yearlings 2
. . R = 0.4045
Regress1on lme
l L
gin 0.83 ....................
=9: 0.6 4 ...............
a 71 fi— .4. A A A
g 0041: ‘. .. . ................. A figflj
o\° 0.2 L; ----------
0 ‘r *g—r" ff— '1' _ “o" * 7* —fi* *r’"
H H I-h H H H l-h H H H
9 9 9 9 9 9 9 9 9 9
co co co 9 9 9 9 9 9 9
\I oo 9 a 1— N u A u- a

Year

47

e) Adult does: geographic group 5

 

% Yearlin gs

 

y = -0.0112x + 0.5381

 

 

A . . R2=0.8418
Regressron lrne
l _ .......
m 0.8 .1... ,,,,,,
E) J
.h 006 J1 A """
a 4 r — A A
0 04 < A + A A A .
>.. . 3 .............. fi,
0
e\ 0.2
0 1 .L_._ 3, - , - L._
H H H H H H H H H H
9 9 9 9 9 9 9 3 9 9
00 co co 9 9 9 9 9 9
\l on 9 O H N N :5 VI 5‘
Year

43

Figure 5. Percent yearling bucks by year and mean percent yearling bucks for the period
1987-1996.

 

 

 

 

 

 

 

a) Adult bucks: geographic group] ‘ % Yearlings
_10yearmean
0.90 T
3’0 0.80 ... . ,,,,,,,
é 4,
S 0.70 A ._
g. 4 ‘ ‘ A A
‘E 0.60 1 A
° A
£5 0.50.7. ...... A ‘
0040 “IT? 4- — fie — +7———-r - ,. L T ‘
5 co Ox 9 —: N m e In 9
co co on 04 en ex ex ex ex ON
ex a as as a as as as as ex
H H H H F! V-I ‘1 F! 1.! fl
Year
b) Adult bucks: geographic group2 ‘ %Yearlings
10 yearmean
0.90 T... . ... . ,, ,, . . _______
En 0.301
.1- 1 A 4
3 0.70 T. .. I' ‘ . ,
>5 .1 ‘ A A A
‘5 0.60 T... ... . .. ,, ....... _ .1 .....
3 1
5 0.50
0.40 -.-; _ ————--+ T_ _L T. .T T __.T.._
1‘ co Ox 9 —1 N n v In so
co co 00 ex ex e~ ex ex ex ex
a ex as 05 01 as as ex a as
F4 H 1‘ III! H v-l H v-i Fl! v-l
Year

49

c) Adult bucks: geographic group 3

 

 

 

__ 10 yearmean
0.90 a ,. ,,,,,
3’» 0.80 A . ‘ .
a f - . = - .
t: 0.70 4 ‘ ‘
0
>. -.
E 0.60 .
0
E .
m 0.50
0.40 4— 7-!— .. i __ u . !
b ca 0‘ Q r-I N M V ID NO
co co no as a a ex a as a
a 5‘ a 0‘ ON Q 5‘ OK 0‘ OK
fi fi v-l Fl! '1 F1 I-I v-I '— VI!
Year
d) Adult bucks: geographic group4 ‘ % Yearlings
_ 10 year mean
0.90 if
m .
”0.80 t" A A A ,, g r ‘
oh _‘ ‘ ‘ -
a 0.70 A- i . a A
0
>‘ 'i
E 0.60
3 .
Emma.
0.40 4__. .,-_?.a_-+ _a ..- A.“ a _i
5 co a c .- N m v m e
co co an a as ex a an ex ex
a a ex ex ex a a an a a
v-t fl !-1 ‘1 fi fi VI! v-I v-i Fl!
Year

50

% Yearlings

A

e) Adult bucks: geographic group 5

10 yearrnean

 

 

 

4| . Ar ..wl . i
0 0 0 0 0
3 8. 7. 6. 5
0 0 0 0 0

$5.39» Hookah

 

i @3—

- mg—

33

. Ma—

r Naa_

33

. c3—

. $3

., awa—

0.40 +_ _

5a—

51

Figure 6. Percent yearling does by year and mean percent yearling does for the period
1987-1996.

a) Adult does: geographic gmupl . %Yearlings
_ 10 year rman

 

Percent yearlings
:
.5
G

 

 

 

 

4 ‘ ‘
" A A A
0.30 . ._ A A _ .............
A
j
a; A
0.20 4— , ....... fl . _ . . “A ,. .1
b no a c 1-4 N m w m e
co co on a a as as ex a as
a as ex ex ex ex ex a as as
1-l 1-1 1-I 1-i 1d 1-‘ 1-! 1-1 1-i 1-l
Year
b Adult does: eo '
) g graphic gmupZ 0/ Year'
‘ 0 hug
_ 10 year mean
0.60 in?
m l
a l
E 0.50
a. .1
3 i
>. 0 40 f A , .. .. _
E ‘ J A A
j A ' A
a 0030 ,._ ......... ‘ _____________ ‘
9 7
Eu 1
0020 — fi—.——~-— . ——4 A. .... __ ....» -_ l
h on as c — N m v m o
co no no ex ex ex Ox ex ex ex
a as as as a as ex a as ex
1-1 1-! 1-1 Fl! Fl! 1-! 1-l 1-1 1-1 1-1
Year

52

‘ % Yearlings
_. 10 year mean

c) Adult does: geographic group 3

A

 

A ,
A . . 0000000 A‘4 . lit 4
A A A .

0 0 0
<~ .3 .a
0 0 0

«ma—La?» «:09qu—

. gag

A. may

 

. ea:

mag
Ng—

r.
E: a

A caa_

. $3

. awa—

A

. baa—

0
2
0

‘ %Yearlings
_ 10 year mean

d) Adult does: geographic group 4

0.60 _

 

A A A
_
A A
A. A
A
w A
, A A
A
A
‘ ,.
, A
A , A
A A
A
A ,
. . A AA... . . . _ ., . A . . b
0 0 0 0
5 4. 3 2
0 0 0 0
3.5.3?» 2.3.8.—

, wag.

A moa—

vam—

mg—

mg—

33

Year

. .33
. ama—

. wwa

ham—

53

 

mm

.m m .

w w

%w

. _
5
n.
u
m A
on
.0
mW A
m
cu
m A
05
m A _
m “at?“ 04A0.
t

,p cm A” 1w

Um no .u no .u
M uni—.39» 239:5
e

eam~

maam

A vaom

. maa~

. Na¢~

. —aa—

. camu

—.
' AA__

0.20 H

awa—

awa—

bwau

Year

54

SAK Model Analysis

Population estimates were determined for each geographic group using the SAK
model. The total buck harvest was calculated from a county level basis to fit the
five geographic groups in Figure 2, and the percent yearling bucks and yearling does as
well as the fawn:doe ratios were obtained from check station biodata. There were two
models calculated for each geographic group, one with firearm biodata only, and the other
using firearm and archery biodata combined. The traditional method of using only
firearm biodata in the SAK model could, therefore, be compared to a model containing
the archery harvest, and any effects that an increasing archery harvest may be having on
model results could be determined. All models were done for years 1987-1996, and the
total buck harvest was used in each model. The lifetime recovery rate was kept constant
at 0.90. Deer-vehicle accident rate data were also aggregated into the five geographic
groups (Figure 2). There were problems with two years of deer-vehicle accident data.
First, no mileage data were available for 1987 and 1992; secondly, deer-vehicle accidents
were collected in only parts of Michigan in 1992. Therefore, deer-vehicle accident data
for these years were not represented on the plots.

Population estimates from both the firearm and combined seasons SAK model
results were plotted on the same graph, along with the deer-vehicle accident data (Figure
7). This was to detect any similarities between the trends in deer-vehicle accidents and
SAK model results. Plots were constructed to determine if model results indicated the
same trends as those of a reliable population index from a completely different database.

In general, the results suggested that the trends were similar, but there were some

55

Figure 7. SAK model results using firearm and combined seasons (CombSeas) data

(firearm and archery) and deer-vehicle accident (D-V Rate) trends plotted against time.

a) Geographic group I

..A Firearm + CombSeas ... D—V Rate

  

 

 

600,000 . -A- A .AA._ AA AAAA A- _ ,
525.000; ...... ,,,,,,,,,,, A? _5’:
450,000; l
E» 375,000 . . . . A ............. *
2.; 300,000i.. :
2 225,000.; L;
150,000 A. . . . . . .. .. F
75,000 , l V A. w. w. , ,, , +
0 AA . __ . A , __ __. AAA _____ ___ ___!"
h 00 ON a — N M V In \0
co co co 0‘ Ox G's as a Ox ON
2 2 9. a 9‘. 2 a a 2 2
Year
b)Geographicgroup2
..A Firearm + Cotheas ..A D-V Rate
l-
8
“B
#-
Q
6
z

56

 

D-V accident rate

D-V accident rate

c) Geographic group 3

No. of deer

_.__ Firearm + CombSeas ... D-V Rate
600,000 77 . __——— A 4 . - 2.80

525,000 3 f

 

450,000 3 .
375,000 1

300,000 .1
225,000 A

ALALA

150,000 7 f ..

.LA—f

75,000 if

 

o i}-..-

l‘ Q 03 c .- N M Q '0 0

co Q on as a 01 ON 0‘ 63 03

03 9‘ OK as a a ON Ox as as

— _ _ _ _ H — — — _
Year

d) Geographic group 4

No. of deer

_._ Firearm + CombSeas _._ D-V Rate
600,000 AAA _A AA -.A ' A_ A- _A_ A__._AA_ AA- AA ___- 2.80
1 -.

525,000 A . , _. ... - 2.40
450,000 - ,w w - -. A ------ ...... E 2.00
375,000; ._ . ._ -, _ ......... ’

  

225,000? _____ - ---------
150,000 % .. _- _ -. ;

75,000 1

 

0 ;A A .- -_ A -AA AAAA AA A AA .-.-AA AAAA- -Al 0.00
\O

h on a c - u v m
a s a a s. a a a s a
Year

57

D-V accident rate

D—V accident rate

e) Geographic group 5

No. of deer

No. of deer

_._ Firearm + CombSeas _._ D-V Rate

 

 

 

 

 

 

 

600,000 AAAA - - - A - _ - AA- A 2.80
525,000 5. . , ., . 2,40
1'
450,000 g- . . . . . . . 2 00
375,000 ? E
300,000 ‘
225,000 1
150,000 f
75,000 3-
0 A . AAA -- ,_ _ i 0.00
h co & O —' N N) V In ‘6
co co Q a 0‘ 0‘ 9‘ ON 0‘ O
a. a a a a a a e a a
Year
1') Statewide
_._ Firearm + CombSeas _._ D—V Rate
2,250,000 :-- A A A -AAA-AAA AA 2.30
2,000,000 3-
1,750,000 L
1,500,000 L _ '
1,250,000 1 _V. .
§ .L
1,000,000 3L ,,,,,,,,, i 1,20
750,000} . . .. ., £
250,000 L L ”'40
0 0 .AAA A A A A AA A, A AA A A A AA. AAA .A3 0.00
b a .— N n v in e
a g a i a 3 a 3 3: 3
Year

58

D-V accident rate

D-V accident rate

deviations. There were also differences within the model results for firearm and
combined seasons data. There were some results that suggested trends were moving in
opposite directions.

Although the two hunting seasons results tracked each other fairly well in all
geographic groups, there were certain years in which differences existed by as much as
12% between the two population estimates (see Appendix B). Charts corresponding to
these analyses can be found in Figure 7. Individual geographic groups had slightly
different results from each other due to the geographic area the data came from, density
independent factors, and regulation processes in each area. Geographic group 1 showed
some divergence between the two model estimates, particularly in years 1989 and 1995,
with deviations of 11% and 9%, respectively (Figure 7a). There was consistency
throughout the ten year period, however, in that population estimates based on firearm
season data were always higher than population estimates based on the combined
seasons. Although the population estimates in geographic group 1 tracked the deer-
vehicle accident rates fairly well, in 1995 and 1996 the deer-vehicle accident rate rose
while the population estimates from the SAK model declined.

There were a few disparities within the results for geographic group 2. Although
the firearm and combined seasons SAK model results generally tracked each other, there
was a 12% difference between the two in 1991 (Figure 7b). The other years in this
geographic group had deviations between 2-8%. As for geographic group 1, the firearm
season estimates were consistently higher than those for the combined seasons data.

Deer-vehicle accidents had a deviation from SAK model results in years 1994-1996

59

(Figure 7b). The deer herd appeared to be stabilizing in these years according to the SAK
model results, but the deer-vehicle accident data suggested that the herd had steadily
increased over the last few years of the study period.

The results in Figure 7c for geographic group 3 showed almost identical
population estimates for both SAK model results, with the largest difference between the
two being 4% in 1995. Unlike geographic groups 1 and 2, in years with deviations,
neither model consistently produced higher population estimates. Comparison of these
outcomes to deer-vehicle accident rates for geographic group 3 generally indicated
similar trends. There was a large discrepancy in 1995, in which deer-vehicle accidents
continued an upward trend, but the combined seasons population estimates dropped from
384,724 in 1994 to 345,004 in 1995, then up to 480,791 in 1996 (Appendix B). This
corresponds to a 10% drop in the deer herd estimates in 1995, then a 28% increase in
1996.

P0pulation estimates based on firearm biodata and the combined seasons biodata
in geographic group 4 were very similar. The largest deviation was 4% in 1993, but six
of the ten years had deviations less than or equal to 1% (Figure 7d). This geographic
group also appeared to track deer-vehicle accident trends (Figure 7d). There were minor
discrepancies in 1990 and 1994, in which the deer-vehicle accident trend was opposite of
the population estimates. Results of geographic group S were expected to be similar to
those of group 4, since both geographic groups are located in southern Michigan. The
firearm and combined seasons population estimates were very similar for both geographic
groups, but firearm season estimates were consistently higher than those for the combined

seasons in group 5 (Figure 7e). Deviations for this geographic group ranged from under

60

1% in 1988-90 and 1992 to 4.2% in 1987 (Figure 7e). The population estimates and
deer-vehicle accident trends seemed to track for geographic group 5, although there were
a few minor discrepancies. In 1989 through 1991, deer-vehicle accidents slightly
decreased, whereas the population estimates increased slightly. The opposite was true for
1993 to 1994.

Statewide SAK model analysis were also done to compare statewide population
estimates of the firearm and combined seasons SAK model results to estimated statewide
population estimates for 1987-1996. Figure 7f shows SAK model results of the two data
sets compared to deer-vehicle accidents. Firearm season population estimates were
consistently higher than those for the combined seasons, deviating from 0.9% in 1987 to
5.2% in 1992 (Figure 70. Both population estimates followed the same pattern. Model
results and deer-vehicle accident rates indicated similar trends statewide. Both increased
from 1993 through 1996, although deer-vehicle accidents were steady from 1989 to 1991,
while SAK model population estimates indicated a slight decline in 1990. Comparisons
of the statewide SAK model results to historical statewide SAK model population
estimates showed a range of differences less than 1% in 1987 and 1993 to 15% in 1988
when compared to the firearm season biodata (Appendix B). Differences in population
estimates ranged from 2% in 1987 to 17% in 1988 and 1995 when the combined seasons
biodata were compared to statewide population projections (Appendix B). This indicated

that the SAK model provided good population trends on a statewide scale.

61

DISCUSSION

This study was done to determine the role archery harvest statistics should have in
a particular harvest-based population model. The SAK population model was developed
as a population estimator for deer herds (Eberhardt 1960). Traditionally, firearm check
station biodata have been used as data sources for population models because very little
data were available from the archery and muzzleloader hunting seasons in Michigan. As
the archery season increased in popularity and became a larger proportion of the total
harvest, the question of how archery harvest biodata should be incorporated into the SAK
model became pertinent.

One component in solving the problem of integrating archery harvest statistics
into the SAK model is determining how the model is being used by managers. If the
SAK model is used to provide an index, then the results of the study only need to
demonstrate the same trends as that of other substantiated indices. For example, this
study compared trends between the SAK model and deer-vehicle accidents. The data sets
were from independent sources, so any similarities in the trends would demonstrate that
SAK is a good index of population fluctuations. If, on the other hand, the SAK model is
being used to provide population estimates, then SAK model results should have
confidence intervals associated with them. This would involve determining variance
estimators for the model itself. Although these confidence intervals would aid managers
in determining the precision of the SAK model results, no variance estimators are

currently available.

62

Sample Size

Having biodata in a usable format was important to this study, as was having an
adequate sample size throughout the study areas. Although biodata were collected
throughout the state each year at highway check stations and field offices, there were both
years and geographic areas for which very little biodata were available. The amount of
biodata available contributed to small sample sizes in the 19605 and 19705, so more
recent years were utilized for the study. Bow hunting started to become very popular in
the 1980s, so more harvested deer from archery season were sexed and aged at highway
check stations and field offices during this time. This led to an overall increase in sample
sizes of check station biodata, with an increase in sample size from the archery hunting
season starting in the mid 19808. Because the increase in archery harvested deer
coincided with an increase in the number of samples at the check stations, data before this
time period were not as critical in determining the effects of the archery season on harvest
statistics.

One of the objectives of this study was to analyze all data at the district level.
This would have provided the district managers a complete analysis of each respective
district. Since check station biodata were collected by county, data were aggregated at
the county level into districts. Once the data were aggregated, however, sample sizes
were very small for some of the districts. Therefore, larger geographic areas were needed
to provide adequate sample sizes for the study. To obtain better sample sizes while
keeping with the intent of providing information to district biologists, Albert’s (1995)
study on similar land types throughout the Great Lakes area was referenced. Information

on similar soil and climatic conditions provided a framework for the five geographic

63

regions shown in Figure 2.

The five geographic areas used in this study were constructed for two reasons.
First and foremost, sample sizes from check station biodata were very small at a county
level, and some of the district level data had small sample sizes, as well. The second
factor involved in the formation of the geographic groups was the applicability of the
study results to different areas of the state. Even though archery sample sizes were small
in some geographic groups, these groups were maintained throughout the study. The
analysis would not have been as usefirl to managers if larger geographic groups were
used. Most of the total sample sizes in Tables 1 and 2 had adequate precision, but it was
the delineation of samples into age classes (i.e. into 1.5 year old and 2.5 years old and
older) that caused sample sizes to drop below the desired level of precision.

Obtaining robust sample sizes for all of the geographic areas was more
complicated than it may appear. Tables 1 and 2 indicated that sample sizes for antlerless
deer and archery hunting season data were the least represented. This may be due to
hunting regulations or to the methods that have been used to collect biodata. For
example, there is no firearm antlerless harvest in some counties, thus contributing to
small sample sizes. The northern tier of counties in the Upper Peninsula did not have any
or had small geographic areas open to firearm antlerless hunting throughout each year of
the study. Although the availability of antlerless permits varied throughout the northern
Lower Peninsula each'year, Crawford and Roscommon counties either had no areas or
very small geographic areas open to firearm antlerless hunting throughout the study
period. Individual years were also variable. Most of the northern Lower Peninsula was

closed to firearm antlerless hunting in 1994, with a scattering of permit availability in the

64

northeastern and northwestern portions, respectively. All of these areas were open for
firearm antlerless hunting in 1989, 1990, and 1996, except for parts of Crawford,

Roscommon, and Kalkaska counties.

Data collection methods may also contribute to small sample sizes. Location and
operation hours of field offices and highway check stations should be evaluated.
Highway check stations are only open during portions of the firearm season. Therefore,
the majority of the archery biodata collected is from hunters checking harvested deer at
field offices. This data collection method may not encourage hunters to have archery
harvested deer checked. Not only are field offices closed on weekends, but they may not
be located near main roads so that archery hunters can conveniently have harvested deer
checked. Increasing the sample size of archery harvested deer may require opening
highway check stations during archery season or to have field offices open on weekends.
If trends in archery harvest continue to increase, the MDNR may want to consider these
options.

Some problems with sample sizes were found in specific geographic areas. In at
least one instance, a single county contributed more samples than the surrounding
counties, thus possibly driving the results for the whole area. In the Upper Peninsula
(geographic group 1), Menominee county had a high deer density and antlerless harvest
was permitted during the firearm hunting season, whereas most of the Upper Peninsula
had not had a consistent antlerless harvest for the years of this study (1987-1996).
Additionally, there were few deer checked throughout the rest of the Upper Peninsula in
relation to Menominee county. For example, no firearm harvested adult does were

checked from Alger, Baraga, Keewanau, Luce, and Schoolcraft counties in 1992.

65

Menominee county, on the other hand, contributed 70 of 168 and 155 of 432 yearling and
2.5 years old and older does, respectively, to the firearm check station biodata in 1992.

There were similar findings for the other nine years of the study. Therefore,
Menonrinee county contributed the majority of samples from this geographic group, and
this should be considered when the results of this study are reported. One solution to
obtaining sex and age data for a larger portion of the Upper Peninsula may be to open a
highway check station near the Mackinac bridge. Theoretically, this would give hunters
who live in the Lower Peninsula, but who hunt in the Upper Peninsula, an opportunity to
have harvested deer checked at a convenient location. This would contribute to larger
sample sizes with broader geographic ranges being represented.

Another area of the state that had small sample sizes was the southernmost two
tiers of counties. In this area, individual counties had few deer checked each year. This
occurred even though hunting was popular, the deer population was healthy, and there
had continually been firearm antlerless permits available. One reason for small sample
sizes in these counties may be due to landowners hunting on their own land. Hunters do
not have to travel as far to go hunting in this area, and may be less likely to bring a
harvested deer to a field office for aging. There are also no highway check stations in the
area. Weekend hours at field stations and deer check stations on county roads may aid in
increasing sample sizes.

Archery hunting season biodata had small sample sizes each year, even when the
geographic groups were considered. The only exception to this was in the northeastern
part of the Lower Peninsula (geographic group 2), in which sample sizes were robust at

the geographic group level. If managers want to have an adequate number of deer

66

checked on a county or management unit level, an effort must be made to increase sample
sizes. If managers could be satisfied with a 10% degree of precision with 95%
confidence, then a sample of approximately 100 known age deer from each county or
wildlife management unit would be needed. If a 5% degree of precision is required, then
at least 385 deer would need to be checked. These sample size estimates are for each
season. Therefore, 100 bucks and 100 does and 100 fawns would be required for each
hunting season in order to have adequate sample sizes for analysis within 95%
confidence. If adequate sample sizes are not met, then data need to be aggregated into
larger geographic groups. As long as the data are used correctly, having adequate sample

sizes ensures that test results will be reliable.

Seasonal Check Station Comparisons

Biodata used for this study were collected over many years by MDNR staff and
volunteers. These data are the major source of statewide deer herd information that is
used for long-term population trends and estimates. As the archery hunting season
increased in popularity over the years, there was concern that different age ratios of deer
were being harvested in each hunting season. The problem was to determine how, if at
all, the archery season was affecting deer herd statistics. Therefore, when changes in the
archery hunting season statistics were observed, an initial study was done in 1993 to
investigate how these changes were affecting hunter success, deer herd composition, and
to investigate whether hunting regulations should be changed due to the changing harvest
statistics (Langenau et a1. 1994). The current study is a continuation of the one in 1993,

emphasizing how archery harvest statistics should be incorporated into a SAK harvest-

67

based population model.

Archery harvest has continually increased in Michigan since the 19605. Archery
biodata have been collected as long as hunters have employed this method, thus giving
the MDNR an opportunity to track changes among the hunting seasons through time.
Differences in sex and age ratios between firearm and archery hunting seasons were the
first questions this study addressed because the SAK model is harvest-based. To
determine how archery harvest data should be incorporated into the SAK model, it was
necessary to determine (1) if archery harvest biodata are significantly different than
firearm harvest biodata, and (2) if the inclusion of archery harvest biodata into the SAK
model altered population trends.

Results of this study suggested that archery hunters checked a different age ratio
of deer at the check stations when compared to firearm hunters for some geographic
groups for some years. Therefore, archery hunters either harvested a different age
composition of deer than firearm hunters, or archery hunters were selective in which deer
were brought to the check stations. There was no indication of hunter selection in the
check station biodata. Hunters have been receiving patches for bringing harvested deer to
check stations since 1972, so this has mitigated any sex or age biases in the data (MDNR
unpublished data). If the assumption of check station biodata adequately representing the
herd was true, then the archery harvest may have affected local herd sex and age
compositions. Since this assumption could not be tested, no definitive conclusions could
be made.

More younger adult bucks were harvested during the archery hunting season than

expected in all years of this study. The same was true for adult does in about half of the

68

results. It was also found that the fawn:doe ratio was larger in the archery season than
expected for approximately half of the study results. These results were similar to those
reported by Langenau and Aho (1983) regarding the impact of firearm and archery
hunting on deer populations. In their study, Langenau and Aho (1983) found that the
proportion of fawns and adult does harvested during archery season was larger than the
same respective age class during the firearm season in the Midwest in 1980. Specific
reports for Michigan stated that the percent of yearling bucks was higher in the archery
season than during the firearm season, as were the percent of adult does (Langenau and
Aho 1983).

It has been reported that archery harvest pressure can have an impact on firearm
hunter success in enclosed areas (Langenau and Aho 1983), but no studies were found
that determined this at county or regional levels. Deer behavior has also been
documented to vary among different sex and age classes (Nixon et al. 1994, Beier and
McCullough 1990), but no studies were found to link these differences to harvest sex and
age biodata. More studies are needed to determine whether biological factors, equipment
bias, or hunter bias are causes for differences in harvest sex and age compositions
occurring between the hunting seasons.

Biological differences have been analyzed by Coe et al. (1980). Their study
focused on the vulnerability of solitary and grouped white-tailed deer, but found no
conclusive results on sex and age ratios. For example, they determined that day-to—day
changes in harvest sex and age ratios suggested which sex and age class of deer were
more vulnerable, thus being dependent on the hunting methods employed. The study did

not differentiate between hunting techniques (Coe et a1. 1980). Comparing the

69

inconclusive results of Coe et al. (1980) to the differences suggested in this study does
not lead to any apparent conclusions. Additional studies are needed to determine if
differences in sex and age ratios of harvested deer between firearm and archery hunting
seasons are due to biological or hunter-related factors.

Although no studies could be found to directly relate the comparison between
firearm and archery hunting seasons, studies have determined that equipment and
experience are factors in archery hunting success rates. Gladfelter et al. (1983) found that
the use of a compound bow gave archery hunters a 1.40 greater chance of harvesting
white-tailed deer than the use of traditional archery equipment. Their study also
determined that previous archery hunting experience increased success rates, but that the
number of days hunted did not have a direct relationship with success rates (Gladfelter et
al. 1983).

Ditchkoff et a1. (1996) found comparable results to Gladfelter et al. (1983) when
success rates between compound bow use and traditional bow use were compared.
Ditchkoff et al. (1996) also determined that although total harvest and the numbers of
bucks and does harvested were greater during compound bow hunts, deer population
estimates and fawn:doe ratios did not change with equipment type. Although the current
study also found no differences in deer population trends between firearm and combined
seasons SAK model results, it was suggested that there were different sex and age ratios
between the seasons. This may be due to the comparison of firearm and archery
equipment instead of the comparison of various types of similar equipment such as the

other studies had done.

70

SAK Model Assumptions

Meeting the assumptions of any model is an important step in having reliable
results. This study assessed some of the SAK model assumptions, and determined if the
deer herd in Michigan, or at least the data collected for the herd, adheres to these model
assumptions. One assumption, that of the harvest being representative of the herd, was
addressed in the interstate comparison part of this study. Another assumption, that fawn
productivity is measured accurately, was assumed to be correct and, therefore, not tested.

The assumption of a stable age distribution in the SAK model was tested by
comparing the percent yearlings in the biodata over a ten year period (1987-1996). In
those geographic groups with significantly different percent yearlings, there was not a
stable age distribution over the ten year period. There were differences in percent
yearling bucks and percent yearling does among years in geographic groups 1 and 2.
Deer from these geographic groups live in an area that typically has harsh winters, and
there is probably a density independent factor involved. Therefore, even though the
overall percent yearlings changed in these areas, it may not be due to the proportion of
deer harvested during the archery season. Severe winters may in fact be determining the
age distributions. For example, if the same proportion of fawns were recruited each year
over a ten year period and there was a heavy over winter fawn loss in years 3 and 7, then
the percent yearlings in the combined harvest would be different in years 4 and 8 without
any influence from the harvest.

Chi-square analyses resulted in the rejection of a stable age distribution for all
geographic groups. McCullough (1979) also found that the deer herd in the George

Reserve did not have a stable age distribution when it was tested with a goodness of

71

fitness test. McCullough (1979) determined that bucks more closely approximated a
stable age distribution than did does. Regression analyses found that one out of five
geographic groups for percent yearling bucks had slopes significantly different than zero.
Two out of five geographic groups had significant slopes for percent yearling does. This
suggested that bucks had a slightly higher proclivity for a stable age distribution than did
does, which concurs with the results of McCullough’s (1979) study.

Percent yearling deviations from long-term percent yearling means indicated that
fluctuations were random. By studying how large the deviations were from each
respective mean, it was determined if the long-term mean should be used to meet the
assumption of a stable age distribution. If the individual percent yearling values are close
to the long-term mean, then the assumption of a stable age distribution may be met by
using these instead of the long-term mean. Conversely, the long-term mean may meet the
assumption of a stable age distribution because it demonstrates the trend within the
population over a number of years. This may be especially important in areas where
density independent factors, such as weather, have a major impact on the deer herd.

Regression analyses were done to determine if the slope for percent yearlings was
significantly different than zero among years. These results indicated that although the
percent yearlings fluctuated between years, the slope was not significantly different from
zero in many of the geographic groups (Figures 3 and 4). Therefore, there were random
fluctuations around each long-term mean. This suggested that the assumption of a stable
age distribution may have been met in those geographic groups. To be sure that the
fluctuations in individual percent yearling deviations were not affecting population

estimates, the SAK model was used as an index rather than as a population estimator.

72

Therefore, population trends were emphasized instead of any absolute population
estimates.

One assumption tested was that the buck harvest pressure is uniform from year to
year. This was tested by the same techniques that were used in determining if there was a
stable age distribution for bucks. According to Burgoyne (1981), the percent yearling
bucks in harvest check station biodata is an expression of the mortality or exploitation
rate, in which the proportion of deer in the youngest age class is approximately equal to
the annual mortality rate. Therefore, the percent yearling bucks is actually used for two
purposes within the SAK model. It is not only a measure of the age structure of the herd,
but it is also a measure of buck exploitation. The same analysis answers both questions.

Since the Chi-square tests rejected the hypothesis of a stable age distribution, the
assumption of a uniform buck harvest was also rejected. However, results indicated that
there were only random deviations around the long-term mean for each geographic group.
These deviations can be accounted for in three ways - either by differential vulnerability
of the age class each year, by a missing cohort that is reflected in later years, or by
sampling error for those geographic groups with slopes of zero in regression analyses.
Secondary factors, such as weather on opening day and throughout the hunting seasons,
standing corn crops, food availability for deer, and hunter distributions may all be factors
affecting the buck harvest pressure.

Results suggested that harvest pressure on bucks was not uniform from year to
year. This may indicate a change in mortality or exploitation each year, but does not
reflect any changes in recruitment (Burgoyne 1981). If the assumption of a uniform buck

harvest is violated, the total buck mortality and the number of bucks predicted will have

73

reciprocal outcomes in the SAK model. For example, if the percent yearling bucks
decreased significantly from year 1 to year 2, then the total buck mortality in the SAK
model would decrease while the number of predicted bucks in the population would
increase. The same holds true if the scenario is reversed, and similar results will occur if
there is no stable age distribution in the percent yearling bucks. Therefore, if the buck
harvest pressure is not uniform from year to year, it will affect the total population

estimates of the SAK model.

SAK Model Analysis

The SAK model was developed at a time when deer herds were smaller, and does
were protected so that herds could expand. The model, therefore, relies heavily on buck
harvest and the percent yearling bucks as data for the SAK model variables. If the
percentage of yearling bucks in the check station biodata begins to change, this will affect
model predictions. Having multiple hunting seasons with varying proportions of the herd
being harvested in each season may also alter the sex and age ratios used in the model if
combined seasons data are not used. I

One of the advantages of using the SAK model is its versatility in regards to
model parameters. Accurate sex and age ratio data are required as model parameters, but
these data can be obtained from either observational indices or harvest data (Creed et al.
1984). The SAK model can incorporate any form of reliable sex and age ratio data in
place of check station biodata. This may be convenient in areas where no or very little
antlerless firearm hunting is allowed. Since the Michigan archery license is either-sex,

samples should always be available from checked deer during the archery season. The

74

only other data source that could be utilized for these parameters in Michigan comes from
annual statewide summer herd observations. Summer herd observations have been
recorded in Michigan since the 19305 (MDNR unpublished data), and were considered an
alternative source of sex and age composition data for the SAK model at the beginning of
this study. Once preliminary analyses were done, however, it was found that this data set
could not be used.

Assessment of summer herd observations determined that the data were not
reliable, and could not be substituted into the SAK model. The major reason for this was
a lack of standardization in data collection methods. In some parts of the state, collection
methods were rigorously followed, and the data were collected in a scientific fashion each
year, while in other areas summer herd observations were not done to any standards. Sex
and age ratios obtained from such data sources were unreliable, so no substitution for
harvest data was done when model parameters were analyzed.

Other studies have also found that herd observations vary across time and habitat.
Downing et al. (1977) found that even with strict methodology, fawns were observed less
often than does in the late summer and early fall, and adult bucks and does had different
observation rates except in August and November. Another study compared behavior of
radio-collared deer to systematic dawn and evening counts (McCullough et al. 1994).

The authors found three major sources of error in herd composition counts: differences in
habitat use, in deer activity, and in deer behavior in relation to the observer.
Standardization of both the methods used and the routes taken controlled some of the
errors associated with herd composition counts (McCullough et al. 1994). If summer

herd observation data are going to be utilized in the future as a resource for the SAK

75

model in Michigan, then data collection methods should be standardized across the state,
and perhaps training courses should be implemented for teaching proper techniques.

The only other data source needed for the SAK model is the number of bucks
harvested in a season or the total buck harvest across all seasons. These estimates were
obtained in Michigan by utilizing mail survey data. Total buck harvest estimates were
used in this study instead of season-specific harvest data because total buck harvest
estimates include all legally harvested deer. Both applications of the SAK model,
therefore, utilized yearly total buck harvest estimates.

The lifetime recovery rate was set at 0.90 throughout all of the geographic group
SAK model analyses. This enabled the analysis to truly test for differences in model
results when each type of seasonal biodata was considered. The nonharvest mortality rate
probably differs by geographic area across Michigan, although there have not been
extensive studies to determine the actual rates. Survival and mortality rates from
localized studies, however, may aid in determining nonharvest mortality at larger scales.
Sitar (1996) determined survival rates for yearling and adult deer in Presque Isle,
Montrnorency, and Alpena counties of Michigan. Nonharvest survival rates for yearlings
in 1994 and 1995 were 0.761 and 0.791, respectively, and were 0.581 in 1994 and 0.572
in 1995 for adult deer (Sitar 1996). A study done in the eastern Upper Peninsula
deternrined annual survival rates of 0.88 for yearling does, 0.29 for yearling bucks, and
adult survival of 0.77 and 0.23 for does and bucks, respectively (Van Deelen 1995).

Another data source for determining nonharvest mortality may be winter severity
indices (WSI) that are recorded each year at stations throughout the state. Some of the

measurements included in this index are ambient temperature, snow depth, air chill, and

76

snow pack yield (V errne 1968). Measurements are recorded weekly across Michigan,
and the severity of the winter is assessed. This index may serve as a measure of density
independent mortality and, therefore, be used as a factor in determining annual
nonharvest mortality rates. These data should be evaluated to determine if WSI values
correlate with other population indices or dead deer surveys.

Deer-vehicle accidents were compared to the SAK model results. Jahn (1959)
concluded that deer-vehicle accidents did not correlate with harvest trends; however, his
study did not account for variable proportions of antlerless deer in the harvest.
McCaffery (1973) determined that deer-vehicle accidents correlated with buck harvest in
a mandatory registration setting. Case (1978) found that the annual numbers of road-
killed animals were correlated with other population indices. Deer-vehicle accidents have
also been found to correlate with the firearm buck harvest in Michigan (MDNR
unpublished data), thus the accident rate is considered a reliable population index.

Different factors affected SAK model results for each of the geographic groups.
Group 1 had similar trends between the firearm and combined seasons population
estimates, but these did not match deer-vehicle accident trends throughout the ten year
study period. There are many reasons why the SAK population estimates may have
differed from deer-vehicle accident trends, among them were variable weather in the
Upper Peninsula, small sample sizes, or the number of antlerless permits available each
year. Variable weather is a density independent factor, hence the lifetime recovery rate
would need to be changed to incorporate nonharvest mortality that might occur due to
weather conditions. Small or clumped sample sizes may also affect trends in SAK model

analysis. Both factors would increase the error in population estimates. Since geographic

77

group 1 is a compilation of the entire Upper Peninsula, it is also difficult to determine if
data from a small proportion of the geographic group is having a larger impact on
population estimates than the area as a whole.

Population estimates for geographic group 2 showed general agreement between
population estimates from the two seasonal data sets, but deer-vehicle accidents differed
from these estimates in 1993-1996. Regression results from the stable age distribution
analysis for this geographic group suggested that although the overall slope for yearling
bucks was not significantly different from zero, yearling does had a highly significant
negative slope (p<0.01). It appeared from the regression data that the herd was not
increasing, and it cannot be determined from available data why the deer-vehicle accident
trends and the SAK model results were so different for these years.

Geographic group 3 had similar trends between SAK model predictions and deer-
vehicle accidents from 1987-1993. In 1994, the deer-vehicle accident rate had an upward
trend, whereas the population estimates showed a decrease in 1995 then an increase in
1996. The drop in 1995 may have been affected by the availability of antlerless permits.
If the number of antlerless permits available to and used by hunters changed dramatically
between 1994 and 1995, then the SAK model would indicate changes in the percent
yearling does and fawn:doe ratios within the check station biodata. For example, the
fawn:doe ratio for geographic group 3 increased fi'om 55% to 82% between 1993 and
1994 (firearm season data), then dropped to 47% and 42% in 1995 and 1996,
respectively. These ratios were compounded by the percent yearling does injthe harvest,
which stayed relatively stable until 1996, when it dropped from about 40% to 28% in the

firearm season data. These numerical changes in model parameters may have been the

78

cause of the large fluctuations in the model predictions, especially since the doe
component reflects recruitment into the herd (Burgoyne 1981).

Comparison of the firearm and combined seasons population estimates in
geographic groups 4 and 5 indicated that the two SAK model predictions produced
similar trends. This suggested that, in these areas, it may not matter if archery season
data are included in SAK model calculations. This may change, though, if the archery
harvest becomes a larger proportion of the total harvest. The overall results for either of
these geographic groups were not unexpected, since there had been a consistent effort to
harvest antlerless deer in these areas throughout the years of this study. Hence, there
have continually been antlerless deer data from these areas to use in the SAK model.
This was due to the availability of firearm antlerless hunting permits each year.
Additionally, severe weather was not a common threat to the deer herd in this part of the
state, so the annual harvest accounted for the majority of the mortality each year.
Therefore, density independent factors would not need to be considered in nonharvest
mortality rates for geographic groups 4 and 5.

The extent of the influence of the lifetime recovery rate on the SAK model is
unknown. MDNR biologists have consistently used a lifetime recovery rate (r) of 0.90
statewide, but this value may need to fluctuate as density-independent factors become
more important in determining herd survival. It must be noted, however, that changing
the lifetime recovery rate is reflected in the SAK model by a similar, but opposite,
multiplication factor. For example, if the SAK model is computed by keeping all
parameters constant with r = 0.90 and the population is calculated as 215,144 deer, then a

10% decrease of r to 0.81 increases the population estimate by 11% to 239,049 (data are

79

from geographic group 5 in year 1993). Since the lifetime recovery rate does not affect
the SAK model predictions except by a multiplication factor, then the actual value of the
lifetime recovery rate can be varied as long as the SAK model is merely used as an index
for trend analysis. This only applies if the lifetime recovery rate remains constant among
years.

The SAK model was found to be a reliable population index when compared to
deer-vehicle accidents. The addition of archery harvest statistics was determined to
change the absolute SAK model estimates in most of the geographic groups, but
differences between firearm and combined seasons model predictions did not alter overall
trends. Density independent factors in geographic groups 1 and 2 may have contributed
to differences between the two SAK model estimate trends, as well as to differences
between SAK model predictions and deer-vehicle accident trends for these groups. In the
southern portion of Michigan, the addition of archery harvest statistics did not affect
trends in SAK model results. If archery harvest statistics continue to increase,
incorporation of these statistics into the SAK model will be imperative for both trend

analysis and absolute population estimation.

80

MANAGEMENT IMPLICATIONS

The size of the geographic area used for management purposes depends on the
sample size of harvest data available and on the effort required to collect an adequate
number of samples. As the size of a management unit decreases, it will take more effort
to collect the minimum required sample size for that area. Since each area managed will
need approximately 100 each of adult bucks, adult does and fawns for 95% confidence
with a 0.10 degree of precision, this needs to be factored into management schemes.

Now that the 13 management districts that were in existence at the beginning of this study
have been reconfigured into 8 management units, it should be easier for managers to
obtain the minimum required sample size for each unit because most of the units are
larger than the original districts. Samples should be collected throughout the entire
management unit, however, to ensure that they are representative of the entire unit.

The SAK population model can be a good resource for managing white-tailed
deer populations. This study showed that the SAK model is a reliable index for deer in
several geographic areas of Michigan, but further studies will need to determine if SAK is
also a reliable population estimator. Although an absolute population estimate can be
determined from the analyses done in this study, it is impossible to decide how accurate
or precise the estimate is. To properly use the SAK model, confidence intervals are
needed for the estimate: There are no known studies that have used confidence intervals
with the SAK model, so further analyses would be required to obtain them. Such a study
involves computer simulation of a deer population, and would require variance estimates

on all of the model parameters as well as the total population estimate.

81

Differences in sex and age ratios between the firearm and archery hunting seasons
may be affecting local deer herds, although this could not be determined directly from
this study. One of this study’s objectives was to determine if harvest statistics have
changed without major regulation changes in the hunting seasons. Hunter success rates
are approximately equal between the firearm and archery seasons, but those hunters who
utilize both seasons have a much higher success rate than season-specific hunters
(Langenau et al. 1994). Regulation changes to control these success rates may alter the
sex and age composition of deer harvested. The current study may serve as a comparison
to future studies to determine how regulation changes affect harvest statistics.

For example, one alternative is to start practicing quality deer management
(QDM) statewide. One of the main issues associated with QDM is how the harvest data
will be affected. If a traditional management scheme of a controlled antlerless harvest
and a liberal buck harvest was switched to an unlimited antlerless harvest and a controlled
buck harvest, the sex and age composition of check station data should change to reflect
these differences. If these data were then used as input into the SAK model as the model
currently stands, there would be erroneous and invalid results. The assumptions of the
model, namely that the data are representative of the herd and that buck harvest pressure
is uniform from year to year, would be violated. In effect, if bucks become limited in the
harvest via regulation changes, they will effectively assume the role that antlerless deer
now have in the SAK model. This would require the SAK model to be inverted by using
the antlerless component in the current role that the buck component has occupied.
Therefore, any regulation changes should be studied to determine potential effects on the

SAK model. One potential problem that would need to be studied is that bucks reflect

82

exploitation and does reflect recruitment (Burgoyne 1981). The assumptions of the SAK
model would need to be reevaluated based on any major regulation change.

An accurate measure of nonharvest mortality is required if the SAK model is to be
used as a population estimator, but this parameter is not so important for trend purposes.
The lifetime recovery rate is a measure of nonharvest mortality throughout the year. If
the equations involved in the SAK model are looked at piecemeal, it is seen that changes
in the lifetime recovery rate affect model predictions by a reciprocal amount of change.
Therefore, proper measures of nonharvest mortality are required so that model estimates
are accurate. Estimates of nonharvest mortality, especially mortality resulting from
density independent factors, vary throughout Michigan. Severe weather affects deer in
the Upper Peninsula much more readily than deer in the rest of the state. A whole fawn
crop could be lost during one winter in the Upper Peninsula, and if this is not accounted
for in the lifetime recovery rate, then the changes in harvested percent yearlings will
reflect incorrect population estimates.

A study that would determine nonharvest mortality rates throughout Michigan is
recommended, especially in the Upper Peninsula. This geographic area has different
climatic patterns on the eastern and western ends (Albert 1995), so a nonharvest mortality
study would have to determine results for both geographic areas. After determining
nonharvest mortality rates for years with both mild and severe winters, a more accurate
lifetime recovery rate in the SAK model could be determined. One data source that is
already collected and could be applied to a nonharvest-based study at both local and
statewide scales is the winter severity index (WSI). Studies are needed to determine if

WSI can be correlated with substantiated population indices throughout Michigan. This

83

would also improve deer management in general, giving concrete nonharvest mortality
data to managers in areas for which there is no extensive data at this time. Although this
will aid managers in the use of the SAK model, it is not the only model parameter that is
affecting SAK estimates.

One of the inconsistencies in the SAK model involves antlerless deer harvest
statistics. In areas where firearm antlerless harvest is not permitted, a different source of
herd composition data may be usefirl. Summer herd observations are a measure of sex
and age ratios that are independent of harvest statistics. Theoretically, this index should
have the capacity to be a substitute for check station biodata in the SAK model. The
index falls short, though, due to data collection methods used throughout Michigan. Poor
experimental design equals poor data, and this study found that because summer herd
observations are not standardized across the state, it was impossible to utilize the data.
Also, problems with observing animals, especially bucks, may bias results. A reliable
alternative data source would provide reasonable sex and age ratios for the SAK model in
areas with little or no antlerless harvest.

The last assumption of the SAK model that should be examined further is that the
harvest biodata represent the herd. Although there was no indication that this was not
true within the confines of this study, testing the assumption will enable managers to
decide if voluntary check stations are adequate. Such a study would answer the question
of whether voluntary check station biodata are biased in regards to particular sex or age
classes. Attempts to answer this question failed in this study. If such a study is
attempted in the firture, it should be investigated within the geographic boundaries of

Michigan, and herd composition should be known beforehand. By keeping the study

84

within Michigan, factors that may cause the study to be invalid, such as different herd
compositions and different regulations, can be mitigated. Results of such a study would
determine if the MDNR should continue to use voluntary check stations or switch to

mandatory check stations to obtain representative samples of the deer herd.

85

 

 

LITERATURE CITED

86

 

LITERATURE CITED

Albert, D. 1995. Regional landscape ecosystems of Michigan, Minnesota, and Wisconsin:
A working map and classification. North Central Forest Experiment Station.

General Technical Report NC-178.

Beier, P. and DR. McCullough. 1990. Factors influencing white-tailed deer activity
patterns and habitat use. Wildl. Monogr. 109, 1-51.

Burgoyne, GB. 1981. Observations on a heavily exploited deer population. Pages 403-
412 in C.W. Fowler, ed. Dynamics of Large Mammal Populations. John Wiley

and Sons, Inc.

Case, RM. 1978. Interstate highway road-killed animals: A data source for biologists.
Wildl. Soc. Bull. 6(1):8-13.

Coe, R.J., R.L. Downing, and BS. McGinnes. 1980. Sex and age bias in hunter-killed
white-tailed deer. J Wildl. Manage. 44(1):245-249.

Creed, W.A., F. Haberland, B.E. Kohn, K.R. McCaffery. 1984. Harvest management:
The Wisconsin experience. Pages 243-260 in L.K. Halls, ed. White-tailed Deer:
Ecology and Management. Wildlife Management Institute.

Ditchkoff, S.S., E.R. Welch, R.L. Lochmiller, R.E. Masters, W.C. Dinkines, and W.R.
Starry. 1996. Deer harvest characteristics during compound and traditional
archery hunts. Proc. Annu. Conf. Southeast. Assoc. Fish and Wildl.
Agencies:50:391-396.

Downing, R.L., E.D. Michael, and RJ. Poux. 1977. Accuracy of sex and age ratio counts
of white-tailed deer. J Wildl. Manage. 41(4):709-714. '

Eberhardt, L. 1960. Estimation of vital characteristics of Michigan deer herds. Ml Dept.
of Conservation Game Division Report No. 2282.

Eberhardt, LL. 1969. Population analysis. Pages 457-495 in R.B. Giles, ed. Wildlife
Management Techniques. 3rd ed. The Wildlife Society, Bethesda, Md.

Gladfelter, H.L., J .M. Kienzler, and KJ. Koehler. 1983. Effects of compound bow use on
deer hunter success and crippling rates in Iowa. Wildl. Soc. Bull. 11(1):7-12.

Hawn, L]. and LA. Ryel. 1969. Michigan deer harvest estimates: sample versus a
complete count. J Wildl. Manage. 33(4):871-880.

Hill, HR. 1995. The 1995 deer pellet group surveys. MDNR-WD Report No. 3232.

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Jahn, LR. 1959. Highway mortality as an index of deer population change. J. Wildl.
Manage. 23(2): 1 87-197.

Johnson, DH. 1994. Population analysis. Pages 419-444 in T.A. Bookhout, ed. Research
and Management Techniques for Wildlife and Habitats. Fifth ed. The Wildlife

Society, Bethesda, Md.

Langenau, E. and R.W. Aho. 1983. Relative impact of firearms and archery hunting on
deer populations. Proceedings from the Midwest Bowhunting Conference.

LaCrosse, WI.

Langenau, E., S.R. Winterstein, and W.E. Moritz. 1994. Allocating deer hunting
opportunities to Michigan hunters. MDNR-WD Report No. 3208.

Langenau, E. 1995. 1995 Deer herd observations. Michigan Department of Natural
Resources (MDNR) unpublished report.

McCaffery, KR. 1973. Road-kills show trends in Wisconsin deer populations. J Wildl,
, Manage. 37(2):212-216.

McCaffery, KR. 1976. Deer trail counts as an index to populations and habitat use. J
Wildl. Manage. 40(2):308-316.

McCullough, DR. 1979. The George Reserve Deer Herd. Univ. of Michigan Press. John
Wiley and Sons, Inc. 271 pages.

McCullough, D.R., F.W. Weekerly, P.I. Garcia, and RR. Evett. 1994. Sources of
inaccuracy in black-tailed deer herd composition counts. J Wildl. Manage.
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Michigan Department of Natural Resources (MDNR). 1976. Deer checking stations data
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Michigan Department of Natural Resources (MDNR). 1979. Deer checking stations data
— 1978. Surveys and Statistical Services Report No. 179.

Michigan Department of Natural Resources (MDNR). 1980. 1980 Michigan deer
seasons. MDNR-WD Report No. 2900.

Michigan Department of Natural Resources (MDNR). 1995. Federal aid to wildlife
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Michigan Department of Natural Resources (MDNR). 1996a. Michigan hunting and
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Michigan Department of Natural Resources (MDNR). 1996b. Expectations of 1996 Deer
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Miller, K.V. and R.L. Marchinton. 1995. Quality wlritetails: The how and why of quality
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Mooty, J .J . and PD. Karns. 1984. The relationship between white-tailed deer track
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Nixon, C.M., L.P. Hansen, P.A. Brewer, J.E. Chelsvig, J.B. Sullivan, T.L. Esker, R.
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survival of male white-tailed deer in Illinois. Illinois Natural History Survey
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Wildl. Manage. 28(1):27-34.

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analyzing white-tailed deer harvest data. Wildl. Monogr. 117, 1-59.

Severinghaus, CW. and HP. Maguire. 1955. Use of age composition data for
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Sitar, KL. 1996. Seasonal movements of habitat use patterns. M.S. Thesis from Michigan
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Thompson, S.K. 1992. Sampling. John Wiley and Sons, Inc. 343 pages.

Van Deelen, TR. 1995. Seasonal migrations and mortality of white-tailed deer in
Michigan’s Upper Peninsula. Ph.D. Michigan State University, East Lansing, MI.
158 pp.

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Verme, L.J. 1968. An index of winter weather severity for northern Michigan deer. J
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89

APPENDICES

90

APPENDIX A

Derivation of a doe:buck ratio for the SAK population model.

Determination of a percent yearling doe:buck ratio for SAK model analysis is
summarized below. It is derived from Severinghaus and Macguire (1955). This
procedure works whether or not the sample sizes are equal. Assume that there are equal
numbers of yearling bucks and does in the population before hunting has occurred. The

following variables are used:

b: number of yearling bucks in population
d: number of yearling does in population
B: total number of adult bucks in population (including yearling bucks)

D: total number of adult does in population (including yearling does)

Now, assume that b=d in the general population. The sex ratio between bucks and does

in the population can be calculated as:

(1)

SIS
eulo-
O—IU

which gives D/B, the ratio of does to bucks in the total adult population. This is

equivalent to

D . B = Percentage of yearling bucks (2)
' Percentage of yearling does

 

91

because
% yearlings bucks = b/B
and

% yearling does = d/D.

Therefore, the D:B ratio can be stated as in (2).

92

APPENDIX B

Table 5. Deer-vehicle accident data and SAK model results for years 1987-1996.

 

 

 

 

 

a) Group 1
Deer-Vehicle Million Miles Total Deer
Year Accidents of Travel Firearm Combined
1987 3,935 427,459 422,205
1988 4,069 2,780 367,424 349,687
1989 5,409 2,967 477,658 429,454
1990 4,963 3,059 3 81,917 365,683
1991 6,419 3,1 12 509,091 469,600
1992 493,361 464,477
1993 5,747 3,080 385,279 351,945
1994 7,3 81 3,059 449,195 420,535
1995 8,553 3,490 512,138 470,649
1996 8,162 3,093 439,308 428,506
b) Group 2
Deer-Vehicle Million Miles Total Deer
Year Accidents of Travel Firearm Combined
1987 6,333 387748 379,717—
1988 7,025 3,662 401,551 375,119
1989 7,422 3,904 491,133 458,242
1990 7,486 4,078 451,317 428,721
1991 7,950 3,841 547,972 491,660
1992 399,928 375,045
1993 6,353 3,827 395,448 364,809
1994 7,594 3,888 377,147 353,324
1995 8,384 3,735 424,180 396,519
1996 9,102 3,876 407,759 383,540

 

93

Table 5 (cont’d).

 

 

 

c) GroupT
Deer-Vehicle Million Miles Total Deer
Year Accidents of Travel Firearm Combined
1987 9,182 374,057— 373,300
1988 10,191 10,355 412,026 412,054
1989 10,963 10,697 457,318 449,579
1990 10,327 10,950 427,557 429,986
1991 10,827 1 1,013 398,794 409,128
1992 272,724 274,010
1993 10,217 11,828 348,890 356,450
1994 12,313 12,006 385,368 384,724
1995 14,325 11,811 358,618 345,044
1996 15,418 12,133 486,294 480,791
d) Group 4
Deer-Vehicle Million Miles Total Deer
Year Accidents of Travel Firearm Combined
1987 10,881 189,603 195,418
1988 12,105 47,958 221,851 219,677
1989 12,742 48,978 215,931 221,402
1990 12,829 49,464 206,814 205,449
1991 12,540 50,103 218,400 217,596
1992 189,390 191,098
1993 13,758 52,797 266,639 255,690
1994 16,071 52,439 281,798 284,856
1995 17,332 52,795 342,707 343,662
1996 20,281 54,006 390,060 382,006

 

 

 

 

94

Table 5 (cont’d).

 

 

 

 

 

 

e) GrouF
Deer-Vehicle Million Miles Total Deer

Year Accidents of Travel Firearm Combined

1987 8,596 157,393 151,103

1988 9,478 12,971 167,791 168,816

1989 10,248 13,340 172,646 171,983

1990 10,340 13,655 177,995 177,221

1991 10,497 13,851 201,420 193,459

1992 186,612 186,807

1993 11,757 14,157 222,764 215,144

1994 13,219 14,191 221,947 213,743

1995 13,899 14,351 240,784 239,118

1996 15,259 14,560 277,171 273,842

f) Waterside

Deer-Vehicle Million Miles Total Deer Statewide
Year Accidents of Travel Firearm Combined Population
1987 38,927 1,535,759 1,521,743 1,547,000
1988 42,868 77,726 1,570,643 1,525,353 1,841,000
1989 46,784 79,886 1,814,687 1,730,661 2,000,000
1990 45,945 81,206 1,645,600 1,607,060 1,700,000
1991 48,233 81,920 1,875,677 1,781,443 1,675,000
1992 1,542,015 1,491,436 1,588,000
1993 47,832 85,689 1,619,021 1,544,038 1,630,000
1994 56,578 85,583 1,715,456 1,657,182 1,760,000
1995 62,493 86,182 1,878,426 1,794,992 2,171,000
1996 68,222 87,668 2,000,592 1,948,685 2,026,000

 

95

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