hm.

I... ‘ . V

. aim.“ . «a1. a
a»? A ., 13».

3...“)?

"renuw . thy

‘. $1
‘

 

x
.12...

Ha“?

ififi.

”calm“.

i I.

g. flaw...“

.1?!
1 u

“M In

wgvtvy

 

tut... :r; .r .
aIiLSaflmww

 

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

DEVELOPING DEMOGRAPHIC MODELS TO INFORM
SELECTION OF ALLIARIA PETIOLATA (GARLIC MUSTARD)
BIOLOGICAL CONTROL AGENTS

presented by
Jeffrey A. Evans

has been accepted towards fulfillment
of the requirements for the

Entomology and
Docto(al degree in Ecology, Evolutionary Biology,
and Behavior

 

 

  

”M Vale“ ”Mme

Major Professor’s Signature

3/?00091
/ F

Date

 

MSU is an Affinnative Action/Equal Opportunity Employer

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 K:/Prolecc&PreleIRC/DaleDuorindd

 

DEVELOPING DEMOGRAPHIC MODELS TO INFORM SELECTION OF ALLIARIA
PE T IOLA TA (GARLIC MUSTARD) BIOLOGICAL CONTROL AGENTS

By

Jeffrey A. Evans

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Entomology
and
Ecology, Evolutionary Biology and Behavior

2009

ABSTRACT

DEVELOPING DEMOGRAPHIC MODELS TO INFORM SELECTION OF
ALLIARIA PE T [OLA T A (GARLIC MUSTARD) BIOLOGICAL CONTROL AGENTS

By
Jeffrey Adam Evans
Biological control is often considered a safe and effective method for controlling
invasive plant species. While methods are available for predicting biocontrol agent host
specificity, biocontrol practitioners currently lack effective tools for predicting agent
efficacy. Demographic models which account for spatial and temporal variation in
population dynamics promise to improve the predictability of weed biological control
programs, while lowering the risks they pose to non-target species. Alliaria petiolata
(garlic mustard) is an obligate biennial forb that is invasive in North American forests. I
analyzed sources of demographic variation in twelve unmanaged A. petiolata populations
in Michigan and Illinois, USA, and over three plant generations. These data were used to
parameterize matrix population models of A. petiolata population dynamics, analyze A.
petiolata responses to simulated management, and inform the selection of effective
biological control agents for potential release in North America. Hierarchical, generalized
linear mixed models (GLMMs) were used to analyze the spatial and temporal structure of
variability in each demographic transition. The degree of variation observed in A.
petiolata demographic rates was greater than expected based on previous studies of this
species. This variation was highly structured in space and time and exhibited negative
density dependence and positive response to precipitation across most of the life cycle.
Estimates of the population growth rate (3») ranged from 0.48 to 5.88 across all sites and

years. Within sites 1. was temporally variable, ranging from 0.80 to 5.88 within one site.

A megamatrix model was used to summarize variation in growth within sites. Site growth

rates (AM) ranged from 0.83 to 3.54 (mean = 1.90). Sensitivity and elasticity analyses of

matrix population models indicated the importance of the seed bank to A. petiolata’s
success. Sensitivity and elasticity rankings varied with 9», indicating that the transitions
with the largest impacts on population growth differ for growing and declining
populations, and within populations during good and bad years, rendering management
options a moving target. Rosette survival (summer and winter) consistently emerged as
the transition with the greatest effects on it in populations with positive growth, as did
germination of new seeds and transitions affecting fecundity. This result is consistent
with past predictions that rosettes should be targeted by management. The model raises
the caveat that rosette survival is only a an effective target when growth is positive; its
proportional effect on it decreases as 9» decreases. These models predict a lower
probability of suppressing A. petiolara with biocontrol than past studies. The simulations
predict that Ceutorhynchus scrobicollis could control up to 5 of 12 populations if
introduced alone. Introducing a second species could extend control 9 populations,
although the probability of success is < 0.1 at 4 of these 9. Better data on the distribution
of agent impacts are necessary to refine predictions. Variance in survival was negatively
density dependent, even when mean survival was not. modeling residual variance in each
vital rate as a function of density, demographic variance and stochasticity themselves
become density dependent functions. This has potentially important consequences for
populations of management concern, as small populations may become more susceptible
to local extinctions. The predictive power of future weed management models may be

improved by incorporating density dependent demographic stochasticity in their designs.

T 0 my mother and father

and to Courtney

iv

ACKNOWLEDGEMENTS

I owe my gratitude to many great individuals and groups. I want to thank my two
co-advisors who have guided me through the fray: thanks to Doug Landis, who brought
me to Michigan, encouraged me, and kept me on track for the last six years. Thanks
equally to Doug Schemske, who has taught me to always think big. Their passion for the
wild things in this world is an inspiration. I look forward to working with each of them
for a long time to come. 1 would not have made it to this point without the guidance and
fiiendship of my collaborator Adam Davis.

Thanks especially to my family. To my partner and wife, Courtney, whose belief
in me and in us has been my only true need. To my parents who remember how hard first
grade was for me but encouraged me at every step. And to my sister, Jocelyn, who just
called me “nature boy”.

This work could not have been done without the help of many people: Thank you
Anna F iedler, Grace Chen, Megan Woltz, Rob Ahem, and my other friends in the Landis
and Schemske labs for your help in the field and for listening to my crazy ideas. Huge
thanks are due to Ashok Ragavendran, my fi‘iend and late night numbers guru who has
probably sweat as much as I have over some of these analyses. Thanks to S. Raghu for
the hard earned data presented here and for more than one critical read of these chapters.
Thanks to Shaun Langley for creating the map in Figure 2.1. Thank you to Tara Lehman,
Molly Murphy, Rob Johnson, Marc Wegener, Susan Post, Jordan Shelley, Erin

Haramoto, Brian Schutte, and the many others who assisted with field and lab work. The

 

Nature Conservancy, The Edward Lowe Foundation, Michigan Department of Natural
Resources, Kent County Parks, Ottawa County Parks, the Shiawassee YMCA Camp, and
the Gasinski and Bartelt families all provided access to field sites. Thank you to Mark
McPeek, Rebecca Irwin, and the Dartmouth College Biology Department for providing a
temporary home away from home for me during the last year of my graduate program.
This work was supported by the National Research Initiative of the USDA Cooperative
State Research, Education and Extension Service (CSREES), grant # 2005-35320-15312,
USDA Specific Cooperative Agreement 58-3611-6-109, and by the Michigan State
University Plant Sciences Fellowship, MSU CNS Dissertation Completion Fellowship,

and EPA Science to Achieve Results (STAR) Graduate Fellowship FP-91650101.

PREFACE

Invasive species constitute a significant threat to native biodiversity globally, and
managing them effectively is an increasing challenge. In some cases invasions are so
devastating that the only way to confront them is by literally clearing the earth and
starting over. During my first year of graduate school I visited Everglades National Park
and saw just that. Brazilian pepper tree (Schinus terebinthifolius) had invaded vast tracts
of fallow farmland that had been incorporated into the park in the 19708. As I drove into
the area, Brazilian pepper was practically the only plant visible - an impenetrable thicket
of waxy leaves dotted with bright red berries. The soil that supported them, I was told,
had been created to promote agriculture. Using heavy equipment, the limestone bedrock
had been macerated to a consistency fine enough that crops could be planted in it.
Because the soil had been so radically altered, when the fields were abandoned, they were
rapidly invaded by Brazilian pepper, which was able to out compete the marl prairie
wetland community native to the area. Three decades later, huge earth moving machines
were being used to scrape away the topsoil that had been disturbed during a century of
agricultural land use, revealing the limestone bedrock beneath. Where this had been done
rich, native vegetation returned to its natural place of prominence within months, and the
Everglades were once again a river of grass.

Sometimes the best way to control invaders and protect native biodiversity is to
scour or scorch the earth. But this is rarely the case. Because plant invaders are more

often diffuse targets of management, standing intermixed with the very species we wish

vii

to preserve, a cautious, more delicate approach to controlling them is necessary. In some
cases, when an invasion is small, hand pulling or spot herbicide treatments can
effectively control a target weed, and quarantines can be used to stop its spread. But
when the target is widespread and well established a more autonomous approach is
necessary.

Enter biological control. Biological control, or biocontrol, is conceptually simple
if not elegant: Everyone has enemies. Use this to your advantage by letting your enemy’s
enemy do the dirty work. More technically, biological control is the practice of using the
natural enemies of a targeted pest species to suppress the pest population. In the case of
weedy invasive plants, herbivorous insects and occasionally plant pathogens are most I
frequently used as biocontrol agents. Although past biocontrol programs have been I
criticized for imprudently releasing agents that have harmed non-target - and even
threatened — species, the culture of biological control practitioners has changed. Great
lengths are now taken to reduce the risk of introducing biocontrol agents that feed on
non-target plant species. Extensive pre-release tests of agent feeding preferences and host
specificity typically take a decade or more to complete, and these still do not guarantee
that permits will be issued to make releases.

But what of the plant? Until recently, the target plant has been something of an
afterthought in the formulation of new biocontrol programs. Biocontrol systems have
historically been ‘designed’ (and I use the term rather loosely) by seeking to introduce as
many host specific biocontrol agent species as can be found until the target is suppressed.
This approach has resulted in a enormous investments of time and money in the

development, testing, and of release of biocontrol agents that ultimately have not

viii

controlled their targets, and that in some cases had wildly unexpected indirect effects on
other species and food webs. There must be a better way...

A more directed approach to finding ‘the right agent’, the one that ultimately does
the heavy lifting and suppresses the target, was proposed by Peter McEvoy and Eric
Coombs. The idea, again, is audaciously simple: Study the plant, determine its
vulnerabilities, and target them explicitly. Drawing from a growing number of studies on
invasive weed demography and conservation biology, they pr0posed that population
models could be developed for a target invasive species that would highlight the stage or
stages in its life history with the greatest effects on population growth. This stage is the
plant’s ‘Achilles’ heel’, and is where management should be directed. Knowing this
information up fi'ont, finding ‘the right agent’ would begin to look less like a lottery and
much more like a directed search. Demographic models, layered with the already
mandatory process of testing agent host specificity, could lead biocontrol researchers
more efficiently towards effective biocontrol solutions for invasive weeds. Perhaps more
importantly, by releasing fewer species of biocontrol agents, the risks to non-target

species posed by biological control programs could simultaneously be reduced.

Adam Davis was the first to apply McEvoy and Coombs’ proposal. Davis and his
coauthors used available data to build a mathematical model of the invasive weed
Alliaria petiolata (garlic mustard) and characterize its vulnerabilities. This model was
then used to make recommendations about how garlic mustard should be managed. My
dissertation work builds from Davis’ model with new studies and analyses of this same

species, garlic mustard. It examines the structure and scale of spatiotemporal variability

ix

in demographic rates and how this variability affects projections of population viability
and the effectiveness of proposed management strategies.

One of the major themes in my dissertation research is variability. A number of
researchers have studied garlic mustard, and a number of these have developed models of
its population dynamics. Looking across these studies and at my own research, what is
really amazing is how incredibly different this one species can be. In some places 10% of
the seedlings survive. In others, 90% survive. In some places the population grows
explosively, while in others it barely persists from year to year. Within populations there
is also incredible variation in survival and growth from year to year as populations cycle
through phases of boom and bust dynamics. In one of my garlic mustard study
populations a year of tremendous growth was followed by two years of population
decline. All of this suggests that to truly understand this plant, we can’t think of its
population biology as a static entity. It does not have one growth rate, nor does it have
one density dependent function. It is unlikely, too, that it has one optimal management
target. This picture only begins to come into focus after watching a dozen populations for

several years.

In the following chapters I will present my dissertation research on garlic
mustard. The central questions I address The first chapter contains background
information on garlic mustard biology, biological control, and some of the goals of my
research. Chapter two describes the statistical analysis of garlic mustard survival and
reproductive rates from the twelve study sites. In this chapter, I examine the spatial and

temporal scales of variability in demographic rates as well as their relationships to

population density and abiotic factors. Chapter three is a detailed critique of a recently
published modeling study of garlic mustard population dynamics by Pardini et al. which
also makes management recommendations. This is a necessary detour, as there were a
number of errors in this model’s construction and parameterization that led to issuing
incorrect management recommendations which some land managers have already begun
implementing. The fourth chapter presents a linear model of garlic mustard population
dynamics which incorporates annual variation in demographic rates within each site. The
model is used to estimate the probability of controlling garlic mustard by simulating the
effects of either single or multiple biocontrol agent species across a range of agent
efficacies. This is the main result of the study. Finally, chapter five contains a reanalysis
of the survival and fecundity data focused on density dependence of demographic
stochasticity. This analysis suggests an important relationship between population density
and the stochasticity of survival probability that should be explored further in future

statistical and population models.

I didn’t think I wanted to be a modeler when I started graduate school. Turns

out... I do. Who knew?

xi

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................ xv
LIST OF FIGURES ........................................................................................................ xviii
Chapter 1 : Developing Demographic Models to Inform Selection of Alliaria petiolata
(Garlic Mustard) Biological Control Agents ....................................................................... 1
Introduction ..................................................................................................................... 2
Biological Control ........................................................................................................... 3
Host Range Testing ..................................................................................................... 4
Benefits of Biological Weed Control .......................................................................... 5
Pitfalls of Biological Weed Control: Non-Target Impacts .......................................... 5
Direct Non-Target Effects ....................................................................................... 6
Indirect Non-Target Effects .................................................................................... 8
Improving Weed Biological Control ............................................................................... 9
The Use of Transition Matrix Models ....................................................................... 10
Demographic Variability ........................................................................................... 13
Study Species ................................................................................................................ 16
Distribution ................................................................................................................ 16
Life Cycle .................................................................................................................. 17
Invasiveness of Alliaria petiolata ............................................................................. 20
Control Strategies .......................................................................................................... 21
Conventional Control ................................................................................................ 21
Biological Control ..................................................................................................... 21
Summary ....................................................................................................................... 23
Chapter 2 : The Scale and Sources of Demographic Variation in Alliaria petiolata ........ 24
Abstract ......................................................................................................................... 25
Introduction ................................................................................................................... 27
Methods ......................................................................................................................... 30
Study Species ............................................................................................................ 30
Study Sites and Data Collection ................................................................................ 32
Germination and Seed Survival ............................................................................. 32
Seedling Survival .................................................................................................. 33
Rosette Survival and Fecundity: ........................................................................... 34
Climate Data .............................................................................................................. 35
Soil Data .................................................................................................................... 37
Statistical Analysis .................................................................................................... 38
Hierarchical Mixed Model Analyses ..................................................................... 38
Environmental Models .......................................................................................... 41
Results ........................................................................................................................... 43
Hierarchical Mixed Model Analyses ......................................................................... 45
Environmental Models: ............................................................................................. 46
Germination ........................................................................................................... 47
Seedling Survival .................................................................................................. 48

xii

Summer Survival ................................................................................................... 48

Winter Survival ..................................................................................................... 50
F ecundity ............................................................................................................... 50
Discussion ..................................................................................................................... 51
Comparisons to Previous Studies .............................................................................. 51
Conclusions ............................................................................................................... 55
Tables: Chapter 2 .......................................................................................................... 59
Figures: Chapter 2 ......................................................................................................... 71
Appendix 2.A : Soil Data .............................................................................................. 83
Appendix 28 : Statistical Model Fitting Notes ............................................................ 85
2.B.i. Model Fitting ................................................................................................... 86
2.B.ii. "Pretending variables" .................................................................................... 88
2.B.iii. Conditional Modeling of Seed Survival ........................................................ 89
2.B.iv. Fecundity estimation ..................................................................................... 90
2.B.v. Estimation of 2007 02 .................................................................................... 93
Appendix 2.C : Environmental Model Predictions ....................................................... 99
Appendix 2.D : Corrections to Meekins and McCarthy (2002) Matrix Model .......... 102
Appendix 2.E : Meekins and McCarthy (2002) Calculations ..................................... 105
Appendix 2.E ............................................................................................................... 106
Chapter 3 : Comment on “Complex Population Dynamics and Control of the Invasive
Biennial Alliaria petiolata (Garlic Mustard) ................................................................... 107
Introduction ................................................................................................................. 108
Study System ........................................................................................................... 109
Management Inference ............................................................................................ l 10
Analyses ...................................................................................................................... 110
Life History ............................................................................................................. 110
Parameterization of Density Dependent Functions ................................................. 1 12
Implementation of Density Dependence ................................................................. 116
Interpretation of Model Output ............................................................................... 117
Conclusions ............................................................................................................. 1 19
Figures: Chapter 3 ....................................................................................................... 121
Appendix 3.A : Summer Density Dependence and multicollinearity ......................... 126
3.A.i. Summer Density Dependence Function (32) ................................................. 127
3.A.ii. Multicollinearity and Parameter Bias ........................................................... 129
Appendix 38 : Refit density dependence equations ................................................... 139
Appendix 3.C : Winter Density Dependence .............................................................. 141
Appendix 3.D : Apply Seedling Density Dependent Mortality .................................. 145
Appendix 3.E : Application of Seedling density dependence ..................................... 149
Appendix 3.F : Multicollinearity Simulation: MATLAB Computer Code ................ 154
Chapter 4 : The Predicted Response of Alliaria petiolata to Biological Control: Linear
Deterministic Demographic Models ............................................................................... 161
Abstract ....................................................................................................................... 162
Introduction ................................................................................................................. 164
Methods ....................................................................................................................... 168
Study System and Data Collection .......................................................................... 168

xiii

Demographic Data ................................................................................................... 170

Matrix Model Construction ..................................................................................... 172
Results ......................................................................................................................... l 80
Population grth rates ........................................................................................... 180
Sensitivity and Elasticity Analyses ......................................................................... 181
Zero Growth Isoclines ............................................................................................. 185
Discussion ................................................................................................................... 1 86
Tables: Chapter 4 ........................................................................................................ 192
Figures: Chapter 4 ....................................................................................................... 196
Appendix 4.A : Raw Zero Growth Contours .............................................................. 207
Appendix 4.B : Annual Zero Grth Contours .......................................................... 210
Chapter 5 : Demographic Variance Across Gradients of Population Density in Alliaria
petiolata ........................................................................................................................... 21 3
Abstract ....................................................................................................................... 214
Introduction ................................................................................................................. 216
Methods ....................................................................................................................... 218
Sampling .................................................................................................................. 218
Statistical Analyses ................................................................................................. 218
Results ......................................................................................................................... 220
Fixed Effects ........................................................................................................... 221
Random Effects ....................................................................................................... 222
Discussion ................................................................................................................... 223
The Importance of Variance .................................................................................... 225
Tables: Chapter 5 ........................................................................................................ 230
Figures: Chapter 5 ....................................................................................................... 235
Literature Cited ............................................................................................................... 246

xiv

LIST OF TABLES

Table 2.1. Names and locations of study sites. Rainfall estimates represent mean values
summed from climatic data used in analyses. See methods section for details. ............... 60

Table 2.2. Timeline of Alliaria petiolata sampling for each demographic parameter. S, F,
W, and Sp indicate summer, fall, winter, and spring, respectively. Boxes enclose the time
interval over which a parameter was measured. The unshaded box indicates the summer
survival transition that was measured in the smaller seedling survival-sized quadrats in
Michigan for the 2005-2006 cohort. Germination data are not presented in Chapter 2. .. 61

Table 2.3. Results of model selection for spatiotemporal differentiation of A. petiolata
life history transitions. Details for each transition include the error distribution (dist) used
in GLMs and GLLMs, the information criterion used for model weighting and selection
(ic), and the dispersion parameter (p used to calculate QAlCc where applicable. Variables:
fixed effects (S=site, Y=year, L=location, I=intercept), Laplace approximated maximum
likelihood (ln(l)), number of observations (n), levels of random quadrat effect (r), number
of parameters including random effects (k), (Q)AIC: AICc or Quasi-AICc for

overdispersed models, delta (Q)AIC (Ai) , and Akaike weight (w,). Models with r=0 were
GLMs with fixed effects only. A maximum of 5 models are shown per vital rate. All

other models with Ai < 11 and w,- > 0 are shown. ............................................................ 62

Table 2.4. Best supported environmental model of germination of newly shed seeds after

one winter (g1). Parameter estimates from GLMM with binomial errors and logit link.
Model ranking was evaluated with QAICc. Akaike weight = 0.853, AQAICc of next best
model = 3.7. All climate data are from time periods which precede germination. Random
quadrat effect was evaluated with a likelihood ratio test by comparing the change in the -

21n(l) from dropping quadrat from the model to a mixture of x2 distributions in
GLIMMIX (SAS Institute 2008). ...................................................................................... 64

Table 2.5. Seedling Environmental Model: Parameter estimates from GLMM of seedling
survival from April until June of the first year with binomial errors and logit link. Model
ranking was evaluated with QAICc. Akaike weight = 0.958, AQAICc of next best model
= 7.8. Random quadrat effect was evaluated with a likelihood ratio test by comparing the
change in the -2ln(l) from dropping quadrat from the model to a mixture of )(2
distributions in GLIMMIX (SAS Institute 2008) .............................................................. 65

Table 2.6. Summer Environmental Model (ssum): Probability of a rosette surviving from
June to October. Summer survival GLMM with binomial errors and logit link. Akaike
weight = 0.993, AQAICc of next best model = 10.01. Random quadrat effect was
evaluated with a likelihood ratio test by comparing the change in the -21n(l) from
dropping quadrat from the model to a mixture of )(2 distributions in GLIMMIX (SAS
Institute 2008). .................................................................................................................. 66

XV

Table 2.7. Winter Environmental Model (swin). Two-stage model of winter rosette
survival (swin). Model r,,.,-,,1 predicts the binary probability of observing an extreme value
(either 0 or 100% survival) versus any other intermediate value and determines whether

an observation proceeds to s,,,,-,,2a or sun-"2b. Higher predicted probabilities fi'om r,,,,-,,l are

more likely to have extreme values and are passed on to sun-"2a. Model swin2a predicts the
binary probability of observing 0% survival versus 100% survival, conditional on

knowledge that the outcome is one of these. Model rwm2b is a binomial GLMM that
predicts the survival probability of a quadrat that does not have an extreme value. For the
first two binary models, the response coded as the "event" whose probability was
modeled is indicated. Akaike weights = 0.343, 0.904, and 0.865 for the three models,
respectively. AAICc of next best models = 1.4, 5.4, and 3.7, respectively. ...................... 67

Table 2.8. Fecundity Environmental Model (I). GLMM with Poisson distributed errors,
log link, and random quadrat effects. Model ranking was evaluated with AICc. Akaike
weight = 0.999, AAICc of next best model = 16.3. Random quadrat effect was evaluated
with a likelihood ratio test by comparing the change in the -21n(l) from dropping quadrat

from the model to a mixture of )(2 distributions in GLIMMIX (SAS Institute 2008). ...... 68

Table 2.9. Comparison of plant densities used in four studies of A. petiolata. Seedling,
Summer, and Winter refer to survival measurements. Plant minimum and maximum

densities have been converted to common units of plants m'z. Geometric mean densities
and 95% confidence intervals of the geometric mean are shown. The mean seedling
density from Pardini et al. (2009) is the arithmetic mean and is based on their report of
marking 469 seedlings across 40 1x1 m quadrats. ............................................................ 69

Table 2A.] Mean soil parameters d: SEM. Site abbreviations in Table 2.1 ..................... 84

Table 2.B.l Parameter estimates from breakpoint linear regression of log10(seeds/plant)
versus log10(siliques/plant). The breakpoint is the number of [untransformed] siliques
above which the slope of the regression changes. The slope for plants with 1-8 siliques is

given by ,6], while the slope for plants with more than 8 siliques is given by ,62. ............ 95

Table 2.8.2. Parameter estimates from generalized linear mixed model of germination
probability of dormant A. petiolata seeds with binomial errors and random site effects.
Type-3 F-tests of parameter significance and parameter standard errors are given .......... 96

Table 3A.] Analysis of simulation results. A random variable 2 was created as a function
of x and y using the formula 2 = 5 + 2x + 6y + random error. Z was modeled as a function
of five different combinations of x and y. M1 represents the ‘true’ form of the function
used to generate 2. Parameter estimates from models without the main effects x and y are
poor, although they have significant P-values. AAICc values correctly identify the M1 as
the model with the greatest support from the data. M1 received > 90% of the Akaike
weights (w) indicate a 90.4% probability that it is the best supported model among the
five competing models. ................................................................................................... 134

xvi

Table 3.8.1. Parameter estimates and fit statistics from refit summer (52) and winter (S3)

A. petiolata density dependence functions. Data were extracted from figures 2a and 2b of
Pardini et al. (2009) A. petiolata winter survival data. ................................................... 140

Table 4.1. Mean observed A. petiolata demographic rates by site, calculated for each of
three years. ...................................................................................................................... 193

Table 4.2. Annual estimates of k for each site Owe“). These were summarized within

each site as the megamatrix 10M), the population growth rate of the average population
within each site calculated from the megamatrix M with uncorrelated environments. The

mean growth rate across sites within each year and across all 1M is given in the bottom
row. The arithmetic mean 1M is the average 1» across the study system. ........................ 194

Table 4.3. The probability of successfully controlling A. petiolata at each site was
graphically estimated as the proportion of the two shaded areas above the zero growth
isoclines in Figure 4.7. The sizes of the shaded areas for C. scrobicollis alone (smaller
rectangle in Figure 4.7) and with C. alliariae (larger rectangle) were 13899 and 26082
pixels, respectively. This analysis assumes a uniform probability distribution for agent
impacts. ..... . ..................................................................................................................... 195

Table 5.1 Comparisons of fixed- and mixed effects models of density dependent survival
and fecundity in A. petiolata. Seedling survival was calculated as the number of rosettes
in June divided by the maximum number of seedlings observed during the spring
germination period. Summer and winter survival were calculated as the proportion of
rosettes surviving from June to October and from October to the following June,
respectivel . All models included fixed effects terms for initial A. petiolata density

(plants In. ), state, year, and state by year interactions. Mixed effects models also
included random effects terms for site within year. In the mixed models, the variance
structure was modeled normally, as an exponential function of the density covariate, and
using the power of the mean (POM) structure. AIC and BIC are the Akaike and Bayesian
Information Criterion, respectively. A AIC and A BIC indicate the difference in fit
between each model and the fit of the best fit model within each set of analyses. Table
5.1. ................................................................................................................................... 231

Table 5.2 Type III F -tests of fixed effects and estimates of covariance parameters from
analyses of arcsine square root transformed seedling, summer, and winter survival

probabilities in A. petiolata. In each model, plant density (# m2) is the number of A.
petiolata plants at the start of the interval over which survival was measured, except for
seedling survival, where seedling density is the maximum density of seedlings observed
during the spring. The estimated density effects are slopes associated with each density
covariate. Random effects are indicated in italics and were evaluated with Z tests.
Congratulations! You’re almost done reading this thing ................................................ 233

xvii

LIST OF FIGURES

Figure 2.1. Locations of seven A. petiolata study sites established in Michigan in 2004
and five sites established in Illinois in 2005. Site Key: 1) Shiawassee, 2) Rose Lake, 3)
Ives Road, 4) Johnson Park, 5) Holland State Park, 6) Edward Lowe Foundation, 7) Russ
Forest, 8) Healy Road, 9) Homer Lake, 10) Illini Plantations, 11) Farmdale, 12) Peoria. 72

Figure 2.2. Schematic diagram of A. petiolata life cycle. Arrows represent one-year
transitions from June to June and are comprised of multiple lower level demographic

transitions. These are abbreviated as follows: g1, germination of new seeds within one
year of seed set; g2, germination of dormant seeds from the soil seed bank; 3, survival of

newly emerged rosettes to the rosette stage in June; ssum, summer survival of new rosettes
from June until late October; s,,.,-,,, winter survival of rosettes to the flowering stage from

October until June; f, fecundity (seeds/plant); ss, survival of dormant seeds in the soil
seed bank. Because seed survival (s3) was measured over a full year but is used twice as

an 8 month, sub-annual transition, SS is raised to the two-thirds power in the seed to
rosette and the flowering plant to rosette transitions to scale its affect ............................. 73

Figure 2.3. Observed mean A. petiolata demographic rates over the study period. Light
gray lines follow mean values within individual sites, averaged across quadrats. Heavy
black lines are mean values (iSEM) of these site means. Year indicates the year during
with each measurement was begun. For example, winter survival 2005 was measured
from fall of 2005 until June of 2006. The three years constitute the three “cohorts” of
plants as grouped in the study, i.e. 2006 germination 1 and 2005 summer survival are
grouped together. *Values of germination 2 from in 2009 are estimations (Appendix
2.B.v). ................................................................................................................................ 74

Figure 2.4. Frequency distributions of A. petiolata demographic rates from this study.
Data shown are raw quadrat level observations. Rosette to flowering plant survival (SJ) is

calculated as rsum’frwm for comparison with previous studies that did not split summer
and winter survival. Letters beneath histograms show observations from previous studies.
References: a (Pardini et a1. 2008); b (Pardini et a]. 2009); c (Anderson et a]. 1996); d
(Meekins and McCarthy 2002); e (Drayton and Primack 1999); f (Nuzzo and Blossey
unpublished data); g (Baskin and Baskin 1992); and h (Cavers et a1. 1979). Overlapping
observations are shown as: 1' (Anderson et a1. 1996, Meekins and McCarthy 2002); j
(Drayton and Primack 1999, Pardini et a1. 2009, Nuzzo and Blossey unpublished data); k
(Cavers et al. 1979, Meekins and McCarthy 2002) ........................................................... 76

Figure 2.5. Predicted versus observed values of A. petiolata seed bank viability (5,),
germination after 1 winter (g1), seedling to rosette survival (5,), summer (ssum) and winter
(swin) rosette survival, per capita fecundity (f), and germination of dormant seeds fiom

xviii

the seed bank after two winters (g2). Fitted values are least squares means estimates for
each site by year combination predicted from the hierarchical GLMs and GLMMs.
Observed values are simple arithmetic means except f. Silique counts were first averaged
across plants within quadrats, then across quadrats for each site and year, and finally
scaled to show the estimated number of seeds per plant. Fitted f, values were modeled as

silique counts and then sealed to generate seed estimates. Only the first two years of g2
are shown, because the third year was estimated fi'om years one and two. Unadjusted R2
are shown because the site by years means are shown (marginal model predictions),

whereas the model was fit with random quadrat effects. All R23 and Adjusted R2 in this
and subsequent figures are calculated in the original data scale. ...................................... 78

Figure 2.6. Predicted versus observed values from environmental models. The five
scatterplots show the demographic rates generated from the BLUPs versus the observed
rates, overlaid with a 1:1 reference line. The vertical axis of the box plot shows the
predicted probability of a winter rosette survival observation resulting in an extreme

value, either 0 or 100% survival, versus a non-extreme value from the rwml binary GLM
versus the actual outcome. Observed extreme values were coded as "Yes" and include all
observations that had either zero or 100% percent survival. Observations in the "No"
category had intermediate survival rates. A well fitting model should predict higher
probabilities for the "Yes" group and lower the probabilities for the "No" group. The

winter rosette survival plot shows the combined results of models run-"2a and rwm2b. For
observed probabilities of 0 and 1 the predicted values represent the probability of an
observation being 1, versus the alternative of it being 0, conditional on knowing that the
outcome will be one of these two extreme values. The remaining points are predicted
survival probabilities as in the upper row of plots. Mean per capita fecundity was
estimated from the predicted and observed numbers of siliques using the breakpoint
regression fimction in Appendix 2.B.iv. ........................................................................... 80

Figure 2.7. Predicted seedling survival is conditioned by interactions among multiple
extrinsic and intrinsic factors. Here, the expected seedling survival probability is
calculated from the best supported seedling model across the observed range of fall rainy
days (rainfall), during the year before germination at the minimum (cool), mean (med.),
and maximum (hot) number of observed hot days during the summer before germination.
The figure illustrates the interaction between population density, spring temperature
(hotsum), and fall rain at population densities of 500 (gray) and 5000 (black) seedlings m“
2. Mean observed values were used for all other variables. The change in slope from

negative to positive results from the interaction between rainfall and hotsum. .................. 82

Figure 2.B.1. Number of seeds versus number of siliques in 142 A. petiolata test (black
dots) and fitted values from breakpoint regression (black line). Inset detail graph shows
the change in slope above the breakpoint value of 8 siliques per plant (vertical dashed
line) .................................................................................................................................... 97

Figure 2.B.2. Fitted versus observed values of pooled A. petiolata germination rates from
dormant seed (g2) overlaid with 1:1 reference line. The first two years of data, which

xix

were used to fit the model, are shown. This relationship was applied to the third year of
data to estimate the unknown values of g2. Model was fit with binomially distributed
errors and g1 and seeds; as fixed effects plus random site effects. ................................... 98

Figure 2.C.1. Observed A. petiolata demographic rates versus up to five independent
variables from the best supported environmental models. .............................................. 100

Figure 2.C.2. Predicted A. petiolata demographic rates versus the same independent
variables in Figure D1 from the best supported environmental models. Predicted values
were generated using the BLUPs, and thus include the random quadrat effects. ........... 101

Figure 2.E.1. Life cycle diagram of A. petiolata showing the upper level transitions
(arrows) and the lower level transitions which comprise them (equations). Symbols are
defined in the text. This version differs from Figure 2.2 in that it follows the notation of
Pardini et al. (2009) and includes parameters for simulation of management. ............... 122

Figure 2.B.2. Bifurcations of A. petiolata populations with simulated management of
rosette survival (left hand panels) and simulated management of per capita fecundity
(right hand panels) using equation set 4. In each case, the unmanaged population is
represented on the far left where additional mortality or reduction in fecundity is zero,
and the dashed reference line shows the maximum equilibrium size of the unmanaged
population. Points above this line indicate potential increases in population size relative
to the unmanaged case, while those below it indicate population decline. Individual
panels show (a,b) the original model as parameterized and published in Pardini et a1.
(2009), (c,d) the effects of adding seed bank morality to the S to S and S to R transitions
and rescaling sub-annual seed mortality as described in the text, (ej), the result of
changing the function for winter rosette density dependence in a-d to a logistic curved
response, and (g,h) the result of correcting the sign of the summer rosette density
dependence function used in a-f. ..................................................................................... 123

Figure 3.A.1. The function used to characterize density dependent mortality of A.
petiolata in summer did not fit the data well. Data extracted from Pardini et al. (2009) are
shown (dots) against the published logistic regression function evaluated at R = A across
the range of total plant density from the study (dashed line). Data extracted fiom Figure
2A in Pardini et a1. using photo editing software were used to refit a new logistic

regression function of survival probability vs. loge(A + R), shown as a solid line. This
new function is used in the modified model in the main text. Because A and R could not
be extracted from the figure, lower-order terms and interactions could not be fit .......... 135

Figure 3.A.2. Surface plot of the published function for density dependent summer

rosette survival (s2) from Pardini et a1. (2009) evaluated at all combinations of A = 0:200
and R = 0:200. ................................................................................................................. 136

Figure 3.A.3. A simulation illustrating how the sum (x + y) and product (x * y) of two

uncorrelated random variables can be highly correlated with each other. The variables x
and y are each comprised of 100 random draws from normal distributions with means 3

XX

and 5, respectively, and standard deviations of 1. The variable 2 was calculated as 2 = 5 +
2x + 6y + random error. Correlation coefficients (r) are shown for each relationship.
Although z is only an additive function of x and y, it appears to be strongly correlated
with both their sum and product. The simulated data plotted here were also used in the
example analysis presented in Table 3.A.1. .................................................................... 137

Figure 3.C.1. Density dependence of winter rosette survival probability using data
extracted from Pardini et al. (2009). Pardini et al. conducted a linear regression of
loge(winter survival) on loge(rosettes + l) with the intercept fixed at 1. Thus the model
predicts that survival probability approaches 100% as population size approaches 0. An

alternative to this is a logistic regression of survival probability on loge(rosettes + 1). This
model has a lower y intercept and is less prone to overestimating survival of low density
populations. The inset detail shows the shapes of the two functions at the y intercept. . 144

Figure 3.D.1 Bifurcations of A. petiolata populations with (a) simulated management of
rosettes in early winter and (b) simulated management of adults in early spring using
equation set C. In each case, the unmanaged population is represented on the far left
where additional mortality is zero, and the dashed horizontal reference line shows the
maximum equilibrium size of the unmanaged population. As all point fall below this line,
any increase in morality results in decreased population size relative to the unmanaged
case. ................................................................................................................................. 148

Figure 3.E.1 Bifurcation of unmanaged A. petiolata populations with varied strength of
seedling density dependence modeled fi'om equation set F. Variability in the strength of
density dependence was expressed by changing the slope parameter in the logistic

function for seedling survival to the rosette stage ([31301]) fiom 0 to -1. The case of no

density dependence is shown on the far left where [915d] = 0 and seedling survival
probability is fixed by the intercept parameter at 0.6225. The dashed horizontal reference
line shows the maximum equilibrium size of the population with no density dependence.
......................................................................................................................................... 152

Figure 3.E.2. Proportional change in A. petiolata equilibrium population densities across
a range of varied strength of seedling density dependence and simulated management of
rosettes (left) and simulated management of Adults (right). The lines show the proportion
of the unmanaged population size for a given strength of seedling density dependence as
the strength of rosette or adult management is increased. Strength of seedling density

dependence increases as values of [313,11 become more negative (see Figure 3.E.1). For

example, when there is no seedling density dependence, (1315,11 = 0, dotted line),
increasing rosette mortality causes an approximately linear proportional decrease in
maximum population size, relative to the size of an unmanaged population with no
density dependence. ........................................................................................................ 153

Figure 4.1. Alliaria petiolata life cycle diagram and corresponding projection matrix A.
Arrows represent one-year transitions from June of year t to June of year t+1 and are
comprised of sub-annual, lower level demographic transitions: per capita fecundity (f),

germination probabilities of new seeds within one year of seed set (g1) and of dormant

xxi

seeds from the soil seed bank (g2), and seedling (Sr), summer rosette (ssum), winter rosette

(Swin)a and dormant seed (s3) survival probabilities. Matrix rows correspond with the life
history stage individuals are transitioning from time t, where rows 1, 2, and 3 (from left)
are seeds, rosettes, and flowering plants. Columns indicate life history stages individuals

are transitioning to in time t+1. For example matrix element a32 represents the transition
from rosettes (column 2) to flowering plants (row 3) in matrix A. Following Davis et al.

(2006), the variables c1 and c2 simulate rosette mortality and fecundity reduction due to
biocontrol, and are shown as (l-cn) to express them in terms of survival. ..................... 197

Figure 4.2. Frequency distribution of A. petiolata megamatrix population growth rate
across all sites (n = 12). The black line indicates the mean value of AM across sites. 198

Figure 4.3. Sensitivities (top) and elasticities (bottom) of A to perturbation of A matrix
elements aij. Sensitivities from the combined 36 site by year matrices are sorted from left
to right by sensitivity matrix element S32 (R—eP), and elasticities are sorted by elasticity
matrix element e11 (S—->S). The sensitivities of 1» to a23 and (113 are small and lie along the
horzontal axis. The elasticities of X to (113 and a2] are equal; the former obscures the latter
in the lower plot. NOTE: The dotted line (all) does not indicate a different density of
data points than the other four line styles and should not be interpreted differently. It is

used because the software which produced the graph (MATLAB) only prints four basic
line styles. ........................................................................................................................ 199

Figure 4.4. Elasticities (eff) of l to A matrix elements an (S—vS) and an (R—rP) (left) and
to lower level transitions seed (s3) survival and E4 (right) versus the population growth
rate A. The elasticities of It to f, 3,, ssum, and SW," were identical and are represented
together with one line, labeled E4. E4 and e32 are equal as well. Among populations with

high growth rates, 1 has the greatest elasticity to an and E4. Logistic regression lines are
overlaid to show trends. .................................................................................................. 201

Figure 4.5. Empirical second derivatives of 1». Observed variation in elasticities of
Alliaria petiolata population growth versus observed variation in the lower demographic
transitions. In each panel the elasticities of A to each lower-level demographic rate from
the 36 site by year matrices is plotted against the observed value of the transition
indicated on the horizontal axis. The eight panels show the same empirical data sorted
differently. The data are sorted from left to right by the transition labeled on the
horizontal axis. In the lower right panel the x axis is shown on a log scale, although the x
axis tick marks are back-transformed to the original scale. Contours were smoothed using
a LOESS smoother (Burkey 2009) to clarify the relationships among variables. This is
why the values in each panel appear different even though they show the same data. The
raw, unsmoothed plots are presented in Appendix A ...................................................... 202

Figure 4.6. Sensitivities of k to lower-level A. petiolata transitions x versus 1» for 36
individual site-years. As A increases, the rankings and magnitudes of the 5,, change to

xxii

favor management of rosettes in winter or summer and germination of new seeds. The
vertical lines differentiate between expanding populations (right) and declining
populations (left). The seven sensitivity contours are split into two panels to improve
readability. LOWESS smoothing was applied to each line to for the same purpose. ..... 204

Figure 4.7. Zero growth isoclines (contours of k = 1, indicating stable A. petiolata
population size) for each study population assuming a random sequence of the three
environments (years) using a megamatrix model. The x and y axes in each plot represent

the efficacy of rosette or fecundity management simulated by increasing the variables c2

or cl, respectively, from 0 to 1. The larger shaded area shows the observed range of seed
reduction and rosette mortality caused by the combined actions of the root and stem
mining weevils Ceutorhynchus scrobicollis and C. alliariae (see Table 2 in Davis et al.,
2006). The smaller rectangle within the shaded area indicates the range of observed
impacts of C. scrobicollis alone, where the upper right corner is the maximum observed
impact of C. scrobicollis. Contours which intersect the larger shaded area represent
populations which could theoretically be controlled by C. scrobicollis and C. alliariae
together at a given level of agent efficacy (e. g. [P would only be controlled if actual agent
efficacy is at the high end of the observed range). Contours which intersect the smaller
shaded area could theoretically be controlled by C. scrobicollis alone. The line from HR

does not appear in the plot because its 1M < 1.Impacts of C. alliariae alone are not shown
because it has not been shown to reduce fecundity under realistic field conditions. ...... 205

Figure 4.A.1 Empirical elasticity contours without smoothing function. Observed
variation in elasticities of Alliaria petiolata population grth versus observed variation
in the lower demographic transitions. In each panel the elasticities of 1. to each lower-
level demographic rate from the 36 site by year matrices is plotted against the observed
value of the transition indicated on the horizontal axis. The eight panels show the same
empirical data sorted differently. The data are sorted from left to right by the transition
labeled on the horizontal axis. In the lower right panel the x axis is shown on a log scale,
although the x axis tick marks are back-transformed to the original scale. .................... 208

Figure 4.3.]. Annual Zero growth isoclines (contours of it = 1) for each site. The
megamatrix result used in the primary analysis is also shown. Within each site, at least
one of the three annual zero growth isoclines crossed the shaded agent—impacts area. In
all sites except HSP, which had positive growth each year, at least one isocline falls
below the origin of the figure. ......................................................................................... 21 1

Figure 5.1 Untransforrned survival and fecundity data plotted against plant density (A.

petiolata plants m'z) at the beginning of the time interval over which survival was
evaluated. Seedling density is the maximum density observed during the spring, summer
and winter starting rosette densities were measured in June and October, respectively.
Each survival parameter estimate shown is a quadrat mean value, calculated as the
proportion of plants marked at the beginning of the time interval that were still alive at
the end of the interval. Fecundity is plotted against the density of rosettes during the
previous October and is shown as the estimated number of seeds produced by each
individual plant within each quadrat rather than quadrat mean values. All plants in a

xxiii

quadrat experience the same starting density and thus align in vertical bands by quadrat in
the figure. Note the differences in the x axes. The maximum plant density steadily
decreases as A. petiolata populations thin over the course of the growing season. ........ 236

Figure 5.2. Observed seedling survival data (dots) and initial seedling density (# m'z)
showing mean predicted trend (solid line) and lower and upper 95% prediction intervals
(dashed lines) for each cohort in Illinois and Michigan based on model results. Dashed

lines show 5th and 95th percentiles of the distribution of survival rates based on simulated
observations generated from the statistical model which was parameterized from the data.
Each distribution is based on 100,000 simulated data sets. Trend lines have been
smoothed to illustrate the overall shape of the relationship between density and the
probability of survival. Analyses were performed on arcsin-square root transformed
survival probabilities and are shown back-transformed to the original scale. Predicted
survival rates with negative values were rounded to zero prior to back-transforrnation to
better illustrate the prediction intervals. .......................................................................... 238

Figure 5.3. Observed summer survival data (dots) and initial rosette density (# m'z) in
June showing mean predicted trend (solid line) and lower and upper 95% prediction
intervals (dashed lines) for each cohort in Illinois and Michigan based on model results.
See Figure 5.2 caption for more details. Note the scale of the X axis for Michigan 2005.
......................................................................................................................................... 240

Figure 5.4. Observed winter survival data (dots) and initial rosette density (# m'z) in fall
showing mean predicted trend (solid line) and lower and upper 95% prediction intervals
(dashed lines) for each cohort in Illinois and Michigan based on model results. See Figure
5.2 caption for more details. ............................................................................................ 242

Figure 5.5. Observed fecundity data (dots, siliques plant-1) and initial rosette density (

# m'z) in fall showing mean predicted trend (solid line) and lower and upper 95%
prediction intervals (dashed lines) for each cohort in Illinois and Michigan based on
model results. Each distribution is based on 50,000 simulated data sets. See Figure 5.2
caption for more details. .................................................................................................. 244

xxiv

Brian (lecturing to large crowd): You're ALL individuals!
The Crowd: Yes! We're all individuals!
Brian: You're all different!

The Crowd: Yes, we ARE all different!

Man in crowd: I'm not...

Life of Brian

Monty Python, 1979

XXV

CHAPTER 1: DEVELOPING DEMOGRAPHIC MODELS TO INFORM SELECTION
OF ALLIARIA PE T IOLA TA (GARLIC MUSTARD) BIOLOGICAL CONTROL

AGENTS

INTRODUCTION

Biological invasions are a major contemporary management problem. Alliaria
petiolata (garlic mustard (M. Bieb.) Cavara and Grande) (Brassicaceae) is one of the
most damaging invasive weeds in North American forests. A native of Eurasia, its
substantial negative impacts on litter and nutrient cycling and its allelopathic and anti-
mycorrhizal effects can disrupt native forbs and tree regeneration (Blossey 1999,
Meekins and McCarthy 1999, Prati and Bossdorf 2004, Stinson et al. 2006).
Conventional strategies have failed to yield effective long term control of any but the
smallest A. petiolata infestations (Nuzzo 1991, 1994, 1996, Nuzzo et al. 1996), and a
search for biological control agents was initiated in 1998 (Blossey et al. 2001b).
Biological control is often considered an environmentally safe alternative to conventional
management. However, a growing awareness of the potential risks to non-target species
posed by some weed biocontrol agents (Louda et al. 1997, Callaway et al. 1999) has
prompted calls for increased rigor in new biocontrol programs (Simberloff and Stiling
1996, McEvoy and Coombs 2000, Louda et al. 2003a) with emphasis placed on a priori
selection of host specific agents that have strong, negative impacts on their intended
target plants (McEvoy and Coombs 2000, Pearson and Callaway 2003, Pearson and
Callaway 2004, Thomas et al. 2004). Matrix population models of target plants and
demographic analysis can improve both the safety and efficacy of weed biocontrol (Shea
and Kelly 1998, McEvoy and Coombs 1999, Rees and Hill 2001). Using demogaphic
models to identify plant life-stages that are most likely to affect a population’s growth
rate if damaged, agent selection and testing can be restricted to species which affect those

optimal target life-stages (McEvoy and Coombs 1999). Additionally, models can suggest

whether single or multiple agents will be necessary to achieve suppression across the
target’s geographic range (Parker 2000). A preliminary model of A. petiolata constructed
from published data (Davis et a1. 2006) suggests that overwintering rosettes should be
targeted initially. However, a more robust, spatially explicit data set is required to address
questions about the range of conditions under which single or multiple agent biological
control are projected to be successful. Developing safe, effective, and economical weed
control strategies will require a combination of new and established empirical and

theoretical ecologically based approaches. This has been the focus of my doctoral studies.

BIOLOGICAL CONTROL

“Biological control is the use of parasitoids, predators, pathogens, antagonists, or
competitor populations to suppress a pest population, making it less abundant and thus less

damaging than it would otherwise be.” (Van Driesche and Bellows I996)

The use of natural enemies to control targeted pest species dates back millennia,
but the use of scientifically rigorous testing to select biological control agents has a
relatively shorter history (Van Driesche and Bellows 1996). Early biological control

efforts were trial and error based and principally designed by intuition. However, as
. . . h
awareness and concern over Impacts to non-target organisms grew during the 20t

century, agent selection became a more focused process and began to address some of

these concerns.

Host Range Testing

Weed biological control in the United States has been regulated since 1957 by the
Technical Advisory Group for Biological Control Agents of Weeds (TAG), a multi-
agency federal panel headed by USDA-APHIS whose purpose is to advise on the practice
of weed biological control “based on consideration of potential non-target impacts and
conflicts of interest” (USDA-APHIS 2006). The goal of agent testing is to predict which
non-target plant species an herbivore is likely to attack if released in a new environment
and is described by Van Driesche and Bellows (1996). The host specificity of candidate
biocontrol agents is evaluated using a centrifugal phylogenetic approach (Wapshere
1974, 1989). A list of test plants is assembled which includes close relatives of the target,
species likely to co-occur with it, and species of economic importance. There are three
stages of testing which are used to discern the agent’s physiological host range (i.e. what
it is capable of feeding and developing on in a contrived, no-choice situation) and its
ecological host range (i.e. what it is likely to feed and develop on under natural field
conditions) (Louda et al. 2005a): (1) in larval feeding trials, larvae of candidate species
are offered test plants tests under no choice conditions in confinement. Rejection by the
larva indicates that it is outside its host range. If it feeds on the plant, (2) a no-choice
adult oviposition trial is conducted in confinement. If eggs are not laid on the plant, it is
deemed not a host. If eggs are laid, (3) a multiple choice oviposition test is conducted in
field cages or in the open field. If eggs are not laid on the plant, it is not a potential host.
If they are laid under these more natural conditions, the non-target plant is within the
agent’s host range, and the agent may be rejected if there is reason to protect the non-

target plant from harm (Wapshere 1989 in Van Driesche and Bellows 1996).

Benefits of Biological Weed Control

Biological control of weeds has several potential advantages over conventional
control methods. Arguments in support of biocontrol include its (1) potential
effectiveness, (2) low resource input requirements, (3) self-perpetuation, (4) low output
of pollutants, (5) reduced non-target impacts, and (6) overall compatibility with alternate
management strategies (McEvoy and Coombs 2000). Cost to benefit ratios for successful
biological control programs can be lower than 1:145 by some estimates (Hoddle 2004a)
and as low as l:12,698 by others (Huffaker et a1. (1976) in Gutierrez et al. 1999) with
gains increasing over time. The successfirl biological control of St. J ohnswort
(Hypericum perforatum L.) (Louda et al. 1997, Whitten and Hoy 1999) and purple
loosestrife (Lythrum salicaria L.) (Blossey et al. 2001a, Landis et al. 2003) in North
America and prickly pear (Opuntia spp.) in Australia and the Caribbean (Bellows 1999)

are frequently cited as evidence of weed biological control’s enormous potential.

Pitfalls of Biological Weed Control: Non-Target Impacts

Non-target impacts of weed biological control programs have been documented
in many systems (e. g. Howarth 1991, Louda et a1. 1997, Stiling and Simberloff 2000,
Louda and O'Brien 2002, Louda et al. 2003a, Pearson and Callaway 2003, Louda and
Stiling 2004), and have inspired discussion about the role biological control should play
in weed management (e. g. Simberloff and Stiling 1996, Pearson and Callaway 2003,
Hoddle 2004b, Louda and Stiling 2004, Pearson and Callaway 2004, Thomas et al. 2004).

The debate focuses on tradeoffs between potential gains from weed biological control

programs and losses incurred through direct and indirect non-target impacts and our
ability (or inability) to accurately forecast the outcomes of these biological control
programs. Decision makers evaluating whether to release new agents must strike a
balance between these. Ultimately, we are forced to weigh the unknown consequences of
introducing an organism into a novel environment against the consequences of either

using conventional control methods or of doing nothing at all.

Direct Non-Target Effects

Most documented cases of direct non-target impacts of weed biological controls
relate either to older weed-control efforts or reflect times when either host-specificity was
not considered important or when certain non-target plants were within the host range of
the proposed agent but were not considered valuable for conservation (e. g. Louda et al.
2005a). Such is the well-documented case of the weevil Rhinocyllus conicus
(ColeopterazCurculionidae) which was released to control invasive European thistles
(Carduus spp.), despite knowledge of its feeding and development on North American
Cirsium thistles from host specificity testing prior to release (Louda et al. 2003b, Rose et
al. 2005). At the time of its release in North America, it was believed that R. conicus’s
preference for Carduus spp. in host specificity trials would limit its impacts on native
thistles (Louda et a1. 1997). Additionally, most thistles, native or otherwise, were
generally considered rangeland weeds without conservation value. Non-target feeding
was reported almost immediately after the initial releases in 1969, and in 1993 the rare
Platte thistle (Cirsz'um canescens) was identified as a preferred host of R. conicus (Louda

et a1. 1997). Further interstate re-distribution of R. conicus was prohibited effective in

2000 (Louda et al. 2003b). Preferential feeding by R. conicus on C. canescens has
resulted in a decrease in C. canescens fecundity and population growth rates and is
predicted to lead to global extinction of C. canescens (Rose et al. 2005). Demographic
modeling indicates that the federally threatened C. pitcheri, a sister species of C.
canescens will rapidly be driven extinct if R. conicus spreads into its habitat (Louda et al.
2005a).

The value of each weed biocontrol program varies regionally. Cactoblastis
cactorum, the same biocontrol agent touted as being enormously successful in the control
of Opuntia spp. in Australia and the Caribbean and the “poster child of biological
control” dispersed naturally from the Caribbean into Florida in the United States in 1989
(Stiling 2002) where it now threatens to drive the endangered native Florida semaphore
cactus 0. corallicola extinct (Louda and Stiling 2004). Although it had been considered
for intentional introduction into the United States on several occasions, introduction was
rejected out of concern for native Opuntia and commercial prickly pear production in
Mexico (Louda et al. 2003b). Because its introduction into North America was
unintentional, some (Hoddle 2004b) suggest that the threat it poses in North America
should not be considered a non-target effect of biological control. However, its deliberate
introduction into Caribbean islands set up the possibility for natural spread to the
mainland United States. This indicates shortsighted planning, as the potential for
redistribution could have been anticipated and considered before introductions were made

(Louda et al. 2003b).

Indirect Non- Target Effects

Indirect impacts on non-target species are more difficult to anticipate and quantify
than direct non-target impacts, and there are relatively fewer examples in the literature.
Conventional biological control theory, based on simple predator-prey interaction
models, postulates that biological control agents impose negative impacts on their target
hosts and thereby confer positive indirect effects on desirable native species. In turn,
reductions in the target host plant negatively impact the control agent and impose
regulation through negative feedbacks. This system is expected to work when control
agents are both highly host-specific and exert strong negative pressures on target
populations (Pearson and Callaway 2003).

The consequences of direct non-target feeding by biocontrol agents can be severe
(Louda et al. 1997, Stiling 2002), but these risks can be quantified a priori (Pemberton
2000). Thus, agent selection processes have increasingly emphasized host specificity
(McEvoy 1996). Host specific agents are presumed to have neutral effects on non-target
organisms. This assumption is used to justify the release of multiple host-specific agents
per target plant when the agents are believed to be host specific (Pearson and Callaway
2003). In this approach, agents are chosen without regard for their potential effectiveness,
and a “lottery” of chance is established in the new environment to determine which of the
agents will succeed in suppressing the target (McEvoy and Coombs 2000). As a result of
this approach, insect species introduced as biological control agents are now more
numerous than their invasive weed target species (McEvoy and Coombs 1999, McEvoy
and Coombs 2000). Despite this, the large majority of weed biological control agents

released do not control their target hosts (McEvoy and Coombs 1999, Denoth et al.

2002). A growing body of evidence suggests that indirect non-target effects can be
mediated by host specific biocontrol agents though “ecological replacement,
compensatory responses, and food-web subsidies” (Pearson and Callaway 2003). These
undesirable indirect effects are much more likely to occur when the introduced control
agents do become established in the introduced range but exert weak pressure on their
targets and fail to control them (Cory and Myers 2000, Pearson and Callaway 2003).
Pearson and Callaway (2003) describe the case of two gall flies, Urophora spp.,
introduced in the 19703 to control the non-native, invasive knapweeds Centaurea
maculosa and C. diffusa. The flies became established in North America and have
remained highly host specific. However, they have not controled Centaurea spp.
populations and subsequently have become highly abundant. Deer mice (Peromyscus
maniculatus) are generalist predators and have increased their overwintering survival
though feeding on the introduced gall fly larvae. Peromyscus maniculatus, in turn, has
become more abundant in this system and negatively impacts native plants and insects
though feeding, other small mammals through competition, and may increase predator
abundances. Irnportantly, as a vector of Hanta virus, P. maniculatus may negatively

impact human populations (Pearson and Callaway 2003).

IMPROVING WEED BIOLOGICAL CONTROL

The key to minimizing the risks of both direct and indirect non-target effects is to
select only highly host specific, highly effective agents and release the minimum number
of agent species necessary to suppress the target (Pearson and Callaway 2003).

Techniques for testing host specificity are relatively well defined, but quantitative

approaches for predicting biocontrol agent efficacy have not yet been used in selection of
agents prior to release. A flush of interest in developing new methods promises to
improve the success rate of biological control and decrease the risk and frequency of non-
target impacts (McEvoy and Coombs 1999, Briese 2006, Davis et al. 2006, Raghu and

van Klinken 2006, van Klinken and Raghu 2006).

The Use of Transition Matrix Models

Matrix population models can be used to interpret a weed species’ population
dynamics and to guide the selection of new biological control agents (McEvoy and
Coombs 1999, Raghu and van Klinken 2006). Caswell (2001) describes their properties,
construction, and interpretation. In past studies, matrix models have been used to
interpret the mechanisms by which biocontrol has succeeded (McEvoy and Coombs
1999), failed (Shea and Kelly 1998, Parker 2000), or had variable outcomes in different
locations (Shea et al. 2005). Recently, attention has turned toward applying them to the
development of new biocontrol programs. While the details of model construction will be
presented in Chapter 4, I will briefly describe some of the ways the model can be used.

A matrix model is an algebraic expression whose components describe the mean
probability of each individual in a population surviving from one life stage to the next
and its reproductive output at each stage in discrete time. These probabilities correspond
with transitions in the organism’s life cycle. The transitions are arranged into a matrix,
abbreviated A (‘the A matrix’) from which a number of useful population statistics can be
calculated. The most pertinent statistics to population management are the population

growth rate (2» , lambda), and the sensitivities and elasticities of lambda to the matrix

10

elements. The population growth rate, 1», is related to the intrinsic rate of increase r from

continuous models as 1. = er or r = 1n 1 (Caswell 2001). When 1» is equal to one, each

individual exactly replaces itself during its lifetime. Values of 1» greater or less than one
indicate expanding or declining populations, respectively. The goal of biological control
is to affect the survival probabilities of a weed such that 1. is driven below one. By
simulating the effects of biological control agents or other management on survival or
reproductive rates, the model can be used to assess the efficacy that management of a
particular stage in the plant’s life cycle would need to achieve to reduce 1» below 1.

The sensitivity of 1 to the each demographic rate is the local slope of 1 as
evaluated at a particular value of the demographic rate. It indicates how much 1» will
change in absolute terms if the transition is perturbed. Elasticities are calculated from the
sensitivities, but are scaled by the proportional contribution of each demographic
transition to 1.. The elasticity of each demographic rate is the proportional change in 1»
expected from a proportional perturbation of the demographic rate. It indicates how much
1 will change in relative terms if the transition is perturbed. Transitions with large
elasticities and large sensitivities are predicted to have large impacts on population
growth and theoretically represent the optimal targets for management.

Elasticity analyses have been used previously to interpret the relative success of
established biological control programs. McEvoy and Coombs (1999) used a post hoc
elasticity analysis of a successful biocontrol program for tansy ragwort Seneciojacobaea
L. (Asteraceae) in Oregon. They attributed successful control of the target to just one of
the two agents released, deeming the other redundant and an unnecessary risk. Parker

(2000) similarly modeled patterns of demographic variation in invasive Scotch Broom

11

Cytisus scoparius along North America’s west coast. She showed significant spatial
heterogeneity in C. scoparius demographic parameters, but elasticity analysis identified
no obviously vulnerable life stage. Her model predicted that nearly 100% and 70% of
seeds would have to be destroyed in prairie and urban populations, respectively, to reduce
1. to less than one, which the introduced biocontrol agents were incapable of achieving.
Shea and Kelly (1998) and Shea et al. (2005) used demographic models to interpret
differential outcomes of biological control agents released against Carduus nutans in
New Zealand and Australia. They found major life history differences between the two C.
nutans populations that drove differences in their elasticity structures. Dynamics of New
Zealand populations were driven by early life stages, whereas rosette longevity was more
important in Australian populations of C. nutans. Of three agents considered in their
analysis, none were able to control C. nutans alone in New Zealand, while in Australia
two were predicted to reduce 1» below one.

Most recently, Davis et al. (2006) used a matrix population model to make a
priori predictions about which stages in the A. petiolata life cycle would be most
susceptible to biological control agents and predicted the levels of mortality that must be
induced by single or multiple hypothetical control agents at each life stage to reduce 1
below one. Their model, parameterized with data from multiple published sources, makes
specific recommendations about which of the potential biocontrol agents being
considered for A. petiolata are most likely to be effective against North American
populations. Davis et al. (2006) found that the greatest elasticity corresponded to the
rosette to flowering transition followed by transitions affecting seed production.

Incorporating the range of impacts the potential agent species have on A. petiolata in

12

laboratory studies, they concluded that multiple agent introductions would be necessary
to extend control of A. petiolata to the greatest number of populations. The weevil
Ceutorhynchus scrobicollis, which disrupts the rosette to flowering transition by mining
in the overwintering rosettes and reduces fecundity by feeding on foliage, was
recommended as a priority agent to be released first. It is predicted to control all but the
most vigorous populations of A. petiolata. For some populations, another supporting
agent that affects fecundity was recommended to be released with C. scrobicollis when
one becomes available. Post-release monitoring will allow biocontrol managers to
interpret which sites and conditions necessitate multiple agents. Taking this “plant first”
approach allows biocontrol practitioners to understand the target’s weaknesses and make
informed agent release decisions. By eliminating ineffective agents from consideration,
the risks of causing non-target impacts can be substantially reduced (McEvoy and
Coombs 1999). In combination with rigorous host-specificity testing, this technique has
the potential to transform the development of new biological control programs from the
traditional “lottery” approach of agent selection (McEvoy and Coombs 2000) into a
directed search for host-specific agents that affect particular life history stages or

transitions.

Demographic Variability

One strategy used to select effective biocontrol agents is to choose and introduce
agents which have been successful elsewhere (Harris 1991). In the case of Cactoblastis
cactorum, redistribution from Australia to the Caribbean resulted in control of the target

in the new location, although the non-target impacts of this choice were costly (Stiling

l3

2002). However, replicating a strategy that had been successful against Carduus nutans
in Australia failed in New Zealand (Shea et al. 2005). The relatively few demographic
studies of plants across spatial or temporal gradients have found significant variability in
demographic rates and statistics (e.g. Bierzychudek 1982, Bierzychudek 1999, Parker
2000). Horvitz and Schemske (1995) studied a tropical rainforest herb for five years in
four locations (n = 16 A matrices) and found variability in 1», in the correlation structure
of demographic parameters, and in the sensitivity and elasticity structure of the
populations both in space and over time. The variation they observed in parameter
sensitivity and demography was not always correlated with variation of other elements in
the environment that the plant could profit from (c. g. presence/abundance of pollinators
during peak flowering). The uncoupled relationship between plant and environmental or
exogenous biotic factors means that variation in a species’ demography does not
guarantee changes in fitness. Rather, demographic variability presents fitness
opportunities or hazards only in concert with conditions that permit realization of a
change in fitness. This suggests that if the target species’ demography and sensitivity
structure vary spatiotemporally, what constitutes an optimal biocontrol strategy will be
conditional on the form and scale of demographic variability and the degree of
parallelism between plant and agent performance and demography across the range of
conditions. Shea et al’s (2005) findings reflect the importance of such variability for
biological control.

Horvitz and Schemske’s (1995) analysis took a factorial approach to
characterizing and interpreting the significance of space (plot) and time (year) in their

model. Another method developed by Horvitz and Schemske (1986), used by Pascarella

l4

and Horvitz (1998), considers the environment itself as a demographic entity with
properties that change over time, in which the study species has demographic rates that
vary as a function of the environmental state. They studied a tropical understory shrub
across a gradient of forest-canopy openness created by a hurricane and the response of
the shrub to the closure of the canOpy over time. The progressive closure of the canopy
was characterized by one set of transition matrices, and the plant’s performance under
each canopy condition was characterized by another. Each patch could transition between
any of seven canopy states, and each plant could transition between any of eight
developmental stages. They nested each of the 8x8 plant demographic matrixes within
each element of the 7x7 forest canopy matrices to create a 56x56 megamatrix which
encapsulated both the environmental dynamics of the system and the organismal
dynamics within each of the possible environmental states. Similar to Horvitz and
Schemske (1995), Pascarella and Horvitz (1998) observed differences between the
elasticity structures of their matrices when considered separately versus when considered
together in their megamatrix. Individually, the matrixes suggested a stable population
dominated by large individuals in closed canopy conditions, whereas the megamatrix
indicated a rapidly growing population whose spread was dependent on the existence of
open patches cleared by the hurricane.

Davis et al.’s (2006) model of A. petiolata biological control was a critical first
step towards the incorporation of predictive ecological models into the decision making
process of invasive species managers. Their approach made use of available data on a
well studied target species and allowed rapid formulation of management

recommendations. However, the data used to parameterize their model were collected

15

from disjunct natural and laboratory populations from Ontario to Kentucky over more
than two decades. These were then pooled to generate ranges across which the
demographic parameters were varied in the simulation analysis. This approach does not
account for the structured correlations between parameters that are shown to have been
important in other study systems. In cases where time is limited, generation of a
demographic model from multiple, unrelated existing data sources to guide selection of
effective agents is much preferred to the “lottery” approach of blindly releasing all
available agents (McEvoy and Coombs 2000). However, when it is possible to do so,
using data collected from distinct populations across the target plant’s spatial range and
over multiple generations or years will allow much more robust management conclusions

to be reached.

STUDY SPECIES
Distribution

Alliaria petiolata is a frequent component of temperate forest understory and edge
communities. It is native to Eurasia where it occurs from England east to Czechoslovakia
and fi'om Sweden and Germany south to Italy (Nuzzo 1993b, 2000). It has been
redistributed into Central Asia, New Zealand (Bangerter 1985) and much of North
America (Nuzzo 2000, Welk et a1. 2002). Alliaria petiolata was first collected in North
America on Long Island, New York, in 1868 (Nuzzo 1993a), where it was likely
introduced by immigrants from the old world. In North America, A. petiolata is most
abundant in New England and the Midwest with populations now present in at least 36

US. States and 4 Canadian Provinces (Nuzzo 2000, USDA-NRCS 2007) from the east

16

coast to Alaska (The Nature Conservancy 2002, Ellen Anderson, USDA Forest Service
personal communication November, 2005). Climate based models of its potential North
American distribution project further range expansion in the future (Welk et al. 2002,

Peterson et al. 2003).

Life Cycle

Evans (2006) reviewed A. petiolata’s biology and life history. Alliaria petiolata is
a disturbance adapted species which profits from anthropogenic and natural disturbances
(Pyle 1995) and can tolerate harsh growing conditions such as lead contaminated soils
(Pichtel et al. 2000). Optimal photosynthetic rates are achieved under light conditions
typical of forest edges, although it can grow under conditions ranging from closed-
canopy forest shade to full sunlight (Dhillion and Anderson 1999, Meekins and
McCarthy 2000, Myers et al. 2005). In forest interiors A. petiolata often colonizes light
gaps where trees have fallen or been removed (Luken et al. 1997).

North American A. petiolata populations have an obligate biennial life cycle
(Cavers et a1. 1979) which can be decomposed into three basic developmental stages:
seeds, first year plants, and second year plants (henceforth “adults”). First year plants can
be further separated into seedlings and rosettes. Seedlings emerge from early spring
through early summer. Rosettes are distinguished from seedlings at some point during the
early summer as those first year plants that survived the germination period early in the
growing season and no longer bare cotyledons. Seeds and rosettes are the only stages

present in autumn and winter.

17

Seeds of A. petiolata require cold stratification to germinate. Dormancy for the
majority of seeds varies from one to two winters (Cavers et al. 1979, Roberts and
Boddrell 1983), although dormant seeds remain viable for nine years or more (N uzzo and
Blossey, unpublished data, ongoing experiment). Germination begins and peaks in early
spring (Baskin and Baskin 1992) under high light, low competition conditions prior to
leaf-out of canopy trees and prior to germination of most native ground layer species

(Myers and Anderson 2003). Seedlings form a low, tight canopy over the forest floor

with population densities as high as 20,000/m2 (Trimbur 1973). Seedlings which survive

the summer overwinter as basal rosettes, bolt the following spring, and flower in early
summer (Cavers et a1. 1979). High seedling mortality results in only 5-9% of seedlings
surviving to form rosettes and only 2-4% of rosettes survivors reaching reproductive age

(Cavers et al. 1979). Nuzzo (1993c) estimated 21.4% winter rosette survival resulting in

mean spring rosette densities of 39.9 (range = 4-102 rosettes/m2) with 9% of the variance

in overwintering surival attributable to fall rosette density. Mature adult plants reach
heights up to 1.8 m (Evans 2006).

Flowers are primarily self pollinating but are visited by generalist pollinators
including Diptera: Syrphidae, and Chironomidae or Ceratapogonidae (described only as
“midges” by Cavers et al. 1979) and Hymenoptera: Apidae, Andrenidae, Halictidae
(Cavers et al. 1979, Anderson et al. 1996, Cruden et al. 1996). Alliaria petiolata
reproduces exclusively by seed (Cavers et al. 1979). Seed production is variable among
individuals (Susko and Lovett-Doust 2000) and populations, with per capita fecundity
ranging up to 7900 seeds (N uzzo 1993b). In dense stands, seed production per square

meter can exceed 100,000 (Cavers et al. 1979). i

18

Several factors affect seed production in A. petiolata. Experiments by Susko and
Lovett-Doust (1999) showed that removal of 50-100% of cauline leaves (leaves along the
stem) from adult plants reduced seed production by 25-46%, and removal of 50-75% of
the root mass of adult plants decreased seed production by 8-13% and reduced the
proportion of seeds maturing by z 4%. Position of flowers within inflorescences and
plant size also affect seed production (Susko and Lovett-Doust 2000). In North America
plants senesce following seed production, although European A. petiolata can perenniate
by production of adventitious buds (Cavers et al. 1979). Dispersal of seeds is limited,
with the majority falling near the parent plant. Long distance dispersal is facilitated by
humans, deer, and mice that transport seeds in muddy footwear and hooves, in fur or
clothing, and automobile tires (Nuzzo 1993a). Seeds have limited ability to float but can
disperse along riparian corridors (Cavers et al. 1979, Nuzzo 1993a).

In newly established populations, first and second year plants are typically not
intermixed within localized patches, creating an effective alternation of generations. Over
time, the seed bank moderates this effect and first and second year plants are found in
unevenly mixed patches. Seedlings that germinate under cover of second year plants have
very high mortality which keeps the generations locally segregated in many areas
(W interer et al. 2005). In areas where it is invasive, A. petiolata spreads in a moving front
as satellite populations ahead of the core establish and fill out, with a positive net rate of
spread in Illinois averaging 5.4 m/y (Nuzzo 1999). A study of seven invaded forests in
southern Michigan documented spatial expansion of A. petiolata in 100% of sites over a

four year period (Evans 2006).

19

Invasiveness ofAlIiaria petiolata

Release from pests or other natural enemies has been proposed as contributing to
the success of some invasive species (Williamson 1996). Damage from herbivore natural
enemies and plant pathogens are frequently found on North American A. petiolata.
However, they do not have significant impacts on its survival or reproduction, suggesting
that natural enemy release may play a role in A. petiolata’s invasiveness (Evans 2006).

Allelopathy has also recently been identified as contributing to increased invasive
ability in several plant species (Bais et al. 2003, Call and Nilsen 2003, Grant et al. 2003,
Weston and Duke 2003, Wolfe and Klironomos 2005). Vaughn and Berhow (1999)
extracted several phytotoxic substances from A. petiolata tissues that negatively impacted
the growth of forbs and grasses. They proposed that these compounds or their derivatives
might additionally inhibit the growth of arbuscular mycorrhizal fungi (AMF). Later
laboratory and field studies showed that AMF growth, abundance, and associations with
vascular plants were reduced or eliminated in seeds or soils treated with A. petiolata
extracts or in which A. petiolata had previously grown (Roberts and Anderson 2001 ,
Stinson et al. 2006). Prati and Bossdorf (2004) demonstrated direct allelopathic inhibition
of germination of a native North American forb grown in soils in which A. petiolata had
been grown, while a congereric forb native to Europe responded positively to the soil
treatment. Disruption of AMF in natural communities could have significant
repercussions for regeneration of trees dependent on AMF associations (Stinson et al.

2006).

20

CONTROL STRATEGIES
Conventional Control

Many conventional methods have been explored to control Alliaria petiolata. Use
of prescribed fire (Nuzzo 1991, Nuzzo et a1. 1996, Schwartz and Heim 1996, Luken and
Shea 2000), herbicide applications (Cavers et al. 1979 and references therein, Nuzzo
1991, 1994, 1996, 2000 and references therein, Carlson and Gorchov 2004), flooding
(Nuzzo 1999, Evans 2006), and mechanical removal (Nuzzo 1991) have resulted in

unsatisfactory control.

Biological Control

In 1998 a search for appropriate biological control organisms for A. petiolata was
launched in Delemont, Switzerland through the cooperative efforts of CABI Bioscience
in Switzerland, Cornell University, and the University of Minnesota (Hinz and Gerber
1998). Blossey et al. (2001b) and Hinz and Gerber (2005) have summarized the search
for biocontrol agents for A. petiolata. From an initial survey of the literature which
identified 69 species of phytophagous insects and 17 fungi in Europe that are associated
with A. petiolata, four weevils belonging to the subfamily Ceutorhynchinae (Coleoptera:
Curculionidae) in the genus Ceutorhynchus are currently considered candidate agents.

Larval Ceutorhynchus alliariae Bristout and C. robertii Gyllenhal mine in stems
and leaf petioles of A. petiolata from March to May and pupate in the soil. Adults emerge
later the same summer and feed on leaves of A. petiolata. Adults overwinter in the litter
and soil, emerge early in the spring, and oviposit in A. petiolata stems and leaf petioles.

In field surveys in Europe, C. alliariae and C. robertii were found either separately or

21

together in 81-100% of A. petiolata plants dissected (Gerber et al. 2002, Gerber and Hinz
2005, Gerber et al. 2008a). Feeding damage from these species results in reduced
fecundity of adult A. petiolata plants.

Ceutorhynchus constrictus (Marsham) has the narrowest host range of the
candidate biocontrol agents tested to date (Hinz and Gerber 2005). Larvae feed on seeds
from May to July and then leave the host plant to pupate in the soil. Adults emerge the
following April to feed on leaves and mate. Each larva consumes and destroys up to three
A. petiolata seeds during its development.

Ceutorhynchus scrobicollis Nerensheimer & Wagner larvae feed in leaf petioles,
buds, and root crowns of overwintering A. petiolata rosettes. Larvae leave the plants to
pupate in the soil by late April. Adults emerge from May to June and aestivate during
summer. Females begin laying eggs in mid September and oviposit continually through
winter into spring. Individual females can produce viable eggs for at least three
consecutive years, although few survive that long and fecundity decreases with age. In
field surveys in Berlin, Germany, C. scrobicollis was found attacking 4-100% of A.
petiolata plants collected and dissected (Gerber et al. 2002, Gerber and Hinz 2005).
Damage from C. scrobicollis leads to direct mortality in overwintering rosettes as well as
reduced fecundity in adult plants.

A petition to release C. scrobicollis in North America was declined by the TAG
in 2008 citing the need for host specificity testing on more plant species and testing of

more western North American species.

22

SUMMARY

Alliaria petiolata is an invasive weed that has the potential to radically alter
native North America forest plant communities. Concerns about the safety and efficacy
of biological control programs require new predictive tools for ensuring that only the
most effective biocontrol agents are released in future programs. The A. petiolata
biocontrol program presents an excellent opportunity to develop and test such tools.

A preliminary plant-based model has been developed to evaluate which stages of
the A. petiolata life-cycle represent optimal targets for management efforts (Davis et al.
2006). However, is model did not account for spatiotemporal variation and covariation in
demographic parameters seen in other studies of this species. Such variation can
significantly affected population trajectories and dynamics (6. g. Horvitz and Schemske
1995, Pascarella and Horvitz 1998). Capturing variability in A. petiolata demographic
rates across its range and over multiple years could be critical to projecting the frequency
of conditions where single or multiple agent biocontrol are projected to succeed. The
linear models used in initial A. petiolata analyses (Davis et al. 2006) may not capture the
true dynamics of natural populations. Observations of early and late spring populations of
A. petiolata suggest that survival is density dependent.

Building from Davis et al.’s (2006) models, we need to ask targeted questions
about the dynamic interactions between A. petiolata and populations of the insect
herbivores that have been proposed as potential control agents. Understanding how
populations of the weed and control agent behave in the presence of one another and
ultimately in a spatial environment will be an important step towards projecting the long-

term outlook for A. petiolata biocontrol.

23

CHAPTER 2: THE SCALE AND SOURCES OF DEMOGRAPHIC

VARIATION IN ALLIARIA PE T [OLA TA

24

ABSTRACT

Variability in demographic rates among natural plant populations can have large
impacts on population structure and cause populations to exhibit subtle or radical
differences in behavior over time. As population modeling studies are increasingly called
upon to guide policy and management decisions, it is important that they accurately
represent the dynamics of their study systems. Quantifying the sources of variability
across the life history of an organism is the first step in this process. I studied the
demography of 12 natural populations of the invasive forb Alliaria petiolata (garlic
mustard) over three generations of its life cycle. Generalized linear models (GLMs) and
hierarchical, generalized linear mixed models (GLMMs) were used to analyze the spatial
and temporal scales of structured variability in each lower level demographic transition
and the intrinsic, edaphic, and climate-driven mechanisms which underlie them. I
developed statistical approaches to deal with common discontinuities, such as zero- and
one-inflation issues, that made conventional analyses problematic. Population density and
climate variables played important roles both in directly affecting morality and in
predicting the fates of individuals later in their life histories. Variation in germination and
survival rates was significantly structured across sites and years, but the distribution of
fecundity varied only across sites. Persistence of dormant seeds in the soil seed bank was
high, with a mean viability of 91 .9% after one year. Germination, seedling, and summer
rosette survival were influenced by negative density dependent feedbacks. Overall winter
rosette survival was not density dependent, although the probability of extremely high (1)
and low (0) winter survival was negatively density dependent. Fecundity was negatively

dependent on final flowering plant density during dry years, but positively dependent

25

during wetter years. The frequency and amount of precipitation early in the life history
were associated with increased survival for the remainder of the life cycle, but increasing
summer precipitation and temperature negatively affected survival. The degree of
variation observed in A. petiolata demographic rates encompasses the results of almost
all previous studies of this species. This variation is highly structured in space and time in
response to biotic and abiotic conditions. Previous studies that have explored subsets of
A. petiolata's demographic parameter space may therefore be limited in the scope and

applicability of their predictions.

26

INTRODUCTION

Spatiotemporal variation in demographic rates of plant populations arises through
a combination of stochastic effects, environmental drivers, and intrinsic factors. The
magnitude and form of this variation has important consequences for both local and
regional population and metapopulation dynamics, particularly with respect to extinction
probabilities. Incorporation of environmental and stochastic demographic variability and
population regulation can greatly improve the accuracy and predictive power of
population models which would otherwise behave asymptotically (e. g. exponentially). As
modeling studies are used more frequently to guide population management, it is
important that they accurately represent the behaviors of the populations they are meant
to simulate (McEvoy and Coombs 1999, Buckley et al. 2003a, b, Briese 2006, Davis et
al. 2006). A single plant species can vary in its life history and demography across its
range to the point where entirely different approaches could be necessary to successfully
manage it in different locations (Parker 2000, Shea et al. 2005). Accounting for variation
among populations becomes especially important for regionally to continentally applied
management such as weed biological control, which utilizes autonomously redistributing
herbivorous or pathogenic agents. Complex indirect non-target impacts can arise when
biocontrol agents spread to areas where they are not effective at controlling the target
species (Pearson and Callaway 2003, Pearson and Callaway 2005). Thus, quantifying
demographic variation among populations and incorporating it explicitly into new
management models presents an opportunity to improve the safety and efficacy of

management tools like biological control.

27

Alliaria petiolata (garlic mustard, Brassicaceae [M. Bieb] Cavara and Grande) is
a broadly distributed, invasive weed in North America that is the target of active
management using various techniques. Numerous studies have quantified aspects of its
biology and ecology, but a comprehensive analysis of variation in its population structure
and dynamics across the landscape is incomplete. A promising initial evaluation of the
known variability in A. petiolata demography assembled from published sources
indicated a gradient of susceptibility to management at specific life history transitions
(Davis et al. 2006). In their study, Davis et al. evaluated the responses of simulated A.
petiolata populations to management of varying intensity that targeted single or multiple
demographic transitions simultaneously. Building from this, the next step towards
predicting the probability of successful A. petiolata management is to determine the
distribution of the species’ demographic rates among natural populations.

Individual A. petiolata survival and reproductive rates reported in the literature
each vary broadly when compared across multiples studies (Davis et al. 2006, Table 1,
and Pardini et al. 2009, Appendix A). For example, Cavers et al. (1979) measured the
annual survival probability of dormant seeds as 0.99 from 1975-1978 in southern Ontario,
Canada. . Thirty years later, Meekins and McCarthy (2002) reported values between
0.30-0.32 from 1996-1998 for the same parameter measured in Athens, Ohio. Variation
in seed survival of this magnitude could mean the difference between a successful
management program versus a failed one because of the resulting differences in longevity
of the seed bank. This is evident in the changing elasticity structures among populations

with different seed survival rates (see Davis et al. 2006, Figure 4A for an illustration).

28

Results of previous A. petiolata studies have suggested two principal guiding
questions from which the experimental and analytical designs were crafted. First, I asked
whether the variation in each demographic transition is hierarchically structured in space
and/or time. In the example above, one would want to know whether the differences in
seed survival resulted from site effects, year effects, both, or if the variation was random.
Also, because A. petiolata growth and photosynthetic rates respond to light intensity
(Dhillion and Anderson 1999, Meekins and McCarthy 2000, Myers et al. 2005), I also
asked whether there were differences within sites between forest edge and forest interior
habitats, as such differences could explain possible variation in population dynamics
within each site. The answers to these questions will be used to determine the hierarchical
levels at which each demographic rate should be pooled for use in future simulations of
A. petiolata population dynamics.

Second, I asked whether the variability in survival and reproductive rates could be
explained by local variation in biotic and abiotic conditions like population density, soil
or climate properties. This second question seeks a mechanistic explanation of
demographic variablity. From this perspective, I would expect any site, year or other
categorical differences to be the net result of differences in the conditions that are
biologically meaningful to plant growth and survival. Addressing this question will allow
pararneterization of survival and reproductive functions which can be combined to build a
more generalized, dynamic model of A. petiolata population growth.

In this study I quantified recruitment, survival, and reproduction of over 60,000 A.
petiolata individuals and seeds at 12 study sites in Michigan and Illinois from 2005

through 2008. I conducted two sets of analyses using generalized linear mixed models

29

(GLMMs) and generalized linear models (GLMs) to address each of the questions posed
above. First I analyzed the spatial and temporal scales at which demographic rates varied
among populations and years. These analyses generated estimates of demographic
parameter distributions for use in predictive population models. Second, I parameterized
survival and reproduction models of each life history stage as a function of population
density and abiotic variables. These functions will be used in future discrete-time
dynamic models of A. petiolata populations. Within each set of analyses I used multi-
model inference to rank and select the best supported model from a set of a priori

candidate models.

METHODS
Study Species

Alliaria petiolata is an understory forb native to western Eurasia. It has been
documented in North America since the 18603 (Nuzzo 1993b) and now occurs in at least
36 US. states and six Canadian provinces (USDA-NRCS 2007). A. petiolata is a shade
and cold tolerant herb (Anderson et al. 1996, Dhillion and Anderson 1999, Meekins and
McCarthy 2000, Myers and Anderson 2003, Myers et al. 2005). Dormant seeds can
remain viable in the soil seed bank for at least ten years (Nuzzo and Blossey, unpublished
data). Density dependence has been observed for survival and fecundity (Meekins and
McCarthy 2000, Winterer et al. 2005, Pardini et al. 2008, Pardini et al. 2009), but not in
germination or recruitment rates. Like other Brassicaceae, A. petiolata has complex
allelochemistry that negatively affects competitors through disruption of soil microbial

and fungal communities (Vaughn and Berhow 1999, Roberts and Anderson 2001, Prati

30

and Bossdorf 2004, Stinson et al. 2006, Stinson et al. 2007, Callaway et a1. 2008, Wolfe
et al. 2008). Few pathogens or herbivores cause significant damage to A. petiolata in its
invasive range (Renwick 2002, Evans 2006, Evans and Landis 2007, Keeler and Chew
2008), although Yates and Murphy (2008) recently found three naturalized herbivore
species that successfully develop on A. petiolata in southwestern Ontario, Canada. They
proposed that these species may merit further investigation as possible biological control
agents for A. petiolata.

The A. petiolata life cycle can be broken into four distinct life stages: seeds,
seedlings, rosettes, and flowering plants (Figure 2.2). Second year flowering plants are
fiequently referred to as “adults” in the A. petiolata literature. Seeds of A. petiolata
germinate in early spring after a period of cold stratification (Baskin and Baskin 1992,
Raghu and Post 2008) and produce dense carpets of seedlings. In the North Central
region of the USA, surviving seedlings mature into low rosettes of petiolate leaves.
Rosettes grow through the summer and fall, holding most of their leaves through the
winter. Surviving rosettes bolt in late April or May the following year in southern
Michigan (mean height = 71 cm, data from Evans and Landis 2007) and flower from May
through June. Flowers are predominantly self pollinated (Durka et al. 2005). Seeds
develop in slender fruits (siliques) along the upper stem and are shed from August
through September after all flowering plants have senesced. Individual siliques contain
14.3 to 20.7 seeds on average (Evans and Landis 2007). Mean per capita fecundity
estimated in eight Michigan forests in a previous study ranged from 0 to 446 (mean =
207) (Davis et al. 2006). Dispersal of seeds is limited. Most fall beneath the parent plant,

although deer are believed to move seeds that get caught in their fur or hooves, and mice

31

are thought to frequently cache them. Past studies have demonstrated large variation in all

A. petiolata vital rates .

Study Sites and Data Collection

Alliaria petiolata demographic rates were measured in 12 forested sites in
Michigan (7) and Illinois (5) from 2005 through 2008 (Figure 2.1, Table 2.1). Sites were
selected based on the presence of established, unmanaged A. petiolata populations and
accessibility. Seven demographic rates were quantified in the field. Four replicate
measures of each demographic rate of were taken at each site for each of three cohorts:
2005-2007, 2006-2008, and 2007-2009. Four groups of sampling quadrats were
established within each site: two near the forest edge and two in the interior. This allowed
comparisons between plants growing in different light environments within each site.
Sampling areas were spaced 20 to 150 m apart as space permitted within each site. Three
types of permanent quadrats were established within each sampling area to estimate rates
of 1) seed germination and seed survival, 2) seedling survival, and 3) rosette survival and

fecundity. A timeline illustrating how data were collected is shown in Table 2.2.

Germination and Seed Survival

I estimated germination rates in 20 x 20 x 2.5 cm deep wire screen trays buried at
the soil surface. Each June (2005, 2006, 2007), topsoil was collected from 3-5 cm depth
in an area fiee of A. petiolata near each sampling area and distributed to each of four
screen trays. Two trays were then randomly selected to receive an addition of locally

collected A. petiolata seeds at rates estimated from mature plants in the rosette survival

32

 

quadrats. The other two trays served as controls for background seed contamination in the
soil. Adult plants were cleared within 2 meters of the seed trays to prevent the
introduction of unrecorded seeds. The following year seedlings were counted
destructively as they emerged from February until germination was complete.

Germination rates of newly shed seeds (g1, Figure 2.2) were calculated as the total

number of seedlings in the seed addition trays minus the number of seedlings in the
control trays divided by the number of seeds added. One pulse tray and one control tray
were collected in June and the remaining seeds were elutriated, counted, and stained with

2,3,5-tetrazolium chloride (AOSA 2000) to determine viability (seed bank survival rate
SS). The second pair of trays was left out for a second winter. Germination rates of older
seeds from the seed bank were measured the following spring, two years after being sown

(g2, Figure 2.2), using the same technique.

Seedling Survival
Estimates of seedling survival to the rosette stage (3,) were made each spring

(2006, 2007, 2008) in 25 x 25 (Michigan sites) or 20 x 20 cm (Illinois sites) quadrats.
Seedling locations were marked on transparent plastic sheets laid over the quadrats every
one to three weeks. Seedling survival rate was estimated as the ratio of seedlings
surviving to the rosette stage in June to the peak number of seedlings observed on any
date in the spring. Second year rosettes were also marked, although they did not occur in

all seedling quadrats.

33

Rosette Survival and F ecundity:

Whereas Davis et al. (2006) estimated survival of rosettes to the flowering stage

over a full year as s,f, I split the measurements of the transition into two periods to
provide greater temporal resolution (Figure 2.2). Summer (sum) and winter rosette

survival (s,,.,-,,) were measured in 50 x 50 (Michigan sites) and 40 x 40 cm (Illinois sites)

quadrats. New rosettes were marked in June (2005, 2006, 2007) on transparent plastic
sheets. Survivors were located during a fall survey in October or November and again the
following June. Summer and winter survival rates were estimated as the ratio of fall to
summer rosettes, and mature flowering plants to fall rosettes, respectively. F ecundity (I)
was estimated for each surviving mature plant by counting the number of siliques and
scaling by the number of seeds per fruit. This relationship was determined from a set of
destructively harvested test plants using a breakpoint linear regression to account for
nonlinearity in the ratio of seeds per fruit between large and small plants (Appendix

2.B.iv). Seed addition rates for the germination trays during the following year were

estimated from these plants as the density of seed rain (seeds m'z) produced by all

surviving plants.

Germination trays vandalized or disturbed by animals during the experiment

(21%) were not used in analyses of g1, g2, or $5. All plant densities were converted to a

common scale of plants rn'2 for use as covariates in analyses of density dependence.

34

Climate Data

Temperature and precipitation data were assembled from the National Climate
Data Center (NCDC) database (www.mcdcnoaagov) using the nearest available weather
station for each site. Missing observations were filled in using data from the next nearest
weather station. Observations from some stations that were difficult to reformat and
assimilate into the database as provided by NCDC were downloaded from a commercial
intemet website (www.wunderground.com) which makes the same data available in a
different format. Daily precipitation (mm), minimum and maximum temperatures (°C)
values were compiled for each site from January, 2004 through October, 2008. These
were then distilled into sets of monthly and seasonal summary statistics to be tested as
predictors of A. petiolata vital rates.

Decisions about how to summarize the climate data were based on A. petiolata's
reported cold tolerance and early season growth (Anderson et al. 1996), and sensitivity to
dry summer conditions (Byers and Quinn 1998) and then refined through exploratory
graphical analysis. Abbreviations for climate statistics are italicized. Temperature data
were processed in five ways. 1) Because A. petiolata is capable of photosynthesizing
during winter when temperatures are above freezing, growing degree days were
calculated using a base temperature of 0°C (gdays). I hypothesized that A. petiolata vital
rates could be driven by threshold-based climate conditions. I calculated the number of
days per month with minimum temperatures: 2) below 0°C (cold days, cold), 3) below -
18°C (very cold days, vcold), and 4) above 0°C (warm days, warm), and 5) with

maximum temperatures above 34°C (hot days, hot). Threshold temperatures used for

35

 

very cold and hot days were based on graphical analysis. Mean, minimum, and maximum
temperatures had weak or no associations with demographic rates.

Precipitation was compiled into three monthly statistics: 1) total monthly
precipitation (mm, prep), 2) the number of days with > 0 mm precipitation (rainy days,
rain), and 3) the number intervals between precipitation events during which the soil
could dry out (drying events, dry). The drying statistic complements the rainy days
statistic as a way of quantifying the fi'equency of precipitation events. For example, the
rainy days statistic might indicate that it rained 14 days in a given month but doesn't
convey any information about whether it rained for two weeks straight and then was dry
for two weeks, or if it rained every other day. Knowing additionally whether there was
one drying event versus 14, we can distinguish between these two patterns of
precipitation.

Seasonal climate statistics were calculated by splitting the “garlic mustard year”

into four stages based on A. petiolata phenology and summing monthly values within

each stage for each year: spring (Spring, January — March of seedling year, used with g],
s,), summer (Sum, May — September of seedling year, used with ssum), winter (Win,

October of seedling year— March of flowering year, used with swin), and flowering period

(fec, February — May of flowering year, used with f). The spring and summer stages were
split further for some analyses. January and February data were grouped, as this seemed
likely to be an important pre-germination time interval, and August and September
drying events, when drought stress seemed most likely to affect summer survival. Finally,
precipitation data from March were used in analyses of seedling survival, and May

precipitation and rainy days were used in summer survival analyses.

36

 

Soil Data

Selected soil chemical and physical properties relevant to plant growth, including
gravimetric water content, particle size distribution, water holding capacity, organic
carbon, pH, P, K, Mg, Ca, and inorganic N were measured at the quadrat level for all
locations. Ten soil cores 1.9 cm in diameter were taken to a depth of 10 cm from the
perimeter of each adult census quadrat at the time of census in June 2007 and bulked to
form a composite sample. Gravimetric soil moisture was immediately determined on a 25
g subsample by oven drying at 65 °C to constant weight (Klute 1986). The remainder of
the composite sample was sent to A&L Great Lakes Laboratories in Fort Wayne, Indiana,
where all other soil analyses were performed. Particle size distribution was measured
using the hydrometer method (Gee and Bauder 1986). Soil water holding capacity was
measured at a matric potential of -1/3 bar (-33 kPa) using the pressure membrane method
(Klute 1986). This matric potential was chosen for measuring soil moisture retention as it
represents field capacity, the point at which all water drainage due to gravity has
occurred, after a soil has been fully saturated (Brady and Weil 1.996). Organic carbon was
measured by loss upon combustion (Nelson and Sommers 1994) and soil pH was
measured in aqueous solution with a hydrogen selective electrode (Thomas 1996).
Available P, K, Mg and Ca were measured using ICP (inductively coupled plasma

spectroscopy) methods (Soltanpour et al. 1996). Finally, inorganic N ions, including both
NO3-N and NH4-N, were measured using automated colorimetric procedures (Mulvaney

1996). The site mean value and standard error of each soil variable are included in

Appendix 2.A.

37

 

Statistical Analysis
The data analysis addressed two principal goals. First, I wanted to determine the

spatiotemporal scales at which most variation occurred for each A. petiolata vital rate to

facilitate pooling of variables at the appropriate scales. For example, if g 1 varies

significantly at the site level but not across years, estimates of germination probability
can be drawn from a common distribution within each site. These parameter estimates
will be used to assemble a set of A matrices for use in future projection models, loglinear
analyses, and Life Table Response Experiments (LTREs) to analyze how variation in
survival rates contributes to differences in population growth and possible responses to
management. Second, I wanted to explore mechanistic sources of variation in vital rates,
and thus constructed a separate set of environmental models which included climatic,

edaphic, and population density covariates

Hierarchical Mixed Model Analyses

I used fixed effects GLMs and GLMMs, which incorporate both fixed and
random effects, to evaluate how each lower level demographic rate varied across the
spatial and temporal structure of the sampling design. These are generalized forms of
familiar linear and linear mixed models which can accommodate data with non-normal
error distributions (Bolker et al. 2009). This is done via a link function that transforms the
predictor to meet the distributional assumptions made about the data. This allows a linear

model to then be fit. The link function used depends on the underlying distribution of the

data. Models of g1, g2, sr, ssum, and swin were fit using a binomial error distribution and

38

logit link. The natural logarithm of fruit production + 1, 1n(f+1), was modeled with a
normal distribution and identity link using the mean siliques/plant as the response
variable weighted by the number of plants in the quadrat. Although I initially modeled

the raw fecundity observations at the plant level, residual diagnostics were unacceptable.
Distributions used to model 5, are described below. All analyses were conducted in the

GLIMMIX procedure in SAS version 9.2 (SAS Institute 2008) except where noted.

For each vital rate, a set of candidate models was developed that embodied
alternative hypotheses about which spatiotemporal levels of the data structure were
important. I then used a multi-model inferential approach based on maximum likelihood

to evaluate which models were best supported by the data (Bumham and Anderson

2002). Models of swim f, g2, and s, were evaluated and ranked using AICc, an information

criterion corrected for small sample sizes (Anderson 2008). Models of gl, 5,, and ssum

were overdispersed and were evaluated with Quasi-AICc (QAICc), which includes an
additional correction for overdispersion (Bolker et al. 2009). AICc and QAICc will both

be referred to as "AIC" in the main text for readability, but will be distinguished in the

tables and appendices where important. The model with the lowest AIC score (AICmin)

within a set of competing models is considered the best model, given the data. More
details about the model fitting and ranking process are provided in Appendix 2.B.i. An
explanation of how spuriously supported models with "pretending variables" (Anderson

2008) were identified is described in Appendix 2.B.ii.

For g1, g2, sr, ssum, swim and fl the full GLMM structure included fixed terms for

Site, Year, Site*Year interaction, and Location (edge vs. interior). Site was included as a

39

fixed effect in this analysis because we are ultimately interested in making site-specific
predictions about A. petiolata population growth and its potential response to
management. Quadrats were modeled as random effects to account for correlations
between observations made within individual quadrats. Although year would ideally have
been modeled as random, there were not enough levels of the year variable (n=3) to test
the assumption that the levels of each random effect are normally distributed. Reduced
models included all factorial combinations of the fixed effects in the full model plus an

intercept-only model for a maximum of ten models per demographic rate.
The seed bank (s3) viability data had an inflated fi'equency of ones, i.e. 100%

viability. These properties made it difficult to fit a GLM or GLMM using a standard error
distribution. Instead, I used a two stage conditional modeling approach similar to that
described by Cunningham and Linenmayer (2005). The data were analyzed by first
modeling probability 7: of observing 100% seed viability in a sample with a binary GLM.
Second, I modeled the non-zero observations with a beta error distribution (see Appendix
2.B.iii for details). As Cunningham and Lindenmayer (2005) point out, this two step
method has an advantage over using zero-inflated or mixture distributions because the
component analyses are orthogonal and can be driven by independent processes. Because

a number of observations were discarded (described above) the 113 " good" observations

of s, were unbalanced with respect to sites and quadrats across years. Although there was

at least one empirical observation of ss per site per year, random quadrat effects and

edge/interior location effects were excluded to avoid overfitting.

40

Environmental Models

The hierarchical analyses are useful for analyzing the structure of variability in
vital rates across sites and years. However, they are not mechanistic and therefore are
limited in how broadly their results can be generalized beyond the study system. I
constructed a second set of GLMs and GLMMs to explore how A. petiolata demographic
rates responded to differences in soil properties, climate variation, and population
density. Following the example of Buckley et al. (2003a), I used GLMMs to evaluate the
response of each lower level demographic transition in the A. petiolata life cycle to a set
of extrinsic and intrinsic variables. For each transition, a set of candidate models with
different combinations of fixed and random effects was defined a priori. Because of the
large number of possible explanatory variables and interactions, preliminary graphical
analysis of the data was necessary to reduce the number of variables included during the
model fitting process. Models were fit to the data in GLIMMIX and ranked using AICc
or QAICc when overdispersion was present. Extrinsic factors included as fixed effects in
models for each transition were combinations of climate statistics for time intervals
relevant to the transition and soil variables in each quadrat. If there were no strong a
priori hypotheses about specific soil variables, versions of full models with different
combinations of soil variables were fit and ranked using AIC. Soil variables from the best
supported models were included in the development of subsequent reduced models. In all
cases, the only soil variables retained in the final models were those which had a priori

support. Intrinsic effects included the natural logarithm of A. petiolata population density

[ln(plants m-2)] at the start of the transition as well as observed A. petiolata densities and

survival rates from previous transitions. For example, both October rosette densities and

41

June adult plant densities were included in analyses of f. Quadrats were modeled as
random effects. Fecundity models were fit using a Poisson error distribution and survival

models were fit with binomial errors except as noted below.

The environmental models of g 1, s, and ssum were overdispersed and were ranked

using QAICc (Appendix 2.B.i). The significance of random quadrat effects was tested for
each model with a likelihood ratio test. The residual deviance explained by the full

GLMM was compared to the residual deviance of a reduced GLM with no random terms.

The drfference 1n devrance explained was compared to a mixture of x distributions With

1 degree of freedom using the covtest / glm option in GLIMMIX to test the null
hypothesis that the random effects did not improve the amount of deviance explained by
the model.

Winter survival had an extreme-value inflated distribution with a high proportion
of both zeros and ones (n = 37). This was accommodated by splitting the winter survival
analysis into a two step conditional process like the seed survival analysis. In the first

step, I estimated the probability of an observation being extreme versus not extreme as a

binary response to a set of predictor variables (model s,,.,-,,1). Second, if the observation

was extreme, I modeled the probability of it having 0 versus 100% survival as a binary

response (model swin2a). If the observation was not extreme (i.e. 0 < swm < 1), it was
modeled with a binomial GLMM (model s,,,,-,,2b). Random quadrat effects did not
improve the fit of the binary models and were dropped from s,,,,-,,l or s,,.,-,,2a. Note that
model swinl predicts the probability of an observation being extreme or not. This

determines whether to proceed to s,,,,-,,2a or Swian- Model swin2a predicts the probability

42

of an extreme observation having a survival probability of either 0 or 1, conditional on

knowing that the observation is extreme. Model s,,,,-,,2b predicts quadrat mean survival

probabilities between 0 and l, conditional on knowing that the observation is not

extreme.

G; was not measured during the third and final season (spring 2009) but was

estimated by modeling the relationship between g1 and g2,and the seed bank size during

the first two years of the study and projecting forward (Appendix 2.B.v). Because the

model used pooled data, there are only site level estimates of g2 during the third year.
Hierarchical models ofgg did not include the estimated rates from the third year. No

environmental analyses were run on g 3.

RESULTS

Alliaria petiolata demographic rates were highly variable across the twelve sites
and over the three years of the study. For survival there were clear site by year interaction
effects, as the indicted by the changes in ranking of the 12 sites over the study period
(Figure 2.3). These interaction plots are also revealing of the relative contributions of site,

year, and site by year interactions in structuring the vital rates spatiotemporally. For
example, variation in germination of new seeds (g1) appears to have been dominated by
year effects, while the site by year interaction had much stronger effects on seedling
survival. These data agree with my general observation that summer survival and g1 were

highest during the first year of the study and then decreased during subsequent years,

43

while patterns of variation in seedling survival over time was much less consistently
across sites.

The distributions of most transitions were heavily right skewed (Figure 2.4), with

high frequencies of zero % survival of summer (25 of 143 observations, mean ssum = 0.22
i 0.03) and winter (30 of 121, mean SW," = 0.33 i 0.03) rosettes. This contrasts with the

more uniform distribution of rosette survival (mean 5, = 0.49 i 0.04), with only four

observations of zero survival out of 144. Seed survival was high in contrast (100% 70 of

113 times, mean 5, = 0.92 i 0.02). Mean g1 (0.31 d: 0.03) and g2 (0.11 d: 0.03) were lower

than comparable mean rates compiled from the literature by Pardini et al. (2009), and are

closer to the means of rates assembled by Davis et al. (2006). Few other A. petiolata

studies have reported measures of ssum and s,,.,-,,. These are more commonly combined
multiplicatively into s,f, the probability of surviving from the rosette to the flowering

stage over a full year. The mean estimated s,f(0.1048) calculated from ssum and s,,.,-,, was

also considerably lower than others' estimates (mean of rates compiled in Davis et al.

2006 = 0.548).

Natural peak seedling densities in the study system ranged from 75-6025 m-2

(median : 877.5), and June rosette densities in the system ranged from 31 .25-3344 m-2
(median : 232). The high densities I observed occurred during the first year of the study,

reaching maxima (median) of 5696 (1096), 6025 (890), and 2650 (704) plants m.2 for

seedlings and 3344 (368), 1092 (210), and 976 (212.25) In.2 for rosettes in 2005-2007,

respectively.

44

Hierarchical Mixed Model Analyses

Demographic rates of A. petiolata were substantially differentiated among sites

and years. Likelihood based evaluations most strongly supported models of g 1, g2, Sr,

35”,", and swim with terms for site, year, and site"‘year interactions (Table 2.3). This

indicates that sites differed in their responses to year effects for these parameters. For

each of these models except swim the second best supported model also included a term

for forest edge versus interior location. Each had a AAIC of approximately 3, but the
extra variable didn’t explain any additional variance in the response, evidenced by the
similarity of the ln(l) values for these models. The additional location term in these
models appears to be a “pretending variable” (Appendix 2.B.ii) and these models were
discarded from consideration. After dropping these models from consideration, the
remaining models in each of these sets had no support from the data.

The best supported model of fecundity included a significant fixed effect for site
only (F 1 1,45 5.00, P < 0.0001 ). Estimated mean values for f are therefore statistically the
same for all years within each site. Models with terms for location also appeared to be
well supported as described above and were excluded from model weighting.

Seed viability in the seed bank was evaluated in two stages because of the high

proportion of ones in the data. In the first step, the data best supported the binomial GLM

with a fixed year effect only. The probability of a population having 100% viability was

lower in 2006 than in either 2005 or 2007 (ls-means difference ’110 = 3.17, P = 0.0020,

and 1110 = -3.32, P = 0.0012, respectively), while the probabilities were approximately

45

equal in 2005 and 2007. Among the remaining observations with less than 100% seed
survival, variability in seed survival was randomly distributed among sites and years with

a mean viability of 0.7847 and beta distributed errors. Note that the second best model for

s, < 1 also appears to be a "pretending variable" model (Table 2.3). Combining the

probabilities from the two seed survival models yields predictions of s, = 0.9462, 0.8668,

and 0.9508 for all sites for the three consecutive years. Plots of the model conditional

predictions (i.e. including random effects) are shown in Figure 2.5.

Environmental Models:

Density dependent feedbacks and responses to climate and intrinsic factors from
previous life stages were common features in models of most demographic rates. In some
cases an earlier population density, climate or survival metric was predictive of a later
survival or reproductive outcome. This suggests that individual success, however
measured, is developed though a cumulative process that conditions individual plants
over their life time. For most A. petiolata demographic rates a single model clearly

received the greatest support from the data, indicated by the Akaike weights and AAIC
scores. The exception to this was SM" 1 , for which the best model received 34% of the
Akaike weights. Because the next best model was only half as well supported, I chose the
top ranked model. The parameter estimates and their standard errors for the best

supported model of each demographic rate are presented in Table 2.4-Table 2.8. Also

shown are the type-3 F -tests of the null hypotheses that each parameter value is not

different fiom zero and the )(2 likelihood ratio tests of the random effects. In models that

46

included and retained random quadrat effects, the random effect is assumed to be

normally distributed with mean 0 and variance as estimated. Random quadrat effects

greatly improved the fit of models of g 1, Sr, 55“,", s,,,;,,2b, and f but were dropped from the

two binary models swinl and s,,,,-,,2a. The goodness of fit of each model to the data is

illustrated in Figure 2.6. This shows the observed and predicted values from each model
generated from the best linear unbiased predictors (BLUPs) which are based on the
parameter estimates for both the fixed and random effects. Interpreting how the
independent variables in each model affect the response can be challenging when there
are significant interaction terms and because the regression coefficients are in a
transformed data scale. Plots of the observed and predicted demographic rates versus the

independent variables help to illustrate these relationships (Appendix 2.C).

Germination

Germination probability of newly shed seed (g 1) was most strongly influenced by
climate conditions in January and February, just prior to germination (Table 2.4). The
best model of g 1 was supported by 85.3% of the Akaike weights and was separated from

the next best model by AAIC of 3.7. Germination was reduced by the frequency of days
with measurable precipitation (rain) in January and February and increased by the
number of warm January and February days. There was an interaction between warm

days and soil water holding capacity that weakened the relationship between warm days

and W.H. C. as W.H.C. increased. Because of its correlation with g I, 2 was not modeled.

47

Seedling Survival
Seedling survival was regulated by a combination of negative density dependent

mortality plus the additive and interactive effects of several climatic and edaphic factors
(Table 2.5). The best supported model of s, received 95.8% of the Akaike weights, while
the next best model had a AAIC of 7.8 (Table 2.5). Seedling survival is negatively
dependent on March precipitation (prcpmm, mm), the natural logarithm of soil water
holding capacity (whc3bar), and the fiequency of warm days in January and February

(warmjf, tmin>0°C) but is positively dependent on total soil inorganic N. The frequencies
of hot days in summer (hotsum, tmax>34°C) and rainy days in autumn (rainfall) during the
year prior to germination affect s, through an interaction illustrated in Figure 2.7. Fall

rain has a negative effect on 5, following a summer with a high number of hot days, but

has a positive effect after a summerwith few hot days. Because survival rates are
bounded on the closed interval [0, 1], the relative magnitude of any single effect is
dependent on the combined magnitudes of all the other factors in the model, as is seen in
the effect of seedling density (Figure 2.7). Although only seedling plots in Michigan
contained both seedlings and second year rosettes, including these in the models with
additive or non-additive terms did not explain any additional variance in seedling

survival.

Summer Survival
The best model of summer rosette survival (ssum) was supported by 99.3% of the

Akaike weights, and was separated fi'om the next best model by a AAIC of 10.0. After

48

accounting for the variability in survival due to other extrinsic factors in the model, the
strength of density dependent mortality during the summer (slope = -0.2951, Table 2.6)

was approximately equal to the rate in spring (slope = -0.2320, Table 2.5). During

summer, this translates to a decrease in survival probability from 1.0 to 0.427 (=e'0‘2951)

for each increase of 1 unit of the log of June rosette density, holding all other variables

constant at zero. The range of June density was ~ 4.6 from the most to the least dense

quadrat, in log transformed units. Density alone would be expected to reduce ssum from

1.0 to 0.257 (=e"2951*4'6), again holding other variables constant at zero. In nature the

variables do co-vary and are non-zero, so the strength of density dependence will again

be scaled by the contributions of other variables. Because of a positive correlation

between the quantity (prcpmay) and frequency (rainmay) of rain events (Pearson's r =
0.7699), increases in either variable positively affect 3mm. There were also negative
correlations between summer hot days hotsum and the number of drying events in August

and September dryas. This indicates s,.,,,,, was lower during cooler summers that

associated with more frequent late summer rain events. Although such strong correlations
among variables can indicate multicollinearity, models including the interaction between
these two variables were more strongly supported than models containing polynomial
functions of either individual variable and other simpler models. Summer heat and May
rain were positively correlated (Pearson's r = 0.5133), so it is possible that the positive
effect of hot summer days is a time-lagged outcome of earlier conditioning from ample

spring rains. Summer survival responded positively to increasing percent sand in soils,

49

 

which was generally higher in Michigan sites, but negatively to increasing soil N through

its interactions with spring rain (pGCMay).

Winter Survival
The three component sub-models of the conditional winter rosette survival
analysis predicted that: (1) the probability of having an extreme survival rate, either 0 or

100%, was negatively density dependent and also decreased with the frequency of

summer rainy days (Table 2.7, Model rm-nl ). (2) Among quadrats that did have extreme

values, the probability of having 100% survival (versus 0%) was greatest at very low

densities and was negatively dependent on summer growing degree days (Table 2.7,
Model r,,,,-,,2a). (3) Among quadrats that did not have extreme values (n = 84), there was a
positive correlation between summer and winter survival probabilities (Table 2.7, Model
rwm2b). Survival in these plots was also negatively dependent on the frequency of

summer rain, soil pH, and the frequency of very cold winter days, but was not density

dependent.

F ecundity

Mean quadrat per capita fecundity, modeled as the mean number of fruits
(siliques) per plant was predicted by two opposing density dependent functions, each
conditional on climate interactions (Table 2.8). First, adult plants were negatively

affected by the rosette density they experienced as rosettes during June of their first year.

The strength of this effect on fecundity was greatest during cool summers (low hot,,,m)

50

but was tempered during hot summers (high hotsum). Second, both the frequency of rain

events during a plant's second spring until flowering (rain/rec) and the log of the final

density of adult plants were positively correlated with per capita fecundity.

DISCUSSION
Comparisons to Previous Studies

The magnitude of variation in A. petiolata demographic rates from this study was
much greater than expected. At the quadrat level, the range of values of each transition
observed in the study system in four years was inclusive of almost all A. petiolata
demographic rates published previously over a thirty year period that I am aware of
(Figure 2.4). The frequency distributions of most vital rates in my data parallel the
distributions of these published rates, evidenced by the correspondence between the
histograms and the clustering of published rates in Figure 2.4. The means of demographic
rates in this study were not significantly different from those of the compiled published
rates based on overlapping 95% confidence intervals using site by year means. The

exceptions to this were geometric mean per capita fecundity (f) [mine: 52.643 (41.51,

66.75); published: 204.194 (93.17, 447.50)] and rosette to flowering survival (s,f) [mine:

0.09 (0.054, 0.126); published: 0.548 (0.443, 0.653)]. The means of each of these rates
were lower in my system. Reduced fecundity may have been related to the same
processes that lead to the low rosette survivorship I recorded. This is suggested by the
mutual dependency of summer survival and fecundity on both June rosette density and

hot summer days.

51

Past studies have also found evidence of stage-specific density dependent
mortality and reproduction (Winterer et al. 2005, Pardini et a1. 2008, Pardini et al. 2009)
or a lack thereof (Rebek and O'Neil 2006) as well as density dependent population
growth (Meekins and McCarthy 2000, but see Appendices D and E for a discussion of
their calculations, 2002). The range of first year rosette densities observed in June and in
October in this study was greater than those evaluated by most previous investigators
(Table 2.9). Meekins and McCarthy's (2002) first year rosette densities fell above the
center of my data range (June from their Figure 3), while Pardini et al.'s (2009) early May
rosette densities fell mostly below it (from their Figure 2A). Rebek and O'Neil's (2006)
fall October densities and Pardini et al.'s (2009) August rosette densities each
encompassed the center of my fall density range. While the Rebek and O'Neil

measurements are comparable to my fall rosette density, Pardini et al.'s August sample is
phenologically earlier than mine. What they measured as 31 from early April-mid May
gives a much more compressed seedling survival period than mine. Similarly, my
measure of summer rosette survival covered J une-late October, while their s2 covered
early May-August. Finally, my winter survival measure ran from October-June, while
their S3 ran from August-May and included most of the mortality attributed to summer

losses. This may be why Pardini et al. found compelling evidence of strong "winter"
density dependent mortality while I did not. Rebek and O'Neil's finding of no density
dependent mortality from October-June concurs with my own.

Seedling densities in my study quadrats fell within the range of other published
accounts (Table 2.9). Winterer et al. (2005, J. Winterer personal communication)

recorded seedling densities within the range I observed. Seedling densities in quadrats

52

used to estimate seedling survival by Pardini et al. (2009) were below this range. Their

empirical measure of s, was based on the survival of 469 marked individuals spread
across 40 1 m2 quadrats for an average density of 11.725 seedlings m'z. These estimates
and my own are all well below Trimbur's (1973) scaled estimate of 20,000 seedlings m'z.
The maximum seedling density recorded in my study system was 142 100 cm'2 (=14,200

me) at the Shiawassee site, but this was outside of the study quadrats (J. Evans, personal

observation).

Second year plants have been shown to negatively impact seedling survival
(Meekins and McCarthy 2002, Winterer et al. 2005). Although I saw this as well in
seedling survival environmental models that included a term for second year plant
density, these models were not strongly supported by the data. Other investigators have
shown that A. petiolata has a plastic response to variation in light availability but reaches
maximum photosynthetic rates under high light. (Dhillion and Anderson 1999, Meekins
and McCarthy 2000, Myers et al. 2005) but I found no differences in any demographic
rates between forest edge versus interior plots. It is possible that the light conditions at
the edge plots were more shaded than those studied by others, or that other unmeasured
differences between edge and interior locations offset the effects of light exposure.

The hierarchical analyses show that there is a significant amount of spatial and
temporal structure underlying this variation (Figure 2.3). I found significant site, year,
and site*year effects in all germination and survival transitions. Germination rates of new
seeds were highest during the first and third years of the study, and were generally

greatest in the southernmost and northernmost sites during all years. Seedling survival

53

exhibited the most pronounced spatial structuring, increasing with latitude and from west
to east within each year. It is possible that this structure is partially driven by climate
related differences in germination phenology, which was up to several weeks later in the
more northern sites during some years. Experimental hierarchical models in which I first
adjusted survival rates to correct for phenological differences among sites produced the
same results (not shown), so I used the original data. The distributions of summer and
winter rosette survival were much more temporally than spatially structured. During the
first year, when summer survival was highest across most sites, it was greatest in the
southernmost Illinois sites and decreased northward. There was much less landscape-
scale spatial structure during the second and third summers, although most individual
sites maintained the same rank in summer survival that they. had the first year (Figure
2.3). In other words, the "best" sites for summer survival in a good year were still the
best, even when conditions were less favorable across the region. Similar maintenance of
site rank was seen across most sites in germination of new seeds and winter survival
probabilities. Winter rosette survival showed an almost opposite temporal pattern to
summer survival, increasing in the second year in most sites and then decreasing the next.
Per capita fecundity was very consistent within sites over time. Only the Homer Lake site
varied in fecundity over time, dropping during the second year and then increasing in the
third. Finally, seed bank persistence was relatively unstructured. It varied by year only in
the proportion of quadrats with 100% seed viability, which was not spatially driven. The
differences in the spatiotemporal structures of these transitions may translate into
differences in their responses to management of specific life history stages and how

locally specialized management of different stages must be (see Chapter 4).

54

Conclusions

These results suggest several important conclusions. First, A. petiolata does not
perform equally well at all times and locations. It has good years and bad years (or better
years), and these vary by site (Figure 2.3). Additionally, the magnitude and direction of
site and year effects differ across life history stages. Germination of new seeds, summer
survival, and winter survival of most sites closely tracked each other over time, indicating
the importance of regional influences on these demographic rates. In contrast, mean
seedling survival did not show such strong inter-site trends across years. Instead, seedling
survival variation was much more locally driven, as evidenced by the lack of parallel
lines in the seedling plot in Figure 2.3.

From the perspective of a natural resource manager, this means that the target
plant is not likely to perform in the same way at all places and times and, thus, should not
be expected to respond to management identically at all locations. The consequences of
making this assumption have been demonstrated previously in other systems where
multiple populations of an invasive weed responded differently to a common
management effort (Shea et al. 2005). In the case of weed management using classical
biological control, implementation of ineffective strategies is of particular concern
because herbivorous or pathogenic natural enemy species cannot be recalled once
released and can be damaging to non-target species (Pearson and Callaway 2003). It will
be important to determine whether differences among life history stages in the
spatiotemporal scales of variation in vital rates will translate into differences in

population dynamics at the same scales. If so, it could mean that life history stages like

55

seedling survival with stronger local structure would require more locally optimized
management plans. Transitions such as germination that are largely shaped by regional
effects may be better suited to implementation of a common management approach
across sites. Future models of A. petiolata population dynamics will have to account for
these spatial and temporal sources of variation in vital rates by making site-specific
models that account for year to year differences in vital rates.

Second, the variation in vital rates is driven by a common set of underlying
mechanisms. Multiple competing environmental models were evaluated to identify the
mechanisms that are collectively quantified as categorical site and year effects in the
hierarchical models. For each demographic transition, a single explanatory model
emerged as the most probable. These models show that individual plants are affected by
both their immediate and past environments at each step through their life history. For
example, seedling survival is greater where there is higher soil N availability, but this
comes at the cost of lower summer rosette survival. Increased rain in May helps condition
rosettes to endure the hottest days of summer. However, plants that experienced high
densities and hot summer days during their first year on average produce fewer seeds
when they mature. Elements like soils and climate patterns and population densities
which feed fiom one life stage into the next are consistent within locations over time and
tie the individual life history stages together into coherent covariance signatures. Based
on this, it may be worth exploring the data structure further using structural equation
modeling or generalized linear latent and mixed models (GLLAMM) in the future
(Skrondal and Rabe-Hesketh 2004) The models as currently parameterized will form the

basis for exploring the consequences of site differences on projected population

56

performance and can be used to predict how populations will respond to perturbations.
Further, because these models quantify the site in terms of continuous variables, it may
be possible to predict the performance of populations at other locations for which the
relevant data are available.

Third, demographic rates of natural A. petiolata populations are more variable
than I expected. The existence of variability in A. petiolata vital rates documented here is
not surprising. What is noteworthy, though, is that nearly the entire range of previously
known vital rates occurs in just a small subset of A. petiolata's North American
distribution and over a relatively short timescale. Modeling studies based on a single site

or a single year of data are very likely to misrepresent the longer term dynamics of the

population. For example, mean seedling survival (s,.) at the Bob-Peoria site was measured
as 0.843, 0.149, and 0.094 over three consecutive years. No single rate characterizes s, at

the site, and it is unlikely that three rates are truly sufficient. Additionally, s, is linked

with other vital rates in the A. petiolata life cycle through density dependent functions
and dependence on common exogenous factors. Previous modeling studies of this
species have explored how population dynamics change across a range of parameter
values (Davis et al. 2006, Pardini et al. 2009) but have been unable to account for the
covariances among parameters. These models likely capture a subset of the range of
population dynamics exhibited by natural A. petiolata populations. However, by holding
dynamic parameter values as fixed during simulations or breaking apart the correlations
among vital rates, they may misunderestimate (sensu George W. Bush, November 6,
2000) the complexity or elasticity structure of natural population dynamics (J. Evans,

unpublished).

57

An important next step to interpreting the behavior of A. petiolata populations
will be to compare a stochastic population model based on a fixed set of matrices for each
site and year with a dynamic model based on the intrinsic and environmental functions
parameterized here. These can then be used to assess the potential interactions between

the different A. petiolata populations and the suite of proposed management tactics.

58

Tables: Chapter 2

59

Table 2.1. Names and locations of study sites. Rainfall estimates represent mean values

summed from climatic data used in analyses. See methods section for details.

 

Latitude Annual

Rainfall (mm)

Site (Abbreviation) State Longitude Site Description

Bob-Peoria

Edward Lowe
Foundation

Farrndale

Healy Road

Holland State
Park

Homer Lake

Illini Plantations

Ives Road

Johnson Park

Rose Lake

Russ Forest

Shiawassee YMCA

(B)

(ELF)

(F)

(HR)

(HSP)

(HL)

(1?)

(IR)

(JP)

(RL)

(RF)

(SH)

IL

MI

IL

IL

MI

IL

IL

MI

MI

MI

MI

MI

40.72205

41.96451

40.67668

42.10862

42.77765

40.06325

40.07925

41.98147

42.92559

42.81234

42.01162

42.88546

60

-89.5055

-85.9962

-89.4878

-88.2148

-86.2025

-87.9787

-88.2107

-83.932

-85.7699

-84.4042

-85.9703

-84.0491

Hardwood
floodplain forest

Second growth
northern hardwood
forest along edge
of old field.
Hardwood
floodplain forest
Mesic second
growth hardwood
forest

Hardwood forest
in dunes along
Lake Michigan
shore

Upland second
growth hardwood
forest

Upland second
growth coniferous
forest

Hardwood forest
bordered by
restored tallgrass
prairie, descending
to hardwood
floodplain forest
Hardwood oak
forest in urban
park

Second growth
hardwood forest in
abandoned crop
field.

Old growth
oak/maple forest
Black locust
(Robim'a
pseudoaccacia)
and degraded pine
plantation

818

978

818

936

774

993

960

743

972

860

978

912

Table 2.2. Timeline of Alliaria petiolata sampling for each demographic parameter. S, F,
W, and Sp indicate summer, fall, winter, and spring, respectively. Boxes enclose the time
interval over which a parameter was measured. The unshaded box indicates the summer
survival transition that was measured in the smaller seedling survival-sized quadrats in

Michigan for the 2005-2006 cohort. Germination data are not presented in Chapter 2.

 

 

 

 

 

 

2005 2006 2007 2008 2009
Cohort SpSFWSpSFWSpSFWSpSFWSpS
2005-2006
Germination y/g VA
Seedling Survival 7
Summer Survival
Winter Survival
Fecundity
2006-2007
Germination 7 A VA
Seedling Survival W2

     

Summer Survival
Winter Survival
Fecundity

2007-2008
Germination
Seedling Survival
Summer Survival
Winter Survival
F ecundity

 

 

61

Table 2.3. Results of model selection for spatiotemporal differentiation of A. petiolata
life history transitions. Details for eaCh transition include the error distribution (dist) used
in GLMs and GLLMs, the information criterion used for model weighting and selection
(ic), and the dispersion parameter (p used to calculate QAICc where applicable. Variables:
fixed effects (S=site, Y=year, L=location, I=intercept), Laplace approximated maximum
likelihood (ln(l)), number of observations (n), levels of random quadrat effect (r), number

of parameters including random effects (k), (Q)AIC: AICc or Quasi-AICc for
overdispersed models, delta (Q)AIC (Ai) , and Akaike weight (w,). Models with r=0 were
GLMs with fixed effects only. A maximum of 5 models are shown per vital rate. All

other models with Ai < 11 and w; > 0 are shown.

62

 

 

 

 

 

 

 

 

 

Transition, Details Fixed Effects ln(l) n r k (Q)AICc At wi
germination 1 (g1) S, Y, S*Y -828.11 137 48 37 352.6 0 0.872
distinomial S, Y, S*Y, L -828.08 137 48 38 356.4 3.8 0.128
ic=QAICC Y 1228.26 137 48 4 379.4 26.8 <0.001

rp=6. 62 Y, L -l228.24 137 48 5 38 I .5 28.9 <0.001

seedling survival (5r) S, Y, STY -513.48 144 48 37 526.6 0 0.820
dist=bin0mial S, Y, S"‘Y, L -512.68 144 48 38 529.7 3.0 0.180
ic=QAICc S, Y -886.93 144 48 15 769.8 243.1 <0.001

(p=2.41 S, Y, L -884.43 144 48 16 770.2 243.6 <0.001

summer srv_ (ssum) S, Y, STY -511.10 143 48 37 387.9 0 0.843
dist=binomial S, Y, S*Y, L -510.47 143 48 38 391.3 3.4 0.157
ic=QAICC Y -846.68 143 48 4 484.0 96.0 <0.001

(0:3.56 Y, L -846.39 143 48 5 485.9 98.0 <0.001

winter srv, (Swin) S, Y, S*Y -240.22 121 48 36 584.1 0 0.541
dist=binomial S, Y, S*Y, L -238.30 121 48 37 584.5 0.3 0.456
ic=AICC Y -294.28 121 48 4 596.9 12.8 0.001

Y, L -293.31 121 48 5 597.1 13.0 0.001

F ecundity Pooled S -81.37 93 48 13 193.3 0 0.946
dist=lognormal S Y -79.99 93 48 16 199.1 5.8 0.052
ic=AICC I Only -100.77 93 48 2 205.7 12.3 0.002

Y -99.61 93 48 5 209.9 16.6 <0.001

germination 2 (g2) s, Y, S*Y -253.91 82 45 25 581.0 0 0.852
dist=binomial S, Y, S*Y, L -253.51 82 45 26 584.5 3.5 0.148
ic=AICC Y -378.88 82 45 3 764.1 183.0 <0.001

Y, L -378.48 82 45 4 765.5 184.5 <0.001

seed srv' (SS) Ones Y '66.97 113 0 3 140.2 0 0.994
dist=bin0mia1 I Only -75.07 1 l3 0 I 152.2 12.0 0.002
ic=AICC S, Y -59.52 113 0 14 151.3 11.2 0.004

S -68.61 113 0 12 164.3 24.2 <0.001

seed SW, (ss) < 1 I Only 25.05 43 0 2 -45.8 0 0.849
dist=beta Y 25.66 43 0 4 42.3 3.5 0.145

ic=AICc s, Y 40.79 43 0 15 -33.8 12.0 0.002

8 36.85 43 0 13 -35.1 10.7 0.004

s, Y, S*Y 45.78 43 0 25 34.9 80.7 <0.001

 

63

Table 2.4. Best supported environmental model of germination of newly shed seeds after

one winter (g1). Parameter estimates from GLMM with binomial errors and logit link.

Model ranking was evaluated with QAICc. Akaike weight = 0.853, AQAICc of next best

model = 3.7. All climate data are from time periods which precede germination. Random

quadrat effect was evaluated with a likelihood ratio test by comparing the change in the -

21n(l) fi'om dropping quadrat from the model to a mixture of )(2 distributions in

GLIMMIX (SAS Institute 2008).

 

 

Parameter Symbol Test Estimate SE
Intercept 11 NA -2.7391 0.3961
WHC3bar wch (F185 = 20.74, P< 0.0001) 0.0624 0.0137
Warm Days (Jan, Feb) wamyf (F1,85 = 647.31. P < 0-0001) 0.3534 0.0139
whc x warmjf vcoldth (F 1,35 = 406.09, P < 0.0001) -0,00899 0,0004
Rainy Days (Jan., Feb.) rainy (1721,85 = 78-18. P < 0-0001) -0.03662 0.0041
Quadrat (random effect) eq (X =5442-66, 4f: 1, P < 0-0001) 0.9787 0.2116

 

64

Table 2.5. Seedling Environmental Model: Parameter estimates from GLMM of seedling

survival from April until June of the first year with binomial errors and logit link. Model

ranking was evaluated with QAICc. Akaike weight = 0.958, AQAICc of next best model

= 7.8. Random quadrat effect was evaluated with a likelihood ratio test by comparing the

change in the -21n(l) from dropping quadrat from the model to a mixture of )(2

distributions in GLIMMIX (SAS Institute 2008).

 

 

Parameter Symbol Test Estimate SE
Intercept 11 NA 0.3937 0.8397
ln(Seedling Maximum Density) dsdl (v) (F 1,89 = 14.74, P = 0.0002) -0.232 0.06043
Precipitation (March, mm) Pmar (F 1,89 = 59.78, P < 0.0001) -0.01301 0.00168
Warm Days (Jan-Feb.) warmwin (F 1,89 = 148-12. P < 0.0001) -0.1238 0.01018
Hot Days (Summer) hotsum (F 1,89 = 241.14, P < 0.0001) 0.6021 0.03878
Rainy Days (Oct-Dec) rain/(,1; (F 1 ’39 = 106.23, P < 0.0001) 0.09 505 000922
hotsum x rainfall hsrf (F 1 ,89 = 158-74, P < 0.0001) -0.01 661 0.00132
1N th (F 1,89 = 31.46, P < 0.0001) 0.07959 0.01419
ln[W.H.C. (1/3 Bar)] whc3q (F1,89 = 21.31. P < 0.0001) -0.8123 0.176
Quadrat(random effect) eq a2 = 404.74,df= 1, P < 0.0001) 0.5760 0.1409

 

65

Table 2.6. Summer Environmental Model (Ssum): Probability of a rosette surviving from

June to October. Summer survival GLMM with binomial errors and logit link. Akaike

weight = 0.993, AQAICc of next best model = 10.01. Random quadrat effect was

evaluated with a likelihood ratio test by comparing the change in the -21n(l) from

dropping quadrat from the model to a mixture of 12 distributions in GLIMMIX (SAS

 

 

Institute 2008).

Parameter Symbol Test Estimate SE

Intercept 11 NA -2. 1092 1 .6265
(F135 = 15.7,

ln(June Rosette Density) dJune P = 0.0002) -0.2951 0.07447
(F135 = 21.61,

Rainy Days (May) minMay P < 0.0001) 0.2825 0.06078
(F135 = 92.34,

Precipitation (May, mm) pmay P < 0.0001) 0.09125 0.009496
(F 1,85 = 99.24,

rainmay x pmay rmpm P < 0.0001) -0.00741 0.000744
(F135 = 24.94,

Soil % Sand sandq P < 0.0001) 0.1100 0.02203
(F 1,85 = 5.2,

Rainy Days (Spring) rainspr P = 0.0251) 0.0837 0.03672
(F1935 = 14.6,

Sand x Rain (Spring) sandxrainspr P = 0.0003) -0.00182 0.000475
(F135 = 51.29,

Soil Total Inorganic N W P < 0.0001) -0.1814 0.02532
(17135 = 53.16,

rainmay x tN rmN P < 0.0001) 0.01072 0.00147
(F135 = 49.52,

Hot Days (Summer) hOIsum P < 0.0001) 0.2580 0.03667

4, (F135 = 199.02,

Drought Events (Aug.Sept.) drysum P < 0.0001) -0.5059 0.03586
(F135 = 31.42,

Hot Days x Drought Events hsd P < 0.0001) -0.02625 0.004683
((2 =425.52, df= l,

Quadrat (random effect) eq P < 0.0001) 1.0298 0.2309

 

66

Table 2.7. Winter Environmental Model (swin). Two-stage model of winter rosette

survival (swin). Model rwinl predicts the binary probability of observing an extreme

value (either 0 or 100% survival) versus any other intermediate value and determines

whether an observation proceeds to swin2a or swin2b. Higher predicted probabilities from

rwinl are more likely to have extreme values and are passed on to swinZa. Model sun-"2a

predicts the binary probability of observing 0% survival versus 100% survival,

conditional on knowledge that the outcome is one of these. Model rwin2b is a binomial

GLMM that predicts the survival probability of a quadrat that does not have an extreme

value. For the first two binary models, the response coded as the "even " whose
probability was modeled is indicated. Akaike weights = 0.343, 0.904, and 0.865 for the
three models, respectively. AAICc of next best models = 1.4, 5 .4, and 3.7, respectively.

 

 

 

 

Parameter Symbol Test Estimate SE
Model ’winl event = extreme
Intercept ll na 1 1.5502 3.0308
ln(Oct. Rosette Density) (10a (F1,118 = 28.9, p < 0000]) -2.5055 0.4661
Rainy Days (Summer) rainsum (Fl,118 = 395, p = 0,0492) -0.0775 0.0390
event = 100%
Model rwinZa
Intercept p na 19.1297 9.2316
ln(October Rosette Density) doc! (171.33 = 499, p = 0,0324) 40.0220 4.4877
Growing Degree Days (Spring) gdspring (17133 = 4,34, 19 = 00350) -0.07713 0.03507
doct x gdsdl drsumfi) (F133 = 5.58, P = 0.0242) 093738 091582
Model ’wiu2b
Intercept p. na 5.0221 3.7513
Summer Rosette Survival Ssum (19135 = 1719, p = 0,0002) 1.3694 0.3428
Rainy Days (Summer) rainsum (F135 = 9.00, p = 00050) 0.02786 0.06026
Soil pH qu (17135 = 923, p = ()0044) -0.3706 0.1298
Cold Days (Winter) caldwin (19135 = 5.07, p = 0.0307) —0.02085 0.009443
Quadrat (random effect) 9,, (x2 = 150.4, df= 1, p < 0.0001) 0.4366 0.1188

 

67

Table 2.8. Fecundity Environmental Model (f). GLMM with Poisson distributed errors,
log link, and random quadrat effects. Model ranking was evaluated with AICc. Akaike
weight = 0.999, AAICc of next best model = 16.3. Random quadrat effect was evaluated

with a likelihood ratio test by comparing the change in the -21n(l) from dropping quadrat

from the model to a mixture of 12 distributions in GLIMMIX (SAS Institute 2008).

 

 

Parameter Symbol Test Estimate SE

Intercept 11 NA 7.4679 1. 1246
ln(June Rosette Density) d Jun 6 (13139 = 0.23, p = 0.6350) -0.0497 0.1039
Hot Days (Summer) h0’sum (F1939 = 2556, P < 0000]) 0.4391 0.08685
dyune x hotsum dJunehotsum (F1339 = 20.61, P < 0.0001) ~0.0705 0.01553
Rainy Days (F ecundity) ram/ac (F139 = 21.72, P < 0000]) -0.1212 0.0260
ln(Flowing Adult Density) df (1171,39 = 19.08, p < 0,0001) -1.6401 0.3754
dfx rainfec djrainfec (131.39 = 20.26, P < 0.0001) 09355 0007875
Quadrat (random effect) eq )6 .0301131-18’ df= 1’ P < 0.2701 0.07244

 

68

Table 2.9. Comparison of plant densities used in four studies of A. petiolata. Seedling,

Summer, and Winter refer to survival measurements. Plant minimum and maximum

. . . -2 . . .
densrtres have been converted to common units of plants m . Geometric mean densrtres

and 95% confidence intervals of the geometric mean are shown. The mean seedling
density from Pardini et al. (2009) is the arithmetic mean and is based on their report of

marking 469 seedlings across 40 1x1 m quadrats.

69

 

 

Min Max
plants plants

_2 _2 Scale of

Transition Time Interval m m Mean (LCL UCL) Measurement Location Ref.
2

Seedling March-June 75 6025 806.9 (693.7-9386) 0-04'0-0625‘“ IL&MI 1
2

Seedling April-May - - 11.725 1m MO 3
2

Seedling March-October 207 2058 - 0-1 m PA 2
2

Summer June-October 31.25 3344 253.4 (2180-2945) 0-163‘0-25’“ IL&MI 1
2

Summer May-August 4 235 - l m MO 3
2

Winter October-June 4 540 47.1(37.2-59.6) 0-16&0-25m IL&MI 1
a,b 2

Winter August-May l 278 6.0 (4.1-8.7) 1 in MO 3
2

Winter October-June 4.47 108.2 - 1 m OH 4
2

Fecundity June 4 540 26.3 (21.1-32.9) 0-16&0-25m IL&MI 1
a 2

Fecundity June—July 1 50 4.4 (3.45.7) 1’“ MO 3

 

References cited are: 1) This study, 2) Winterer et al. (2005), 3) Pardini et al. (2009), and 4) Rebek and
O'Neil (2006).

a Means and confidence intervals from Pardini et al (2009) were obtained by extracting x and y pixel

coordinates fiom each data point in their printed figures 28 and 2C using photo editing software. Because

they reported sampling winter survival in 34 quadrats but only 18 points are visible in their Figure 23, I

«2
inferred that the remaining 16 quadrats had rosette densities of 1 plant m .

b It appears that Pardini et al. (2009) mistakenly reported that 1795 rosettes were used in calculating winter

survival. Data extracted from their figure 2B reveal that there were approximately 1340 rosettes used in this
calculation. This corresponds closely with the 1346 rosettes they report marking for measurements of
summer survival. Thus, I interpret that the number of plants indicated in the text for summer and winter

rosette survival must be reversed in the text on page 390 of their paper. See Chapter 3.

 

70

Figures: Chapter 2

71

:1

 

 

 

 

 

 

Flgur

in. ~
~14. ill

1
lg.
., It

first.

 

 

 

 

 

 

 

“7 ,l‘f'f.‘ \
/ .~\
‘. \2
2:) ' L‘vx N
/’ -‘ 1 t
,4 l ’ - L‘»
54'? f' K W E
' I 1 ‘-
’ l
S
w/y’ /\“\
I
Mlchlgan *,
4 1 i
l 2 i
1.5 o . o ,
1. ""’“-"**~~~-*-j, . ‘
_ .8 ‘ ,’ 6 '7 .3
,1" /.
J}, .22222..--_ . ,. -
' l
f 1
1' 12
(my. .
.45: .' 11 _ l
= ; . Illinois 4 ;
Xx l 'l ' I ' 1
\ ,2
l
l P
(if e ”if; [ 1 l l | 1 1 1 |
.2 o 75 150 300 Kilometers

 

 

 

Figure 2.1. Locations of seven A. petiolata study sites established in Michigan in 2004
and five sites established in Illinois in 2005. Site Key: 1) Shiawassee, 2) Rose Lake, 3)
Ives Road, 4) Johnson Park, 5) Holland State Park, 6) Edward Lowe Foundation, 7) Russ

Forest, 8) Healy Road, 9) Homer Lake, 10) Illini Plantations, 11) F armdale, 12) Peoria.

72

 

  
   
 

 
    
 

S sums win

 
  
  

 
   
    

 

Dormant
Seeds

Flowering
Plants

 

 

Rosettes

Figure 2.2. Schematic diagram of A. petiolata life cycle. Arrows represent one-year

transitions from June to June and are comprised of multiple lower level demographic

transitions. These are abbreviated as follows: g1, germination of new seeds within one
year of seed set; g2, germination of dormant seeds from the soil seed bank; s, survival of
newly emerged rosettes to the rosette stage in June; ssum, summer survival of new rosettes
from June until late October; swim winter survival of rosettes to the flowering stage from
October until June; f, fecundity (seeds/plant); Ss, survival of dormant seeds in the soil
seed bank. Because seed survival (53) was measured over a full year but is used twice as

an 8 month, sub-annual transition, 3, is raised to the two-thirds power in the seed to

rosette and the flowering plant to rosette transitions to scale its affect.

73

Figure 2.3. Observed mean A. petiolata demographic rates over the study period. Light
gray lines follow mean values within individual sites, averaged across quadrats. Heavy
black lines are mean values (iSEM) of these site means. Year indicates the year during
with each measurement was begun. For example, winter survival 2005 was measured
from fall of 2005 until June of 2006. The three years constitute the three “cohorts” of
plants as grouped in the study, i.e. 2006 germination 1 and 2005 summer survival are
grouped together. *Values of germination 2 from in 2009 are estimations (Appendix

2.B.v).

74

2007 2008
Year

2006

 

g 8 (8. <3

V
(ureId/spoos) Aitpunood

l
\ -

~°9~9<t°a<
COCO

[mi/sins Bunpoos

Year

 

 

 

 

 

 

 

 

 

 

 

 

* l\
§ 8
N N
H
\O
°8° 8 g g
N >4 N >4
‘ xx In
8 8
N N
~ «2 ‘0. 4r. «T o H «a ‘0. V. N. <>
0 O O O O o O O
z uopeuiuuag) [mums auasou .19111] AA
00 l\
8 8
N N
H
\O
y g g 8 8
N >" N >‘
\O V‘-
§ §
~ °°. 0. v. N. <3 — 69 w. V. es 0
o O O o O O O O
1 uopeulunag [ml/Ling 9119503 learning

75

Figure 2.4. Frequency distributions of A. petiolata demographic rates from this study.

Data shown are raw quadrat level observations. Rosette to flowering plant survival (s,f) is

calculated as rsum*rw,-,, for comparison with previous studies that did not split summer

and winter survival. Letters beneath histograms show observations from previous studies.
References: a (Pardini et al. 2008); b (Pardini et a1. 2009); c (Anderson et al. 1996); d
(Meekins and McCarthy 2002); e (Drayton and Primack 1999); f (Nuzzo and Blossey
unpublished data); g (Baskin and Baskin 1992); and h (Cavers et al. 1979). Overlapping
observations are shown as: 1' (Anderson et a1. 1996, Meekins and McCarthy 2002); j
(Drayton and Primack 1999, Pardini et al. 2009, Nuzzo and Blossey unpublished data); k

(Cavers et al. 1979, Meekins and McCarthy 2002).

76

ooaoimcom xe~nu8m
_ Wo

fizgm 3.532» 9 ozomom
Wo

fiztsm ocomom 8E5»

 

 

 

 

Eztsm otomom 555m
o _ o _ WC W0
0
.C v o x v u
8
ov
S
cm
oo—
cfiemcae £238 293% méusm N 535.500 H comes-2500
oofl o9: com c W0 0 ~ We We
a u _ :3. :

 

Aouanboi :1

 

77

Figure 2.5. Predicted versus observed values of A. petiolata seed bank viability (SS),
germination after 1 winter (g 1), seedling to rosette survival (Sr), summer (3mm) and winter
(Sm-n) rosette survival, per capita fecundity (I), and germination of dormant seeds from

the seed bank after two winters (g 2). Fitted values are least squares means estimates for

each site by year combination predicted from the hierarchical GLMs and GLMMs.
Observed values are simple arithmetic means except f. Silique counts were first averaged
across plants within quadrats, then across quadrats for each site and year, and finally

scaled to show the estimated number of seeds per plant. Fitted f, values were modeled as
silique counts and then sealed to generate seed estimates. Only the first two years of g 2
are shown, because the third year was estimated from years one and two. Unadjusted R2

are shown because the site by years means are shown (marginal model predictions),

whereas the model was fit with random quadrat effects. All st and Adjusted R2 in this

and subsequent figures are calculated in the original data scale.

78

035/ 33030

 

 

 

 

EEsmBomeaéoa
o._ wd ed vd Nd do
.Nd
.vd
.od
.wd
- O O O .
.8. 2 oust;
gasses-Sassoon Eyes-m 362%
So cow 8N oo o._ md ed vd Nd do
.Nd
com . .
e e 2V6
. ed
.8...
id
Scum:
com d

 

 

 

 

 

 

R225 888m SEE?
o4 wd ed vd Nd do
.- o .Nd
. O
O O O
.vd
. ..
o . .od
o .md
~3an
.#
Nzozmfictomv
o._ wd 0d vd Nd do
Nd
vd
.od
wd
_

 

 

E>E=m 288% $885
o4 wd ed vd Nd

 

4

    

O

.Nd

.vd

.cd

wd

 

 

86 n N:

_ assuage

d._ wd ed vd Nd d

 

o

Nd

.vd

.cd

.wd

 

enlBA 1391115

79

Willie:
glam she“
_‘:51\ll‘tl&ld l
tied prob:
silt either 0
2: it: it‘ll
initials t
3:;7; had ?
T."?‘l‘f.ll‘.l€‘$ ‘
critter:
a: 3:01
mm b
3 till
513:} prob;
Tad {Tor

1‘” 1'. ‘
i‘nlllvln m“

Figure 2.6. Predicted versus observed values from environmental models. The five
scatterplots show the demographic rates generated from the BLUPs versus the observed
rates, overlaid with a 1:] reference line. The vertical axis of the box plot shows the

predicted probability of a winter rosette survival observation resulting in an extreme

value, either 0 or 100% survival, versus a non-extreme value from the rwml binary GLM

versus the actual outcome. Observed extreme values were coded as "Yes" and include all
observations that had either zero or 100% percent survival. Observations in the "No"
category had intermediate survival rates. A well fitting model should predict higher

probabilities for the "Yes" group and lower the probabilities for the "No" group. The

winter rosette survival plot shows the combined results of models rw,-,,2a and rwm2b. For

observed probabilities of 0 and 1 the predicted values represent the probability of an
observation being 1, versus the alternative of it being 0, conditional on knowing that the
outcome will be one of these two extreme values. The remaining points are predicted
survival probabilities as in the upper row of plots. Mean per capita fecundity was
estimated from the predicted and observed numbers of siliques using the breakpoint

regression function in Appendix 2.B.iv.

80

assessed £880.;

 

ddd_ com o

23 n N: .3

 

 

 

Rita—m 86m om 5883

M mgd d

 

 
  

 

 

 

odN

.oov

.ooc

.oow

doo—

-

‘2“
1 i v" v I

023/ 69,830
22.55 seam sag»
mgv d

 

 

.23m .863? oEobxm
mo> oz

 

. u do
so
... . . 9o

we

3o u N: +3..

lll d

 

 

 

 

+ M
+
1+.
+
+
..+n
+.
A:
a
+

 

 

 

 

 

29,33 museum
2 o

 

 

 

 

 

 

 

NAV

.VAV

.dgv

.wgd

 

enleA 1391115

81

, , Low Dens., Cool 1

-- " Low Dens., Med. !
" Low Dens., Hot l
. """ High Dens., Cool i
"-High Dens., Med;

 
   
   

Predicted Seedling Survival
O

2o 25" 7 3:0 35 4'0 * 4:5 7' ‘ 50
Fall Rainy Days

Figure 2.7. Predicted seedling survival is conditioned by interactions among multiple
extrinsic and intrinsic factors. Here, the expected seedling survival probability is

calculated from the best supported seedling model across the observed range of fall rainy
days (rainfall), during the year before germination at the minimum (cool), mean (med),

and maximum (hot) number of observed hot days during the summer before germination.

The figure illustrates the interaction between population density, spring temperature

(hotsum), and fall rain at population densities of 500 (gray) and 5000 (black) seedlings m-
2. Mean observed values were used for all other variables. The change in slope from

negative to positive results from the interaction between rainfall and hot,,,,,,.

82

APPENDIX 2.A: SOIL DATA

83

n-HP~ n h I
null-«Ill 2.... i Han/u 1 an .

5“]. ‘Jniofil. 0‘ U l“ - val. IU‘Q’.
. .l .
v . u .9) , .

Table 2.A.l Mean soil parameters i SEM. Site abbreviations in Table 2.1

 

:m

 

2.8% 6.86.26 6.833 6.83» 6.83 6.8: 6.83. :88 6; 6.86.8 6.86.? 6.88
am

6.83 6.88%: 6.682: @838. 688... 6.85 6.23.: 686.3 6.86 386.2 6.82% 6.86.2
am

6.83. 6886.5. 6.836 66:88. 2.88% 6.83. 6.83. 6.82 Em 6.86.: 6.86.: 682.8
x:

68% 68.886 68.86.: 68? 6.38% 68*; 6.82 6.80: A866 6.82: 6.8% 683.2
6.8 E

6.86.6 6.8882 6.33% 6.88% 6.8: 6.86.» 6.88: 6.83m 02 6.86.3. 6.83.6 6.80%
6.8 a

6.83 6.880882 6.688868 6.wm8w.m6_ 6.8% 6.806 6.888.: 686.2 6.2 2.828. 6.8M: 6888
mm:

6.8: 6.9829 6.83: 6.82% 6.802 68$ :83 :83 6.82 6.83 6.25% 6.86
a:

6.83 2.3882 6.08306 6.88am 6.8% 83 6.822 6.882 :82. 6.838. 665% 6.8m:
.E

6886 6.886.288 6.6862 6336 68.8.8 6.83. 6.838 6.83% 6.8: 6686.6 6.886.: 6.83m
6.8 a

2.83 6.2835 6.wm8m.$~ 6.838 6.88 6.866 6.83 6.82; 5: 6.8.8. 6.8? 686.2
5w

6.83 886.85 6.082. 68828 6.83». 6.83. 6.83 2.86.8 6.8w 6.8% 6.83 6.88:
m

6.83 66686.52 6.83% 6.86.60 6.8” 6.83 6.8 ”.2 2.888.: A82 68%.. 6.89 6.882
232: 82 :98... 6 m2 8 m 00 M4“? 5 68m 0% sow 222m

 

84

APPENDIX 2.B: STATISTICAL MODEL FITTING NOTES

85

IICIO

We:

made

the di

sum

CORE:

2.B.i. Model Fitting

Maximum likelihood (ML) and the Laplace approximation of the maximum
likelihood were used to fit GLMs and GLMMs for model selection, respectively.
Akaike's Information Criterion with a correction factor for small sample bias (AlCc) was
then used rank models by their relative support from the data as described by Anderson
(2008). AICc is based on Kullback—Leibler information and is an estimate of the distance,
in arbitrary units of "information", from a model to the full reality of the processes or
factors driving a system. Models which better describe the variation in the data have

lower AICc scores and are interpreted to more closely approximate reality. Competing
models of each vital rate were compared with AAIC (Ai), calculated for each model i as
the difference between its AICc and that of the best supported model. Thus, the best
supported model always has a A,- of 0. Models with A,- less than approximately 10 are
considered plausible alternatives to the best model (Anderson 2008). The Akaike weight

(w,-) is the probability that model i is actually the best model within the set. The wis are
estimated from the Ais and sum to 1 within each set of competing models.

Models of swim f, g2, and SS were evaluated using AICc. Models of g 1, sr, and ssum

were overdispersed. In models with binomial errors the expected variance is a function of
the mean, p, expressed as y(1-,u). Overdispersion occurs when the observed variance
exceeds this expectation. This can indicate that important covariates are missing from the
model, poor model specification, or an inappropriate error distribution (Crawley 2007).
Although overdispersion often has little effect on parameter estimates (e. g. slopes,

intercepts), it can cause underestimation of parameter standard errors (Joe and Zhu 2005)

86

andtha

onthet

in} as

Pearsor

estima:

farmer

and thereby inflate the type I error rate. Selection among overdispersed models was based
on the Quasi-Akaike Information Criterion (QAICc), which is interpreted in the same

way as AICc but also includes a scale parameter in its calculation, [3, calculated as the

Pearson's ledf statistic (Bolker et a1. 2009). For each overdispersed vital rate [1 was

estimated from the fill] model and applied to the QAICc calculation of all reduced models
for model selection.

Overdispersed hierarchical models were then refit using pseudo quasi-likelihood
(PQL) estimation where possible. This allowed using an overdispersed quasibinomial
distribution by fitting multiplicative scale parameter I] to the variance structure of the

overdispersed models using the random _residual_ statement in GLIMMIX. Parameter

estimates and standard errors for g1 and 3,. are derived from these re-fit PQL models. The
best supported hierarchical model of ssum, would not converge using PQL. Parameters for

ssum were estimated using the Laplace approximation and are uncorrected for

overdispersion. The standard errors for this model may be underestimations and should

be interpreted with caution.

The overdispersed environmental models of g 1, s, and ssum were fit and ranked

using QAICc scores calculated from the Laplace-approximated maximum likelihoods.
Although I then refit the best supported model for each vital rate with a quasibinomial
distribution that corrects for overdispersion, SAS can only fit this distribution using PQL,
which produces less accurate parameter estimates than the Laplace approximation. The
residual diagnostics of the quasibinomial environmental models were poor, and the fit of

the model predictions to the observed data was much worse than the overdispersed

87

Laplace estimated models. All final environmental models therefore were fitted with the
Laplace approximation (= better parameter estimates) but were uncorrected for
overdispersion (= possible underestimation of parameter standard errors). Type-3 F -tests
for parameter estimates may have inflated risks of type-1 errors and should be interpreted
conservatively. The significance of random quadrat effects was tested for each model
with a likelihood ratio test. The residual deviance explained by the full GLMM was

compared to the residual deviance of a reduced GLM with no random terms. The

difference in deviance explained was compared to a mixture of X2 distributions with 1

degree of freedom using the covtest / glm option in GLIMMIX to test the null hypothesis

that the random effects did not improve the amount of deviance explained by the model.

2.B.ii. "Pretending variables"

Anderson (2008) describes a scenario that arises in model selection in which two
competing models spuriously appear to have nearly equal support from the data. In these
cases, the ln(l) scores of both models will be nearly identical, and the second model will
differ from the better supported model only by having one or more additional
independent variables that parameters do not explain any additional variance in the
response. Because AIC scores are based on the ln(l) scores plus a penalty for the number
of parameters estimated, the difference in AIC between these two models will be equal to
the penalty imposed for the extra parameters. The Ai of the competing model may
suggest at first that it is a reasonable altemative to the reduced model. However, if the
AIC differ only by the penalty for fitting extra parameters but the ln(l) are equal, the extra

variables do not actually improve the model fit. Anderson (2008) refers to this as the

88

"pretending variable" phenomenon, where a parameter with an effect size of zero is
"pretending" to improve model fit. Models with pretending variables are identified in the

text when they occur.

2.B.iii. Conditional Modeling of Seed Survival
Because the seed survival date contained a high proportion of ones, the data were

analyzed in two steps. First, the probability 7: of observing 100% seed viability in a
sample was modeled as a Bernoulli process: each quadrat-level estimate of S3 with 100%

seed viability was coded as a one, and all other observation were coded as zeros. The
recoded binary data were then fit with a set of binary GLMs with different competing
fixed effects structures. Second, I modeled the subset of observations with values less
than one using a beta distribution. Thus the process for simulating n new observations is
to first generate a set of n random Bernoulli variables with probability 1: (determined in
the binary GLM) of success (i.e. having a 100% viability rate). If 5 random trials are
successes, then the remaining n - s trials have probabilities < 1 and are simulated from the
fitted beta distribution. Tests of this simulation process faithfully reproduce the observed
mixture distribution. This approach is similar to Cunningham and Lindenmayer's (2005)

solution for modeling zero-inflated distributions.

89

2.B.iv. Fecundity estimation

Measuring per capita fecundity directly in the field was not feasible. Instead, I
nondestructively counted the number of siliques on each surviving mature plant in the
rosette quadrats. The number of siliques was then multiplied by the number of seeds per
silique to estimate total per capita seed production.

The number of seeds per silique increased with plant size. To estimate the shape
of this function, a set of 145 test plants was destructively harvested and the number of
siliques and seeds per plant were counted. Test plants were collected from seven field
sites in southern Michigan and Illinois in 2004 and 2005. Individual test plants ranged
from having 0-266 siliques and from 0-3864 seeds.

Three plants had zero siliques and hence had zero seeds. The 142 remaining
plants were analyzed to determine the relationship between total seeds per plant and total
siliques per plant. The number of seeds and siliques per plant were each loglo
transformed to stabilize the variance. Exploratory graphical analysis suggested a linear
relationship with a break in the slope close to ten siliques per plant. I created a program in
PROC NLMIXED in SAS version 9.2 (SAS Institute 2008) to fit a breakpoint linear
regression which estimated the location of the break in slope as well as the two slopes

and the intercept.

The fitted model had a maximum likelihood estimated breakpoint of 8 siliques per

plant (Table 2.B.1) and had an adjusted R2 of 0.975 (Figure 2.8.1). The estimated number

of seeds per plant, after the back-transformation, in plants with 1-8 seeds is:

90

pair

"1'
eq“,

fimctit

loglOlseedSsiliquesSS ) = 160 + fll X 10g10(5 iliq “es )
= 0.5860 +1.5022 x log10(siliques)

00.5860+l.5022Xlog10(siliques)

seedssiliquesSfS = 1

where fig and ,8, are the slope and intercept estimates. Seeds in plants with more than 8

siliques are estimated as:

10g10(seedssiliques >8 ) = «'60 + fl] X10g10(break))+ 32 X

((log10(siliques )— loglo (break — 1))
= ((0.5860 + 1.5022 xlog10(8))+ 1.027 x...

((10g10(3i1iqu65 )- l0g10(8 '1»

= (0.5860 +1.5022 x0.9031)+1.027 x...
(16g10 (siliques )- 0.8451)

= 1.9426 +1.027 x (10g10(siliques )- 0.8451)

_ 1.9426+l.027x lo sili ues 0.8451
seedssiliques >8 — 10 ( g10( q )_ )

where break is the estimated breakpoint, ,62 is the slope, intercept is the maximum value

predicted by the equation for smaller plants. Using this as the intercept in the second

equation and subtracting log10(break +1) from the silique count ensures that the two

functions transition smoothly into each other.

The Michigan plants used in this analysis were previously used to generate the
seed-silique function in Evans and Landis (2007). This re-analysis includes additional test
plants from Illinois and accounts for the nonlinearity between silique number and per

capita fecundity in small plants. Complete SAS code and data for the analysis is provided

below.

91

data allo;

0 0 61 4
O O 45 S
O 0 51 5
1 1 53 5
l 1 55 5
2 1 57 5
2 1 75 5
3 1 49 6
4 1 52 6
5 1 67 6
7 1 93 6
8 l 43 6
6 2 38 7
10 2 44 7
12 2 56 7
17 2 73 7
18 2 82 7
22 2 87 7
23 2 94 7
24 2 121 7
20 3 15 8
21 3 7O 8
21 3 83 8
23 3 89 8
19 4 97 8
34 4 67 8
37 4 86 8
40 4 104 9
42 4 107 9
47 4 116 10
data allo; set allo;

logsil=loglO<siliques);
10gseed=log10(seeds);
run;

title

input seeds siliques;

118
137
146
155
148
135
140
165
181
183
131
166
175
201
111
200
149
151
208
163
199
205
214
243
139
193
237
308
231
61

'Fit Breakpoint Regression';

* drop plants with zero siliques;

proc nlmixod
data=allo(where=(siliques>0));

* range of breakpoints to try;
parms break 2 to 200;
if siliques <= break then

* regression for smaller

plants;
eta = b01 + bl*logsil;
else
* regression for larger
plants;
eta = (b01 + b1*log10(break))+

b2*(logsil-loglO(break—1));

* fit model;

model logseed ~ normal(eta,V);
* generate fitted values;
predict eta out=pred;

cards;

10 181 18 656
10 201 18 786
10 138 19 869
10 222 19 816
10 270 20 817
11 281 20 850
11 264 21 661
11 296 21 891
11 309 21 874
11 257 22 811
12 357 25 1094
12 449 25 1031
12 328 25 839
12 368 26 1145
13 47 27 1339
13 346 27 1125
14 393 27 469
14 401 27 1527
14 341 30 1923
14 336 34 2091
15 373 35 2762
15 506 39 2724
16 598 41 3786
16 627 42 3718
17 565 43 3864
17 683 44 ;

17 772 45

17 663 46

17 685 46

18 623 48

run;

49
50
50
52
54
54
55
56
64
65
73
75
76
77
79
84
86
91
127
151
173
209
248
249
266

* backtransform predicted values;

* calculate residuals;
data pred; set pred;
backpred = 10**pred;
resid = pred-logseed;
run;

* plot results;
title 'Predicted and Observed
Values versus Siliques';
axisl order=(0 to 4500 by 500);
symboll color=black height=2;
symb012 colorzred value=dot;
proc gplot data=pred;

plot seeds*siliques/
vaxis=axisl;

plot2 backpred*siliques /
vaxis=axisl;
run; quit;

title 'Residual Plot';
proc gplot data=pred;

plot resid*logseed;
run;qu1t;

2.B.v. Estimation of 2007 6‘2

Germination of A. petiolata seeds from the soil seed bank (g2) afier two winters of
dormancy was measured for the first two experimental cohorts (2005-2006, and 2006—

2007). No measurements of g2 were made for the 2007-2008 cohort, which would have
been sown in 2007 and germinated in 2009. g2 for this third cohort was estimated fi'om

the relationship between g1 and g2 in previous years. A generalized linear mixed model
was fit to the first two years of data as:
820.41) = g1(v+1) + seedszwz) + time ~N(0,62)
with binomially distributed errors, where y is the year that seeds were sown, g, is

the proportion of seeds that germinated after one winter, seedsz is the estimated number

of ungerminated seeds remaining in the soil in year y+1, estimated as the number of

seeds added in year y — the number of seeds that germinated in year y+ 1 , g2 is the

proportion of seedsz that germinated in year y+2, and 85,-“, is the random error due to site.

Because a number of data points were suspected of being inaccurate (e. g. were
vandalized, damaged by animals, etc...) pooled parameter estimates were calculated from
the remaining good observations from each site within each year. This was done by

adding the number of individuals from all good quadrats at within a given time interval

and then calculating summary values from these. For example, if three of four g1 quadrats

were deemed useable, pooled g1 was calculated as the total number of seedling that

emerged from the three good quadrats divided by the total number of seeds added to the

three good quadrats. Using pooled values precludes analyses of density dependence, as

93

different individual quadrats had different densities of seeds and seedlings. The primary
analyses of g1 and g2 in this study were conducted on the raw, quadrat level data, not the
pooled values. Analyses of g2 excluded the pooled values estimated here for 2009.

The fit of the model to the data is illustrated in Figure 2.8.2, and the parameter
estimates and model fit statistics are given in Table 2.B.2. One observation (Homer Lake

2006) was an outlier and was omitted from model parameterization

94

Tah

IBIS

_._- h.
. ' J

l

Table 2.B.1 Parameter estimates from breakpoint linear regression of log10(seeds/plant)

versus log10(si1iques/plant). The breakpoint is the number of [untransformed] siliques

above which the slope of the regression changes. The slope for plants with 1-8 siliques is

given by fi 1, while the slope for plants with more than 8 siliques is given by fig.

 

 

Parameter Estimate Standard Error DF t Value Pr > M
breakpoint 8 3.259 142 2.5 0.0
Intercept 0.586 0.052 142 1 1.3 <.0001
181 1.5022 0.090 142 16.7 <.0001
fiz 1.027 0.048 142 21.4 <.0001
V 0.03133 0.004 142 8.3 <.0001

 

95

Table
proba

T1118

Table 2.B.2. Parameter estimates from generalized linear mixed model of germination

probability of dormant A. petiolata seeds with binomial errors and random site effects.

Type-3 F-tests of parameter significance and parameter standard errors are given.

 

 

Parameter Test Estimate SE
Intercept na 6.6141 0.5907
81 (F1,9 = 141 .37, P < 0.0001) -3.5725 0.3005
seedsz (F19 = 276.07, P < 0.0001) -1.3836 0.03327
Random Site Q2 = 363.54, 4f: 1, P < 0.0001) 1.0847 0.2381

 

96

Scccis [our I’lant

Fig“ ff

1751 a

flit).

4000

T

3500

l

3000

N
Ur
O
O

 

    

Seeds per Plant
8
8

 

Seeds per Plant
N
o
o

O
O

 

 

 

 

 

 

500 0 .
0 10 20
0 4 1 1 Siliques per Plant .
0 50 100 150 200 250 300
Siliques per Plant

Figure 2.B.1. Number of seeds versus number of siliques in 142 A. petiolata test (black
dots) and fitted values from breakpoint regression (black line). Inset detail graph shows
the change in slope above the breakpoint value of 8 siliques per plant (vertical dashed

line).

97

fl.

0.6“

   

Adj. R2 = 0.96

  

0 ‘1 012 0.4 0.6
g 2 Observed

Figure 2.B.2. Fitted versus observed values of pooled A. petiolata germination rates from

dormant seed (g2) overlaid with l :1 reference line. The first two years of data, which

were used to fit the model, are shown. This relationship was applied to the third year of

data to estimate the unknown values of g; . Model was fit with binomially distributed

errors and g1 and seedsz as fixed effects plus random site effects.

98

APPENDIX 2.C: ENVIRONMENTAL MODEL PREDICTIONS

99

Figure 2.C.1. Observed A. petiolata demographic rates versus up to five independent

variables from the best supported environmental models.

 
 

  
 

 

 

980 88% handbag 889 com 8885 88 8:83— 085. 88 85$ 8.39%
00 O? on ON o“ o ooov OOON O CO? CON 0
o o . o
86 . com .. com
88 s... 88 88 e 8 86 .6
Cmmv 88D on 9:380 TED band 888%.. Goo Hv . 8 when 200 3323 .5885 N- 3 M a 0
00¢ CON o CA: On Q Om_ 9: cm g Wd 0 com: 00m 0
o o
o 0‘
.. . O C . ‘O
o e on. _ 0J3=o ~
2 6e :8 885 we be .883. 683 A .8 85 a: . as 82888 83
cm 0 A: com o 000? ooom o

 

Z .8... wow A8308 88m :88 A063 A :8 983 so:

     

  

.r ..
O O
a. u.
6.8.3 9 :53 :3 Sam 88-8.
88 86 o

  

 
 

 

cm on A: o ocm

Pann— 883 hen—-83.

om

 

3

    

 

o

l_1u12[d

spoosf

[mi/1mg
191mm

[eAIAmS
Jowums

[mums
30110998

1 uoueuruuog

100

variables in Figure D1 from the best supported environmental models. Predicted values

Figure 2.C.2. Predicted A. petiolata demographic rates versus the same independent
were generated using the BLUPs, and thus include the random quadrat effects.

 
 

 

 

   
 

$89 85 b88508 995 .2; 883m 88 8:681 68: 88 8:65 86<
88 cc ON on 2 o ooov 888m o 89. com o
o o o
0
com o o 6 com com
82 s... 88 88 . .
6ng when. .30 wEBEO .0..me .883— 8885 Goo uv .. 8 when 00 >385 888% 88 88.30% 80
2 E .
cow oom oo 00— On 88 of 82 one _ We 0 000— com
.. 3.. w. . m m
a. .— u 8 8 6o . m. w
"a o o O o. o 0.0 o A 9
O m. J

 
 
 

_ . _

 

Rug

 
 
 
  
 

Z 80,—. =0m 883m wEEQ dom.ms< A063 A a 830 “on A888 End .922 88 88.80% 08:.
on 2 8 cm 3 8 88m oo. 8 88¢ ooom o
o S S
0.. 0 . . m m
o: m o m o m.
J. A w
o _ _ o _ m1 1
RUE
Z .68. now 6.88 8mm :8“— 663 A 8 869 com 888 and 882 8 8 85:83
8m 8 8 8m 0 cow 83 o ooow ooov o

 

 

 

 

 

o

o 6 8. 8o 8 o o

.él . 2.. ... _ ....

6f... 2 KhWAnou .... no .% 8 1.. no

0 am. 0' «M a o . oo

_ _ _ _ 2
0.8.3 x :53 man 85. 8.8.8 was :53 88.8. 8m 8 0.8.3

088— com cm 2 oo on

o
co o.o 0002‘“ o
:3 8 . 8...: 8

g _

   

[BAIAJnS
301113998

 

 

1 uorreuruuog

101

APPENDIX 2.D: CORRECTIONS TO MEEKIN S AND MCCARTHY (2002)

MATRIX MODEL

102

The calculations of A for A. petiolata in Meekins and McCarthy (2002) are
problematic for two reasons. First, the life history is incorrect. Seeds of A. petiolata either
germinate in the spring afier they were produced or after a more prolonged period of
dormancy in the seed bank as described by Meekins and McCarthy (2002) in their
introduction. Meekins and McCarthy’s model omits this first pathway, whereby seeds are
produced in June, germinate the following spring, and are rosettes by June. This life
history pathway should appear as a non-zero entry in the flowering plant (FP) to summer
rosette (RS) transition of their A matrix. An identical error was made in another earlier
study of A. petiolata demography (Drayton and Primack 1999) and was later identified
and corrected by Rejmanek (2000).

The second problem pertains more generally to transition matrix models. All
upper level transitions in a matrix population model must represent equal-length time
intervals equal to the projection interval of the model (Caswell 2001). Meekins and
McCarthy’s (2002) model violates this assumption. For example, they show the seedling
to rosette transition taking as long as the seed to seed transition in their figure 7. It is
unclear from their methods what time interval the seed to seed transition represents (May
to October or October to May?). In recalculating ,1 from their data I assume that the seed
to seed transitions as given are correct and represent one full year of seed survival in the
seed bank. Lower level transitions of variable time-lengths can be combined
multiplicatively into equal length upper level transitions to meet the assumption of equal
time intervals.

I reanalyzed the data in Table 3 of Meekins and McCarthy (2002), combining

their mean lower-level transition estimates into a 3x3 annual projection matrix based on

103

the life cycle in Figure l of Davis et al. (2006). Only one germination rate estimate was
provided in Meekins and McCarthy, whereas Davis et al. used different germination rates
for newly shed seeds and seeds that had been dormant in the seed bank. Here I assume
that both of these rates are the same. Additionally, the annual transitions from seed to
rosette and from flowering plant to seed in the corrected model include sub-annual seed
dormancy transitions. To account for this I use the square root of Meekins and
McCarthy’s annual seed to seed transition assuming that seed survival accounts for half

of the annual projection interval. Estimates of X in the original paper were 1.451, 1.375,
and 1.256 in their quadrats that had 16, 40, and 80 rosettes m'z, respectively, during the

first year of their study. Re—calculated values of l» are 2.14, 1.84, and 1.43.
A printout of a spreadsheet is provided in Appendix 2.EAppendix 2.E which
shows how Meekins and McCarthy’s transitions were combined for this re-analysis.

Estimates of K were calculated using the fiee PopTools plug-in for Excel (Hood 2006).

104

APPENDIX 2.E: MEEKINS AND MCCARTHY (2002) CALCULATIONS

105

Meekins and McCarthy Low Density Matrix

S SL RS RF 2R
S 0.301 O 0 0 0
SL 0.158 0 O O 0
RS 0 0.935 0 0 0
RF 0 0 0.672 0 0
2R 0 0 0 0.787 0
FP 0 0 0 0 0.925

Meekins and McCarthy Medium Density Matrix

S SL RS RF 2R
S 0.31 l 0 0 0 0
SL 0.153 0 0 0 0
RS 0 0.972 0 0 0
RF 0 O 0.724 0 0
2R 0 0 0 0.802 O
FF 0 0 0 0 0.96
Meekins and McCarthy High Density Matrix

S SL RS RF 2R
S 0.316 0 0 O 0
SL 0.147 0 0 0 0
RS 0 0.958 0 O 0
RF 0 0 0.569 0 0
2R 0 0 0 0.663 0
PP 0 0 0 0 0.940

Meekins and Mchy Abbreviations
Seeds

S
SL Seedlings March
RS Rosettes in June
RF Rosettes in October
2R

Second Year Rosettes
Flowering
FP Plants

FP
102.14

OOOOO

FP
62.997

OOOOO

FP
58.766

OOOOO

106

 

Adjusted Matrix

3 r p
3 0.253 0 25.88
r 0.081 0 8.27
p 0 0.489

Adjusted Matrix

3 r p
8 0.263 0 16.59
r 0.083 0 5.22
p O 0.557

Adjusted Matrix

3 r p
s 0.27 0 15.8
r 0.079 0 4.65
p 0 0.355

Adjusted Matrix Abbreviations

8 Seeds in June
r Rosettes in June
p Flowering Plants in June

7
9

4
5

4
2

0

Rosette Density

M&M 7t

16

1.375 1.451

1.843

1.256
1.426

Corrected 3»

2.143

CHAPTER 3: COMMENT ON “COMPLEX POPULATION DYNAMICS AND
CONTROL OF THE INVASIVE BIENNIAL ALLIARIA PE T [OLA T A (GARLIC

MUSTARD)

107

INTRODUCTION

Demographic models are powerfiil tools for understanding the dynamics of
natural populations. As analytical methods and computing power become more
accessible, population models are increasingly being used to guide or interpret the
development of population management plans. Recently, two studies of the invasive
weed Alliaria petiolata (garlic mustard, Brassicaceae [M. Bieb] Cavara and Grande) have
been published which did just that (Davis et al. 2006, Pardini et a1. 2009). Each identified
optimal stages in the plant's life history to target with management actions, but they reach
contrasting conclusions. Pardini et al.'s (2009) stage-classified model, which included
density» dependent rosette mortality and fecundity, predicted that management of newly
recruited rosettes would have to reduce survival by 95% to be effective. The authors also
predicted that rosette management could be counterproductive and increase population
density if managers killed fewer than 95% of individuals. This result differs from the
elasticity analysis of Davis et al.'s (2006) linear, deterministic model, which indicated
that rosette survival was one of three lower level demographic transitions, along with
fecundity and seedling survival, that was likely to have the greatest effect on population
growth rate (,1). Several critical errors in the construction and parameterization of the
model by Pardini et al. (2009, henceforth PDCK after the authors' initials) result in
management recommendations are incorrect. Because the published recommendations
are potentially already being implemented by some natural resource managers (Adam
Davis, personal communication), it is important that these problems in the model be

corrected.

108

The problems stem from omission of demographic transitions in the A. petiolata
life cycle, errors in the statistical estimation of parameters in two density dependent
functions, incorrect implementation of density dependent functions in the model, and
questionable interpretation of the model output itself. I will briefly discuss each of these
and show the effects of sequentially correcting them. A revised version of their model
based on information extracted from the published article makes different management
predictions than the original model. This new model indicates that any management that
decreases rosette or adult survival probability or decreases per capita fecundity will
reduce population sizes. Further, the reworked model predicts stable population dynamics
rather than the chaotic or cyclical dynamics predicted by the original model. Readers
should consult PDCK or Davis et al. (2006) for more background and details on model

specifics.

Study System

Alliaria petiolata is a biennial forb and a frequent invader of forested habitats in
North America. Its life history is well documented (e. g. Cavers et al. 1979, Nuzzo 2000,
Rodgers et a1. 2008). The life cycle diagram in Figure 2.E.1 shows the life history stages
present at an annual census point in mid-June just prior to seed set. These are: dormant
seeds in the soil that are one or more years old (S), new rosettes which germinated several
months earlier in spring (R), and second year flowering plants referred to as "adults" (A).
The arrows represent transitions individuals can make over the course of one full year

and are comprised of one or more sub-annual transitions: per capita fecundity (f),

germination probabilities of new (g1) and dormant (g2) seeds, and seed (v), seedling (51),

109

summer rosette (S2), and winter rosette (S3) survival probabilities. The parameters C] and

c2 are varied from between 0:1 to simulate the effects of management as a proportional

reduction in rosette or adult density. Notation alert: in this chapter I follow the
abbreviation scheme for demographic transitions from PDCK to facilitate direct

comparison with the original paper by PDCK.

Management Inference

Pardini et al.'s management conclusions were drawn from bifirrcation plots which
show the equilibrium sizes of A. petiolata populations (vertical axis) across a range of
simulated management efficacy (horizontal axis). I have reproduced PDCK’S bifurcation
plots using Equation 5 from their paper as the starting point for the reanalysis. The
reproduced original result is shown without modification in Figure 2.E.2a, b. I then

incrementally modify the bifurcation plots as each successive correction is made to the

model. In each plot either 01 or C; is varied from 0:1 by 0.00] while the other is fixed at

1. Populations were projected for 2000 years and the first 500 years of population sizes

were discarded to eliminate transient dynamics. Population size (adults plus rosettes) was

then plotted against c1 or Q.

ANALYSES
Life History
In Figure 2.E.l I show three corrections made to PDCK’s published life cycle

diagram. As presented in PDCK, the model applies a seed survival probability

110

(abbreviated v in their paper) to newly produced seeds (Figure 1, PDCK) but not to older
seeds in the seed bank. The only source of seed loss from the population after the first
winter in PDCK’s A. petiolata life cycle is by germination, shown as the seed to seed

loop in the life cycle diagram (Figure 2.E. 1). This loop is parameterized in their model as

l-gz, where g2 is the probability of an older, dormant seed in the seed bank germinating

during any given year. This means that the number of seeds remaining in the soil every
year is the proportion that did not germinate. Seeds in the soil seed bank as modeled in
PDCK are therefore effectively immortal. However, seeds are lost from the seed bank to
mortality as well. Accounting for this requires modification of two transitions. First, it is

necessary to multiply the S to S transition by an annual seed survival probability,

abbreviated s, in Davis et al. (2006) and v in PDCK, to account for seed mortality or loss

from the seed bank by paths other than germination (Drayton and Primack 1999,
Rejmanek 2000, Meekins and McCarthy 2002, Davis et al. 2006). Second, the transition
fi'om dormant seeds in June of one year to rosettes in the next must also account for
losses via seed mortality prior to germination. This partial-year seed mortality over 8

months (2/3 of the 1 year model projection interval) is first scaled by raising it to the two-

thirds power (v2/3) and then multiplied by the existing S to R transition as v2/3gzsr.

Finally, because the losses from seed mortality during the P to R transition are only a

. . . . . 2/3
partial year lower-level transrtron, thrs parameter is also rescaled as v
PDCK’s model included seed mortality (v) in the A to S (013; matrix notation

refers to analogous transitions in Davis et al. 2006 and in Chapter 4) and A to R (a23)

transitions. Although Pardini et al. state that omitting seed mortality from the S to S

111

transition ((11 1) changes the bifurcation result (i.e. the effect of simulated management)

only qualitatively (which is true), they also omitted it from the S to R (an) transition.

Adding full and partial year seed mortality to the base model as described above and
shown in Figure 2.E.1 changes the model predictions substantially (Figure 2.E.2c, d).
Unmanaged populations exhibit chaotic instead of cyclic dynamics. More importantly,
whereas PDCK concluded that proportionally raising rosette mortality between 0-95%
caused maximum population size to increase when v was omitted from several
transitions, restoring v to these transitions results in population suppression as rosette
mortality is increased to about 47.5%. Reducing per capita fecundity, which PDCK
describe as reducing adult plant density (discussed later), up to about 39% results in an
increase in population size relative to unmanaged populations. Thus, it is important that

seed bank mortality not be omitted from the model.

Parameterization of Density Dependent Functions

Summer Survival, s2: The function for density dependent summer rosette survival

(52) was estimated by PDCK using a multiple logistic regression (PDCK Equation 2) of

survival versus the sum of adult and rosette density (T=A+R) and the product of adult and
rosette densities (U =A *R). The authors developed this function by comparing regression
models with different combinations of A, R, T, and U as predictors. Parameter
significance (i.e. P-value) was used to decide which parameters were retained in the final
model. The major issue with the statistical analysis using the above predictors is that it

ignores muticolinearity between U and T, which violates the assumption of independence

112

among predictors in the multiple regression. Additionally, the inclusion of an interaction
term U without the main effects A and R can result in biased estimates of model
parameters. These specific issues set up a scenario that favors spuriously identifying
variables as important if P-values are used to select parameters. The resulting density
dependence function used in PDCK’s population model does not fit the data well and
predicts survival probabilities that do not make biological sense (Appendix 3.A, Figure
3.A.1). In the absence of adults, rosette survival probability asymptotically approaches
100% as rosette density increases. For example, this function predicts 100% rosette

survival probability (to within the machine precision limits of my computer) when rosette
density is 1000 m.2 and adult density is 1 m'z. This is incongruous with other estimates of
A. petiolata summer rosette survival rates between 10-40% (Anderson et al. 1996, Byers
and Quinn 1998, Evans Chapter 4) The details of these issues are discussed at greater
length in Appendix 3.A and demonstrated in a MATLAB script (The MathWorks 2008)

in Appendix 3.F.

I re-parameterized the summer survival function by fitting a logistic regression of

survival probability to T and to loge( T+l). Data were obtained from Figure 2a in PDCK

by extracting x and y pixel coordinates from each data point in the published PDF graph
using photo editing software. Because it was not possible to determine values of R or A

from the graph, models including A, R, or U were not evaluated. The model which used
loge( T +1) as the covariate was better supported by the data (AAICc = 1.9), although not

overwhelmingly. While this function fits the data reasonably well (Appendix 3.A, Figure

3.A. l ), alternative functions should be re-fit using the complete dataset and evaluated

113

using an information criterion such as AlCc rather than parameter significance (Appendix
3.A). The re-fit function is:

1
32“) ' 1+e—(50s+fl1s(At+Rt +1» (3")

 

where [903 and [913 are the summer intercept and slope, respectively, and the covariate is

the sum of rosette and adult densities at the beginning of summer in year t. Note that in
the back transformation of a logistic regression the negative of the exponentiated term

(the linear predictor) is taken (N eter et al. 1996). It is not clear whether PDCK did this in

their original model of s2 (Appendix 3.A). Parameters for the refit function are given in

Table 3.B.1 (Appendix 3.B).

Winter Survival, S3: The density dependent rosette survival function. was

estimated using a linear regression of loge(survival) on loge(R, + 1). The back

transformed survival rate at time t was estimated from rosette density as

S30) = 8131”” logem’ +1) (32)

where fllw is a slope parameter estimate for winter survival.

There are two problems with this analysis. First, it appears that the authors may
have inadvertently dropped a number of observations of 0% survival from their analysis
by using a log transformation of the survival response. In their Figure 2b, the only
observations with either 0% survival or 100% survival were those with only a single

rosette (singletons). Dropping all of the 0% observations by log transforming them

[loge(0) = ~00] leaves all remaining estimates of singleton survival as 100% (PDCK

114

Figure 2b, inset). By excluding all of the observations with 0% survival from the
analysis, the survival probability of populations at very low densities will be
overestimated by the fitted regression model. Second, because PDCK did not estimate an

intercept in the model, fixing it at zero on the log-transformed scale, the intercept is fixed

at unity (S3 = 100% survival) on the back-transformed scale. Winter survival probability

therefore always goes to one as population size approaches zero because e'B loge (0+1) = 1
for any B. This results in a deterministic overestimation of A. petiolata's ability to persist
or invade when rare. While in the “real world” the survival probability of less than one
individual is meaningless, fractional individuals exist in the “model world” and model
predictions can be significantly impacted by this type of error.

Variance stabilizing transformations can be problematic when applied in models
used for making predictions, as demonstrated above, and the model-predictions do not
always make sense when back-transformed to the original data scale. For example a
linear model of arcsin-square root transformed proportion data could predict negative
values that cannot be back-transformed to proportions in a meaningful way. When the
goal of analysis is to interpret pattern, working in a transformed scale can be the most
straightforward option for meeting the assumption of normality in a linear model.
However, caution is required when the goal is to make predictions in the original data
scale. A better solution is to use a generalized linear model (GLM) or a generalized linear
mixed model (GLMM) with an embedded link fiJnction appropriate to the distribution of

the data (Bolker et al. 2009).

I fit a logistic regression of winter survival probability versus loge(R, + l) to data

obtained from Figures 2b and 2c using photo editing software (Appendix 3.C). This

115

model is appropriate for survival data and fits the data satisfactorily (Figure 3.C.1).
Substituting the new density dependence functions for summer and winter rosette
survival changes the population dynamics. The bifurcation analysis of this corrected
model indicates a single stable equilibrium at any management efficacy (Figure 2.E.2e, f).
Any management which reduces either rosette survival or fecundity is predicted to reduce
population size. This is an important difference from PDCK’s prediction that populations
would exhibit cyclical or chaotic dynamics, or that management could cause an increase

in population size.

Implementation of Density Dependence

The two rosette density dependence fimctions (summer and winter) each reference
the same rosette density (R,) in their calculations. This is incorrect, as it is not how the

functions were parameterized. Calculation of the winter survival rate must be based on
the density of rosettes at the beginning of winter. This requires creating an intermediate
age class of winter rosettes, Rw, that is passed from the summer survival function to the

winter survival function. This change also requires distinguishing between management

of rosettes in summer versus winter. The new calculation of AH 1, simulating reduction of

winter rosette survival (c2), is given in two equations:

 

1
Rw = R
t t 1+ e‘(flsO +fisl 1082(At+Rt+1))

1
1+e—(flu0+16wl 1083(th'1'1)

(3.3a)

A,“ = (1— cz )Rw, (3.3b)

 

With these changes incorporated, the strength of winter density dependent mortality is

decreased because summer mortality is accounted for, and the predicted population size

116

at equilibrium is greater (Figure 2.E.2g, h). The model predicts that any management that

reduces rosette survival or fecundity will reduce population size.

Interpretation of Model Output

In the analyses of A. petiolata’s response to management, PDCK refer to
management of rosettes versus management of adults. They simulate these scenarios by
including an extra parameter in the model which proportionally reduces one of the
demographic rates. The equation set below is modified from PDCK equation 5 to include

all of the changes described in the previous sections and was used to produce Figure

 

 

2.E.2g and h:
St+1 = v(1 — g1)<1— coAte/jof’mf” + S.v(1- g2) (3.4a)
a,+1 = V” 3gp] (1 — c1)A,e'60f ”If/1‘ + V” 3g231S, (3.4b)
Rw’ 2 R’ 1 + e‘(160s+161s1108e(14t +12; +1» (34")
AH] = (1 - c2)Rw, H e_( 30W, [31W loge ( Rw, +1) (3.4a)
where e'BOf +13 If A’ is the density dependent fecundity function .

The effect on population dynamics of managing a particular life history stage

depends on when the management is applied. I refer to C] as a simulation of managing

fecundity rather than adult density, as PDCK describe it, because it is only inserted in the
equation set where it affects the number of plants contributing new seeds to the rosette

stage and to the seed bank without affecting the relationship of adult density to other life

117

history stages. In this respect, it is identical to the simulation of reducing per capita
fecundity in Davis et al.’s (2006) linear model of A. petiolata.

Things are more complicated in a nonlinear model. To simulate the effect of
increasing adult mortality, one must be explicit about where and when the impacts of
reducing adult density occur. Adult management as modeled in PDCK is analogous to
hand pulling a fraction of the adult p0pulation as they senesce, just before seed dispersal.
Management could be applied at different times, though. For example, reduction of adult

plant density earlier in the spring could affect per capita fecundity as well as summer
rosette survival. To simulate this, adult density (A ,) should be adjusted by (1 -c1) in the

density dependence functions for per capita fecundity in the A—+S and A—+R transitions,
and in the summer rosette survival function. Similarly, managing rosettes early in winter
could reduce the strength of density feedbacks on rosette survival. Making these changes
further alters the population dynamics of the model system by decreasing the
population’s responsiveness to rosette management (Appendix 3D). The types of
management likely to be implemented should therefore be considered. The effects of
management timing relative to sub-annual transitions and subsequent impacts on density
dependent fimctions can then be explored by varying where the management parameters
are inserted into the equation set.

Finally, the effects of density dependent seedling mortality should also be
explored. PDCK cite the low survival rate of seedlings to justify not including density
dependent rosette mortality in their model. Alliaria petiolata seedling survival
probabilities are variable, though, ranging from 0.13 to 0.63 (Table l in Davis et al. 2006)

and higher (Chapter 2). Adding a density dependent seedling survival function to

118

 

Equation set 3.4 has a large effect on the stable equilibrium population size as the
strength of the density feedback is increased (Appendix 3.E). More importantly, it greatly

changes how populations respond to management Appendix 3.E, Figure 3.E.2).

Conclusions

The study of A. petiolata by Pardini et al. (2009) presented a model of A.

petiolata population dynamics based on a study of a single cohort of plants in 40 1 m2

 

sampling quadrats at a single study site. The authors quantified density dependence in
summer and winter rosette survival and per capita fecundity, but did not to quantify
density dependent seedling survival, which may be important in this species given its
variable population density (Trimbur 1973, Nuzzo 2000, Evans Chapter 2, Chapter 5).
Using this model, the authors recommended that management of A. petiolata should be
focused on reducing adult density. Because their model predicted that incomplete
removal of rosettes could cause increases in population size, PDCK also recommended
that management of rosettes should be avoided. Given the limited geographical and
temporal scope of the data, the numerous quantitative errors in formulating the model,
and the known spatiotemporal variability in A. petiolata demographic rates, the
management recommendations made by Pardini et a1. (2009) should not be applied at this
point or until the modeling framework is examined more thoroughly for the
inconsistencies reported here. The suggestion that rosette management could increase
population density is particularly concerning. This should include: 1) a recalculation of
the density dependence functions for winter and summer rosette survival using

appropriate statistical models and parameter selection tools, 2) consideration of how

119

. .
.P
.. .
L" I.
, e ,.
.: I
.1
I
1-
I' - .
1'1
, ,
.Z’ a
t;
l .
..
'-‘
r
.
l;
..
7‘
..
r."
‘3
.
.
..
.n‘
:‘
z“
.
2‘,
‘7
-
‘.
..
..
..
.3 ‘
"x
_.;
E-v
.‘J
.13
‘ .
-
-..
..—_
.r.’
..-
‘ ~.
:‘fil‘.
a-“
.
.
.33.?
‘92
.
._...
.‘3
..
'.
.1. .~
'—. 'o
.
«:5.
u‘O‘.
.1":-
.‘y‘
r:
.-".
.' ,.'
1‘65
‘1'.
D..-
.. h
\
h

 

management might actually be implemented in the field and testing models which reflect
this, 3) experimentation with density dependent seedling survival, and 4) revisiting the
analyses of the sensitivity of population dynamics to variation in the lower level
demographic rates which was included in a supplement to the original paper. Because
some of the proposed management strategies for A. petiolata affect both rosette survival
and fecundity (Davis et al. 2006), the authors should also look at the population responses
to combinatorial variation in simulated management these two demographic transitions.

In contrast to PDCK’s conclusions, the population dynamics of A. petiolata
appear to be driven by stable equilibria in simulations of both unmanaged and managed
populations based in the final model parameterized from PDCK’s data (Figure 2.E.2 g, h).
There is also compelling evidence for the importance of modeling seed bank mortality.
Most reconfigurations of the model predicted that management of either rosettes or adults
in the study population should be an effective strategy. However, it will be necessary to
think more carefully about how and where in the model to apply the simulated
management if the goal is to simulate ways that populations might be managed in the
field. While the predictions generated in this re-analysis represent an improvement over
the original model, they should not be taken as conclusive. More and better long term
empirical data are needed on the seed bank dynamics of A. petiolata and density
feedbacks on seeding survival and other transitions. Because of the tremendous
spatiotemporal variability in A. petiolata demographic rates, more general management
recommendations will need to come from a larger set of demographic data that has
greater coverage in space and time. The results of Pardini et al., once the model is

corrected, should be expected as a subset of the many possible models of A. petiolata.

120

3
r
e
m.
a
h
C

Figures

 

121

 

 
   
   
  

(l-Cllfi’U-gl)

 
     

122/3&51 (1 -cz)s2 "‘s3
Rosettes

Dormant
Seeds

 

Flowering
Plants

 

v (1 -g2) (1-c1)fi22/3gls1

Figure 2.E.1. Life cycle diagram of A. petiolata showing the upper level transitions
(arrows) and the lower level transitions which comprise them (equations). Symbols are
defined in the text. This version differs from Figure 2.2 in that it follows the notation of

Pardini et al. (2009) and includes parameters for simulation of management.

122

Figure 2.E.2. Bifurcations of A. petiolata populations with simulated management of
rosette survival (left hand panels) and simulated management of per capita fecundity
(right hand panels) using equation set 4. In each case, the unmanaged population is
represented on the far left where additional mortality or reduction in fecundity is zero,
and the dashed reference line shows the maximum equilibrium size of the unmanaged
population. Points above this line indicate potential increases in population size relative
to the unmanaged case, while those below it indicate population decline. Individual
panels show (a,b) the original model as parameterized and published in Pardini et al.
(2009), (c,d) the effects of adding seed bank morality to the S to S and S to R transitions
and rescaling sub-annual seed mortality as described in the text, (ej), the result of
changing the function for winter rosette density dependence in a—d to a logistic curved
response, and (g,h) the result of correcting the sign of the summer rosette density

dependence function used in a-fl

123

-2

Total Population Density at Equilibria (no. rosettes plus adults m )

2000

1500'

1000'

(II
C
O

0

2000

O

    

 

_ aRosettes:
Pardini et al. (2009)

 

 

 

c Rosettes: +
Add seed bank mortality l

 

 

 

 

0 0.2 0.4 0.6 0.8
Proportional Increase in Rosette Mortality

124

600

500 '
400 i

300 '

200

.
100

000

1800 '

EJOOO

O .
1.0 0

. b Fecundity:
Pardini et al. (2009)

 

 

 

1 d Fecundity: l

 

eed bank mortality

7:

 

0.2 0.4 0.6 0.8 1.0
Proportional Reduction in Fecundity

Figure 2.E.2 cont'd.

Total Population Density at Equilibria (no. rosettes plus adults m '2)

 

 

 

 

 

 

 

 

 

 

e Rosettes:
500L Correct rosette DD firnctions 500
4001 1 400'
300» 300-
200 ~ 200 *
100 100
0 4 O
fiRosettes: f
1200 ewrnter densityin .3s calculation 1200
1000~ 1000
800 t 1 800
600 . - 600
400 - . 400 ~
200 l- ‘ 200 ’
O 1 1 x I O
0 0.2 0.4 0.6 0.8 1.0

Proportional Increase in Rosette Mortality

125

 

l

fFecuirdity.
Correct rosette DD functions

 

 

 

 

 

l

h Fecundity.

Use winter density in s3 calculation

 

 

 

 

0

0.2 0.4 0.6 0.8
Proportional Reduction in F ecundity

1.0

APPENDIX 3.A: SUMMER DENSITY DEPENDENCE AND

MULTICOLLINEARITY

126

3.A.i. Summer Density Dependence Function ($2)

The function for density dependent summer rosette survival (52) in Pardini et al.

(2009, henceforth abbreviated 'PDCK') does not fit the data which were used to
parameterize it, which are shown in Figure 2a of PDCK. The function is given in PDCK
Equation 2. Parameters were selected for inclusion in the model based on significance

(i.e. P—values). The authors may have been lead to conclude that this function fit their
data well based on its parameters’ P-values and its R2 value (0.79). Because the
distribution of plant densities used to parameterize the function were clustered, rather
than continuous (PDCK, Figure 2a), the function they used only intersects the two

clusters of data by chance (Figure 3.A. l , dashed line). If there had been more continuous

variation in A. petiolata rosette density, it is unlikely that this model would have garnered

much support via R2. The original function for summer survival in PDCK is given as:

1
_ 1+ efl0+fl1(.4+R)+fl2(A*R)

 

52

(3.A.1)

where e is the base of the natural logarithm, ,80 is the intercept, £1 and ,82 are the slopes of

the covariates, and A and R are the densities of adults and rosettes, respectively, at the
beginning of summer. In PDCK, the sum A+R is abbreviated T, and the product A*R is
abbreviated U. These are expanded here for clarity.

Because the lower-order terms for A and R were dropped, predicted rosette

survival probability is symmetrical with respect to A and R. For example, this means that
s2 is the same whether there are 100 rosettes and 5 adults, or 5 rosettes and 100 adults. A

surface plot of the predicted rosette survival rates versus adult and rosette densities

127

illustrates some of the problems with this function (Figure 3.A.2). When adult density is
zero, survival probability increases asymptotically, approaching 100% survival as rosette
density increases. This does not correspond with the data plotted in PDCK Figure 2a or
with the known biology of A. petiolata. The symmetry of the function means that the
same is true when rosette density is extremely low and adult density is increased.
Survival only decreases when there are both rosettes and adults present, dropping most
rapidly when A = R. This apparent Allee effect that occurs at low densities or when the
ratio of A:R is uneven occurs because the sign of coefficient for T is actually positive,
although it is shown as negative in PDCK Table 1. The reason for this and consequences
if this assumption is incorrect are explained below in the section on back transforming
logistic regressions.

There are two related statistical problems with this function. The first is the
inclusion of a term for the interaction U without its constituent lower-order effects A and
R. Used in this way, the interaction lacks biological meaning, although it has a large
effect on model predictions.

The additive term T implies that the linear effect of rosettes on survival is the

same as that of adults, and thus, that the slopes and intercepts of $2 with respect to A and

R are equal. If this is true, how do they interact? If there is a significant interaction
between A and R, the main effects for these lower—order terms should be retained in the
model even if they are not significant. Removing them from the regression can cause a
shifi in the function relative to the origin and alter its curvature. Depending on the signs
and magnitudes of the terms in the model, this will result in over or under estimation of

the intercept and of the remaining slope parameters. Unless there is compelling evidence

128

to do otherwise, lower order terms should always be retained if they are included in
higher order terms (see chapter 12.3 in Draper and Smith 1998). Without them, the
interaction term lacks meaning, and the regression model predictions are likely to be

flawed.

3.A.ii. Multicollinearity and Parameter Bias

Second, the additive and multiplicative density terms T and U should not both be
included in the model. Given two random variables x and y, (x + y) and (x * y) will often
be strongly, positively correlated, even if x and y are uncorrelated. If 2 is a function of (x
+ y), it will spuriously appear to be a function of (x * y) as well. If 2 is an additive
function of x and y, it can also appear to be a function of (x*y) and/or (x+y), depending on
the signs, magnitudes, and correlations among x and y. When there is strong correlation
among predictor variables in a regression model, there can be multiple solutions to the
regression (parameter estimates) that fit equally well. In such cases where there is
multicolinearity among the predictors, the parameter estimates will not be unique, and
alternate solutions to the model will generate different, unrelated predictions. Neter et al.
(1996) discuss this issue with useful examples in Chapter 7.7 of their text. Model
selection based on variable significance (P-values) will not be able to distinguish
effectively among these models, because the parameter estimates will be significantly
different from zero, even though they are unrelated to the process driving variation in 2.
These issues are explored and illustrated more fully in a supplemental MATLAB

program (Appendix 3.F).

129

The results of one simulation from Appendix 3.F illustrating the correlations
among x, y, and z, are shown in Figure 3.A.3 for those without access to MATLAB. In
this figure, x and y are randomly generated variables with means 3 and 5, respectively,
standard deviations of 1, and 100 ‘observations’ each. The random variable 2 is a linear

function of x and y, calculated with Model Function A in Appendix 3.F as:
z=5+2x+6y+e 8~N(O,1) (3.A.2)

where a is added as random error. Three linear models were then fit to the data with

different combinations of parameters:

Ml z=fl0+fl1x+fl2y

M2 Z=fl0+flix+fl2y+fl3w
M3 2 =fl0+fl1(x+y)

M4 z=fl0+fl1xy

M5 Z=flo+.B1(x+y)+,32xy

Models were then compared using parameter significance as well as AICc. AlCc
is based on Kullback-Leibler information and is a relative measure of the distance, in
arbitrary units of ‘information’, from a given model to the full reality of the underlying
processes driving the variance in the data (Anderson 2008). The model with the lowest
AICc score is thus the closest to describing the truth among a set of competing models

and is considered the best model. AAICc is calculated as the difference between each
model’s AICc and that of the best model (AAlchest = 0). The Akaike weight (w) for
each model is the probability that it is the best among a set of competing models, and is
calculated from the AAICc scores. Anderson (2008) offers a very user fiiendly

introduction to the subject which is more accessible than the more comprehensive volume

by Burnham and Anderson (2002). The simulation was run in MATLAB (The

130

MathWorks 2008), and the analysis was conducted in PROC GLIMMIX in SAS (SAS
Institute 2008).

The results of this exercise, including parameter estimates, P-values, and
Akaike’s Information Criterion adjusted for sample size (AICc) are given in Table 3.A.l.
The analysis of the simulation highlights the potential pitfalls of model selection based on
parameter significance alone. All parameters were highly significant (P < 0.0001) in all
models except for the interaction term in M2, which was correctly estimated as non-
significant. The interaction term was only identified as significant when the lower order
terms for x and y were dropped (M4, M5). Model selection based on parameter
significance can therefore easily lead to retention of spuriously significant terms. In
models where this happened (M3-M5), the parameter estimates were highly inaccurate.
The true intercept was 2. In M3, it was estimated as 9.5, in M4 it was estimated as 29.9,
and in M5, which has the same form as PDCK’s summer survival function, it was
estimated as -12.3. The other parameters in these models were not part of the process
underlying the variance in z and so have no ‘true’ values, although the estimates of these
parameters vary substantially across models. The parameter estimates in the true model,
M1, were reasonably close to the true parameter values, as were those in M2.

Comparison of models using AICc correctly ranked M1 as the best model, given
the data. As 90.4% of the Akaike weight was assigned to M1, there is a 90.4% probability
that M1 is the best model among the five. M2 was ranked second with 9.6% of the
Akaike weights. All other models had approximately 0% probability of being the best

model and thus are discarded as unlikely.

l3]

In summary, when an interaction term is retained, its lower-order terms should
also be retained because the function can become shifted relative to the origin (Draper
and Smith 1998) and the remaining parameter estimates will likely be inaccurate if lower
order terms are dropped. If U is kept in the model, A and R should be kept as well, even if
they are not significant. Because of the high probability that U and T are strongly
correlated, if U is included in the model, T should not be. If T is included, it should be the
only covariate, as A, R, and U cannot be included with it. Model selection based on
parameter significance can be misleading and result in incorrect acceptance of an
inappropriate model. Model selection based on information theory represents a better
alternative. One very effective way of assessing whether a fitted model is appropriate or
not is to plot its predictions across a range of values and judge whether it reflects the
patterns in the data. If it does not, then the model likely mischaracterizes the underlying

processes.

Notes on Logistic Regression Back-Transformation

A logistic regression model linearizes the relationship between the independent
variables, which can be categorical or continuous, and the dependent response variable,
which is the probability of observing p “successes” (e. g. survivors) out of q trials (e. g.

initial plants). The linearized form of the logistic model is
72'
loge[1—:—7;]= ,30 + .lel + . . flux” (3.A.3)

where the right hand side of the equation is collectively called the linear predictor, x1,. ..

xn is the set of n predictor variables, [1b. B1,. .. A, are the estimated intercept and slope

132

parameters, a is the response probability of interest, and the left hand side of the equation
is the logit of it (Neter et a1. 1996). Solving Equation 3.A.3 for 7: in terms of the x,- by
taking the antilog of both sides allows predictions of survival probabilities to be made

from the fitted model if the x,- are known:

efl0+fl1x1+...flnxn
=1+efl0+fl1x1+...flnxn
__ 1
1+ e-(flo +filxr+---flnxn)

7r (3.A.4a)

 

 

(3.A.4b)

These are equivalent expressions. PDCK used the form in Equation 3.A.4b in their
summer rosette density dependence function, reprinted here as Equation 3.A.1. Because
they do not indicate taking the negative of the exponentiated linear predictor, the
implication is that they either took the negative of the individual terms before presenting

them in Table 1 of their paper, or that they omitted this step. Assuming the former, this
means that the ‘true’ signs of all the coefficients for s2 are reversed from their signs on
the linear scale as printed in PDCK Table 1, the slope of T is positive, and the slope of U
is negative. This assumption was made in plotting Figure 3.A.2 and in reproducing the

original bifurcation plots shown in Figures 2a and 2b of the main paper (this paper). If

this assumption is wrong, failure to take the negative of the linear predictor in the back-
transformation would reverse the sign of the density dependent function for $2 and would

result in an additional set of problems. To visualize what this would do to the function,

stand on your head while looking at Figure 3.A.2.

133

Table 3.A.1 Analysis of simulation results. A random variable 2 was created as a

function of x and y using the formula 2 = 5 + 2x + 6y + random error. Z was modeled as a

function of five different combinations of x and y. Ml represents the ‘true’ form of the

function used to generate 2. Parameter estimates from models without the main effects x

and y are poor, although they have significant P—values. AAICc values correctly identify

the M1 as the model with the greatest support from the data. M1 received > 90% of the

Akaike weights (11) indicate a 90.4% probability that it is the best supported model

among the five competing models.

 

 

 

 

 

 

Model Effect Estimate SE (if t-Value P-value -2LL AICc AAICc w

Ml Intercept 5.701 0.582 97 9.80 <.0001 294.9 303.3 0.0 0.904
x 1.865 0.097 97 19.29 <.0001
y 5.934 0.095 97 62.18 <.0001

M2 Intercept 4.603 1.451 96 3.17 0.002 297.2 307.8 4.5 0.096
x 2.248 0.473 96 4.75 <.0001
y 6.151 0.280 96 22.00 <.0001
x *y 0076 0.092 96 -0.83 0.4105

M3 Intercept 9.557 1.860 98 5.14 <.0001 526.1 532.3 229.0 <0.001
x + y 3.928 0.229 98 17.18 <.0001

M4 Intercept 29.877 1.295 98 23.08 <.0001 603.4 609.6 306.3 <0.001
x ‘y 0.744 0.080 98 9.27 <.0001

M5 Intercept -12.331 1.952 97 -6.32 <.0001 424.7 433.1 129.8 <0.001
x + y 9.138 0.407 97 22.44 <.0001
x *y -l.326 0.098 97 -13.56 <.0001

 

134

    
 

 

 

 

 

 

 

m \‘
03 I
a 0.8 ‘
>~ 1
f: 1‘
m I
8 0.6 1"
PD I
O I
“ 1
.9..." 0.4 ,
a o b
.2 , .
a 0 2 L 0 Observed Values II
(1:) ' '--- Published Function ||
-— Logistic vs. log (T) |
O l I e ' I I . 1‘\_ _.
1 5 10 25 50 100 200 400

Total Density (Rosettes + Adults)

Figure 3.A.1. The function used to characterize density dependent mortality of A.
petiolata in summer did not fit the data well. Data extracted from Pardini et a1. (2009) are
shown (dots) against the published logistic regression function evaluated at R = A across
the range of total plant density from the study (dashed line). Data extracted from Figure

2A in Pardini et al. using photo editing software were used to refit a new logistic
regression function of survival probability vs. loge(A + R), shown as a solid line. This

new function is used in the modified model in the main text. Because A and R could not

be extracted from the figure, lower-order terms and interactions could not be fit.

135

Summer Rosette Survival ( s2 )

 

. ‘\
”Ida/[D 100 \\ /// 100 0693‘“
e
3093“

Figure 3.A.2. Surface plot of the published function for density dependent summer

rosette survival (5;) from Pardini et al. (2009) evaluated at all combinations of A = 0:200

and R = 0:200.

136

Figure 3.A.3. A simulation illustrating how the sum (x + y) and product (x * y) of two
uncorrelated random variables can be highly correlated with each other. The variables x
and y are each comprised of 100 random draws from normal distributions with means 3
and 5, respectively, and standard deviations of l. The variable 2 was calculated as 2 = 5 +
2x + 6y + random error. Correlation coefficients (r) are shown for each relationship.
Although z is only an additive function of x and y, it appears to be strongly correlated
with both their sum and product. The simulated data plotted here were also used in the

example analysis presented in Table 3.A.1.

137

 

 

 

 

r=-0.06 O I
.. 800838”
O O
>~ W (goo o
00
O O O 0
4r
0% 81300o
o o
2 A .
0 4
X

 

 

 

 

 

 

 

 

20

15

X*Y

 

 

 

 

40 .
r=094
30» 6’
20*
10'
00
O . .
0 5 10
X+Y

 

 

 

 

 

 

 

 

 

20

138

40

APPENDIX 3.B: REFIT DENSITY DEPENDENCE EQUATIONS

139

Table 3.B.l. Parameter estimates and fit statistics from refit summer (52) and winter (S3)

A. petiolata density dependence functions. Data were extracted from figures 2a and 2b of

Pardini et al. (2009) A. petiolata winter survival data.

 

 

 

Model Parameter Test Estimate SE
32 Intercept (t2; = 1.81, P = 0.0840) 3.5626 1.9682
loge(rosettes+l) ([22 = -2.28, P = 0.0325) -l.0850 0.4753
S3 Intercept 032 = 3.837, P < 0.0001) 1.1928 0.3108
log£.(rosettes+l) (I33 = -7.344, P < 0.0001) -0.4752 0.0647

 

140

 

APPENDIX 3.C: WINTER DENSITY DEPENDENCE

141

Extraction of winter rosette survival data

Several problems were noted in Pardini et al.’s (2009) function for density

dependent survival of A lliaria petiolata rosette in winter (53). The most significant of

these was the omission of an intercept, which forces survival probability to 100% as
densities approach 0. Data to re-parameterize this survival function were obtained from
Figures 2b and 2c in PDCK by extracting x and y pixel coordinates from each data point
in the published PDF file using photo editing software. Because they reported sampling

winter survival in 34 quadrats but only 18 points are visible in their Figure 2b, it was

inferred that the remaining 16 quadrats had rosette densities of 1 plant m.2 and obscure

each other in the figure. The number of survivors in these 18 singleton quadrats was
obtained from the number of fecundity estimates made in plots with a single plant in their
figure 2c. None of the other non-singleton plots had survival rates low enough to leave
them as singletons the following spring. Thus, of these 18 singleton quadrats, 12 must
have had 100% survival and six had 0% survival. Data extracted from PDCK figure 2b
reveal that there were approximately 1340 rosettes used in this calculation. It seems that
PDCK mistakenly stated that 1795 rosettes were used in calculating winter survival
(PDCK, pg. 390). This corresponds closely with the 1346 rosettes they report marking for
measurements of summer survival. Thus, the number of plants indicated in the text for
summer and winter rosette survival must be reversed in the text on page 390 of their
paper.

Re-running PDCK’s linear regression of loge(survival probability) on loge(rosette

density+1) in SAS (SAS Institute 2008) using the extracted data reproduced their original

result very closely. This estimate of B1,, was -0.2 804, compared with their estimate of -

142

0.2890 (PDCK Table 1), and confirms that the data extraction was successful. As
expected, the six quadrats with 0% survival were dropped from the analysis by taking the

natural logarithm of 0, which is -00. Model fit to the untransformed data was good with

the 0% survival observations excluded (Adj. R2 = 0.86) but not when the dropped
observations were included (Adj. R2 = 0.09). Adding a small fraction (IO-7) to

observations with 0% survival resulted in poor model fit (Adj. R2 = 0.018), and fitting an
intercept predicted survival probabilities greater than one.
A new logistic regression of survival probability as a function of loge(rosette

density +1) was fit to the extracted data in PROC GLIMMIX in SAS (SAS Institute
2008). The parameter estimates for the new function are presented in Table 3.8.1
(Appendix 3B). The refit winter survival function fits the data similarly across most of
the range of observed densities (Figure 3.C.1). The functions diverge most prominently at
low densities as they approach the y axis (Figure 3.C.1, detail). The original function

increases and intercepts the axis at 1, while the y intercept of the back-transformed refit

function is 0.767. Incorporating this new function for S3 into the population model further

changes the model’s management predictions.

143

Figure 3.C.1. Density dependence of winter rosette survival probability using data

extracted from Pardini et a1. (2009). Pardini et al. conducted a linear regression of
loge(winter survival) on loge(rosettes + 1) with the intercept fixed at 1. Thus the model
predicts that survival probability approaches 100% as population size approaches 0. An
alternative to this is a logistic regression of survival probability on loge(rosettes + 1). This

model has a lower y intercept and is less prone to overestimating survival of low density

populations. The inset detail shows the shapes of the two functions at the y intercept.

 

 

 

 

 

 

 

   
 

 

1 o
__ - 0 Observed Survival
2 l ' Pardini et a1
0.8 53’: 0.8 log-log linear regression
§ ................ wgistic regression
g 0.6 \
0'6 0 i 2 3

Rosette Density

  

.9
.rs

 

 

 

Winter Survival Probability

 

 

50 100 150 200 250 300
Rosette Density

144

APPENDIX 3.D: APPLY SEEDLING DENSITY DEPENDENT MORTALITY

145

The implementation of simulated A. petiolata rosette and adult morality in Pardini
et al (2009) was limited to overall survival functions and was not incorporated into the
density dependence functions that comprised the upper level demographic rates. Here,
rosette and adult mortality are applied to simulate: 1) the effect of increasing rosette
mortality during the winter survival period and 2) increasing adult mortality early in the

spring. Equation set 3.4 in the main paper is used as the starting point. The new equation

 

 

set is:
Sz+1 = v11— 1:1 >(1 - c1>A.e/3°f+fl‘f’4’ + S.v(1— g2) (3.D.1a)
R,+1 = v2 / 3glsl(l — cl)A,eflOf +13” ’4‘ + 112/3gzslS, (3.D.1b)
RW’ 2 R’ 1 + e-(flos +flrs log:<<(1—c-1>A. +11, )+1)) (3'11”)
At+l = (1- C2 >sz H [wow/31w jogeapczmwt +1) (3.D.1d)

where increasing the parameter c, reduces adults survival proportionally and c2 reduces

rosettes survival. In scenario 1, management of rosette density is simulated to occur early
enough in the winter that it decreases the negative feedback of rosette density on the
remaining survivors. In scenario 2, management of adult density is simulated to occur

early enough in the spring that the negative effects of adults on rosette survival are

decreased, although not early enough to reduce per capita fecundity. To run scenario 1, C;

is varied from 0:1 and cl is fixed at 1 (Figure 3.D.1a). To explore the effects of rosette

management the reverse is done (Figure 3.D.1b).
The results of these simulations are qualitatively similar to the results of the model in the
main paper (Figure 2.E.2 g, h). Comparison of the curvature of the equilibrium density

curve in Figure 3.D.1 a with Figure 2.E.2g in the main text shows that the changes made

146

in the density dependent functions here slow a population’s response to management.

This is evidenced by the increased curvature in Figure 3.D.la.

147

Figure 3.D.1 Bifurcations of A. petiolata populations with (a) simulated management of
rosettes in early winter and (b) simulated management of adults in early spring using
equation set C. In each case, the unmanaged population is represented on the far left
where additional mortality is zero, and the dashed horizontal reference line shows the
maximum equilibrium size of the unmanaged population. As all point fall below this line,

any increase in morality results in decreased population Size relative to the unmanaged

 

 

 

 

case.
1200 f .. . 2 1200 - - . -
3. a Reduce Wmter Rosettes b Reduce Spring Adults
g 1000- 4000’
d)
a 800 * . 800 .
.9.
33’ soor J 600*
:3
Q.
a? 400- 1 400»
'3
+5 200~ « 200-
E—.

 

 

 

 

 

 

O i A L 1 0 J 1 1 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Proportional Reduction in Rosettes Proportional Reduction in Adults

148

APPENDIX 3.E: APPLICATION OF SEEDLING DENSITY DEPENDENCE

149

Alliaria petiolata populations frequently reach high initial seedling densities
(Davis et al. 2006) and have variable seedling mortality rates (2006). To explore the
possible affects of density dependent seedling mortality on A. petiolata’s population
dynamics and response to management, a density dependent function for seedling
survival can be added to the model developed in Appendix 3.D of this paper. A sub-

annual seedling age class (Sdl) is created to which a logistic density dependent function
then applied to estimate the number of rosettes at time t+l (RM) that survive from the
seedling stage at time t. Note that the number of seedlings at time t is calculated from the
number of seeds germinating from the soil at time t and the number of new seeds

contributed from adult plants at time t, thus making the seedling stage temporally

intermediate to time t and time t+l:

 

 

+ A . .
s,+1 = v(1— g1)(l — cl)A,e'BOf fl‘f ’ + s,v(1— g2) (3.E.la)
Sdl, = 1’2/3glsl(l -cl)Ate'BOf+'BlfAt + v2/3g25, (3.E.lb)

1
R’ +1 = Sdl’ 1+ e-(fl05d1+flisdl logetSd11+D> (3310)
1
= 3.E.1d
Rw‘ R’ 1+ e—(fl05+fl25(1—CI)AIRI +fl251At (1—c1)+R1)) ( )
1
An = (1- 62)th (3.E.1e)

 

1 + e—(flOW‘l‘fllw l088(th (1‘03“)
By setting [305d] to 0.5, the maximum seedling survival rate is 0.6225 when the

strength of density dependence is zero. This is approximately equal to the highest rate

compiled from the literature by Davis et al. . As fllsdl is varied from 0: -l, the strength of

the density dependent feedback on seedling survival probability increases. In the absence

of management (fixing cl and c2 at 0) the maximtun density of the unmanaged population

150

decreases sharply as ,Blsd/ increases, although the population dynamics remain stable

(Figure 3.E.l ).

To explore the effects of managing rosettes or adults across this range of
increasing seedling density dependence, c1 and C; were varied from 0:1 as 515d] was
varied from 0:-1 (Figure 3.E.2). The lines in Figure 3.E.2 were created by running a 2000
year simulation from Equation set F with each combination of c1 or C; as ,8] 5d; was varied
from 0 to l and discarding the first 500 years of population sizes to eliminate transient
dynamics. For each level of seedling density dependence (,81 5d,), the proportion of the

unmanaged population size from each simulation was calculated by dividing the
maximum population size at each value of along the x axis by the maximum population

size when x = 0. Hence, all lines cross they axis at 1. In each case, increasing the strength
of seedling density dependence (as 315,11 becomes more negative) reduces the
responsiveness of the population to management. At the strongest level of seedling

density dependence simulated (fllsd/ = -1), increasing rosette management actually causes

an increase in population size, whereas increasing adult management still suppresses
population size.

Seedling density could negatively affect the responsiveness of the population to
rosette management if it is strong enough. Dismissing its potential effects on population

dynamics an management may be unwarranted.

151

Figure 3.E.l Bifurcation of unmanaged A. petiolata populations with varied strength of
seedling density dependence modeled from equation set F. Variability in the strength of

density dependence was expressed by changing the slope parameter in the logistic
function for seedling survival to the rosette stage (31 say) from 0 to -l. The case of no
density dependence is shown on the far left where ,Blsd/ = 0 and seedling survival

probability is fixed by the intercept parameter at 0.6225. The dashed horizontal reference

line shows the maximum equilibrium size of the population with no density dependence.

 

 

 

 

 

a I T I I I T I f I

-: 5000- ‘
r2

3*

u: 4000+ —
*5

.8’

:3 300m -
Q)

Q

i:

.2 2000- a
E

8.

53 10001 -
S

O

H O I l 1 I L 1 ' 1 1

0 -0.1 -02 -03 -04 -05 -0.6 -0.7 -0.8 -09 -1.0

Strength of Seedling Density Dependence ( '31 5d,)

152

n1“

‘I‘II‘-I‘\.'."
.u-
I .~

Figure 3.E.2. Proportional change in A. petiolata equilibrium population densities across
a range of varied strength of seedling density dependence and simulated management of
rosettes (left) and simulated management of Adults (right). The lines show the proportion
of the unmanaged population size for a given strength of seedling density dependence as

the strength of rosette or adult management is increased. Strength of seedling density

dependence increases as values of A M] become more negative (see Figure 3.E.1). For

example, when there is no seedling density dependence, (615d; = 0, dotted line),

increasing rosette mortality causes an approximately linear proportional decrease in

maximum population size, relative to the size of an unmanaged population with no

 

 

 

 

 

 

 

 

 

 

 

 

 

 

density dependence.
8 1
.55.
g“ 0.9- 83?“.
V1 0.7t "~
:3 1::
“-1 .8 0.6 7
° N 0.51
G 3
.fé 3 0.4L
8 an 0.3 t
8 0.2-
9-1 0.1- . .
0 r 1 1 1 .° 0 l 4 . 1
0 20 40 60 80 100 0 20 40 60 80 100
Reduction in Rosettes (%) Reduction in Adults (%)

153

APPENDIX 3.F: MULTICOLLINEARITY SIMULATION:

MATLAB COMPUTER CODE

154

% Appendix B from J. Evans: Response to Pardini et al. (2009)

% Multicollinearity Simulation

% Created with MATLAB 7.6.0.324a (R2008a)

% To run this program, open a new editor in MATLAB and paste the entire
% script below into it. Save the file as Wulticollinearity_Demo.m'.

% The product of two random variables, x and y, will be correlated even

% when x and y are independent. If 2 is an additive function of x and y

% (Model Function A below) or a linear function of the sum of x and y

% (x+y), (Model Function 8 below), 2 will also be strongly correlated with
% their product (x*y). This can lend false support to regression models

% with an interaction term for x*y if the additive terms for x and y are

% excluded.

%

°/o The simulations below illustrate this. First run the script with model

°/o function A. The figure will show the relationships among x, y, z, x+y,

% and x*y, including correlation coefficients. If the MATLAB statistics

°/o toolbox is installed, four linear regressions will be run relating z to

% different combinations of x and y. Because we know the relationship of z
% to x and y, we can judge which correlations are 'true' and which are

°/o spurious.

%

% When 2 is a linear function of x and y with no interaction (Model

% Function A), both (x+y) and (x*y) are spuriously picked up as significant
°/o predictors of 2 if the main effects of x and y are excluded from the

% model, as seen below in the output of regressions (m3) and (m4). If the
°/o main effects are retained (m5), the regression correctly identifies the

"/0 interaction term as non-significant. The same is true when 2 is a

°/o function of (x+y) (Model Function B).

%

°/o When there is a significant interaction between x and y, substituting the
% sum of x and y (x+y) for the two independent main effects of x and y

"/0 results in incorrect parameter estimation. Run Model Function C and

% compare the parameter estimates for the intercepts and interaction terms
°/o in regression analyses (m3), (m4) and (m5). When the regression includes
% both main effects and the interaction (m5), the parameter estimates are
% accurate, even thought the P-values for the main effects are not always
% significant. However, substituting (x+y) for the main effects results in

% underestimation of the interaction coefficient and gross underestimation
°/o of the intercept (m3). Excluding just the main effects x and y results in
°/o overestimation of the intercept and the interaction term (m4).

°/o

% This is true also when the main effects are small but the interaction is

% significant and is one of the principal reasons to not drop non-significant
% main effects. Run Model Function D. It is identical in form to C, but the
% slopes for the main effects of x and y are an order of magnitude smaller
% than in C. Compare the regression output from (m3), (m4) and (m5). In
"/0 (m5), when the main effects are retained, the parameter estimates are
% close to their 'true' values. In (m3), where the main effects are

% replaced with the sum of x and y, the parameter estimate for the

% interaction is reasonably close to its true value of 2, although

"/0 underestimated. The intercept is also underestimated and, because we know
"/0 that z is a function of x and y, not (x+y), the result of a highly

°/c significant fit of (m3) to the data is spurious, due to the correlation

°/o between (x+y) and (x*y). In (m4), where the main effects for x and y are
°/o dropped, both remaining coefficients are overestimated. However, without
°/o the main effects, the increase in 2 as either x or y is increased will be

155

°/o an underestimate.

%

% Therefore, it is important to retain the main effects in the model, even
% though they could be non-significant. Information-theoretic statistics
°/o such as Akaike's Information Criteria (AlCc) may provide clearer guidance
°/o for model selection than variable significance alone.

%

%

% Version Date 6/27/2009 Jeffrey Evans

%

%

°/oWWWWVVWWWWWV\/W\NWWVWWW

%% Begin Simulation

clear all; close all;

% The simplest way to run the code is to set 'modelFun' below and press F5.
"/0 Figure will be created, and regression output will appear in the command
°/o window if the statistics toolbox is installed.

% Model function A: z = 5 + 2x +6y;

% Model function B: 2 = 5 +3(x+y);

°/o Model function C: 2 = 5 + 2x + By + 2(x*y);

°/o Model function D: 2 = 5 + 0.2x + 0.6y + 2(x*y);
% Choose which model function to use by typing 'A', 'B','C', or '0' between single quotes:
modelFun = 'b';

% Use a large sample size in simulation The sample size is set by
% changing the value of 'reps'.
reps = 100;

% generate two random, normally distrusted variables, x and y. x has a
% mean 3 and standard deviation of 1. y has a mean 5 and standard
% deviation of 1.

x = random('normal',3,1,reps,1);

y = random('normal',5,1,reps,1);

% Select among functional relationships between 2, x, and y The random
% number generation for each parameter simulates the effects of process
% error in the relationship of z to x and y.
if ~isempty(strmatch('A',modelFun))

z = 5 + 2.*x+6.*y + normmd(0,1,reps,1);

t = 'z = 5 + 2x +6y'; °/o title for figure

elseif ~isempty(strmatch('B',modelFun)) || ~isempty(strmatch('b',modelFun))
2 =5 4» 3.*(x+y) + normrnd(0,1,reps,1);
t= 'z = 5 +3(x+y)'; % title for figure

elseif strmatch('C',modelFun) % with significant interaction term
2 = 5 + 2.*x+ 6.*y + 2.*(x.*y) + normrnd(0,1,reps,1);
= 'z = 5 + 2x + 6y + 2(x*y)’; % title for figure

elseif strmatch('D',modelFun) % with small main effects and significant interaction term
2 = 5 + 0.2.*x + O.6.*y + 2.*(x.*y) + normrnd(0,1,reps,1);
t = 'z = 5 + 0.2x + 0.6y + 2(x*y)‘; % title for figure

end

156

%% Create Scatterplots

% Set size and aspect ratio of figure. Defaults will be restored if entire

°/o code is run (by pressing F5) or when MATLAB is closed and restarted.
scrsz = (get(0,'ScreenSize'));

set(0,'DefaultFigurePosition',[50 50 scrsz(4)*.5 scrsz(4)*.75]);

figure(1);

% plot y vs. x

subplot(3,2,1);

plot(x,y,'ok')

set(gca,'FontName',Times')

xlabel('X',‘FontName','Times');ylabel('Y',‘FontName','Times');

text(0.1,0.9,['\rm\itr\rm = ' num2$tr(corr(x,y),'%3.2f\n')],...
'Units','Normalized',...
'EdgeColor',‘k','BackgroundColor','w',...
'FontName','Times') °/o overlay correlation coefficient

axis square

°/o plot x*y vs x+y
subplot(3,2,2);
plot(x+y,x.‘y,'ok');
set(gca,'FontName',"l’imes')
xlabel('X+Y','FontName',‘Times');ylabel('X*Y','FontName','Times');
text(0.1,0.9,['\rm\itr\rm = ' num2$tr(corr(x+y,x.*y),'%3.2f\n')],...
'Units','Normalized',...
'EdgeColor','k','BackgroundColor',‘w',...
'FontName','Times') °/o overlay correlation coefficient
axis square

°/o plot 2 vs. x

subplot(3,2,3);

plot(x,z,'ok');

set(gca,'FontName',"l’imes')

xlabel('X',‘FontName','Times');ylabel('Z','FontName','Times');

text(0.1,0.9,['\rm\itr\rm = ' num2str(corr(x,z),'%3.2f\n')],...
'Units','Normalized',...
'EdgeColor','k',‘BackgroundColor','w',...
'FontName','Times') % overlay correlation coefficient

axis square

% plot 2 vs. y

subplot(3,2,4);

plot(y,z,'ok');

set(gca,'FontName',Times')

xlabel('Y','FontName','Times');ylabel('Z','FontName','Times');

text(0.1,0.9,['\rm\itr\rm = ' num23tr(corr(y,z),'%3.2f\n')],...
'Units','Normalized',...
'EdgeColor’,'k',‘BackgroundColor','w',...
'FontName','Times') °/o overlay correlation coefficient

axis square

"/0 plot 2 vs. x+y
subplot(3,2,5);

157

plot(x+y,z,'ok');
set(gca,'FontName‘,'Times')
xlabel('X+Y','FontName','Times');ylabe|('Z','FontName','Times');
text(0.1,0.9,['\rm\itr\rm = ' num23tr(corr(x+y,z),'°/o3.2f\n')],...
'Units','Normalized',...
'EdgeColor','k','BackgroundColor','w',...
'FontName','Times') % overlay correlation coefficient
axis square

% plot 2 vs. x*y

subplot(3,2,6);

plot(x.'y,z,'ok');

set(gca,'FontName',"l'imes')

xlabel('X‘Y','FontName','Times');ylabel('Z','FontName','Times');

text(0.1,0.9,['\rm\itr\rm = ' num2$tr(corr(x.*y,z),'%3.2f\n')],...
'Units','Normalized',...
“EdgeColor','k','BackgroundColor','w',...
'FontName','Times') % overlay correlation coefficient

axis square

% Set title for figure. Code modified from 'suplabel' by Ben Barrowes °/o
°/o Copyright information at bottom of script.
h=axes('Units','Normal','Position',[.08 .08 .87 .87],'Visible','off');
set(get(h,‘Title'),'Visible',’on')

title(t,'FontSize',14);

t_ax=get(h,'Title');
set(t_ax,'VerticalAlignment',‘middle','FontName','Times')

°/oVWVWVV\N\/\NV\NVVVV\NV\NVVV\NV\N\NW

%% Compare Regressions
°/o Note: This section requires that the MATLAB statistics toolbox be
% installed.

% Run four linear regressions of 2 vs. different combinations of x and y.
% The four regression models are:

% (m1) 2 = b0 + b1x + b2y (m2) 2 = b0 + b1(x+y) (m3) 2 = b0 + b1(x+y) +
°/o b2(x*y) (m4) 2 = b0 + b2(x*y) (m5) 2 = b0 + b1x + b2y +b3(x*y)

% where b0 is the intercept and b1, b2, and b3 are slope estimates

°/o The regression parameter estimates and associated p-values will be output
% in the MATLAB command window.

[b1 dev stats1] = glmfit([x y],z,'normal');

[b2 dev statsZ] = glmfit([x+y],z,'normal'); °/o#ok<NBFiAK>
[b3 dev statsS] = glmfit([x+y x.*y],z,'normal');

[b4 dev stats4] = glmfit([x.*y],z,'normal'); %#ok<NBRAK>
[b5 dev stats5] = glmfit([x y x.*y],z,'normal');

OUt‘I = CGII(4,3);

outt {1 ,1 } ='Param eter';
out1 {2,1} ='lntercept'; out1{3,1} ='X'; out1{4,1} ='Y';

158

out1{1,2} = 'Coefficient';

out1{2,2} = b1(1); out1{3,2} = b1(2); out1{4,2} = b1(3);

out1{1,3} = 'P-Value';

out1{2,3} = stats1.p(1); out1{3,3} = statst .p(2); out1 {4,3} = statst .p(3);
disp('(m1): z = b0 + b1x + b2y'); diSp(out1)

out2 = cell(3,3);

out2{1,1} ='Parameter';

out2{2,1} ='lntercept'; out2{3,1} ='X+Y';
out2{1,2} = 'Coefficient';

out2{2,2} = b2(1); out2{3,2} = b2(2);

out2{1,3} = 'P-Value';

out2{2,3} = stat52.p(1); out2{3,3} = stat32.p(2);
disp('(m2): z = b0 + b1(x+y)'); disp(out2)

out3 = cell(4,3);

out3{1 ,1 } ='Param eter';

out3{2,1} ='lntercept'; out3{3,1} ='X+Y'; out3{4,1} ='X'Y';

out3{1,2} = 'Coefficient';

out3{2,2} = b3(1); out3{3,2} = b3(2); out3{4,2} = b3(3);

out3{1,3} = 'P-Value';

out3{2,3} = stats3.p(1); out3{3,3} = stat33.p(2); out3{4,3} = stats3.p(3);

disp(sprintf('M3 is analogous to the summer rosette\n survival function in Pardini et al. (2009)'));
disp('(m3): z = b0 + b1(x+y) + b2(x‘y)');disp(out3)

out4 = cell(3,3);

out4{1,1} ='Parameter'; out4{2,1} ='lntercept'; out4{3,1} ='X'Y';
out4{1,2} = 'Coefficient';

out4{2,2} = b4(1); out4{3,2} = b4(2);

out4{1,3} = 'P-Value';

out4{2,3} = stats4.p(1); out4{3,3} = stats4.p(2);

disp('(m4): z = b0 + b2(x'y)'); disp(out4)

out5 = cell(5,3);

out5{1,1} ='Parameter'; out5{2,1} ='lntercept'; out5{3,1} =‘X';

out5{4,1} ='Y';out5{5,1} ='X*Y'; out5{1,2} = 'Coefficient‘;

out5{2,2} = b5(1); out5{3,2} = b5(2); out5{4,2} = b5(3); out5{5,2} = b5(4);

out5{1,3} = 'P-Value';

out5{2,3} = statsS.p(1); out5{3,3} = stat55.p(2); out5{4,3} = stat35.p(3); out5{5,3} = stat35.p(4);
disp('(mS): z = b0 + b1x + b2y +b3(x*y)'); disp(outS)

% Restore default screen size settings
set(O,‘DefaultFigurePosition',scrsz);

°/o°/o Copyright lnfonnation for redistribution of 'suplabel' code

°/o Used to place equation on figure with subplots.

%

°/o Code available at Mathworks file exchange:

°/o http://www.mathworks.com/matlabcentral/fiIeexchange/7772

%

% Copyright (c) 2004, Ben Barrowes All rights reserved.

%

% Redistribution and use in source and binary forms, with or without

% modification, are permitted provided that the following conditions are

159

% met:

%

% ‘ Redistributions of source code must retain the above copyright

% notice, this list of conditions and the following disclaimer.

% * Redistributions in binary form must reproduce the above copyright

% notice, this list of conditions and the following disclaimer in the

°/o documentation and/or other materials provided with the distribution

%

°/o THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
”AS

% IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
% THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
% PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR

°/o CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,

°/o EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,

% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR

% PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
OF

% LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING

% NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS

°/o SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

160

CHAPTER 4: THE PREDICTED RESPONSE OF ALLIARIA PET [OLA T A TO

BIOLOGICAL CONTROL: LINEAR DETERMINISTIC DEMOGRAPHIC MODELS

161

ABSTRACT

Temporal and spatial variation in the demographic rates of invasive weed species
can affect the outcome of management. When classical biological control is applied as a
management tool, the introduction of ineffective agents can increase the risk of impacts
to non-target species. Building from an earlier published model of the invasive weed
Alliaria petiolata (garlic mustard), I evaluated the sensitivities and elasticities of the
asymptotic population growth rate OI.) to both annual and sub-annual demographic
transition probabilities. The model was parameterized using data from twelve sites in
Michigan and Illinois, USA, and over three plant generations. Annual estimates of It
ranged from 0.48 to 5.88 across all sites and years. Population growth rates within sites

were highly variable, ranging from 0.80 to 5.88 within one site. I used a megamatrix
model to summarize variation in growth within sites. Site growth rates (AM) ranged from

0.83 to 3.54 with an arithmatic mean of 1.90. Sensitivities and elasticities varied with 3.,
indicating that the transitions with the largest impacts on population growth differ for
growing and declining populations. This makes management options dependent on
population growth rate. Rosette survival (summer and winter) consistently emerged as the
transition with the greatest effects on A in populations with positive growth, as did
germination of new seeds and fecundity. This result is consistent with previous
predictions by Davis et al. (2006) that rosette survival should be targeted by management.
My model raises the caveat that rosette survival is only a target transition when growth is
positive; its proportional effect on It decreases as 1 decreases. I predict a lower
probability of successfully managing A. petiolata with biocontrol than Davis et al. My

simulations predict that the root-crown mining weevil Ceutorhynchus scrobicollis is

162

 

[hl

likely to control up 5 of 12 populations, while introducing a second species could extend
control to as many 9 populations, although the probability of success is very low (< 0.1)
at 4 of these 9 sites. Better data on the distribution of agent impacts is necessary to refine

these predictions.

163

INTRODUCTION

Demographic analyses are increasingly being used to interpret the ecology of
invasive plant species and to guide the development of population management plans
(e.g. Vitousek and Walker 1989, Byers and Quinn 1998, Shea and Kelly 1998, Parker
2000, Sakai et al. 2001, Buckley et al. 2003a, b, Koop and Horvitz 2005, Shea et al.
2005). McEvoy and Coombs (1999) proposed that demographic analyses of weed
populations could contribute especially to improving success rate of weed biological
control and to reducing possible negative effects on native communities. Some of the
safety concerns about weed biocontrol relate to the common practice of releasing
multiple agent species per target as a means of finding one that successfully suppresses
the target (the "lottery model", McEvoy and Coombs 1999, McEvoy and Coombs 2000,
Denoth et al. 2002). There are two principal concerns with this approach. First, biocontrol
agent species which establish but do not suppress their hosts are more likely to become
abundant in the absence of negative feedbacks from their host plants. Indeed, the
establishment of one or more ineffective biocontrol agents is a common occurrence
(McEvoy and Coombs 1999, Denoth et al. 2002). This increases the risk of the agent
indirectly affecting non-target species at higher trophic levels by altering food web
structures (Pearson and Callaway 2003, Ortega et al. 2004, Pearson and Callaway 2005).
To minimize this risk, it is desirable to release the smallest number of agents necessary to
suppress the target weed. Second, testing the feeding preferences and host specificity of
agents that do not ultimately control the target is an unprofitable investment of monetary

resources and scientist time. Testing and introduction of each agent species cost $460,000

164

US. dollars in 1997 (McFadyen 1998 $611,155 in 2009,
http://www.bls.gov/data/inflation_calculator.htm).

Using sensitivity and elasticity analyses of matrix population models, life history
transitions in the target species’ life cycle that have a large effect on the population
growth rate (,1) can be easily identified (Caswell 2001) before biocontrol agents are
released. This information can then be applied as a filter to the biocontrol agent selection
process. By increasing emphasis on species that disrupt these critical transitions,
biological control researchers can conduct a more directed search for agents that are most
likely to have a large impact on the target plant (McEvoy and Coombs 1999). This could
serve to reduce the total number biocontrol agent species introduced, thereby reducing
the risk of non-target impacts, as well as the costs of testing ineffective agents.

Davis et al. (2006) were the first to apply predictive plant demographic models to
the development of a new biocontrol program before the introduction of any biocontrol
agents. A biological control program for the invasive biennial forb Alliaria petiolata
(garlic mustard, Brassicaceae [M. Bieb] Cavara and Grande) has been in development
since 1998 (Blossey et al. 2001b) with efforts focused on testing the host specificity of
four European weevils in the genus Ceutorhynchus (Coleoptera: Curculionidae) that
affect A. petiolata at different stages in its life cycle. Davis et al. (2006) used a linear,
deterministic matrix population model of A. petiolata to estimate the probability of
successfully controlling it with either one or two biocontrol agent species. Their model
was parameterized using the ranges of reported A. petiolata demographic rates from
multiple published sources. It generated predictions about the efficacy required of

biocontrol agents that attack different stages in the life cycle to suppress the target

165

species, defined here as the reduction of it to 1.0 or less, This is the level at which
individuals exactly replace themselves. Comparing their model predictions to data on the
impacts of the candidate biocontrol agents from host specificity trials in Europe, Davis et
al. concluded that the majority (72%) of simulated populations were likely to be
controlled effectively by a single agent that simultaneously reduces per capita
reproductive output of mature plants by 49% and survival of rosettes to the flowering
stage by 43%.

One other demographic model of A. petiolata has been published which made
predictions about which life history stages should be targeted for management (Pardini et
al. 2009). Unfortunately, a number of biological and statistical problems in the
conception and implementation of this model as published render its predictions about A.
petiolata population dynamics and management questionable. An extensive discussion of
Pardini et al.’s model is presented in Chapter 3.

The approach used by Davis et a1. (2006) considers the potential effects of
managing one or two life history transitions simultaneously. This is likely a reflection of
the kinds of impacts that would be seen if either one or two of the candidate biocontrol
agents were introduced and performed at its maximum possible efficacy. However, the
Davis model only considered the asymptotic dynamics of individual populations by
holding the transition probabilities within populations static through time. Although they
looked at the projected responses of A. petiolata across a range of demographic rates,
their analysis did not account for the possibility that demographic rates vary through time
within populations. Because natural populations can be highly variable (in population

structure, dynamics, etc...) across locations and over time, it is important to consider how

166

the variation in a population’s demographic rates over time will affect its long-term
response to perturbations (i.e. management). The transition matrices in Davis et al.’s
analysis were assembled by varying the demographic parameters individually using a
single natural population as a starting point. Because of this, the matrices they used do
not necessarily reflect the correlations among parameters likely to be found in natural
populations.

I have previously shown that A. petiolata demographic rates are highly variable
across its range within the North Central Region of the United States (2006, Chapter 2)
This variation is highly structured across populations and over multiple plant generations
as a function of population density, climate, and soil attributes. This finding suggested
that a static matrix modeling approach in which the transition probabilities are fixed
through time likely does not accurately represent A. petiolata's population dynamics. In
this paper, I build on the matrix models of A. petiolata by Davis et al. (2006) and extend
them using data from multiple natural populations of A. petiolata. My goal was to assess
variation in population growth rates and population structure of A. petiolata across its
demographic parameter space. Here, I examine the effects of variation in the observed A.
petiolata demographic rates on estimated population grth rates (,1), the sensitivities and
elasticities of 3. to variation in transition probabilities among the study populations, and
the projected response of populations to different combinations of simulated biological
control management. I do this using linear, deterministic matrix population models and
with “megamatrix” models (sensu Horvitz and Schemske 1986, Pascaraella and Horvitz,
1998) which account for temporal variation in vital rates within sites by cross-classifying

individuals by life stage and habitat condition.

167

 

C/J
I'L‘

METHODS
Study System and Data Collection

Alliaria petiolata is a common invasive weed of forested ecosystems across
much of North America (USDA-NRCS 2007). Its general biology and ecology are well
studied and have been summarized in several reviews (Cavers et al. 1979, Nuzzo 2000,
Rodgers et al. 2008). I will briefly review its biology as recorded in Michigan and
Illinois. All demographic statistics refer to data from Chapter 2 unless noted otherwise.

Seeds germinate in March or April in Michigan and Illinois producing dense carpets of

seedlings with densities (seedlings m'z) ranging 75—6025 (mean = 1171 , median = 878).

Seedling survival (annual proportion surviving in 0.16-0.25 m'2 plots) is variable (range

= 0-1, mean = 0.486) and negatively density dependent. Seedlings that survive form low
rosettes of basal leaves by June. Rosettes persist over the winter as green plants. All
surviving rosettes bolt and flower by May of their second year. Between 0 and 20%
(median = 1.5%) of seedlings that emerge in the spring survive to flower. The majority of
individuals self-pollinate (Durka et al. 2005). Seeds are produced in slender fruits
(siliques) along the upper stem. The number of seeds per silique increases nonlinearly
with plant size, reaching an asymptote of around 14 seeds per silique in large plants in
my system (see Appendix 2.B.iv). All second year plants senesce by August and set their

seeds over the summer as the siliques dry and become brittle. Individual plants produced
0-1705 (mean = 85.7 seeds plant-]) seeds (Chapter 2). Seeds require cold stratification to

germinate (Baskin and Baskin 1992, Anderson et al. 1996, Raghu and Post 2008).

Between 6.1-68.2% (mean =30.l%) of newly shed seeds germinate after one winter,

168

 

although there is strong inter-annual variation in this rate. Seeds which do not germinate
can remain dormant for twelve or more years in the soil (Nuzzo and Blossey, unpublished
data). Annual seed survival probability is high (mean = 0.919), while germination
probabilities of dormant seeds after two winters ranged from 0.001-0.569 (mean = 0.110).
These each contribute to the longevity of A. petiolata's seed bank.

The search for biocontrol agents for A. petiolata was initiated in 1998. From an
initial pool of over 70 phytophagous insects known to feed on A. petiolata in Europe,
four weevil species in the genus Ceutorhynchus were considered the most promising and
have been studied in feeding preference trials (Blossey et al. 2001b, Davis et al. 2006,
Gerber et al. 2007b, Gerber et al. 2007a, 2008a). The four weevils each complete their
life cycle on A. petiolata. All feed on A. petiolata foliage as adults and decrease fecundity
by reducing photosynthetic capacity. As larvae they affect A. petiolata at different stages.
The multivoltine root crown feeder C. scrobicollis aestivates during summer in Europe
and oviposits on rosette leaves from mid-September through April while mean
temperatures are above -5°C (Gerber et al. 2007a). Larvae hatch from eggs laid in buds,
leaves, and petioles and mine in the root crown over the winter. In spring, C. scrobicollis
larvae leave A. petiolata and pupate in the soil, emerging as adults in May-June (Gerber
et al. 2007a). The univoltine stem-borers C. alliariae and C. robertii each oviposit on A.
petiolata in early spring (Gerber et al. 2008a). Larvae mine within stems and petioles
until late spring and pupate in the soil. Adults emerge in June and July, feed on A.
petiolata foliage, and overwinter in the litter. Finally, C. constrictus feed on developing

seeds in June and July as larvae. Each larva consumes 2-3 seeds on average before

169

 

migrating to the soil to pupate (Gerber et al. 2008b). Ceutorhynchus constrictus
overwinter as pupae and emerge as adults in the spring.

Host specificity testing of C. scrobicollis and C. alliariae are the closest to
completion and these species are the most likely of the four to be introduced first (Hinz
and Gerber 2005). The impacts of these two species varied across several feeding trials
conducted in greenhouse and common garden experiments from zero effect on seed
production by either agent (Gerber et al. 2007a, 2008a), zero effect on rosette survival by
C. alliariae (Gerber et al. 2007b) and 7% reduction of rosette survival by C. scrobicollis
(data from Hinz and Gerber 2001). By itself, C. scrobicollis has caused up to a 49%
reduction in fecundity and a 45% increase in rosette mortality (Gerber et al. 2002). The
combined action of the two agents caused up to 82% and 50% reductions in rosette
survival and fecundity, respectively (Gerber et al. 2002) Given the small sample sizes
used and wide range of impacts caused by these species in different experiments, it is
hard to know exactly what effects they might have on A. petiolata if released in North
America or what kinds of error terms to associate with their predicted efficacies. This
uncertainty makes demographic models potentially useful in estimating impacts by

allowing simulation of different scenarios.

Demographic Data

Plant demographic data were collected from 12 A. petiolata populations in
southern Michigan (n = 7) and Illinois (n = 5) between 2005 and 2008 (Table 2.1). Site
selection was based on accessibility and on the presence of established, unmanaged A.

petiolata populations. Demographic rates were measured during three sampling periods

170

denoted here by the year in which the sampling period began (year = 2005, 2006, and
2007). Beginning in 2005, four replicate measures of each demographic rate were made
at each site during each sampling period. Four sampling areas were established within
each site (n = 48 experimental units total): two at the forest edge and two in the forest
interior. Analysis of spatiotemporal variation in demographic rates indicated no
differences between edge and interior quadrats for any demographic rate, so all replicates
were treated equally Chapter 2.

Survival rates were recorded in three quadrats within each sampling area.

Seedling survival to the rosette stage (5,, seedling survival) was recorded in 20 x 20 cm

(IL) and 25 x 25 cm (MI) quadrats between late February and June of each year. Davis et

al. (2006) modeled rosette survival from June to June as a single survival parameter
abbreviated s,f. I split this transition into two lower-level demographic rates to improve
the temporal resolution of the analysis and model. Rosette survival from June to October
(ssum, summer survival) and from October to June the following year (swim winter

survival) were recorded in 40 x 40 cm (IL) and 50 x 50 cm (MI) quadrats. The positions
of individual rosettes within each quadrat were marked on transparent plastic data sheets

in June each year. Survivors were located in October and again the following June using
the transparency as a map. SSW, and s,,,.,-,, can be multiplied together to generate s,fin the

same temporal currency of Davis et al.’s parameter. Fecundity was estimated from all
survivors in the rosette quadrate in J une of the second year by counting the number of
siliques per plant and scaling by the number of seeds per silique estimated from nearby

plants not included in the demographic censuses (Appendix 2.B.iv).

171

Germination of one-year-old and two-year-old seeds and seed survival from June
to June were followed in 20 x 20 cm stainless steel wire mesh trays buried at the soil
surface. Each experimental seed tray was paired with a control tray that did not receive

seeds. This yielded estimates of the probability of germination of new seeds after one

winter (g1) and the probability of germination of older dormant seeds from the soil seed

bank (g2). The annual survival probability of dormant seeds (s,) was also measured fi'om

these seed trays. Greater detail on all sampling procedures can be found in Evans et al.
(unpublished manuscript). Mean values of each demographic rate were calculated within
each site during each year for use in the present analysis (n = 36 site x year mean rates).
Replicate measures of some demographic rates were lost to vandalism or animal
disturbance. In other cases, demographic rates could not be measured because there were
zero plants at the beginning of a transition interval (e.g. if all rosettes died in summer,
winter rosette survival could not be estimated). In each of these cases, the replicate was

omitted from the calculation of the mean transition rate.

Matrix Model Construction

Davis et al. (2006) described the construction of a matrix model for A. petiolata
which I reiterate here with some modifications and apply to the parameterized matrices
from the 12 study sites. The life cycle of A. petiolata in the northern continental United
States is described in terms of the three life history stages present in mid-summer just
before seed set: dormant seeds in the soil seed bank (S), first year rosettes (R), and
flowering second-year plants (P) about to set seed (Figure 4.1). In this life cycle diagram,

each arrow represents a transition that an individual can make between two stage classes

172

over the course of a full year (e. g. S—vR, R—->P). Following the terminology in Caswell
(2001), transitions which occur over one full projection interval of a model (one year, in
this model) are referred to as upper-level transitions. Transitions that do not occur in
North American A. petiolata populations were assumed to have zero probability of
occurring and are not represented in Figure 4.1. Newly shed seeds produced by flowering
plants in June of year 1 can either germinate after one winter and become rosettes in year
2 with some probability (P—->R transition) or they can remain dormant and enter the soil
seed bank in year 2 (P—->S). Note that the P—rR transition only occurs via seed
production. Flowering plants do not perenniate or become rosettes. Dormant seeds in the
seed bank in year 1 can either germinate in the spring to become rosettes in year 2 (S-—>R)
or can remain dormant for another year (S—nS). There is no stasis in the rosette stage.
Because A. petiolata does not flower in the year that it germinates, rosettes in year 1
either transition to the flowering plant stage in year 2 (R—>P) or die.

The upper-level transitions are quantified as the products of sub-annual, lower-
level transitions. For A. petiolata, the five nonzero upper-level transitions are composed
from combinations of seven lower-level transitions which I measured in the field and
appear as the equations alongside each arrow. The lower-level demographic rates

quantify the probabilities associated with each lower level transition. Three changes were
made from the model in Davis et al. (2006). First, the R to P transition (s,fin Davis et al.)
was split into the lower-level transitions SSH," and SW, because summer and winter

survival were measured in separate quadrats in Michigan in 2005. Summer survival was

measured in the smaller seedling quadrats that year, and summer and winter survival was

measured in the larger rosette quadrats thereafter. Second, because seed survival (5,.) was

173

quantified in the field over a full year but is used twice as a sub-annual transition (P —>R,

S—->R), I scaled the observed value proportionally to account for s, over 8 months in these
transrtrons by rarsrng it to the two-thirds power as s,2 3. Third, followrng Davrs et al., the
variables c1 and c2, which simulate rosette mortality and fecundity reduction, are shown

as (l-cn) to express them in terms of survival. The transition probabilities in the life cycle

diagram make up the entries in the projection matrix A. The A matrix has one row and
one column for each life history stage in the population (Figure 4.1). The 3 x 3 A matrix

for A. petiolata has rows 1, 2, and 3 and columns 1, 2, and 3 for seeds, rosettes, and

flowering plants, respectively. The individual elements in the A matrix are “the aij” (the

. . h . . .
entry in the 1’ row and the 11" column number) and represent probabilities of an

individual in life stage j at time t transitioning to stage i at time t + 1 (Caswell 2001).

Thus a32 is the probability of individuals that are rosettes (stage 2) at time t surviving to

becoming flowering plants (stage 3) at time t + 1, while an corresponds with the

transition from flowering plants at time t to rosettes at time t + 1. One A matrix was
parameterized for each site during each year using the mean lower-level parameters,
yielding 3 matrices per site, for a total of 36 A matrices

The numbers of individuals in each stage class are tracked in a column vector, 11,

which has one row for every life history stage. The entries in rows 1-3 (n1, n2, and n3)

represent the numbers of seeds, rosettes, flowering plants, respectively, in the population

at a given time. Given a population vector n,, the population size can be projected

174

forward to time t + 1 using matrix multiplication to multiply the transition matrix by the

population vector as
n1+1 = Asynt (4-1)

where n,+1 and n, are the population vector at times t + 1 and t, respectively, and A,y is

the projection matrix for site 5 in year y. The population growth rate (A) was calculated as
the dominant eigenvalue of the A matrix (Caswell 2001). When It > 1, the population size
increases, whereas )1 < 1 indicates population decline. In terms of demography, the goal

of A. petiolata management is to persistently drive A below 1. The sensitivities and

elasticities of It to perturbation of the ag- were used to analyze which transitions have the

greatest impact on A. The sensitivity of each matrix element is the partial first derivative

of A with respect to aij. The sensitivities are the local slope of A at a given value of aij

(Caswell 2001) and are compiled in the sensitivity matrix S as:

at

day-
Elasticities of A to perturbation of the aij scale the sensitivities (sij) by their proportional
contributions to A. For each matrix A,y the elasticity matrix E contains the elasticities of

lambda to the aij. These are calculated as

firfli

where eij is the elasticity of It to a proportional change in matrix element ail, aft/dail- is the

sensitivity of k to an additive perturbation of aij, calculated as the partial derivative of A

175

with respect to aij, and the eij sum to 1 within each matrix E (Caswell 2001). Because

management of A. petiolata is likely to be applied at the level of the lower-level

transitions, which are components of the of] (e. g. management of fecundity, management

of seedling survival, etc. . .), it is useful to analyze how A responds to perturbations of the

lower-level transitions. The sensitivities of A to the lower-level transitions are:

x ax ij day- Bx '
and the elasticities of A to the lower-level transitions are:
x all x 61 a "
E - J- (4.5)

“tax-x 1.]. 3a,,- ax

where E x is the elasticity of it to a proportional perturbation of the lower level transition x

(Caswell 2001).
I used two previously described methods (Davis et a1. 2006) to visualize the
potential impacts of the proposed biological control agents on A. petiolata. I first

calculated the sensitivity and elasticity of it to each of a) the five non-zero upper level
transitions (a1 1, a21, a32, a23, and a13,) and b) the seven lower-level transitions (SS, 5,, g1,
g2, ssum, Swim and j) for each of the 36 A matrices. The sensitivity and elasticity of

lambda to each of these transitions was then plotted against the observed transition

values. For example, the elasticities (Ex) of A to each of the lower-level transitions were

plotted against g1 to show how the rankings of the Ex change as g1 changes. This is,

effectively, a set of empirical second derivatives of lambda with respect to each

transition. It illustrates how the response of lambda to a proportional perturbation in one

176

of the lower-level transitions changes across the observed range of each transition. This is
used to interpret the relative potential magnitudes of the response of A to management of
each lower-level transition. Rankings of the sensitivities and elasticities were compared
among populations with low and high growth rates. Pearson correlation coefficients
between the elasticities and A were used in some cases to help elucidate these patterns.
The natural logarithm of A was used in these calculations to meet the assumption of
normality. Because lower-level elasticities do not sum to 1 as the upper-level statistics
do, they are not interpretable as proportional contributions to A in the same way (Caswell
2001)

In the second set of analyses, I used a megamatrix model (Pascarella and Horvitz
1998) for preliminary exploration of the effects of Markovian environmental variation on
projected biocontrol outcomes. Note that the megamatrix analysis with uncorrelated

environments is equivalent to a conventional analysis of the weighted mean matrix A

created from the means of the aij across the three years within a site (Tuljapurkar et al.

2003). I chose to pursue the megamatrix approach because it set up a flexible analytical
framework that can be adapted in future models as additional environmental data
becomes available, and because of difficulty in estimating appropriate weights associated
with the mean A matrix. In a megamatrix model, individual plants are cross-classified by
life stage and by the state of the environment, defined here by the three annual A matrices
within each site. The three annual A matrices parameterized for each site characterize a
portion of the local variability in A. petiolata demographic rates which is driven by a
combination of intrinsic and extrinsic biotic and abiotic factors (see Chapter 2). For the

purpose of this analysis I assume these are representative of the true variation in A for

177

each site. For the megamatrix analysis, I create a 3 x 3 matrix P of environmental
transition probabilities with one row and one column for each of three environmental

states (A matrices) parameterized for each site. The P matrix characterizes how the

environment changes over time. Each entry pk] in P is the probability that the

environment in state I at time t will transition to state k at time t+l, where the time
interval t to t+1 is the same as the projection interval of the population matrix A and the
probabilities within each row of P sum to 1. The m x n population projection matrix A is
combined multiplicatively with the p x q environmental transition matrix P to create the
mp x nq megamatrix M, whose entries quantify the probability that an individual in stage
j in environment I at time t transitions to stage i in environment k at time t+1. See

Pascarella and Horvitz (1998 Appendix B) for details on the parameterization of M. The
dominant eigenvalue of M, AM, is the asymptotic growth rate of the population as the

environment changes according to P. In the analysis presented here, I assumed that the

environments were uncorrelated, where the probabilities pk] in P were equal for all k,l and

generate a stochastic sequence of environments. The 3 x 3 environmental matrix is
"A % A
P = % y3 % (4.6)
A A 8-

and was used to generate the megamatrix M.

 

 

For each site I created zero growth isoclines (contours of A = 1) from the

megamatrix by calculating AM for all factorial combinations of c1 and (’2 between 0 to 1

178

in increments of 0.001, and then creating a contour plot of M4 = 1 versus c1 and c2. These

were interpreted by overlaying them on plots showing the expected range of biocontrol
agent impacts on A. petiolata rosette survival and fecundity estimated from common
garden and greenhouse studies during agent host specificity testing (Gerber et al. 2007b,
Gerber et al. 2007a, 2008a, E. Gerber and H. Hinz, personal communication). Sites
whose zero growth isoclines intersected the plotted range of biocontrol impacts can
potentially be controlled. The empirical probability distributions of agent impacts on A.
petiolata are unknown. We only know that the range of impacts each agent has is from
zero to an observed maximum. The probability of successfully controlling A. petiolata at
each site was assessed from the plots assuming a uniform probability distribution for
agent impacts (i.e. an agent is equally likely to have any impact from zero up to its
maximum). For each site, the ranges of possible impacts from C. scrobicollis alone and
from C. scrobicollis with C. alliariae were each plotted as shaded rectangles, and the
zero grth isoclines were plotted over them. The probability of success was then
estimated as the proportion of the shaded area above the zero growth isocline.

I also considered the annual variation in the response to biocontrol, although
management recommendations are based on the megamatrix results. For each site I
created zero growth isoclines (contours of )t. = 1) from the three annual A matrices, and
varied rosette mortality and per capita fecundity to simulate the effects of the proposed

biocontrol agents. The annual zero growth isoclines were created by solving the

characteristic equation of each matrix for c1, the simulated reduction in per capita

fecundity, in terms of the observed demographic rates, 71, and Cg, the simulated reduction

in per capita rosette survival:

179

c1 = r3 — 55(1-82)/12 +102l-ssfl -82)fss2/3813r)+
(4.7)

2 / 3 2 / 3
k2 (fis ngrSsumSwin )+ CZ (135“ — g1)Ss gZSrSsumSwin )J
Equation 4.7 is based on Equation 4 in Davis et al. (2006) but incorporates changes in the

calculation of vital rates described above. Details on its derivation are available in the

Appendix in Davis et al. (2006). By setting A to 1 and varying c2 fiom 0 to 1, I was able

to calculate combinations of c1 and c2 that correspond with stable population size and

plot zero growth isoclines for each annual matrix within each site.

RESULTS
Population growth rates

Years: There was considerable temporal variation in population growth rates (3.)
within each site. Over the three years of study, A varied among the twelve sites from 0.48
to 5.88 (Table 4.2). Some sites consistently had low annual population growth rates. Two
(HR, RL) never reached a 71 of 1. Five sites had positive growth during a single year only,
four during two years only, and just one site, HSP, had positive growth during all three
years. Within five sites (41%) A was greatest during the first year of the study and
decreased in years two and three. Temporal variation in A across all sites is summarized
by comparing the column arithmatic means of the annual 7t estimates in Table 4.1 .
Overall, A was greatest in 2005 and was nearly identical thereafter, dropping from 1.825

to 1.014 and 1.019 successively.

Sites: Spatial variation in 71. across sites is evaluated with AM, the megamatrix A for

each site (Table 4.2). Estimates of 3M ranged from 0.932 (HR) to 3.543 (B) and were

180

frequently greater than even the highest annual A within a site Figure 4.2. For example,
the highest annual I. in the JP site was 1.595 (2006), while AM was 2.298. There were no
consistent geographic patterns in the spatial distribution of A within years, although the

two sites with the highest AM were both in southern Illinois. The overall mean of the12

AM estimates was 1.897, meaning that on average the A. petiolata study sites supported

rapid positive growth. This number is within the range of published estimates of A. for A.
petiolata from previous studies which vary from 1.2 (V. Nuzzo and B. Blossey,
unpublished data in Davis et al. 2006) to 4.4 (Drayton and Primack 1999, Rejmanek
2000). Only one site had negative growth (HR). The two sites with the highest site mean
A, both in Illinois, each had a A > 5 during 2005 (Table 4.2), and in one of these sites (B)

2. dropped to below 1 during the following two years.

Sensitivity and Elasticity Analyses
Upper-Level Transitions: Across the study populations, management which

reduces the transition of rosettes to the flowering stage (R—->P) is expected to cause the

greatest absolute reduction in It. The sensitivity of It to perturbation of the aij varied in

rank order among the 36 A matrices. These are shown in Figure 4.3 (upper panel) sorted

from left to right by S32, the sensitivity of A to an (R-+P). The population growth rate A
most frequently had the greatest sensitivity to perturbation of a32 (R—+P) followed by a21
(S—+R). This is a biologically intuitive result, as a32 is the proportion of A. petiolata

individuals that survive to reproductive maturity. Raising a21 similarly increases the rate

181

at which dormant seeds exit the seed bank to become rosettes and can progress toward

reproductive maturity. Sensitivity of A to am was only large when S3 2 was small. The

mean sensitivity to a32 was over twice that of (131 (5.7 vs. 2.4), and the sensitivities of A
to all other upper-level transitions were comparatively low.

In contrast, the elasticity (eij) of A to an (S—>S) was, on average, much greater

than the other elasticities. However, e11 was strongly, negatively correlated with loge(A)
(log transformed to meet assumption of normality) across the 36 A matrices

(r = —0.9118); e11 was large almost exclusively among poorly performing populations
with A near or below 1. This occurred because 011 was largely-driven by seed survival
(s3), which had relatively little variation and was almost universally high, while there was
much more variation in the other a,-j and lower-level transitions (Table 4.1). The elasticity
of A to al 1 becomes inflated when reductions in the other more variable transition
probabilities cause A to decrease. When this happens, a1 1/A, which is multiplied by the
sensitivity of A to all (511) to calculate e11 (Equation 4.3), becomes disproportionately

large and drives up e11. Thus, although a“ appears to rise in importance in a number of

cases, it does so somewhat passively by not changing in synch with other transitions and
only makes large contributions to A in populations where A is already low (Figure 4.4,
left). Russ Forest (2007) is the most extreme example of this, where there was 100%
summer mortality in all quadrats which forced winter survival and fecundity to 0. The A

and E matrices for this site in 2007 were:

182

70.7688 0 0

 

 

A: 0.0388 0 0 (4.8)
_ 0 0 0‘
and
'1 0 0'
E: 0 0 0 (4.9)
_0 0 04

 

 

Because the individuals transitioning to the rosette stage in (221 (S—+R) at time t have 0
survival probability thereafter (because a33, R—>P, = 0), a proportional change in an has
no effect on A. Only individuals in an (S—>S) contribute to the next time step, and A =
a] 1: 0.7688. This was not the most robust population.

After a1 1, a3; (R—rP) made the next largest contributions to A (Figure 4.3,

bottom). The elasticity of A to a32 (e32) was positively correlated with loge(A) (r =

0.8152) and was greater than all other elasticities in the populations and years with the
highest A (Figure 4.4, left). Based on this, the transition from rosettes to the flowering

stage is the most important management target among the fastest growing and most

problematic populations. Transition a23 (P—->R) caused the next largest proportional

response in A followed by 013 (P—>S) and 021, (S—rR), which had approximately equal eij

(Figure 4.3).

183

Lower-Level Transitions: The population growth rate A had the greatest elasticity
to perturbation of dormant seed survival (SS) in most sites and most years (Figure 4.5).
Elasticities of A to g1 and tof, 5,, 5m", and SW, were positively associated with increases

in each of those five lower-level demographic rates, and were most strongly correlated
with increasing 35",” and g1. The elasticities of A to f, s,, ssum, and swim (abbreviated E4)

are shown with a single line (solid line, Figure 4.5) because their values are equal across
the range of the data. E4 exceeded E ,1, at the higher levels of ssum, (dash-dot line, Figure
4.5). Seed survival (s5) had low variability (Table 4.1) and was only weakly correlated

with loge(A) (r = 0.2838), while ssum was positively correlated with loge(A) (r = 0.7059),

and s, and ssum were uncorrelated (r = 0.0256). This and the plot of the elasticities versus
A (lower right, Figure 4.5) suggest that this reversal in ranking parallels what was seen in

the upper-level elasticities (Figure 4.4, right). It results not from a tradeoff between s, and

sum, but rather from the response of A to increasing Ssum as s, remains stable and large in
the background. The higher A becomes, the greater its proportional response is to
perturbation of all transitions except 5, and g3. The sensitivities of A to the lower level
transitions reveal that this is accompanied by a larger increase in the magnitude of A’s

response to additive perturbation of swim g1, and ssum (Figure 4.6). Thus, the more rapidly

A. petiolata grows, the more vulnerable it becomes [demographically] to management of
rosette survival and germination. Management should be preferentially directed at these

transitions.

184

Zero Growth Isoclines

Alliaria petiolata showed a range of responses to the simulation of management
(Figure 4.7). In Figure 4.7, the larger shaded area represents the ranges of increased
rosette mortality (x-axis, 0-50%) and reduction of fecundity (y—axis, 0-82%) induced in
A. petiolata during several studies of the candidate biocontrol agents C. scrobicollis and
C. alliariae (Gerber et al. 2002, Gerber et al. 2007b, Gerber et al. 2007a, 2008a, E.
Gerber personal communication). The smaller shaded area shows the range of observed
impacts of C. scrobicollis, acting by itself, on fecundity (0-49%) and rosette survival (0-
45%) across all experiments. Zero growth isoclines which intersect the shaded area or fall
below the origin (and thus are not visible) indicate combinations of A. petiolata
demographic rates and agent efficacy which suppress A below 1. Predicted management
outcomes are based on interpretation of the megamatrix zero growth isocline for each
site. Annual zero growth isoclines are shown in Appendix 4.B

Nine of the twelve (75%) A. petiolata study populations are potentially
controllable if C. scrobicollis and C. alliariae are released together. This assumes that
management efficacy is at the extreme high end of the expected range for both agents
(top right comer of shaded area, Figure 4.7). Of these eight sites, four have a predicted
probability of being successfully controlled below 0.1 (Table 4.3). Fewer sites are
predicted to be controlled if the agents perform below this level. If C. scrobicollis is
released alone and performs at its maximum observed efficacy, A. petiolata could be
suppressed at up to five sites (41%; HR, F, SH, RL, and RF). One of the five sites (RL) is
predicted to have a 0.007 probability of being successfully controlled. However, if C.

scrobicollis only reduces rosette survival by 7% (Hinz and Gerber 2001) and has no

185

effect on fecundity (Gerber et al. 2007a), this number drops to one site (HR), which is not

an increase over the number of unmanaged sites with AM < 1.

The annual variation in demographic rates within each site caused considerable
differences in agent efficacy required to suppress growth during individual years..Annual
zero grth isoclines are shown in Appendix 4.B. At each site, at least one of the three
annual zero growth isoclines crossed the shaded agent-impacts area. In all sites except
HSP, which had positive grth each year, at least one isocline also falls below the

origin of the figure.

DISCUSSION

Improving the predictability of weed biological control remains a common goal of
weed scientists, biocontrol practitioners, and conservation managers (McEvoy and
Coombs 1999, Louda et al. 2003b, Pearson and Callaway 2003, Briese 2006, Davis et a1.
2006, Raghu and van Klinken 2006). Because biological control management of A.
petiolata is a longer-term endeavor, management decisions should not be made based on
data from individual years. Four demographic models of A. petiolata have been published
previously (Drayton and Primack 1999, but see Rejmanek 2000, Meekins and McCarthy
2002, but see Evans et al. unpublished manuscript Appendix D, Davis et a1. 2006, Pardini
et al. 2009, but see Evans unpublished manuscript), two of which made specific
management recommendations. Of these four previous models, three had significant

errors that required later correction (hence the “but sees”). Drayton and Primack’s model
incorrectly characterized A. petiolata’s life history by omitting a23 (P—->R). Meekins and

McCarthy used sub-annual transitions as upper-level transitions, thus introducing errors

186

in the model’s projection interval. Pardini et al.’s model incorporated errors from the

parameterization of several density dependent functions and omitted seed bank mortality
from two transitions (an and a21), which together sabotaged their management

recommendations.

Davis et al. explored a parameter space centered on the demographic rates of a
natural A. petiolata population (Meekins and McCarthy 2002) and made a number of
specific predictions about the expected variability of successful management. One of
their main conclusions was that the elasticity structure, at least in terms of relative
rankings of the elasticities, was fairly constant as each vital rate was sequentially varied
from 0 to 1 while the others were held fixed (Figure 3 in Davis et al. 2006). As they
acknowledge, this method did not account for correlations or covariance among the vital
rates likely to occur in natural populations. Because the matrices in my analysis were
parameterized from natural populations and were fixed, the analysis implicitly accounts

for these correlations and avoids having to make assumptions about the relationships

among the ag- (van Tienderen 1995).

In this study, I have shown that A. petiolata’s demographic parameter space is, in
fact, larger and more varied than what Davis et al. modeled or than previous reports in the
literature indicated. One of my most important findings is that, contrary to Davis et al.’s
conclusion, neither the magnitudes nor rankings of either the lower or upper level
elasticities are constant in space or time. We know that spatial variation in the importance
of individual life history pathways can drive significant differences in population
dynamics and response to management among isolated populations (Shea et al. 2005) and

even within populations (Parker 2000). I show here that temporal variation in life history

187

within populations can also contribute significantly to variation in long-term population
performance. A lliaria petiolata populations fluctuate over time through periods of rapid
growth and expansion and periods of survival. As these fluctuations occur, the population
dynamics change from being driven primarily by growth and reproduction, to being
driven by the persistence of the seed bank. This is evidenced by the varying elasticity

structures within populations over time. When A was low, the survival of dormant seeds
in the seed bank (s5 and a1 1) had the largest proportional effect on growth, although the
absolute magnitude (sensitivity) of this effect was small relative to other transitions. In

contrast, when A was high, the transition from rosettes to flowering plants (a32) had the

largest proportional effect on A (Figure 4.5, bottom right panel). This effect was largely
dependent on variation in summer rosette survival, which was the largest demographic
bottleneck in the system. Other lower-level transitions with large proportional effects
when A was large were germination of new seeds, seedling survival, fecundity, and winter
survival. The sensitivity analysis highlights the importance of winter and summer rosette
management among populations where A is large. Collectively, the elasticity and

sensitivity analyses indicate that management which reduces the survival of rosettes to

the flowering stage (a23) or which reduces the transition from the flowering to rosette

stages (a32), either via reducing fecundity, seedling survival, or germination of new

seeds, will have the greatest impact on A during years with the highest growth rates.
The high variability in A both among and within populations could also have
significant consequences for the outcome of biological control. As a population

experiences a sequence of years with alternating positive and negative growth, the

188

rankings and magnitudes of the elasticities and sensitivities can change. For example the

‘Bob’ site (Peoria) had a A of 5.78 in 2005 and 0.79 in 2006. In 2005,the lower level

elasticity of A to s, (E,_,.) was 0.29, while the elasticity to E4, which includes ssum and swim

was 0.4989. The following year, the rankings were reversed, and E5, was 0.9666 while E4

dropped to 0.0235. Practically speaking, this means that when a transition probability is
driven to a small value relative to other transitions, a proportional change in its value

would have to be very large to have a meaningful impact on A. This could help A.

petiolata buffer against biocontrol management of the transitions in E4 such as rosette

survival and fecundity if their effects on A consistently diminish when populations are
suppressed. If so, it would allow A. petiolata a means of recovering from biocontrol
suppression after its grth rate is initially reduced. This would be exacerbated if the
biocontrol agents’ efficiency is negatively dependent on A. petiolata density, for example
if they spend more time searching for the plant at low densities. This highlights one of the
limitations of using static, linear population models, as there are no built-in feedbacks of
density on the vital rates or the elasticity of A to them. Future nonlinear models will need
to explore this possible feedback mechanism in greater detail.

The two candidate biocontrol agent species, C. scrobicollis and C. alliariae, are
well matched to A. petiolata in terms of affecting it at the appropriate life stages. Because
it can affect both rosette survival and fecundity simultaneously, the root mining weevil C.
scrobicollis has the potential to suppress A. petiolata in as many as five of the 12 study
populations (41%) if it performs at its maximum efficacy. Using the same basic approach
applied here, Davis et al. (2006) concluded that C. scrobicollis would control A. petiolata

in 13 of the 18 (72%) scenarios they modeled. They also concluded that introducing the

189

weevil C. alliariae could broaden the impacts to include control A. petiolata in of 16 of
the 18 (88%) simulations. It is important to note that these numbers represent the best
possible outcome, given the models in Davis et al. and in this study, and assume that the
biocontrol agents perform at the maximum efficacy recorded from among at least four
different feeding and impacts trials. In reality, the impacts of either agent will likely be
lower than the maximum and, thus, those numbers are likely overly optimistic. Given
these caveats, both studies agree that C. scrobicollis is likely to suppress at least some A.
petiolata populations if released on its own. Davis et al. found that introducing a second
agent, C. alliariae, could extend control to an additional 16% of the scenarios modeled.
My analysis predicts potentially higher returns from the release of a second agent by
extending the possibility of control to an additional 33% of the study populations.
Whether either species is capable of consistently delivering a strong enough impact on
rosette mortality or reproduction to suppress populations remains unclear from currently
available data. Without knowing what the mean or distribution are of the agents’ impacts
below the reported maxima, it is not possible to assess the degree of uncertainty in the
probability of success. The estimated probabilities of successfully managing A. petiolata
presented here should be interpreted with this understanding. Better data on the
distributions of candidate agent impacts are needed from well replicated field trials and
should be sought. These should include information on insect demographic rates and
density dependence, as well as the insects’ demographic responses to A. petiolata
densities and environmental conditions. From these, a coupled plant-herbivore model
could be developed which links the demography of A. petiolata with the biology of the

biocontrol agents. This would allow generation of much more refined predictions.

190

The lack of ability or desire to make these kinds of evaluations prior to releasing
biological control agents has been criticized as a major historical shortcoming of weed
biocontrol programs. However, the last decade since McEvoy and Coombs (1999) has
seen the beginnings of a cultural shift in the philosophy of weed biocontrol. The number
of studies on agent impacts and target plant demography continues to grow, and
biological control is transforming into a more rigorous practice guided by scientific

principles and founded on ecological theory.

191

Tables: Chapter 4

192

Table 4.1. Mean observed A. petiolata demographic rates by site, calculated for each of

three years.

 

Site
B

State
IL

Year

2005
2006
2007

81
0.682
0.239
0.070

82
0.049
0.031
0.071

Sr
0.843
0.149
0.094

Ssum

0.648
0.119
0.119

Swin
0.369
0.500
0.321

f
276.857
59.027
79.527

SS
0.823
0.806
0.975

 

ELF

MI

2005
2006
2007

0.445
0.1 l 1
0.190

0.019
0.068
0.267

0.357
0.702
0.832

0.342
0.213
0.095

0.408
0.617
0.037

46.170
48.576
56.877

0.988
1.0
1.0

 

IL

2005
2006
2007

0.360
0.129
0.061

0.143
0.019
0.072

0.167
0.125
0.087

0.578
0.151
0.136

0.492
0.333
0.175

86.446
83.543
106.959

1.0
0.642
1.0

 

HL

IL

2005
2006
2007

0.403
0.245
0.389

0.021
0.269
0.032

0.198
0.273
0.429

0.872
0.138
0.054

0.823
0.286
0.250

445.234
572.051
126.388

1.0
0.880
0.969

 

HR

IL

2005
2006
2007

0.577
0.110
0.166

0.1 12
0.048
0.039

0.222
0.429
0.195

0.492
0.094
0.187

0.406
0.389
0.125

23.301
46.540
20.079

0.778
0.505
0.979

 

HSP

MI

2005
2006
2007

0.529
0.106
0.238

0.021
0.161
0.266

0.528
0.935
0.685

0.216
0.073
0.311

0.185
0.403
0.325

59.891
105.165
122.102

1.0
0.975
0.979

 

IP

IL

2005
2006
2007

0.546
0.395
0.480

0.075
0.367
0.288

0.128
0.205
0.403

0.447
0.267
0.085

0.308
0.146
0.806

108.276
71.698
124.029

0.839
0.894
1.0

 

IR

MI

2005
2006
2007

0.421
0.273
0.41 1

0.001
0.047
0.207

0.273
0.798
0.388

0.393
0.048
0.081

0.352
0.370
0.156

44.425
310.587
217.960

0.875
0.882
0.867

 

JP

MI

2005
2006
2007

0.661
0.177
0.660

0.062
0.144
0.440

0.606
0.617
0.523

0.309
0.357
0.1 11

0.350
0.552
0.092

68.905
63.669
56.877

1.0
0.983
1.0

 

RF

RL

SH

M1

M1

M1

2005
2006
2007
2005
2006
2007
2005
2006
2007

0.362
0.130
0.109
0.163
0.151
0.340
0.297
0.152
0.377

0.064
0.129
0.077
0.031
0.157
0.189
0.026
0.569
0.169

0.609
0.533
0.566
0.835
0.810
0.899
0.550
0.667
0.849

0.036
0.331
0.0
0.067
0.013
0.113
0.197
0.044
0.111

193

0.1 14
0.421
0.0
0.161
0.333
0.152
0.569
0.298
0.365

140.325
63.173
0.0
15.849
152.414
20.079
22.737
5.717
34.090

0.900
0.859
0.833
1.0
0.969
1.0
0.977
0.907
1.0

Table 4.2. Annual estimates of A for each site (Ayear). These were summarized within

each site as the megamatrix A (AM), the population growth rate of the average population
within each site calculated from the megamatrix M with uncorrelated environments. The

mean growth rate across sites within each year and across all AM is given in the bottom

row. The arithmetic mean AM is the average A across the study system.

 

 

 

 

 

Site State A2005 A2006 A2007 7M
B IL 5.883 0.798 0.927 3.543
ELF MI 1.097 1.212 0.793 1.586
F IL 1.453 0.642 0.945 1.120
HL IL 5.061 1.586 0.959 3.405
HR IL 0.855 0.530 0.945 0.832
HSP MI 1.014 1.184 1.856 2.082
1P IL 1.064 0.809 1.509 1.887
IR MI 0.880 1.207 0.922 2.370
JP MI 1.763 1.595 0.709 2.298
RF MI 0.862 1.212 0.769 1.285
RL MI 0.973 0.908 0.870 1.233
SH MI 0.995 0.483 1.029 1.123
Column Means: 1.825 1.014 1.019 1.897

 

194

Table 4.3. The probability of successfully controlling A. petiolata at each site was

graphically estimated as the proportion of the two shaded areas above the zero growth
isoclines in Figure 4.7. The sizes of the shaded areas for C. scrobicollis alone (smaller
rectangle in Figure 4.7) and with C. alliariae (larger rectangle) were 13899 and 26082

pixels, respectively. This analysis assumes a uniform probability distribution for agent

 

 

 

 

 

 

 

impacts.
Shaded Pixels Above Isocline Probabilitv of Control
C. alliariae + C. alliariae +

Site State C. scrobicollis C. scrobicollis C. scrobicollis C. scrobicollis
B IL 0 0 0 0
ELF MI 0 408 0 0.016
F IL 8074 20173 0.581 0.773
HL IL 0 0 0 0
HR IL 13 899 26082 1.000 1.000
HSP MI 0 0 0 0
IP IL 0 2327 0 0.089
IR MI 0 208 0 0.008
JP MI 0 103 0 0.004
RF MI 2469 13827 0.178 0.530
RL MI 98 8056 0.007 0.309
SH MI 8951 21050 0.644 0.807

Mean: 0.201 0.295

 

195

Figures: Chapter 4

196

 

(l‘c1ifis(l‘g1)

 
   
   
  

 

 

 

S 2/3 I-C Ssu win
Dormant s gZS’ ( 2) ms Flowering
Rosettes
Seeds Plants

SS (l-gz) (1-61m32/3glsr

011=Ss(1-82) 012:0 013=(1-01)f$s(1-g1)

A = 021 = SSZ/3gzs, a22 = 0 on = (1- cl)fi32/3gls,.

_a31 = 0 032 = (1-02)Ssum3win 033 = 0 A

 

Figure 4.1. Alliaria petiolata life cycle diagram and corresponding projection matrix A.
Arrows represent one-year transitions from June of year t to June of year t+1 and are

comprised of sub-annual, lower level demographic transitions: per capita fecundity (f),

germination probabilities of new seeds within one year of seed set (g1) and of dormant
seeds from the soil seed bank (g2), and seedling (sr), summer rosette (ssum), winter rosette

(swin), and dormant seed (53) survival probabilities. Matrix rows correspond with the life

history stage individuals are transitioning from time t, where rows 1, 2, and 3 (from left)

are seeds, rosettes, and flowering plants. Columns indicate life history stages individuals

are transitioning to in time t+1. For example matrix element a3; represents the transition
from rosettes (column 2) to flowering plants (row 3) in matrix A. Following Davis et al.

(2006), the variables el and c2 simulate rosette mortality and fecundity reduction due to

biocontrol, and are shown as (l-cn) to express them in terms of survival.

197

 

M

Mean AM = 1.8968 '

  

A

 

Frequency
"3

 

 

2- _

1- _

00 1 1 2' 3 4
KM

Figure 4.2. Frequency distribution of A. petiolata megamatrix population growth rate

across all sites (n = 12). The black line indicates the mean value of AM across sites.

198

Figure 4.3. Sensitivities (top) and elasticities (bottom) of A to perturbation of A matrix

elements (1,}. Sensitivities from the combined 36 site by year matrices are sorted from left
to right by sensitivity matrix element S32 (R—rP), and elasticities are sorted by elasticity

matrix element e11 (S—>S). The sensitivities of A to a23 and on are small and lie along the
horzontal axis. The elasticities of A to an and a2] are equal; the former obscures the latter

in the lower plot. NOTE: The dotted line (011) does not indicate a different density of

data points than the other four line styles and should not be interpreted differently. It is
used because the software which produced the graph (MATLAB) only prints four basic

line styles.

199

 

 

 

25 4
6T 3- ,i
O 20 ‘ 5': i n
H .I'
c< .i’
9H 15 ' ._ I' I _
O ’.
3. E ."
,_ _ : I _
> 10 i ,...i
CE . T 3' I”.’
g 5 .— ...o o : =- i I ’ ..... I _
CI)

 

Low (— Sensitivity of A to a3 -—> High

 

 

 

 

 

 

 

 

2

l

CIT
0.8 ' f
8 --O— a” (S —)S)
c< ---_
8H 0.6 ' (1'3 (P 9.5) (_
0 ~ P ——)
35 O 4 _ \\ a23 ( R)
.g . ~-._.—.v.~.’_\. .~ ........ (12I (S —)R)
I; .‘Kn-n
'53 02 — _- ’ :;~u---.‘. ----- (132 (R HP) _
’ \ .~ ‘~-——

In sv’ v \V’I «Mu-“‘m...

. M

 

Low (— Elasticity of Ato all —> High

200

 

 

 

 

 

f?
6
O
‘51

 

 

 

 

 

 

 

 

  

   

 

 

 

 

“JR >., .2 0&8 0 all (S .9 S) ’5' 009, 0 E33
'0 0.. 0 % 0......
5:": O 8 o 8...? O 032 (R -—)P) o .558“ . E4
3 ‘3 O o
o 0.6 .‘..
:2 " o q c or
“a 0.4-
2:
'8
E 0.2
8.5 1 2 34560.5 1 2 3456
A

Figure 4.4. Elasticities (eij) of A to A matrix elements an (S—>S) and an (R—vP) (left)
and to lower level transitions seed (53) survival and E4 (right) versus the population
growth rate A. The elasticities of A to f, Sr, 55",", and s,,..,-,, were identical and are
represented together with one line, labeled E4. E4 and e32 are equal as well. Among

populations with high growth rates, A has the greatest elasticity to a3; and E4. Logistic

regression lines are overlaid to show trends.

201

 

Figure 4.5. Empirical second derivatives of A. Observed variation in elasticities of
Alliaria petiolata population growth versus observed variation in the lower demographic
transitions. In each panel the elasticities of A to each lower-level demographic rate from
the 36 site by year matrices is plotted against the observed value of the transition.
indicated on the horizontal axis. The eight panels show the same empirical data sorted
differently. The data are sorted from left to right by the transition labeled on the
horizontal axis. In the lower right panel the x axis is shown on a log scale, although the x
axis tick marks are back-transformed to the original scale. Contours were smoothed using
a LOESS smoother (Burkey 2009) to clarify the relationships among variables. This is
why the values in each panel appear different even though they show the same data. The

raw, unsmoothed plots are presented in Appendix A.

202

K Egm gm bison £96 E 533 has»
cm v m N M md _ ad wd 5d ed 8* SN o wd ed vd Nd d

 

       

 

 

 

 

 

3
d1! \\ C
..... \Ii“ . x l
.... ..:.:. . ................. ..:. . \ ..:.:.... .. |
.\ l... . .:V\ 10.} .HS'Funuu-ao-MV‘ .0. m
s .. p .10
\ 4 \\ ... u b
\ \ 0o n
\ \ o u
\ \ u -
IIIIIIIIIII\\ \\ .4 v.0
. .l.l.l.l .
.I.’ 1.!
. .I .1. .
mm ..:.:. I. .I I. . O O
o. .p |. . I. \I.
_M IIII v —m .\u I. I. I \. Io
- — 0‘ In, I ‘5’ o'e‘. ’
m .33 r . .~ .I. I . I. .I
.83 um I _ . .. .s Ii. Y x a . .1. w o
. .1 \ I.I .I II
a \n‘.‘ —. o ~I. . II..-
mm lull-I -\ VS [.1 — flu

 

 

 

 

 

 

 

 

~w>E=m 0330M .5885 3325 mam—doom N gonna—500 H domaEEBO
wd 0d vd Nd o wd ed vd Nd wd vd md Nd _d ed vd Nd

  

 

I nun-cg...
l n:-
. I :-
uo - l'l incl-..:.:.:-

  

\ I u I III \\
\s . . Inn-ii
\
\
\
l
.I.I. \\\ .\ \\
I. .... \\ v O
I.I ...‘ a
. .. I
I. .. .I
I .. .
.I. 3.. I.I .
I.’ u. . .I. 0 O
. |u|nlcl I.
I. \II I \nlulo n\-\-\- llo‘iI-I I.In
l u\- n 0’ ‘u‘. I \u‘ . 'uI-I.'-’~
. ‘\ .l. I .\. t I .
f u‘ n’ ’0 o
.r I. . i a. . r. :w o
.I.\. t a. Ii
. .
_ 1 l
A

 

 

 

 

 

 

 

 

 

191m 011/ J0 5110118913
203

"me01

f1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sx (Sensitivity of A to variation in x)

 

 

 

 

 

Figure 4.6. Sensitivities of A to lower-level A. petiolata transitions x versus A for 36

individual site-years. As A increases, the rankings and magnitudes of the Sx change to
favor management of rosettes in winter or summer and germination of new seeds. The
vertical lines differentiate between expanding populations (right) and declining

populations (left). The seven sensitivity contours are split into two panels to improve

readability. LOWESS smoothing was applied to each line to for the same purpose.

204

Figure 4.7. Zero growth isoclines (contours of A = 1, indicating stable A. petiolata
population size) for each study population assuming a random sequence of the three

environments (years) using a megamatrix model. The x and y axes in each plot represent

the efficacy of rosette or fecundity management simulated by increasing the variables c2

or cl, respectively, from 0 to l. The larger shaded area shows the observed range of seed

reduction and rosette mortality caused by the combined actions of the root and stem
mining weevils Ceutorhynchus scrobicollis and C. alliariae (see Table 2 in Davis et al.,
2006). The smaller rectangle within the shaded area indicates the range of observed
impacts of C. scrobicollis alone, where the upper right corner is the maximum observed
impact of C. scrobicollis. Contours which intersect the larger shaded area represent
populations which could theoretically be controlled by C. scrobicollis and C. alliariae
together at a given level of agent efficacy (e. g. [P would only be controlled if actual agent
efficacy is at the high end of the observed range). Contours which intersect the smaller

shaded area could theoretically be controlled by C. scrobicollis alone. The line from HR

does not appear in the plot because its AM < 1.Impacts of C. alliariae alone are not shown

because it has not been shown to reduce fecundity under realistic field conditions.

205

AXV 528.88 6338 E 6382: “:8an

 

09 On do 0v dN doe ow do 9. ON dog ow do ow ON doe ow do dv dN

 

 

 

 

 

o

 

 

 

 

 

 

. o
.. .om

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

2 m 2 / z 8
v3.” .A RN“ .x J7 cam“ 4“
8.0. n 2K 2.] a: n 2.x a onwn 2,“ .5 mi u 2.A

/ w a

.2.

/ .5. 8

2 E 2 .2... cm

MS “3 . E m: u g 5 N: u g a man ,A m:

 

 

 

 

 

 

 

 

(%) 1nd1no pass at uononpor moored

206

APPENDIX 4.A: RAW ZERO GROWTH CONTOURS

207

Figure 4.A.1 Empirical elasticity contours without smoothing function. Observed
variation in elasticities of Alliaria petiolata population grth versus observed variation
in the lower demographic transitions. In each panel the elasticities of A to each lower-
level demographic rate from the 36 site by year matrices is plotted against the observed
value of the transition indicated on the horizontal axis. The eight panels show the same
empirical data sorted differently. The data are sorted from left to right by the transition
labeled on the horizontal axis. In the lower right panel the x axis is shown on a log scale,

although the x axis tick marks are back-transformed to the original scale.

208

 

 

     
 
   

0
§
‘O—I—I—U‘.—'.

2:.

u"
o"'
’0

r I'U'uz-lg.-..-..-

0’.

3'".

Ell-Immune.—
--

w._--.'—'==l|"-—

 

 

 

Win-"nun...

“..:.o-.-'-.-.
w ...:::-u.

b'v' ‘7 I ‘
n1." -. 3
‘-~ 0
pug-.-Jlflnuun
,, io-c-u-I-o-v . -
I‘ ~ 0
I”. ~ .~
«I ' a
.-.MIIIIC ‘-

 

0’. ..."l:.~~
I
‘3'..-.-. ..
> I..:::...., :..
O .0...
’O‘.‘» ~..
’I
dl‘=-l-I-u-|-I, .1
I. ”g
m‘gl-‘I.-I- ..
0-0-o-.. #‘
l . I I A. I

 

 

 

 

 

 

 

 

 

 

 

 

0.2 0.4 0.6 0.8

Summer Rosette Survival

0

0.8

0.6

0.4

Seedling Survival

0.2

0.2 0.3 0.4 0.5

GerminatiOn 2

0.1

l

erminatlon

'G

 

 

sr, sum,

..OIIII- £;S

 

-.-.-o-I.-‘--

 

 

 

‘. .....'IIIII
....II
rfl=:=:=:lfllillllillo .
unlillllfli-‘iz-‘h
‘-
l-au-"Ullfln'n'c-go-h
. ~r°.-u-I-'-'-'
II Il..-..-..'

2:»-
o
'g r
V w
“‘uwu-oh .
s. IIIIIOII'..-'

 

 

  
     
  
 

 

 

0.6 0.7 0.81 0.9

 

 

("I

 

.----.-..-‘.%Ei-..ICEI
comma-97'3", "’

 

 

‘..
L .‘g'

 
 

-.‘I-.-'..
.'-..-.-III
.II.II..I..I.II..

 

 
 

 

    
     

 

r:
"x u; uopetreA 011/ JO Anonselg

209

“l
o

 

460
Per Capita Fecundity

 

 
  
   

0.8

0.6

 

 

0.2

3456

0.5

1

'val

SeedbankS

200

O

0.4

“Winter Survival

 

APPENDIX 4.B: ANNUAL ZERO GROWTH CONTOURS

210

Figure 4.B.1. Annual Zero growth isoclines (contours of A = l) for each site. The
megamatrix result used in the primary analysis is also shown. Within each site, at least
one of the three annual zero growth isoclines crossed the shaded agent-impacts area. In

all sites except HSP, which had positive growth each year, at least one isocline falls

below the origin of the figure.

 

211

OOO Om O0 OV ON OOO_ Ow OO OV ON OOOH Ow OO O.v ON OOO~ Om O0 OV ON O

axed 3:388 6338 E 335$ 308$

 

://

 

 

BOON ...........
meow .......
meow ......

ggmoE I

 

 

mm

O
. om

 

 

 

 

 

 

 

 

 

 

 

E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_--_-------- nun—
—
v

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(%) 1nd1n0 peas III uoponpor moored

212

CHAPTER 5: DEMOGRAPHIC VARIANCE ACROSS GRADIENTS OF

POPULATION DENSITY IN ALLIARIA PE T [OLA TA

213

ABSTRACT

Demographic models of the invasive plant Alliaria petiolata (garlic mustard,
Brassicaceae) have been developed previously to inform the selection of effective
biological control agents. Understanding how density dependent feedbacks affect vital
rates and vary spatiotemporally among populations may further the refinement of these
model predictions and lend an important regional perspective to future management r
models. From 2004 to 2007, I studied the survival and reproduction of A. petiolata in 13
natural populations in Illinois and Michigan, USA, across a natural density gradient

spanning over three orders of magnitude. Using mixed effects models I quantified the

 

contributions of population density, region, cohort, and site effects to variability in
demographic rates. Seedling and summer survival and fecundity parameters varied
significantly between Michigan and Illinois and between cohorts, but winter survival did
not. In contrast to other studies of A. petiolata, only mean seedling survival and fecundity
were negatively correlated with initial density, while summer and winter rosette mean
survival were not. Instead, I found that the residual variance in each analysis was
negatively dependent on population density, even when the mean response to density was
not significant. By explicitly modeling the residual variance in each vital rate as a
function of plant density, I show that the demographic variance and stochasticity are
themselves density dependent functions; the maximum possible value of each
demographic rate decreases as density increases, but vital rates vary below these density
dependent upper bounds. Thus, survival and fecundity can be broadly distributed at low
densities but funnel into narrow distributions with lower maxima at high densities. The

scaling of demographic stochasticity with population density has potentially important

214

consequences for populations of management concern, as small populations may become
more susceptible to local extinctions. The robustness of predictive weed management
models may therefore be improved by incorporating elements of environmental and

density dependent demographic stochasticity into their designs.

215

INTRODUCTION

Density dependent processes and demographic variability are important in natural
populations (Horvitz and Schemske 1995, Turchin 1999). Failure to incorporate them
properly into predictive management models could lead to inaccurate characterization of
the demography of the study species. Density feedbacks can vary in importance (Elliott
and Hurley 1998) and even direction (Goldberg et al. 2001) among life history stages,
which suggests that linear population models may oversimplify complex biological
processes. Similarly, a single species can exhibit life history differences across its range,
in different habitats, or over time that could affect how it responds to management
(Parker 2000, Shea et a1. 2005). For species with large geographic distributions, this
means either that different management approaches need to be implemented in different
areas, or that a single strategy must be applied which maximizes the outcome at the
greatest number of locations.

When biological control is considered for management of invasive weeds, this
latter, probabilistic approach may be the most appropriate option. Because herbivorous
insect agents with strong dispersal capabilities are not likely to stay where they are
locally released (Simberloff and Stiling 1996, Stiling et al. 2004, Louda et al. 2005b),
weed biocontrol management decisions should ideally be made on a scale equivalent to
the potential distribution of the proposed biocontrol agent(s) (Louda et al. 2003a).
Modeling a target species’ biology should ideally account for demographic variability
across the species’ range that could affect the outcome of management, including

possible variability in density dependence. The critical question then is how to best

216

account for this variability and create a model of invasive species control that is robust in
its predictions across a wide range of environments.

I considered this problem in an ongoing study (Davis et a1. 2006) of the invasive
weed Alliaria petiolata (garlic mustard, Brassicaceae [M. Bieb] Cavara and Grande) for
which biological control has not yet been implemented but is likely forthcoming (Gerber
et al. 2008b). This species has been the subject of several previous studies that quantified
various aspects of its demography (Cavers et al. 1979, Baskin and Baskin 1992,
Anderson et al. 1996, Drayton and Primack 1999) and indicated negative density
dependent feedbacks in survival and reproduction (Meekins and McCarthy 2000, Pardini
et al. 2009). Data from Meekins and McCarthy (2002) also shows density dependence of
A. petiolata population growth rates (1), although the estimates of A in the original paper
were calculated incorrectly (see Appendix 2.D). These studies provide valuable estimates
of A. petiolata transition probabilities across a large geographical area in eastern North
America (Kentucky to Ontario), but none accounts for the variability in demographic
rates and population density feedbacks on vital rates at large spatial or temporal scales.

Here, I present a re-examination of density dependence in the A. petiolata
demographic data described in previous chapters. Using these data, I asked (1) if there
were differences in demographic rates between Michigan and Illinois populations, (2)
whether populations were variable from year to year, and (3) whether there were density
dependent feedbacks that contribute to this variability. I used mixed effects models to
explore the spatial and temporal variability in survival and reproduction and evaluate the
importance of density dependent feedbacks across the observed gradient of population

density measured in my study system. This study differs from the analysis in Chapter 2 in

217

 

the way that residual variance was modeled and interpreted. While the generalized linear
models and generalized linear mixed models parameterized in Chapter 2 can be used to
predict survival rates, they have limited flexibility in the way they handle residual
variance and overdispersed data. The linear mixed models explored here offer a different
view of the data structure and highlight some of the most interesting aspects of A.

petiolata’s demography.

METHODS

Sampling

Study site descriptions and sampling methods are presented in Chapters 2 and 4. Note
that as in previous chapters, demographic rates were grouped into “cohorts” for analysis
based on the June to June annual projection interval used in previous A. petiolata studies
(Davis et a1. 2006). This required grouping rosettes from one year in the same cohort as
seedlings that germinated the following year. For example rosette survival in the 2005-
2006 cohort was measured from June 2005 until June 2006 when those plants matured

and produced seeds. Seedling survival was measured during the spring of 2006.

Statistical Analyses

The main objective of this study was to evaluate the contributions of location,
time, and density to differences in demographic rates between A. petiolata populations. I
constructed linear mixed effects models with a 2 by 3 factorial fixed effects structure to
analyze the variability in seedling, summer, and winter survival and in per capita

fecundity. Fixed factors in the analyses included region (Illinois and Michigan), cohort

218

 

(2005-2006, 2006-2007, 2007-2008), and initial A. petiolata density to test for density
dependence. Site nested within year was included as a random factor assuming that each
site is a random sample from the population of all possible study sites and therefore
contributes to the observed variation in the data. The nesting structure accounts for the
covariance of observations across sites within each year. To avoid introducing
multiplicative errors into the fecundity analysis, I modeled the number of siliques per
plant as the response rather than the estimated number of seeds per plant. However, seeds
per plant and siliques per plant are strongly correlated (Appendix 2.B.iv), so model
predictions will be applicable to seed production. In the three analyses of survival, each
observation was weighted by the number of plants used in its calculation. For example, a
survival rate estimated from a sample of 100 plants would be more heavily weighted than
one estimated from 50 plants. Data used in the analysis of fecundity were not weighted
because these were exhaustive counts of the true number of siliques on each plant in each

sampling quadrat.
Maximum seedling density and June and fall rosette densities (plants m'z) were

used as density covariates in analyses of seedling, summer, and winter survival,
respectively. Fall rosette density was used as the covariate in the analysis of fecundity.
All survival probability response variables were arcsine square root transformed, and
silique counts used in the fecundity analysis were square root transformed to meet the
assumptions of the analyses.

Initial statistical analyses indicated that there was overdispersion in the survival
data (i.e. the residual variance was greater than expected under a binomial distribution,

where the variance is a function of the mean (Littell et a1. 2006)) even after applying

219

 

variance stabilizing transformations. The fecundity data were also overdispersed. Two
alternative structures for the residual variance were fitted in each analysis to correct for
this: the power of mean (POM) fimction and an exponential firnction in which the
residual variance is a function of the density covariate. Denominator degrees of freedom
were approximated using the Satterthwaite method (Littell et al. 2006). Each analysis was
run with fixed effects only, fixed effects plus random site within year effects, and finally
with all fixed and random effects including the alternative residual variance structures.
The best-fit model was selected using the information-theoretic methods (Littell et al.

2006)

RESULTS

Alliaria petiolata initial population densities varied approximately lOO-fold for
each life stage. Maximum seedling densities ranged from 75 to 6025 plants In2 (Figure
5.1). Summer and fall rosette densities used as covariates in the summer and winter

survival. analyses ranged from 31 to 3344 plants 111-2 and from 4 to 540 plants m'z,

respectively (Figure 5.1). Bayesian Information Criteria (BIC) (Littell et al. 2006)
indicated that, for each of the three survival transitions analyzed, the data best supported
the full model which included random effects terms and the variance modeled as a
function of density (Table 5.1). There was equivalent support for the POM and density
dependent variance functions in the fecundity analysis (ABIC = 0.4). For ease of
biological interpretation, I present the results of the density dependent variance model of
fecundity. Model fit statistics are presented in Table 5.2 including slope and variance

parameter estimates for covariates. Many of the highest starting densities in the summer

220

 

survival analysis occurred in the smaller quadrats that were monitored through the

summer in Michigan during 2005. Re-running the model without these data points did not
change sign or significance of the density covariate (F1, 32 = 4.13, P = 0.0504) nor the

general conclusions about the exponential variance term; the results presented include

these data.

Fixed Effects

Mean seedling survival (F1, 373, = 43.05, P < 0.0001) varied between Michigan
and Illinois (Table 5.2), but not between cohorts. Summer survival varied both between
regions (F1, 349 = 5.32, P = 0.0272) and cohorts (F2, 32.7 = 18.0, P < 0.0001). The
region*cohort interaction in the summer survival analysis was significant as well (F 2, 32.2

= 5.59, P = 0.0082), indicating that year to year differences in mean summer survival
were not consistent between Michigan and Illinois. Mean winter survival rates were not

significantly different between regions or cohort groups (Table 5.2), though mean

fecundity varied between regions (F 1, 26.4 = 5.76, P = 0.0237).

Density dependent effects on survival were strongest early in the life cycle and for

seed production. Maximum seedling density negatively affected seedling survival (slope

= -0.00004, F1, 45,; = 8.88, P = 0.0046). The effect of rosette density on summer survival
was also negative (slope = -0.00002) but not significant (F 1, 183 = 0.61, P = 0.4456), and

reversed to significantly positive (slope = 0.0006, F1, 424 = 6.61, P = 0.0137) in winter.

This reversal was driven by two influential experimental units (quadrats) with high

221

 

leverage during the winter that had both high starting densities and high survival rates.

Dropping these data points from the analysis changed the sign of the slope to negative

(slope = -0.00018) but non significant (F1, 572 = 0.24, P = 0.6241). Because the

interpretation of the slope of the density covariate for winter rosette survival was entirely

dependent on these two observations, I chose to drop them from further analysis.

Fecundity responded negatively to initial A. petiolata density (slope = -0.0055, F1, 595,
P < 0.0001) and varied between regions as well (F 1, 264 = 5.76, P = 0.0237), but not

between cohorts (F2, 259 = 0.85, P = 0.4378). Although the absolute values of the slope

estimates are small, the ranges of the dependent variables were also small relative to the
independent variables. Thus, shallow slopes such as these can be biologically meaningful.
All three-way interactions (region*cohort*density) were non-significant and were

dropped from the models.

Random Effects

The random effects of sites nested within cohorts were significant for all response
variables (Table 5.2), indicating that plants growing together at the same site likely
experienced more similar biotic and abiotic conditions than those growing at different
sites and in different years. This effect was least significant during the winter, suggesting
that winter survival is less dependent on local site conditions.

Perhaps more significantly, the residual variance in each vital rate decreased as a
function of initial density. The slope estimates for the variance terms were negative and

significant in all analyses: seedling survival (SIOpe = -0.0007, Z = -4.81, P < 0.0001),

222

 

survival in summer (slope = 0001, Z = -2.84, P = 0.0045) and winter (slope = -0.0096, Z
= -6.1 l, P = < 0.0001), and fecundity (slope = -0.0049, Z = ~6.81, P < 0.0001). The
consequence of this is reflected in the decreasing ranges of the response variables with

increasing initial density. At low population densities, survival probability estimates in

each model ranged from 0 to 1, and fecundity ranged from 0 to over 120 siliques plant.l

(Figure 5.1). As the population density increased, the variation around the mean survival
probabilities and fecundity declined exponentially (Figure 5.2), such that at high plant

densities survival probabilities were rarely greater than 0.5, and fecundity rarely
exceeded 20 siliques plant-l. This pattern is evident in the data as the decreasing upper

boundaries and the more subtly increasing lower boundaries of the parameter space
across the gradient of increasing density in the raw data (Figure 5.1) and in the prediction
intervals generated from the parameterized models (Figure 5.2-5.5). Thus, although the
density covariate slopes of the summer and winter survival analyses were not different

fiom zero, survival rates did respond to initial plant density.

DISCUSSION

Population density is one of several important factors influencing the survival and.
reproduction of A. petiolata across the 12 Illinois and Michigan study sites. These effects
appear to be at least partially seasonal. Negative density dependent feedbacks were
demonstrated in all transitions except winter using generalized linear mixed models with
additional covariates in Chapter 2. Using simpler linear mixed models of transformed
data here, the main effects of population density appear more variable. Negative density

dependent feedbacks were strongest during the spring recruitment phase (seedling to

223

 

rosette). During this period, seedling populations reached high initial densities in some
locations and then thinned over the remainder of the plant’s life cycle until senescence in

the summer of the second year. It was only during this recruitment stage, when

population densities reached almost 7000 m'z, that there was a significant negative effect

of plant density on mean survival (Figure 5.2, Table 5.2). Though still negative, this

relationship weakened through the summer (Figure 5.3) and winter (Figure 5.4), when the

highest starting density was only 360 plants In.2 (Table 5.2). Winter rosette density had a

negative effect on seed production during the spring of the second year in A. petiolata’s
life cycle. This switching of the covariate slope from negative to zero may reflect the
importance of intraspecific competitive or interference interactions early in the life cycle
later becoming subordinate to abiotic or stochastic factors once self thinning of seedlings
has increased the spacing between individuals and reduced the likelihood of further
competitive interactions (Goldberg et al. 2001). Altemately, because fecundity was
density dependent as well, it could indicate that spring is a critical period in the life cycle
during which differences in resource availability or growing conditions have the potential
to interact with population density.

The failure to detect density dependence in summer and winter rosette survival
rates may be either exclusion of other important covariates or that natural population
densities were too low after thinning of seedlings in spring to have further effects (sensu
Smith et al. 2003). Biased selection of low density rosette populations could also obscure
density dependence, especially if its effects are subtle or absent at these low densities.
Quadrat placement was not biased against high densities. If it had been biased, I would

not have captured the exponentially declining variance of survival and fecundity as

224

density increased. Thus, the data show that mean demographic rates are relatively
constant across the naturally occurring density gradient after recruitment with only the

variance exhibiting a strong negative density response.

The Importance of Variance

The slope of the density covariate in the fixed effects is an estimate of the
relationship between initial density and mean survival or reproductive rates. When this
slope is not significantly different from zero, the conventional interpretation is that the
response variable and covariate are unrelated. However, I find that population density is
strongly connected with the variance of demographic rates in A. petiolata, even when the
main effect of density is not significant. This was true of the density dependent models
presented in Chapter 2 as well, although it was not possible to explicitly account for the
density-variance relationship within the generalized linear modeling framework used
there. Modeling the variance as a random exponential function of the density covariate
reveals a decreasing upper bound to the distribution of lower level demographic rates as
density increases even in the absence of an overall mean trend. For example, the slope of
the summer survival density covariate was not significantly different from zero. Mean

summer survival was nearly the same in both the high and low density plots: the mean

summer survival rates of the lower and upper 50th percentiles of quadrats were 0.207 and

0.224, respectively. But summer survival in low density quadrats ranged from 0 to 1,

while there were no measurements of summer survival greater than 0.5 at densities above

~600 plants m.2 (Figure 5.1). Maximum survival probability is limited or capped at any

given density but can vary below that maximum. This limit decreases as density

225

 

increases. Vital rates show a broad distribution in the range of values they can attain at
low densities where abiotic and stochastic factors are likely most limiting and are
firnneled into a more restricted range of values as density increases and crowding and
competition dominate. Predicting population behaviors will therefore be less precise at
low densities.

Ecological data from natural populations are characteristically noisy. Unmeasured
factors such as habitat quality, microsite conditions, and environmental and demographic
stochasticity undoubtedly contribute to the observed variance in demographic rates.
Decoupling these from the effects of density requires controlled experiments. What
observational studies such as this one can provide are important estimates of the actual
distribution of demographic parameters among natural populations and over time. For
application to a regional management strategy like biological control, understanding this
variability in vital rates will be essential to determining what proportion of populations
across the landscape will respond to a given control strategy. Linking results from
observational studies of natural populations with experiments conducted under known
gradients may be usefirl for further partitioning the observed variance into density
dependent, environmental, and stochastic components.

My mixed model approach to estimating demographic rates in A. petiolata
suggests a significant negative feedback of population density on survival probability and
fecundity across multiple populations and corroborates findings of other studies of this
species (Meekins and McCarthy 2000, Smith et al. 2003, Winterer et al. 2005, Rebek and
O'Neil 2006). More interestingly, though, I did not see strong effects of plant density on

mean demographic rates after the recruitment phase. Rather, density dependence in this

226

 

system was best characterized by the negative relationship between demographic
variance and population density for all demographic parameters. Density dependence is
an important factor structuring A. petiolata populations, but is only important relative to
other factors at high densities. The estimated ranges of demographic parameters changed
from spanning the entire range of possible values at low densities to having increasingly
restricted distributions at higher densities. Thus, the demographic rates in these models
effectively change from behaving like stochastic variables to behaving in a more
deterministic fashion with increasing density, and density dependence becomes the most
important factor limiting the response variable.

Demographic variability is predicted to be dependent on population size when
there is density dependence in survival and reproductive rates (Engen et al. 1998). This
has been observed empirically in a songbird population (Saether et al. 1998) as well as in
experimental populations of Daphnia magna in which demographic stochasticity
appeared to have density dependent components (Drake 2005). Incorporating density
dependent demographic stochasticity into a stochastic population model greatly improved
Drake’s ability to accurately predict extinction rates of the experimental populations. This
suggests future models of A. petiolata biocontrol that incorporate density dependent
stochasticity as well as site and regional demographic differences will provide more
accurate predictions of population responses to biocontrol. Graphical analysis of the data
shows strong density dependent mortality in some sites during certain years, but not
others. Density feedbacks are therefore important in this system, but might better be
thought of as effects that rise and fall in importance relative to other mortality factors

across space and time.

227

 

It is uncertain exactly how these elements will interact in future A. petiolata
biocontrol models. There is a tension between the generally stabilizing effects of density
dependent survival and reproduction (e. g. Saether et a1. 1998, Buckley et al. 2001) and
the destabilizing effects and increased extinction probabilities resulting from density I
dependent stochasticity (Drake 2005). Conceivably, these processes could interact to
enhance biocontrol effectiveness. An effective herbivore that reduces a vital rate such as
survival could increase the relative importance of stochasticity. Mortality induced in early
life history stages will truncate the distribution of population densities in later, non-
density dependent stages. By driving populations towards densities that are more
susceptible to demographic stochasticity, a biocontrol agent could thus increase a
population’s probability of stochastic extinction. Complex dynamics between herbivore
and plant densities could complicate this relationship.

Populations of A. petiolata exhibit spatiotemporal variability in demographic
rates. Dynamic stochastic feedbacks on demographic rates clearly play an important role
in this variability and should not be overlooked. Because populations whose
demographics are dissimilar may not succrunb a common control tactic (Parker 2000,
Shea et al. 2005), incorporating these estimates of the spatiotemporal variance and
density dependence of demographic rates and stochasticity in the A. petiolata system into
predictive management models could potentially indicate whether different management
strategies will be required in different areas. The role of demographic variance scaling
across population density gradients should be explored further in future models of A.
petiolata population dynamics and biological control. The models presented here are

useful for interpreting patterns in these data. However, because the data were transformed

228

before analysis, the models cannot be used in a predictive context. Doing so will require
development of new generalized linear mixed models that can accommodate modeling

the residual variance as a function of a covariate. .

229

Tables: Chapter 5

230

.7"?

 

Table 5.1 Comparisons of fixed- and mixed effects models of density dependent survival
and fecundity in A. petiolata. Seedling survival was calculated as the number of rosettes
in June divided by the maximum number of seedlings observed during the spring
germination period. Summer and winter survival were calculated as the proportion of
rosettes surviving fi'om June to October and from October to the following June,

respectively. All models included fixed effects terms for initial A. petiolata density
(plants m'z), state, year, and state by year interactions. Mixed effects models also
included random effects terms for site within year. In the mixed models, the variance
structure was modeled normally, as an exponential function of the density covariate, and
using the power of the mean (POM) structure. AIC and BIC are the Akaike and Bayesian

Information Criterion, respectively. A AIC and A BIC indicate the difference in fit

between each model and the fit of the best fit model within each set of analyses. Table 5.1.

231

 

-2 Res. Log

 

 

 

 

Transition
Model, Covariance Structure likelihood AIC A AIC BIC A BIC
Seedling Survival Mixed, exp(seed1ings) 35.4 41.4 0.0 46.2 0.0
Mixed, POM 50.1 56.1 14.7 60.8 14.6
Mixed, normal 54.0 58.0 16.6 61.1 14.9
Fixed, normal 80.1 82.2 40.9 85.1 38.9
Summer Survival Mixed, exp(June rosettes) 24.6 30.6 0.0 35.3 0.0
Mixed, POM 31.3 37.3 6.7 42.0 6.7
Mixed, normal 44.9 48.9 18.3 49.8 14.5
Fixed, normal 46.0 48.0 17.4 50.9 15.6
Winter Survival Mixed, exp(Oct. rosettes) 130.5 136.5 0.0 141.1 0.0
Mixed, normal 159.2 161.2 24.7 162.8 21.7
Fixed, normal 159.2 161.2 24.7 163.9 22.8
Fecundity Mixed, POM 2687.2 2693.2 0.0 2697.7 0.0
Mixed, exp(Oct. rosettes) 2687.5 2693.5 0.3 2698.1 0.4
Mixed, normal 2733.7 2737.7 44.5 2740.8 43.1
Fixed, normal 2815.7 2817.7 124.5 2822.4 124.7

232

Table 5.2 Type III F -tests of fixed effects and estimates of covariance parameters fi'om

analyses of arcsine square root transformed seedling, summer, and winter survival
probabilities in A. petiolata. In each model, plant density (# m'z) is the number of A.

petiolata plants at the start of the interval over which survival was measured, except for
seedling survival, where seedling density is the maximum density of seedlings observed
during the spring. The estimated density effects are slopes associated with each density
covariate. Random effects are indicated in italics and were evaluated with Z tests.
Congratulations! You’re almost done reading this thing. 1 will buy a beer for any

committee member who finds this text and mentions it at my defense.

233

 

 

 

 

 

 

Transition Effect Estimate Num DF Den DF Test Statistic P
Seedling Survival Region 1 27.3 43.05 <.0001
Cohort 2 26.7 0.58 0.5664
Region*Cohort 2 27 1.76 0.1910
Maximum Seedling -0.00004 1 45.2 8.88 0.0046
Density
Sile(C0hort) 0.0287 2.67 0.0038
exp(Seed/ing Density) -0.0007 —4.81 <.0001
Residual 0.0902 4. 8 8 <.0001
Summer Survival Region 1 34.9 5.32 0.0272
Cohort 2 32.7 18.03 <.0001
Region*Cohort 2 32.2 5.59 0.0082
Summer Density -0.00002 1 18.8 0.61 0.4456
Site(C0h0rt) 0.0198 2.46 0.0069
exp(Summer Density) -0.001 1 -2.84 0.0045
Residual 0.0634 5.24 <.0001
Winter Survival Region 1 46.9 0.03 0.8588
Cohort 2 49.7 1.25 0.2946
Region*Cohort 2 38 1.04 0.3628
Winter Density -0.00018 1 57.2 0.24 0.6241
Site(C0h0rt) 0.0175 1.7100 0.0435
exp( Winter Density) -0.0096 -6.1 100 <.0001
Residual 0.2904 5.4700 <.0001
Fecundity Region 1 26.4 5.76 0.0237
Cohort 2 25.9 0.85 0.4378
Region*Cohort 2 23.9 ' 0.18 0.8392
Winter Density -0.00551 1 595 44.89 <.0001
Site(Cohort) 0.4183 2.12 0.0172
exp( Winter Density) -0.0049 -6.81 <.0001
Residual 3.71 7.53 <.0001

 

234

 

Figures: Chapter 5

235

Lil“

 

 

Figure 5.1 Untransformed survival and fecundity data plotted against plant density (A.

. -2 . . . . . .
petzolata plants m ) at the beginning of the time interval over which survrval was

evaluated. Seedling density is the maximum density observed during the spring, summer
and winter starting rosette densities were measured in June and October, respectively.
Each survival parameter estimate shown is a quadrat mean value, calculated as the
proportion of plants marked at the beginning of the time interval that were still alive at
the end of the interval. Fecundity is plotted against the density of rosettes during the
previous October and is shown as the estimated number of seeds produced by each
individual plant within each quadrat rather than quadrat mean values. All plants in a
quadrat experience the same starting density and thus align in vertical bands by quadrat in
the figure. Note the differences in the x axes. The maximmn plant density steadily

decreases as A. petiolata populations thin over the course of the growing season.

236

I

 

$9. 358$ 26ch __mn_

 

 

 

ooo ooo oou ooN oo. o2 oo o
o. o .
. H2.5“. ”madam”. 3.}
CCC

00’

.u

C

o o.

C

o

 

 

 

 

 

 

£258".
AwE $2305 36ch .mEesm
oooo ooom ooom ooor ooo. ooo o
o o o. t -
o o o o. o~ ”“0
O O O O...
o o a
O O .0. O
o o
C C C
o o 0000 o
u to» o
O.
on.
.2555

o:
rueld Jed sanbms

00l-

OSL

9'0 #0 2'0 0'0.
Anuqeqwd IBM/ms

8'0

01

 

$5 8:805 328 __o”_

 

 

 

 

 

 

03 com OmN OON Omp OOF on O
. o o . 00'
o o o o o o o
n C C C ' C C .C ’ C C
C C : C C C
o. o o e one 00
O O O
o o o o oo 0 one o o H 00 o
o $
0 o o
o 0
on. o.
.253
me 85689 £28 x84
Doom OOOm OOOv Doom OOON OOO _. O
. .O .p
o o o o o o. o. o 00’ “of
C e C C
o o co Q. Q.
I “one o
o o o o o 0000’"
o o I 0000 ..o
o o o to.
'0. O. O O
o o 00. o o
o o 00‘ a“:
o v 0 cl 0
o o o
o 0-0

 

 

mmc=umom

9t) rt) 31) or)
Mriiqeqmd IBAwns

90

Cl

0'0

2'0

910 7'0
Miqueqmd IeAwns

8'0

O'L

237

Figure 5.2. Observed seedling survival data (dots) and initial seedling density (# m-Z)

showing mean predicted trend (solid line) and lower and upper 95% prediction intervals

(dashed lines) for each cohort in Illinois and Michigan based on model results. Dashed

lines show 5th and 95th percentiles of the distribution of survival rates based on simulated

observations generated from the statistical model which was parameterized from the data.
Each distribution is based on 100,000 simulated data sets. Trend lines have been
smoothed to illustrate the overall shape of the relationship between density and the
probability of survival. Analyses were performed on arcsin-square root transformed
survival probabilities and are shown back-transformed to the original scale. Predicted
survival rates with negative values were rounded to zero prior to back-transformation to

better illustrate the prediction intervals.

238

 

0.6 0.8 1.0

Seedling Survival Probability: 2006
0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4

Seedling Survival Probability: 2007

0.8 1.0 0.0

0.6

Seedling Survival Probability: 2008
0.2

0.0

Prediction Intervals for Illinois

 

 

0.6

 

 

 

 

 

 

 

0.4

 

 

 

. “‘
V
:5
o
o
o . N
o . ° :5
o . 0 .
e
o----! ----------------- g
1000 3000 5000
C?
\\\ w
o
\\\\ (Q
‘~.\ O
. \\‘\~\
0 ' ‘~-\ v
0 ‘ <5
0
o
. . O N
O
C . . .. .
.C
_____________________________ c;
o
1000 3000 5000
O.
a)
\\\ d
\\\ (D
O
C . \\\
“I
0 ° ' o
.0 o
N
o .. o
.-_°.-...2----.’ 0.
O
1000 3000 5000

Peak Densitv (Seedlings m2)

239

Prediction Intervals for Michigan

 

1.0

0.8

 

-“
‘s.
‘s
s
s
\
x
s
\
x“
‘
.0 ~.‘
0 \
~ ‘\
C ‘~‘
‘
C C.
C

 

 

0 1000

 

 

 

O 1000 3000 5000

 

 

 

o 1000 30100 5000
. . -2
Peak Densrtv (Seedlings m 1

 

 

 

 

Figure 5.3. Observed summer survival data (dots) and initial rosette density (# m'z) in

June showing mean predicted trend (solid line) and lower and upper 95% prediction
intervals (dashed lines) for each cohort in Illinois and Michigan based on model results.

See Figure 5.2 caption for more details. Note the scale of the X axis for Michigan 2005.

240

Summer Survival Probability: 2006 Summer Survival Probability: 2005

Summer Survival Probability: 2007

to

Prediction Intervals for Illinois

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: . °
CO
c5
.0
‘Q .__: .° 0
C
o e. . °
v; o
0
Cd. 0
o ........
e
0
c5
0 200 400 600 800 1000
c;
a)
c5
(0
<5 ‘ ....
0 ““~-
V:, o
O
o
0
(Y
C’ o o '
o 0
~
0 C
o- coo-o--—+—-—
0 200 400 600 800 1000
C?
co
c5
‘9.
o A“
v. ‘\
O
o
o
. 0
2i' 0 ‘
$
C : . U
3 oo--o----o--'
0 200 400 600 800 1000

Summer Density (rosettes m'2)

LO

08

06

04

02

00

06 08 10 00 02 04- 06 08 10

04

02

00

241

Prediction Intervals for Michigan

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\\.
\\“
o. ‘\“‘ ““““““““““
C
C . .
° 0
W
.0 0 . 0
~ C
C ____________
o--—o -----------
0 500 1500 2500 3500
‘~-:
o‘. ~~~~~~
o . °
. C
C
C .. .
0 o
. C
0 o
._’_’-C___’__-__.. _______
O 200 400 600 800 1000
C
o 0 T ‘‘‘‘‘‘‘‘‘‘
C
O o
o . ° . 0 o
C . i.
ar-o- ------- o ------ 1--o
0 200 400 600 800 1000

Summer Density (rosettes m2)

Figure 5.4. Observed winter survival data (dots) and initial rosette density (# me) in fall

showing mean predicted trend (solid line) and lower and upper 95% prediction intervals
(dashed lines) for each cohort in Illinois and Michigan based on model results. See Figure

5.2 caption for more details.

242

Prediction Intervals for Michigan

Prediction Intervals for Illinois

 

. e
s —
~ —
~ _
\ —
x _
‘ —
Q .
s C —
\ —
\ CC .
xx 0 .
x O _
x 0 .—
\ C
x o .
\ C o
x 0 _
\ C C
x C.
\ _
x C C
\ C
\ e o u
x
x O O _
x C _
x C _

 

360

160

 

 

o“. o.o o.o so No o.o

 

300

 

5
—-—_-———'

 

 

Oé

wad

0d

vd

Nd

Od

ooomooom ӣ5805 .9428 .223

400

200

400

200

100

 

 

 

 

 

 

 

 

Oé

Od

mo

.10

NO

Od

NOONOOON SEE—onen— _m>_>5m EES>

200 300 400

100

200 300 400

100

 

\
C
”---—---—--—--—-

 

100
Fall Density (rosettes m

 

 

c>
‘-
x>
c:
<9
:3
‘V
c>
N
c:
c:
c>

 

100
Fall Density (rosettes m

 

.
-
.
-
-
_
s C m
..

 

 

Oé

md

QO

YO

NO

Od

OOONKOON “Eznmnoi _m>_>5w 5E;

300 400

200

300 400

200

-2)

-2)

243

Figure 5.5. Observed fecundity data (dots, siliques plant'l) and initial rosette density (#

m'z) in fall showing mean predicted trend (solid line) and lower and upper 95%

prediction intervals (dashed lines) for each cohort in Illinois and Michigan based on
model results. Each distribution is based on 50,000 simulated data sets. See Figure 5.2

caption for more details.

244

 

Prediction Intervals for Michigan

Prediction Intervals for Illinois

 

 

 

100

 

 

 

 

 

 

 

 

o? 8? oo oo ov om
CC C ‘~\CC
\\
C‘sCCCCC C C
. . x. .2..-
C CC C CC\\\C CC
o9 ooo oo oo ow om

OOON-mOON ucm_a\mmnc_=m

300 400

200

200 300 400

00

1

 

 

 

300

 

 

ON?

OOF on O0 ov ON

 

 

 

 

ON?

ooF oo oo ov ow
38-88 ”Eo_n=8=o___m

400

200

100

0 200 300 400

0

1

 

 

To?)
Fall Density (rosettes m

400

-2)

300

200

 

 

 

 

.C
c .
a .
o .
o _
. .
~ .
. .
o .
C C C o C
\ O
\ C
\s C .
\ C
xx C C“
ON? OOF ow O0 ov ON O
s. C C .
\ u
. u
x
.. ..m
\\ C C _

0

200 300 400

Fall Density (rosettes m'z)

100

 

 

o9 o2 oo oo ov oo o
ooomgoom ocoaaoogom

245

LITERATURE CITED

 

246

Anderson, D. R. 2008. Model based inference in the life sciences: a primer on evidence.
Springer.

Anderson, R. C., S. S. Dhillion, and T. M. Kelley. 1996. Aspects of the ecology of an
invasive plant, garlic mustard (Alliaria petiolata), in central Illinois. Restoration
Ecology 4:181-191.

AOSA. 2000. Tetrazolium testing handbook for agricultural seeds : contribution no. 29 to
the Handbook on seed testing. Association of Official Seed Analysts. Tetrazolium
Testing Committee, North Brunswick, NJ.

Bais, H. P., R. Vepachedu, S. Gilroy, R. M. Callaway, and J. M. Vivanco. 2003.
Allelopathy and exotic plant invasion: From molecules and genes to species
interactions. Science 301 : 1 377-13 80.

Bangerter, E. B. 1985. New and interesting records of adventive plants from the
Auckland Institute and Museum Herbarium: 11. Records of the Auckland Institute
and Museum 22:41-45.

Baskin, J. M., and C. C. Baskin. 1992. Seed-gerrnination biology of the weedy biennial
Alliaria petiolata. Natural Areas Journal 12:191-197.

Bellows, T. S. 1999. Whither hence, Prometheus? Pages 1011-1015 in T. S. Bellows and
T. W. Fisher, editors. Handbook of Biological Control. Academic Press, New
York.

Bierzychudek, P. 1982. The demography of jack-in-the-pulpit, a forest perennial that
changes sex. Ecological Monographs 52:335-351.

Bierzychudek, P. 1999. Looking backwards: Assessing the projections of a transition
matrix model. Ecological Applications 9: 1278- 1 287.

Blossey, B. 1999. Before, during and after: The need for long-terrn monitoring in
invasive plant species management. Biological Invasions 1:301-31 l.

247

Blossey, B., R. Casagrande, L. Tewksbury, D. A. Landis, R. N. Wiedenmann, and D. R.
Ellis. 2001a. Nontarget feeding of leaf-beetles introduced to control purple
loosestrife (Lythrum salicaria L.). Natural Areas Journal 21:368-377.

Blossey, B., V. Nuzzo, H. Hinz, and E. Gerber. 2001b. Developing biological control of
Alliaria petiolata (M. Bieb.) Cavara and Grande (garlic mustard). Natural Areas
Journal 21:357-367.

Bolker, B. M., M. E. Brooks, C. J. Clark, S. W. Geange, J. R. Poulsen, M. H. H. Stevens,
and J .-S. S. White. 2009. Generalized linear mixed models: a practical guide for
ecology and evolution. Trends in Ecology & Evolution 24:127-135.

Brady, N. C., and R. R. Weil. 1996. The nature and properties of soils. 11th edition.
Prentice Hall, Upper Saddle River, NJ.

Briese, D. T. 2006. Can an a priori strategy be developed for biological control? The case

of Onopordum spp. thistles in Australia. Australian Journal of Entomology
45:3 1 7 -3 23.

Buckley, Y. M., D. T. Briese, and M. Rees. 2003a. Demography and management of the
invasive plant species Hypericum perforatum. 1. Using multi-level mixed-effects
models for characterizing growth, survival and fecundity in a long-terrn data set.
Journal of Applied Ecology 40:481-493.

Buckley, Y. M., D. T. Briese, and M. Rees. 2003b. Demography and management of the
invasive plant species Hypericum perforatum. 11. Construction and use of an
individual-based model to predict population dynamics and the effects of
management strategies. Journal of Applied Ecology 40:494-507.

Buckley, Y. M., H. L. Hinz, D. Matthies, and M. Rees. 2001. Interactions between
density-dependent processes population dynamics and control of an invasive plant

species, Tripleurospermum perforatum (scentless chamomile). Ecology Letters
4:551-558.

Burkey, J. 2009. LOWESS smoothing function for MATLAB,
http://www.mathworks.com/matlabcentral/fileexchange/22470.

Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference : a
practical information-theoretic approach. 2nd edition. Springer, New York.

248

Byers, D. L., and J. A. Quinn. 1998. Demographic variation in Alliaria petiolata
(Brassicaceae) in four contrasting habitats. Journal of the Torrey Botanical
Society 125:138-149.

Call, L. J ., and E. T. Nilsen. 2003. Analysis of spatial patterns and spatial association
between the invasive tree-of-heaven (Ailanthus altissima) and the native black
locust (Robinia pseudoacacia). American Midland Naturalist 150:1-14.

Callaway, R. M., D. Cipollini, K. Barto, G. C. Thelen, S. G. Hallett, D. Prati, K. Stinson,
and J. Klironomos. 2008. Novel weapons: Invasive plant suppresses fungal
mutualists in America but not in its native Europe. Ecology 89: 1 043-1055.

Callaway, R. M., T. H. DeLuca, and W. M. Belliveau. 1999. Biological-control
herbivores may increase competitive ability of the noxious weed Centaurea
maculosa. Ecology 80:1196-1201.

 

Carlson, A. M., and D. L. Gorchov. 2004. Effects of herbicide on the invasive biennial
Alliaria petiolata (garlic mustard) and initial responses of native plants in a
southwestern Ohio forest. Restoration Ecology 12:559-567.

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation.
2nd edition. Sinauer Associates, Sunderland, MA.

Cavers, P. B., M. I. Heagy, and R. F. Kokron. 1979. Biology of Canadian weeds. 35.
Alliaria petiolata (M Bieb) Cavara and Grande. Canadian Journal of Plant
Science 59:217-229.

Cory, J. S., and J. H. Myers. 2000. Direct and indirect ecological effects of biological
control. Trends in Ecology and Evolution 15:137-139.

Crawley, M. J. 2007. The R book. Wiley, Chichester, England ; Hoboken, NJ.

Cruden, R. W., A. M. McClain, and G. P. Shrivastava. 1996. Pollination biology and
breeding system of Alliaria petiolata (Brassicaceae). Bulletin of the Torrey
Botanical Club 123:273-280.

Cunningham, R. B., and D. B. Lindenmayer. 2005. Modeling count data of rare species:
Some statistical issues. Ecology 86:1135-1142.

249

Davis, A. S., D. A. Landis, V. Nuzzo, B. Blossey, H. Hinz, and E. Gerber. 2006.
Demographic models inform biocontrol agent selection for garlic mustard

(Alliaria petiolata). Ecological Applications 16:2399-2410.

Denoth, M., L. Frid, and J. H. Myers. 2002. Multiple agents in biological control:
improving the odds? Biological Control 24:20-30.

Dhillion, S. S., and R. C. Anderson. 1999. Growth and photosynthetic response of first-
year garlic mustard (A lliaria petiolata) to varied irradiance. Journal of the Torrey
Botanical Society 126:9-14.

Drake, J. M. 2005. Density—dependent demographic variation determines extinction rate
of experimental populations. Plos Biology 3:1300-1304.

Draper, N. R., and H. Smith. 1998. Applied regression analysis. 3rd edition. Wiley, New
York.

Drayton, B., and R. B. Primack. 1999. Experimental extinction of garlic mustard (Alliaria
petiolata) populations: implications for weed science and conservation biology.
Biological Invasions 1: 1 59-167.

Durka, W., O. Bossdorf, D. Prati, and H. Auge. 2005. Molecular evidence for multiple
introductions of garlic mustard (A lliaria petiolata, Brassicaceae) to North
America. Molecular Ecology 14: 1697-1 706.

Elliott, J. M., and M. A. Hurley. 1998. Population regulation in adult, but not juvenile,
resident trout (Salmo trutta) in a lake district stream. Journal of Animal Ecology
67:280-286.

Engen, S., O. Bakke, and A. Islam. 1998. Demographic and environmental stochasticity -
Concepts and definitions. Biometrics 54:840-846.

Evans, J. A. 2006. Impacts of herbivores and plant communities on establishment and
spread of Alliaria petiolata (garlic mustard) in Michigan. MS. Thesis. Michigan
State University, East Lansing, MI.

Evans, J. A., A. S. Davis, S. Raghu, A. Ragavendran, D. A. Landis, and D. W. Schemske.
unpublished manuscript. The scale and sources of demographic variation in the
invasive plant Alliaria petiolata.

250

 

Evans, J. A., and D. A. Landis. 2007. Pre-release monitoring of Alliaria petiolata (garlic
mustard) invasions and the impacts of extant natural enemies in southern
Michigan forests. Biological Control 42:300-307.

Gee, G. W., and J. W. Bauder. 1986. Particle-size analysis. Pages 383—411 in A. Klute,
editor. Methods of soil analysis: Part 1: Physical and mineralogical methods.
American Society of Agronomy : Soil Science Society of America, Madison, WI.

Gerber, E., and H. Hinz. 2005. Biology, impact and interactions of potential biocontrol
agents on garlic mustard. Pages 4-6 in Symposium on the biology, ecology, and
management of garlic mustard (Alliaria petiolata) and European buckthorn
(Rhamnus cathartica). USDA Forest Service, University of Minnesotta, St. Paul,
MN.

Gerber, E., H. L. Hinz, and B. Blossey. 2007a. Impact of the belowground herbivore and
potential biological control agent, Ceutorhynchus scrobicollis, on Alliaria
petiolata performance. Biological Control 42:355-364.

Gerber, E., H. L. Hinz, and B. Blossey. 2007b. Interaction of specialist root and shoot
herbivores of Alliaria petiolata and their impact on plant performance and
reproduction. Ecological Entomology 32:357-365.

Gerber, E., H. L. Hinz, and B. Blossey. 2008a. Pre-release impact assessment of two
stem-boring weevils proposed as biological control agents for Alliaria petiolata.
Biological Control 45:360-367.

Gerber, E., H. L. Hinz, and G. Cortat. 2008b. Biological control of garlic mustard,
Alliaria petiolata. Annual report 2007. Unpublished Report, CABI Bioscience
Switzerland Centre, Delemont, Switzerland.

Gerber, E., H. L. Hinz, N. Guazzone, J. McKenney, S. Michler, and M. Zuefle. 2002.
Biological control of garlic mustard, Alliaria petiolata (Bieb.) Cavara & Grande.
Annual report 2001. Unpublished Report, CABI Bioscience Switzerland Centre,
Delemont, Switzerland.

Goldberg, D. E., R. Turkington, L. Olsvig-Whittaker, and A. R. Dyer. 2001. Density
dependence in an annual plant community: Variation among life history stages.
Ecological Monographs 71:423-446.

251

Grant, D. W., D. P. C. Peters, G. K. Beck, and H. D. Fraleigh. 2003. Influence of an
exotic species, Acroptilon repens (L.) DC. on seedling emergence and grth of
native grasses. Plant Ecology 166:157-166.

Gutierrez, A. P., L. E. Caltagirone, and W. Meikle. 1999. Evaluation of results:
economics of biological control. Pages 243-252 in T. S. Bellows and T. W.
Fisher, editors. Handbook of Biological Control. Academic Press, New York.

Harris, P. 1991. Classical biocontrol of weeds - Its definition, selection of effective
agents, and administrative political problems. Canadian Entomologist 1232827-
849.

Hinz, H., and E. Gerber. 2005. Summary of host specificity testing conducted in
Switzerland and Brassicaceae taxonomy. Pages 12-16 in Symposium on the
biology, ecology, and management of garlic mustard (Alliaria petiolata) and
European buckthorn (Rhamnus cathartica). USDA Forest Service, University of
Minnesotta, St. Paul, MN.

Hinz, H. L., and E. Gerber. 1998. Investigations on potential biological control agents of
garlic mustard, Alliaria petiolata (Bieb.) Cavara & Grande Annual Report 1998.
Unpublished Report, CABI Bioscience Switzerland Centre, Delemont,
Switzerland.

Hinz, H. L., and E. Gerber. 2001. Investigations on potential biological control agents of
garlic mustard, Alliaria petiolata (Bieb.) Cavara & Grande. Annual Report 2000.
Unpublished Report, CABI Bioscience Switzerland Centre, Delemont,
Switzerland.

Hoddle, M. S. 20043. Restoring balance: Using exotic species to control invasive exotic
species. Conservation Biology 18:3 8-49.

Hoddle, M. S. 2004b. The strength of biological control in the battle against invasive
pests: a reply. Conservation Biology 18:61-64.

Hood, G. M. 2006. PopTools version 2.7. Available free on the intemet. URL
http://www.cse.csiro.au/noptools/. Albany, Western Australia.

Horvitz, C. C., and D. W. Schemske. 1986. Seed dispersal and environmental .
heterogeneity in a neotropical herb: a model of poopulation and patch dynamics.

252

 

Pages 169-185 in A. Estrada and T. H. Fleming, editors. Frugivores and seed
dispersal. Dr W. Junk, Boston.

Horvitz, C. C., and D. W. Schemske. 1995. Spatiotemporal variation in demographic
transitions of a tropical understory herb - projection matrix analysis. Ecological
Monographs 65:155-192.

Huffaker, C. B., F. J. Simmonds, and J. E. Laing. 1976. Theoretical and empirical basis
of biological control. Pages 41 -7 8 in C. B. Huffaker and P. S. Messenger, editors.
Theory and practice of biological control. Academic Press, New York.

Joe, H., and R. Zhu. 2005. Generalized Poisson distribution: the property of mixture of

Poisson and comparison with negative binomial distribution. Biometrical Journal
47:219-229.

Keeler, M. S., and F. S. Chew. 2008. Escaping an evolutionary trap: preference and
performance of a native insect on an exotic invasive host. Oecologia 156:559-568.

Klute, A. 1986. Water retention: laboratory methods. Pages 635-662 in A. Klute, editor.
Methods of soil analysis: Part 1: Physical and mineralogical methods. American
Society of Agronomy : Soil Science Society of America, Madison, WI.

Koop, A. L., and C. C. Horvitz. 2005. Projection matrix analysis of the demography of an
invasive, nonnative shrub (Ardisia elliptica). Ecology 86:2661-2672.

Landis, D. A., D. C. Sebolt, M. J. Haas, and M. Klepinger. 2003. Establishment and
impact of Galerucella calmariensis L. (Coleoptera : Chrysomelidae) on Lythrum

salicaria L. and associated plant communities in Michigan. Biological Control
28:78-91.

Littell, R. C., G. A. Milliken, W. W. Stroup, R. D. Wolfinger, and O. Schaebenberger.
2006. SAS for mixed models. 2nd edition. SAS Institute, Cary, NC.

Louda, S., D. Kendall, J. Connor, and D. Simberloff. 1997. Ecological effects of an insect
introduced for the biological control of weeds. Science 277 :1088-1090.

Louda, S. M., A. E. Arnett, T. A. Rand, and F. L. Russell. 2003a. Invasiveness of some
biological control insects and adequacy of their ecological risk assessment and
regulation. Conservation Biology 17:73-82.

253

 

Louda, S. M., R. W. Pemberton, M. T. Johnson, and P. A. Follett. 2003b. Nontarget
effects - The Achilles' Heel of biological control? Retrospective analyses to
reduce risk associated with biocontrol introductions. Annual Review of
Entomology 48:365-396.

Louda, S. M., T. A. Rand, A. E. Arnett, A. S. McClay, K. Shea, and A. K. McEachern.
2005a. Evaluation-of ecological risk to populations of a threatened plant from an
invasive biocontrol insect. Ecological Applications 15:234-249.

Louda, S. M., T. A. Rand, F. L. Russell, and A. E. Amett. 2005b. Assessment of
ecological risks in weed biocontrol: Input from retrospective ecological analyses.
Biological Control 35:253-264.

Louda, S. M., and P. Stiling. 2004. The double-edged sword of biological control in
conservation and restoration. Conservation Biology 18:50-53.

Luken, J. O., L. M. Kuddes, and T. C. Tholemeier. 1997. Response of understory species
to gap formation and soil disturbance in Lom’cera maackii thickets. Restoration
Ecology 5:229-235.

McEvoy, P. B. 1996. Host specificity and biological pest control - How well is research
on host specificity addressing the potential risks of biological control. Bioscience
46:401-405.

McEvoy, P. B., and E. M. Coombs. 1999. Biological control of plant invaders: Regional
patterns, field experiments, and structured population models. Ecological
Applications 9:387-401.

McEvoy, P. B., and E. M. Coombs. 2000. Why things bite back: unintended
consequences of biological weed control. Pages 167-194 in P. A. Follett and J. J.
Duan, editors. Nontarget effects of biological control. Kluwer Academic
Publishers, Boston.

McFadyen, R. E. C. 1998. Biological control of weeds. Annual Review of Entomology
43:369-393.

Meekins, J. F., and B. C. McCarthy. 1999. Competitive ability of Alliaria petiolata
(garlic mustard, Brassicaceae), an invasive, nonindigenous forest herb.
International Journal of Plant Sciences 160:743-752.

254

 

Meekins, J. F., and B. C. McCarthy. 2000. Responses of the biennial forest herb Alliaria
petiolata to variation in population density, nutrient addition and light availability.
Journal of Ecology 88:447-463.

Meekins, J. F ., and B. C. McCarthy. 2002. Effect of population density on the
demography of an invasive plant (Alliaria petiolata, Brassicaceae) population in a
southeastern Ohio forest. American Midland Naturalist 147:256-278.

Mulvaney, R. L. 1996. Nitrogen—inorganic forms. Pages 1123-1184 in D. L. Sparks,
Soil Science Society of America, and American Society of Agronomy., editors.
Methods of soil analysis. Part 3, Chemical methods. Soil Science Society of
America : American Society of Agronomy, Madison, WI.

Myers, C. V., and R. C. Anderson. 2003. Seasonal variation in photosynthetic rates
influences success of an invasive plant, garlic mustard (Alliaria petiolata).
American Midland Naturalist 150:231-245.

Myers, C. V., R. C. Anderson, and D. L. Byers. 2005. Influence of shading on the growth
and leaf photosynthesis of the invasive non-indigenous plant garlic mustard
Alliaria petiolata (M. Bieb) Cavara and Grande grown under simulated late-

winter to mid-spring conditions. Journal of the Torrey Botanical Society 132:1-
10.

Nelson, D. W., and L. E. Sommers. 1994. Total carbon, organic carbon, and organic
matter. Pages 961-1010 in R. W. Weaver and Soil Science Society of America,
editors. Methods of soil analysis. Part 2, Microbiological and biochemical
properties. Soil Science Society of America, Madison, Wis., USA.

Neter, J ., M. H. Kutner, C. J. Nachtsheim, and W. Wasserrnan. 1996. Applied linear
regression models. 3rd edition. Irwin, Chicago, Ill.

Nuzzo, V. A. 1991. Experimental control of garlic mustard [Alliaria petiolata (Bieb.)
Cavara & Grande] in Northern Illinois using fire, herbicide, and cutting. Natural
Areas Journal 11:158-167.

Nuzzo, V. A. 1993a. Current and historic distribution of garlic mustard (Alliaria
Petiolata) in Illinois. The Michigan Botanist 32:23-33.

Nuzzo, V. A. 1993b. Distribution and spread of the invasive biennial Alliaria petiolata
(garlic mustard) in North America. Pages 137-145 in B. N. McKnight, editor.

255

 

Biological pollution: The control and impact of invasive exotic species:
proceedings of a symposium held at the University Place Conference Center,
Indiana University-Purdue University at Indianapolis on October 25 & 26, 1991.
Indiana Academy of Science, Indianapolis.

Nuzzo, V. A. 1993c. Natural mortality of garlic mustard (Alliaria petiolata (Bieb.)
Cavara & Grande) rosettes. Natural Areas Journal 13:132-133.

Nuzzo, V. A. 1994. Response of garlic mustard (Alliaria petiolata Bieb - Cavara and
Grande ) to summer herbicide treatment. Natural Areas Journal 14:309-310.

Nuzzo, V. A. 1996. Impact of dormant season herbicide treatment on the alien herb garlic
mustard (Alliaria petiolata [Bieb.] Cavara and Grande) and groundlayer
vegetation. Transactions of the Illinois State Academy of Science 89:25-36.

Nuzzo, V. A. 1999. Invasion pattern of the herb garlic mustard (Alliaria petiolata) in high
quality forests. Biological Invasions 1: 169-1 79.

Nuzzo, V. A. 2000. Element stewardship abstract for Alliaria petiolata (Alliaria
oflicinalis) garlic mustard. The Nature Conservancy.

Nuzzo, V. A., W. McClain, and T. Strole. 1996. Fire impact on groundlayer flora in a
sand forest 1990-1994. American Midland Naturalist 1362207-221.

Ortega, Y. K., D. E. Pearson, and K. S. McKelvey. 2004. Effects of biological control
agents and exotic plant invasion on deer mouse populations. Ecological
Applications 14:241-253.

Pardini, E. A., J. M. Drake, J. M. Chase, and T. M. Knight. 2009. Complex population
dynamics and control of the invasive biennial, Alliaria petiolata (garlic mustard).
Ecological Applications 19:387-397.

Pardini, E. A., B. J. Teller, and T. M. Knight. 2008. Consequences of density dependence
for management of a stage-smctured invasive plant (Alliaria petiolata). American
Midland Naturalist 160:310-322.

Parker, 1. M. 2000. Invasion dynamics of Cytisus scoparius: A matrix model approach.
Ecological Applications 10:726-743.

256

 

Pascarella, J. B., and C. C. Horvitz. 1998. Hurricane disturbance and the population
dynamics of a tropical understory shrub: Megamatrix elasticity analysis. Ecology
79:547-563.

Pearson, D., and R. Callaway. 2003. Indirect effects of host-specific biological control
agents. Trends in Ecology & Evolution 18:456-461.

Pearson, D. E., and R. M. Callaway. 2004. Response to Thomas et a1: biocontrol and
indirect effects. Trends in Ecology & Evolution 19:62—63.

Pearson, D. E., and R. M. Callaway. 2005. Indirect nontarget effects of host-specific
biological control agents: Implications for biological control. Biological Control
35:288-298.

Pemberton, R. W. 2000. Predictable risk to native plants in weed biological control.
Oecologia 125:489-494.

Pichtel, J ., K. Kuroiwa, and H. T. Sawyerr. 2000. Distribution of Pb, Cd and Ba in soils
and plants of two contaminated sites. Environmental Pollution 110:171-178.

Prati, D., and O. Bossdorf. 2004. Allelopathic inhibition of germination by Alliaria
petiolata (Brassicaceae). American Journal of Botany 91:285-288.

Pyle, L. L. 1995. Effects of disturbance on herbaceous exotic plant-species on the
floodplain of the Potomac River. American Midland Naturalist 134:244-253.

Raghu, S., and S. Post. 2008. Cold stratification requirements for germination of Alliaria
petiolata. Invasive Plant Science and Management 1:315—318.

Raghu, S., and R. D. van Klinken. 2006. Refining the ecological basis for agent selection
in weed biological control. Australian Journal of Entomology 45:251-252.

Rebek, K. A., and R. J. O'Neil. 2006. The effects of natural and manipulated density
regimes on Alliaria petiolata survival, growth and reproduction. Weed Research
46:345-352.

Rees, M., and R. L. Hill. 2001. Large-scale disturbances, biological control and the
dynamics of gorse populations. Journal of Applied Ecology 38:364-3 77.

257

 

Rejmanek, M. 2000. On the use and misuse of transition matrices in plant population
biology. Biological Invasions 2:315-317.

Renwick, J. A. A. 2002. The chemical world of crucivores: lures, treats and traps.
Entomologia Experimentalis et Applicata 104:35-42.

Roberts, K. J., and R. C. Anderson. 2001. Effect of garlic mustard A lliaria petiolata
(Beib. Cavara & Grande) extracts on plants and arbuscular mycorrhizal (AM)
fungi. American Midland Naturalist 146:146-152.

Rodgers, V. L., K. A. Stinson, and A. C. Finzi. 2008. Ready or not, garlic mustard is
moving in: Alliaria petiolata as a member of eastern North American forests.
Bioscience 58:426-436.

Saether, B.-E., S. Engen, A. Islam, R. McCleery, and C. Perrins. 1998. Environmental
stochasticity and extinction risk in a population of a small songbird, the geat tit.
The American Naturalist 151:441-450.

Sakai, A. K., F. W. Allendorf, J. S. Holt, D. M. Lodge, J. Molofsky, K. A. With, S.
Baughman, R. J. Cabin, J. E. Cohen, N. C. Ellstrand, D. E. McCauley, P. O'Neil,
I. M. Parker, J. N. Thompson, and S. G. Weller. 2001. The population biology of
invasive species. Annual Review of Ecology and Systematics 32:305-332.

SAS Institute. 2008. The SAS System Version 9.2. Cary, NC.

Shea, K., and D. Kelly. 1998. Estimating biocontrol agent impact with matrix models:
Carduus nutans in New Zealand. Ecological Applications 8:824-832.

Shea, K., D. Kelly, A. W. Sheppard, and T. L. Woodbum. 2005. Context-dependent
biological control of an invasive thistle. Ecology 86:3174-3181.

Simberloff, D., and P. Stiling. 1996. How risky is biological control? Ecology 77 :1965-
1974.

Skrondal, A., and S. Rabe-Hesketh. 2004. Generalized latent variable modeling:
multilevel, longitudinal, and structural equation models. Pages xi, 508 p.
Chapman & Hall/CRC, Boca Raton.

258

 

Smith, G. R., H. A. Dingfelder, and D. A. Vaala. 2003. Effect of plant size and density on
garlic mustard reproduction. Northeastern Naturalist 10:269-276.

Soltanpour, P. N., G. W. Johnson, S. W. Workman, J. Benton-Jones Jr., and M. R. O.
1996. Inductively coupled plasma spectroscopy. Pages 91-140 in D. L. Sparks,
Soil Science Society of America, and American Society of Agronomy., editors.
Methods of soil analysis. Part 3, Chemical methods. Soil Science Society of
America : American Society of Agronomy, Madison, WI.

Stiling, P. 2002. Potential non-target effects of a biological control agent, prickly pear
moth, Cactoblastis cactorum (Berg) (Lepidoptera: Pyralidae), in North America,
and possible management actions. Biological Invasions 4:273-281.

Stiling, P., D. Moon, and D. Gordon. 2004. Endangered cactus restoration: Mitigating the
non-target effects of a biological control agent (Cactoblastis cactorum) in Florida.
Restoration Ecology 12:605-610.

Stinson, K., S. Kaufinan, L. Durbin, and F. Lowenstein. 2007. Impacts of garlic mustard
invasion on a forest understory community. Northeastern Naturalist 14:73-88.

Stinson, K. A., S. A. Campbell, J. R. Powell, B. E. Wolfe, R. M. Callaway, G. C. Thelen,
S. G. Hallett, D. Prati, and J. N. Klironomos. 2006. Invasive plant suppresses the
grth of native tree seedlings by disrupting belowground mutualisms. Plos
Biology 4:el40 http://dx.doi.org/l 10.1371/joumal.pbio.0040140.

Susko, D. J ., and L. Lovett-Doust. 1999. Effects of resource availability, and mu and
ovule position on components of fecundity in Alliaria petiolata (Brassicaceae).
New Phytologist 1442295-306.

Susko, D. J ., and L. Lovett-Doust. 2000. Patterns of seed mass variation and their effects
on seedling traits in Alliaria petiolata (Brassicaceae). American Journal of Botany
87:56-66.

The MathWorks. 2008. MATLAB. Natick, MA.
The Nature Conservancy. 2002. http://tncweeds.ucdavis.edu/success/ak001.html.

Thomas, G. W. 1996. Soil pH and soil acidity. Pages 475-490 in D. L. Sparks, Soil
Science Society of America, and American Society of Agronomy., editors.

259

 

Methods of soil analysis. Part 3, Chemical methods. Soil Science Society of
America : American Society of Agronomy, Madison, WI.

Thomas, M. B., P. Casula, and A. Wilby. 2004. Biological control and indirect effects.
Trends in Ecology & Evolution 19:61-61.

Trimbur, T. J. 1973. The ecological life history of Allarz'a oflicinallis, a deciduous forest
"weed". MS. Thesis. The Ohio State University, Columbus, OH.

Tuljapurkar, S., C. C. Horvitz, and J. B. Pascarella. 2003. The many growth rates and
elasticities of populations in random environments. American Naturalist 162:489-
502.

Turchin, P. 1999. Population regulation: a synthetic view. Oikos 84:153-159.

USDA-APHIS. 2006. Technical Advisory Group for Biological Control Agents of Weeds
home page, http://wwwaphisusda.gov/ppg/permits/tag. USDA.

USDA-NRCS. 2007. The PLANTS Databse, Version 3.5 (http://nlants.usda.gov). Data
compiled from various sources by Mark W. Skinner. National Plant Data Center,
Baton Rouge, LA 70874-4490 USA.

Van Driesche, R. G., and T. S. Bellows. 1996. Biological Control. Chapman & Hall,
Detroit.

van Klinken, R. D., and S. Raghu. 2006. A scientific approach to agent selection.
Australian Journal of Entomology 45:253-258.

van Tienderen, P. H. 1995. Life-Cycle Trade-Offs in Matrix Population-Models. Ecology
76:2482-2489.

Vaughn, S. F., and M. A. Berhow. 1999. Allelochemicals isolated fi'om tissues of the
invasive weed garlic mustard (Alliaria petiolata). Journal of Chemical Ecology
25:2495-2504.

Vitousek, P. M., and L. R. Walker. 1989. Biological Invasion by Myricafaya in Hawaii -
Plant Demography, Nitrogen-Fixation, Ecosystem Effects. Ecological
Monographs 59:247-265.

260

if".

Wapshere, A. J. 1974. Strategy for evaluating safety of organisms for biological weed
control. Annals of Applied Biology 77:201-21 1.

Wapshere, A. J. 1989. A testing sequence for reducing rejection of potential biological-
control agents for weeds. Annals of Applied Biology 114:515-526.

Welk, E., K. Schubert, and M. H. Hoffrnann. 2002. Present and potential distribution of
invasive garlic mustard (A lliaria petiolata) in North America. Diversity and
Distributions 8:219-233.

Weston, L. A., and S. 0. Duke. 2003. Weed and crop allelopathy. Critical Reviews in
Plant Sciences 22:367-389.

Whitten, M. J ., and M. A. Hoy. 1999. Genetic improvement and other genetic
considerations for improving the efficacy and success rate of biological control.
Pages 271-296 in T. S. Bellows and T. W. Fisher, editors. Handbook of
Biological Control. Academic Press, New York.

Williamson, M. 1996. Biological invasions. lst edition. Chapman & Hall, London ; New
York.

Winterer, J ., M. C. Walsh, M. Poddar, J. W. Brennan, and S. M. Primak. 2005. Spatial
and temporal segregation of juvenile and mature garlic mustard plants (Alliaria

petiolata) in a central Pennsylvania woodland. American Midland Naturalist
153:209-216.

Wolfe, B. E., and J. N. Klironomos. 2005. Breaking new ground: Soil communities and
exotic plant invasion. Bioscience 55:477-487.

Wolfe, B. E., V. L. Rodgers, K. A. Stinson, and A. Pringle. 2008. The invasive plant
Alliaria petiolata (garlic mustard) inhibits ectomycorrhizal fungi in its introduced
range. Journal of Ecology 96:777-783.

Yates, C. N., and S. D. Murphy. 2008. Observations of herbivore attack on garlic mustard
(Alliaria petiolata) in Southwestern Ontario, Canada. Biological Invasions
10:757-760.

261

 

   

”‘lllllllllllllljlllflilllllllslllllllillllf