ABSTRACT

Title of Dissertation: THE ECONOMICS OF SPRUCE BUDWORM
MONITORING AND MANAGEMENT
IN EASTERN CANADA

Alexandre I.E. Holm Perrault
Doctor of Philosophy, 2024

Dissertation Directed by: Professor Lars J. Olson
Department of Agricultural and Resource Economics

This dissertation uses techniques that were developed for renewable natural resource and

invasive pest management to describe the two principal challenges of eastern spruce budworm

(SBW) monitoring and management in Eastern Canada, with a specific focus on the province

of Quebec. The primary empirical components of this dissertation can be found in Chapters 2

and 3. Chapter 1 provides the necessary historic, entomological, ecological and policy context to

understand Chapters 2 and 3. Chapter 4 provides a conclusion to this dissertation by proposing

extensions that would make the models presented in Chapters 2 and 3 more readily applicable to

real-world spruce budworm management. These extensions involve making the models spatially

explicit, as the models presented in Chapters 2 and 3 are spatially crude for the sake of tractability.

Chapter 2 describes the management of an endemic irruptive forest pest and, using the

spruce budworm-balsam fir forest interaction, proposes an optimization model that determines

optimal pest treatment and forest harvest levels for a single, dimensionless forest stand that is



currently undergoing an active budworm outbreak. Budworms cause both growth reductions and

mortality on the forest biomass stock, and increasing forest biomass will provide budworms with

more prey, causing their growth rate to increase. Treatment decisions are limited to three discrete

possibilities (0, 1 or 2 on the landscape) that impose mortality on budworms, while harvests

remove a proportion of the forest biomass. Using a numerical solution algorithm, we find that

the optimal policy is generally to apply treatments over budworms and to harvest the forest at a

sustainable rate, which confirms that the current management programs used in Eastern Canada

are welfare-improving relative to letting an outbreak run its course. The time path for our baseline

scenario indicates that budworms can be treated down to endemic levels quickly. Sensitivity

analysis describes scenarios where budworm levels will rebound every year as well as scenarios

where the optimal policy is to clearcut the forest as quickly as possible.

Chapter 3 considers the pre-outbreak monitoring phase for spruce budworm management.

This context is informed by the Early Intervention Strategy, a management practice that is cur-

rently being successfully employed in New Brunswick and other Maritime provinces. EIS re-

quires extensive monitoring and proactive treatment. As such, we adapt a model known as CE-

SAT to determine the locations for which EIS would yield positive net benefits in eastern Quebec.

Under our baseline scenario, we find that EIS is optimal in some zones bordering New Brunswick,

which indicates that EIS is unlikely to be welfare-improving over current management practices

used in Quebec. Under different assumptions, however, we find that EIS is optimal across a much

larger landscape, yielding millions of CAD net benefits over a thirty year horizon.



THE ECONOMICS OF SPRUCE BUDWORM
MONITORING AND MANAGEMENT IN EASTERN CANADA

by

Alexandre Ismaël Eliot Holm Perrault

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Doctor of Philosophy

2024

Advisory Committee:
Professor Lars J. Olson, Chair/Advisor
Professor Rebecca Epanchin-Niell, Co-Advisor
Professor Maureen Cropper, Dean’s Representative
Professor Erik Lichtenberg
Professor Jorge Holzer



© Copyright by
Alexandre Holm Perrault

2024



Dedication

Dedicated to the memory of Pamela Holm.

ii



Acknowledgments

I would like to thank my dissertation director and advisor, Professor Lars J. Olson, for

his patient help and guidance over the last six years, first through my first-year paper and then

through this doctoral dissertation. The theoretical component of this dissertation draws directly

from material that he taught our cohort in my first year at the University of Maryland. Ever

since he agreed to be my director, Lars has provided me with both invaluable advice and moral

support, especially during the pandemic. Without him, I would not have been able to complete

this dissertation.

I would also like to thank my co-advisor, Professor Becky Epanchin-Niell. From our first

meeting in January 2020, I hoped that she would be able to join the AREC faculty at the Univer-

sity of Maryland, due to the similarities in our research interests. I am fortunate to have been first

her research assistant and later her co-author. She has helped me to become a better researcher

and programmer. My problem-solving skills have grown significantly in the past four years, and

I have used these skills in a number of professional contexts.

Additional thanks are due to professors Maureen Cropper, Erik Lichtenberg and Jorge

Holzer for agreeing to serve on my dissertation committee and to review this manuscript.

The AREC department has incredible staff, all of whom helped me immensely, and all

of whom deserve my thanks. Thank you to Pin-Wuan Lin and Dany Burns for supporting me

throughout all the paperwork and deadlines. Jeff Cunningham and John Jensenius both provided

iii



me with extensive and patient technical assistance, which were especially important given how

much of this dissertation was completed remotely.

My deepest thanks go to my partner Lily, who accepted to move with me down to the

United States, sight unseen. It was tough, but we got through it, with the help of Tache, and of

Miette, who I believe is still with us.

Merci à ma mère, Valérie. Tu m’as tellement soutenu au cours des dernières années. Ce fut

tellement difficile de ne pas te voir pendant la pandémie, et je suis vraiment heureux de ne plus

être loin de ma famille montréalaise.

Thanks to my dad, Barry, who is always just a phonecall away. Thank you for always being

there to listen te me when I needed it.

Merci à mes grands-parents, Paul et Nicole, qui ont toujours cru en moi et qui m’ont inspiré

par leur parcours et leur persévérance.

I got through this process with the help of my cohort and of other AREC students outside

of my cohort. I owe particular thanks to Alejandro López and Dan Kraynak, both of whom were

in my Covid bubble. When I first came to the University of Maryland, I was able to count on the

mentorship of Chris Holt. Later on, as I completed my coursework and became a candidate, I got

invaluable advice from Haoluan Wang, who helped me to avoid numerous pitfalls.

I would like to acknowledge the many Canadian public servants and researchers who

guided me throughout this process. In particular, I would like to thank Rob Johns and Drew

Carleton, who provided me with detailed descriptions of the EIS program in New Brunswick.

Particular thanks are also due to Alain Dupont of la SOPFIM, who provided me with inspiration

for this topic back in January of 2020.

Après tout cela, il ne reste qu’une chose à dire : enfin, tabarnak!

iv



Table of Contents

Dedication ii

Acknowledgements iii

Table of Contents v

List of Tables ix

List of Figures x

List of Abbreviations xiv

Chapter 1: Introduction: The Biology, Ecology and Economics of Eastern Spruce Bud-
worms and their Forests 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Invasive and irruptive endemic insects . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 The economics of invasive and irruptive species control . . . . . . . . . . 8
1.2.2 Fast and slow processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.3 The economics of tipping points . . . . . . . . . . . . . . . . . . . . . . 15

1.3 The biology of spruce budworms . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 The life cycle of spruce budworms . . . . . . . . . . . . . . . . . . . . . 17
1.3.2 Two theories of budworm dynamics . . . . . . . . . . . . . . . . . . . . 18
1.3.3 Model: the budworm cycle . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.4 Parameterization of the budworm cycle model . . . . . . . . . . . . . . . 23

1.4 The ecology of spruce budworms . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 The hosts and predators of spruce budworms . . . . . . . . . . . . . . . 23
1.4.2 Timeline of spruce budworm outbreaks . . . . . . . . . . . . . . . . . . 25
1.4.3 A history of Canadian spruce budworm outbreaks . . . . . . . . . . . . . 27
1.4.4 Model: interactions between budworms and forests . . . . . . . . . . . . 28
1.4.5 Parameterization of the interaction model . . . . . . . . . . . . . . . . . 31

1.5 Managing budworm outbreaks . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.5.1 A history of spruce budworm management in Canada . . . . . . . . . . . 32
1.5.2 Early intervention or foliage protection? . . . . . . . . . . . . . . . . . . 34
1.5.3 The importance of additionality in budworm treatments . . . . . . . . . . 37
1.5.4 Sampling and monitoring spruce budworm populations . . . . . . . . . . 37
1.5.5 The economics of spruce budworm control . . . . . . . . . . . . . . . . 39

v



1.5.6 Model: valuation of forests . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.5.7 Parameterization of the forest valuation model . . . . . . . . . . . . . . . 45

1.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter 2: Optimal Management of an Endemic Irruptive Forest Pest (with. Prof. Lars
J. Olson) 47

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.2 An overview of current management practices . . . . . . . . . . . . . . . . . . . 49
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.3.1 Summary of model parameters and primitives . . . . . . . . . . . . . . . 51
2.3.2 Generalized framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.3 Generalized economic model . . . . . . . . . . . . . . . . . . . . . . . . 55
2.3.4 Specific ecological models for budworms and tree stands . . . . . . . . . 56
2.3.5 Integrating the generalized framework with the specific ecological models 69
2.3.6 Simulating the marginal impacts of budworm density on defoliation, growth

loss and mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.4 Empirical strategy and available data . . . . . . . . . . . . . . . . . . . . . . . . 75

2.4.1 Available data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.4.2 Calculating parameter values for the model . . . . . . . . . . . . . . . . 79
2.4.3 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.5.1 Simulation model results: baseline scenario . . . . . . . . . . . . . . . . 86
2.5.2 Time paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.5.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
2.6.1 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 142
2.6.2 Discussion of sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . 142
2.6.3 Implications of sensitivity analysis for management . . . . . . . . . . . . 146
2.6.4 Limitations of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Chapter 3: Managing Spruce Budworm Outbreak Risks Through Optimized Surveil-
lance Strategies (with. Prof. Rebecca Epanchin-Niell) 149

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.2 Literature review: surveillance in invasive pest management . . . . . . . . . . . . 152

3.2.1 Emerald ash borer management, the portfolio approach, and acceptance
sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

3.2.2 Asian longhorned beetle management and the CVaR approach . . . . . . 155
3.2.3 Spongy moth, slowing the spread and the hot spot approach . . . . . . . . 157

3.3 Surveillance for a spruce budworm early intervention strategy . . . . . . . . . . . 161
3.3.1 Background on current spruce budworm sampling . . . . . . . . . . . . . 162
3.3.2 Aerial and satellite surveys . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.3.3 Hot spots, establishment and long-distance spruce budworm spread . . . 165
3.3.4 Short-distance spruce budworm spread . . . . . . . . . . . . . . . . . . . 167
3.3.5 Treatment under EIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

vi



3.4 Conceptual framework of the model . . . . . . . . . . . . . . . . . . . . . . . . 169
3.4.1 Modeling approach: CESAT . . . . . . . . . . . . . . . . . . . . . . . . 170
3.4.2 Model application to EIS for SBW . . . . . . . . . . . . . . . . . . . . . 172
3.4.3 Budworm arrival and establishment . . . . . . . . . . . . . . . . . . . . 173
3.4.4 Budworm spread across the landscape . . . . . . . . . . . . . . . . . . . 174
3.4.5 Surveillance, treatment and penalties . . . . . . . . . . . . . . . . . . . . 174
3.4.6 A graphical description of the model . . . . . . . . . . . . . . . . . . . . 175

3.5 Mathematical specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
3.5.1 The age-class model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
3.5.2 Detection probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
3.5.3 Net present value of expected costs and damages . . . . . . . . . . . . . 181
3.5.4 Model with multiple zones . . . . . . . . . . . . . . . . . . . . . . . . . 183
3.5.5 Objective function with and without a constraint . . . . . . . . . . . . . . 186
3.5.6 Summary of model parameters and primitives . . . . . . . . . . . . . . . 187

3.6 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.6.1 Sampling spruce budworms . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.6.2 Calibrating treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
3.6.3 Defining the landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
3.6.4 Calibrating infestation establishment and risk . . . . . . . . . . . . . . . 193
3.6.5 Calibrating local growth . . . . . . . . . . . . . . . . . . . . . . . . . . 195
3.6.6 Calibrating value and damages . . . . . . . . . . . . . . . . . . . . . . . 197
3.6.7 Simulation of surveillance and management . . . . . . . . . . . . . . . . 199

3.7 Results and analysis of results . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
3.7.1 Model results: baseline scenario with an unconstrained budget . . . . . . 202
3.7.2 Model results: baseline scenario with a constrained budget . . . . . . . . 206
3.7.3 Model results: net benefits and marginal net benefits as functions of in-

vestment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
3.7.4 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
3.7.5 Summary of model results . . . . . . . . . . . . . . . . . . . . . . . . . 231

3.8 Further discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
3.8.1 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 233
3.8.2 Discussion of sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . 234
3.8.3 Limitations of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Chapter 4: Conclusion and Extensions 237
4.1 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

4.1.1 Summary of main research results and contributions . . . . . . . . . . . . 238
4.1.2 Management implications . . . . . . . . . . . . . . . . . . . . . . . . . 239

4.2 Future perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
4.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

4.3 Modeling endemic pests on complex landscapes . . . . . . . . . . . . . . . . . . 242
4.3.1 Current spruce budworm multi-spatial management tools and practices . . 243
4.3.2 Modeling a generic endemic pest on a complex landscape, with dispersal 245
4.3.3 Modeling multi-spatial spruce budworm treatment and harvest . . . . . . 249

4.4 Multi-spatial spread monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

vii



4.4.1 Multi-spatial spread monitoring in literature . . . . . . . . . . . . . . . . 252
4.4.2 Modeling multi-spatial monitoring and early treatment . . . . . . . . . . 254
4.4.3 Ease of access and the monitoring budget . . . . . . . . . . . . . . . . . 256

4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
4.5.1 The benefits of multi-spatial modeling . . . . . . . . . . . . . . . . . . . 258
4.5.2 Limitations to multi-spatial modeling . . . . . . . . . . . . . . . . . . . 259
4.5.3 Future perspectives for spruce budworm control in Eastern Canada . . . . 260

Bibliography 262

viii



List of Tables

2.1 Model state variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2 Model parameters: forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3 Model parameters: budworms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5 Defoliation midpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.6 Growth loss (% of DBH increment) and five year mortality due to defoliation . . 82
2.7 One-year basal area growth increment to budworm density relationship . . . . . . 82
2.8 Results of equation (2.32) regression . . . . . . . . . . . . . . . . . . . . . . . . 83
2.9 Five year mortality to budworm density relationship . . . . . . . . . . . . . . . . 83
2.10 One year mortality to budworm density relationship . . . . . . . . . . . . . . . . 84
2.11 Results of mortality regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.12 Parameters of the baseline simulation . . . . . . . . . . . . . . . . . . . . . . . . 86
2.13 Parameters: fourth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.14 Parameters: fifth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.15 Parameters: eighth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.16 Parameters: ninth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
2.17 Parameters: twelfth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
2.18 Parameters: thirteenth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2.19 Parameters: sixteenth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
2.20 Parameters: seventeenth run . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.1 Model primitives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
3.2 Cost and damage parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.3 Spread variables and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.4 Survey variables and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.5 Results of equation (3.9) regression . . . . . . . . . . . . . . . . . . . . . . . . . 197
3.6 Table of baseline and sensitivity analysis scenarios . . . . . . . . . . . . . . . . 200
3.7 Results: unconstrained analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
3.8 Results: constrained analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

ix



List of Figures

2.1 Uncontrolled Budworm Transition . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.2 Uninfested Forest Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.3 Baseline optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . 89
2.4 Baseline optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . 90
2.5 Baseline optimal budworm transition contours . . . . . . . . . . . . . . . . . . . 90
2.6 Baseline optimal budworm transition contours . . . . . . . . . . . . . . . . . . . 91
2.7 Baseline optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . 92
2.8 Baseline optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . 92
2.9 Baseline optimal budworm transition as a function of forest . . . . . . . . . . . . 93
2.10 Baseline optimal forest transition as a function of budworms . . . . . . . . . . . 94
2.11 Baseline forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.12 Baseline budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.13 Baseline treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.14 Baseline harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.15 Time path of initial (st) and post-harvest (xt) forest . . . . . . . . . . . . . . . . 98
2.16 Run 4 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.17 Run 4 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 100
2.18 Run 4 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 101
2.19 Run 4 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 101
2.20 Run 4 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 102
2.21 Run 4 optimal budworm transition as a function of forest . . . . . . . . . . . . . 102
2.22 Run 4 optimal forest transition as a function of budworms . . . . . . . . . . . . . 103
2.23 Run 4 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.24 Run 4 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.25 Run 4 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.26 Run 4 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.27 Time path of initial (st) and post-harvest (xt) forest for Run 4 . . . . . . . . . . . 105
2.28 Run 5 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.29 Run 5 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 106
2.30 Run 5 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 107
2.31 Run 5 optimal budworm transition as a function of forest . . . . . . . . . . . . . 108
2.32 Run 5 optimal forest transition as a function of budworms . . . . . . . . . . . . . 108
2.33 Run 5 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.34 Run 5 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.35 Run 5 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.36 Run 5 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.37 Time path of initial (st) and post-harvest (xt) forest for Run 5 . . . . . . . . . . . 110

x



2.38 Run 8 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.39 Run 8 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 111
2.40 Run 8 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 112
2.41 Run 8 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 112
2.42 Run 8 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 113
2.43 Run 8 optimal budworm transition as a function of forest . . . . . . . . . . . . . 113
2.44 Run 8 optimal forest transition as a function of budworms . . . . . . . . . . . . . 114
2.45 Run 8 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.46 Run 8 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.47 Run 8 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.48 Run 8 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.49 Time path of initial (st) and post-harvest (xt) forest for Run 8 . . . . . . . . . . . 116
2.50 Run 9 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . . 116
2.51 Run 9 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 117
2.52 Run 9 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 117
2.53 Run 9 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 118
2.54 Run 9 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 118
2.55 Run 9 optimal budworm transition as a function of forest . . . . . . . . . . . . . 119
2.56 Run 9 optimal forest transition as a function of budworms . . . . . . . . . . . . . 119
2.57 Run 9 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.58 Run 9 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.59 Run 9 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.60 Run 9 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
2.61 Time path of initial (st) and post-harvest (xt) forest for Run 9 . . . . . . . . . . . 121
2.62 Run 12 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . 122
2.63 Run 12 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 123
2.64 Run 12 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 123
2.65 Run 12 optimal budworm transition as a function of forest . . . . . . . . . . . . . 124
2.66 Run 12 optimal forest transition as a function of budworms . . . . . . . . . . . . 124
2.67 Run 12 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.68 Run 12 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.69 Run 12 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.70 Run 12 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2.71 Time path of initial (st) and post-harvest (xt) forest for Run 12 . . . . . . . . . . 126
2.72 Run 13 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . 127
2.73 Run 13 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 127
2.74 Run 13 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 127
2.75 Run 13 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 128
2.76 Run 13 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 128
2.77 Run 13 optimal budworm transition as a function of forest . . . . . . . . . . . . . 129
2.78 Run 13 optimal forest transition as a function of budworms . . . . . . . . . . . . 129
2.79 Run 13 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.80 Run 13 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.81 Run 13 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.82 Run 13 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

xi



2.83 Time path of initial (st) and post-harvest (xt) forest for Run 13 . . . . . . . . . . 131
2.84 Run 16 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . 132
2.85 Run 16 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 132
2.86 Run 16 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 133
2.87 Run 16 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 133
2.88 Run 16 optimal budworm transition as a function of forest . . . . . . . . . . . . . 134
2.89 Run 16 optimal forest transition as a function of budworms . . . . . . . . . . . . 134
2.90 Run 16 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
2.91 Run 16 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
2.92 Run 16 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
2.93 Run 16 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
2.94 Time path of initial (st) and post-harvest (xt) forest for Run 16 . . . . . . . . . . 136
2.95 Run 17 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . 137
2.96 Run 17 optimal treatment contours . . . . . . . . . . . . . . . . . . . . . . . . . 137
2.97 Run 17 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 137
2.98 Run 17 optimal budworm transition contours . . . . . . . . . . . . . . . . . . . . 138
2.99 Run 17 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 138
2.100Run 17 optimal forest transition contours . . . . . . . . . . . . . . . . . . . . . . 138
2.101Run 17 optimal budworm transition as a function of forest . . . . . . . . . . . . . 139
2.102Run 17 optimal forest transition as a function of budworms . . . . . . . . . . . . 139
2.103Run 17 forest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
2.104Run 17 budworm time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
2.105Run 17 treatment time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
2.106Run 17 harvest time path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.1 Plot of IEQM blocks used in this chapter . . . . . . . . . . . . . . . . . . . . . . 192
3.2 Plot of zones within blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
3.3 Elevation by zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
3.4 Relative (normalized) outbreak likelihood by zone . . . . . . . . . . . . . . . . . 195
3.5 Losses per hectare by block-zone (baseline scenario) . . . . . . . . . . . . . . . 200
3.6 Losses per hectare by block-zone (1% discount rate) . . . . . . . . . . . . . . . . 201
3.7 Losses per hectare by block-zone (3 year average introduction rate) . . . . . . . . 201
3.8 Total investment by block-zone (baseline scenario) . . . . . . . . . . . . . . . . 203
3.9 Total surveys by block-zone (baseline scenario) . . . . . . . . . . . . . . . . . . 203
3.10 Zones of block 22B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
3.11 Total investment by zone in block 22B (baseline scenario) . . . . . . . . . . . . . 205
3.12 Total surveys by zone in block 22B (baseline scenario) . . . . . . . . . . . . . . 206
3.13 Survey investment by zone in block 22B, 25% budget reduction . . . . . . . . . . 207
3.14 Survey investment by zone in block 22B, 50% budget reduction . . . . . . . . . . 208
3.15 Survey investment by zone in block 22B, 75% budget reduction . . . . . . . . . . 209
3.16 Net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
3.17 Marginal net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
3.18 Combined net benefit and marginal net benefit curves . . . . . . . . . . . . . . . 211
3.19 Total investment by block-zone (1% discount rate) . . . . . . . . . . . . . . . . . 213
3.20 Total surveys by block-zone (1% discount rate) . . . . . . . . . . . . . . . . . . 213

xii



3.21 Total investment by zone in block 22B (1% discount rate) . . . . . . . . . . . . . 215
3.22 Total surveys by zone in block 22B (1% discount rate) . . . . . . . . . . . . . . . 215
3.23 Losses under an outbreak scenario in block 22B (1% discount rate) . . . . . . . . 216
3.24 Survey investment by block-zone (1% discount rate), 25% budget reduction . . . 217
3.25 Survey investment by block-zone (1% discount rate), 50% budget reduction . . . 218
3.26 Survey investment by block-zone (1% discount rate), 75% budget reduction . . . 219
3.27 Net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
3.28 Marginal net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
3.29 Combined net benefit and marginal net benefit curves . . . . . . . . . . . . . . . 221
3.30 Total investment by block-zone (3-year intro rate) . . . . . . . . . . . . . . . . . 222
3.31 Total surveys by block-zone (3-year intro rate) . . . . . . . . . . . . . . . . . . . 222
3.32 Relative (normalized) outbreak likelihood by zone (3-year intro rate) . . . . . . . 223
3.33 Relative (normalized) outbreak likelihood by zone (baseline) . . . . . . . . . . . 224
3.34 Total investment by zone in block 22B (3-year intro rate) . . . . . . . . . . . . . 224
3.35 Total surveys by zone in block 22B (3-year intro rate) . . . . . . . . . . . . . . . 225
3.36 Losses under an outbreak scenario in block 22B (3-year intro rate) . . . . . . . . 226
3.37 Survey investment by block-zone (3-year intro rate), 25% budget reduction . . . . 227
3.38 Survey investment by block-zone (3-year intro rate), 50% budget reduction . . . . 228
3.39 Survey investment by block-zone (3-year intro rate), 75% budget reduction . . . . 229
3.40 Net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
3.41 Marginal net benefit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
3.42 Combined net benefit and marginal net benefit curves . . . . . . . . . . . . . . . 231

xiii



List of Abbreviations

EIS Early Intervention Strategy
FP Foliage Protection
CESAT Cost-efficient Surveillance Allocation Tool
DSS Decision Supporty System

Btk Bacillus thuringiensis var. Kurstaki
DDT Dichlorodiphenyltrichloroethane

DBH Diameter at breast height

SBW (Eastern) Spruce budworm
SM Spongy moth (formerly Gypsy moth)
ALB Asian longhorn beetle
EAB Emerald ash borer
MBP Mountain pine beetle
L2 Second larval instar
L4 Fourth larval instar

IEQM Inventaire écoforestier du Québec méridional (Ecoforest Inventory of Southern Quebec)
BMMB Bureau de mises en Marché des bois du Québec (Quebec Timber Marketing Board)
FPL Forest Protection Limited (New Brunswick)
SOPFIM Société de protection des forêts contre les insectes et maladies

(Forest Insect and Disease Protection Corporation of Quebec)

NPV Net present value
CGE Computable general equilibrium

xiv



Chapter 1: Introduction: The Biology, Ecology and Economics of Eastern Spruce

Budworms and their Forests

1.1 Introduction

The eastern spruce budworm (Choristoneura fumiferana) is an economically and ecologi-

cally significant pest in eastern Canada and New England1. Budworm caterpillars eat the nettles

of coniferous trees; their preferred hosts are balsam fir, white spruce, and red spruce, and they

can also be found in black spruce, tamarack, eastern hemlock, and white pine [Talerico, 1983].

The spruce budworm belongs to the genus Choristoneura, which consists of moths that feed on

coniferous foliage.

At low population densities, budworm feeding does not cause significant harm to trees, and

budworms form an integral part of the ecology of eastern forests. Periodically, however, budworm

densities increase to the point where they completely defoliate trees. Several (3-5) consecutive

years of severe defoliation will cause trees to die [Huff et al., 1984]. Even in the absence of tree

mortality, pronounced defoliation will reduce growth rates and increase injury in trees. Three

1Throughout this dissertation, I use the terms "budworm" and "spruce budworm", as well as the abbreviation
"SBW", interchangeably to refer to the eastern spruce budworm. This is common practice in the literature (see, for
example, Talerico [1983]). All such references should thus be understood as shorthand for eastern spruce budworm.
The western spruce budworm, mentioned briefly in this chapter, is a closely related species that does not form the
basis of this study. Nonetheless, lessons from the study of eastern spruce budworm are applicable to the study of
western spruce budworm.

1



years of defoliation are generally enough to kill a terminal leader [Huff et al., 1984]. Widespread

tree deaths cause economic, social and ecological damage, especially as trees are left to rot and

lose their value.

In this chapter, I present literature, models and empirical research on the biology, ecology

and economics of spruce budworms and the forests they inhabit, and I complement these contri-

butions with insights from invasive species and fragile ecosystems literature. This chapter will

help guide research presented in subsequent chapters. However, these chapters will have novel

models that were developed to each address one aspect of budworm management. This disserta-

tion covers three aspects: the harvest-treatment aspect, the pre-outbreak surveillance aspect, and

the multi-spatial interdependence aspect.

Chapter 2 presents a bioeconomic model for harvest and treatment decisions for an es-

tablished outbreak. This chapter employs a novel modeling approach where biomass stocks of

budworm pests and forest resources are modeled in discrete time (as opposed to continuous time

approaches such as Ludwig et al. [1978] and Ludwig et al. [1979]), with each time step hav-

ing before and after phases. The two choice variables are the proportional harvest of the forest

biomass and the discrete application of treatments to suppress the budworm biomass. Chapter

2 was developed with the foliage protection strategy in mind, which is why the initial spruce

budworm infestation level is assumed to be high.

Chapter 3 models surveillance decisions in a pre-outbreak context under an early interven-

tion program, and thus assumes that the initial spruce budworm infestation level is very low. It

adapts the CESAT model [Epanchin-Niell, 2020] to the spruce budworm management question

and specifically to an examination of the early intervention strategy by employing a single de-

tection method, a single treatment program, and a pest that can enter all parts of the landscape

2



rather than through a single point of entry. There is a single choice variable, which is the number

of surveys sent into each part of the landscape. Treatment is a response to a survey outcome

rather than a model choice. Chapter 3 analyzes choices with and without a limited budget and

determines how survey resources might best be placed in Eastern Quebec to minimize the total

expected damages from outbreaks and costs from a survey and treatment program.

Chapter 4 provides descriptions of how the Chapter 2 and Chapter 3 models should be

adapted to a multi-spatial context. Chapters 2 and 3 were developed without considering spatial

pathways. In Chapter 2, this meant restricting ourselves to a single, dimensionless landscape.

In Chapter 3, this meant modeling budworm infestation events as an exogenous and continuous

process. If early detection of developing outbreaks and active treatment of advanced outbreaks

minimizes budworm spread across the landscape, this will capture additional benefits that were

not considered in Chapters 2 and 3.

This chapter distinguishes between the ecology of spruce budworms and their biology. I

use biology to refer to the behavior and life cycle of spruce budworms, and ecology to refer to

their interactions with their forest habitat. A forestry planner hoping to design and implement a

forest protection program must understand both.

From an economic modeling perspective, two aspects of budworm biology are relevant:

the year-over-year reproduction rate within a tree stand and the dispersal rate across a forested

area. Year-over-year reproduction is a simplification of the budworm life cycle. This life cycle is

described in subsection 1.3.1.

In terms of budworm ecology, planners are principally interested in the rate at which bud-

worm larvae consume foliage, the natural predation and stressors to which budworms are subject,

and the effects of treatments on local budworm densities. Biology and ecology are linked: pre-

3



dation is a key component of year-over-year reproduction, since it determines the survival rate

of larvae. Budworms suffer from high natural mortality: over 90% of early-instar larvae will

die before they can become moths, due to starvation, parasitism, or predation. A forest manager

seeking to minimize budworm damages must apply treatments that cause additional mortality to

budworms; optimal timing and the importance of additionality are explored in section 1.4.

Despite recent and rapid advancements in knowledge, budworm dynamics are still not fully

understood due to the fact that outbreaks have generally been observed only after the outbreak

phase had begun. Entomologists have, therefore, been forced to work backwards from limited

sample data to determine how endemic outbreaks become epidemics. Two competing hypothe-

ses have emerged, based on the same set of data from a research project in Green River, New

Brunswick that was carried out from 1945 to 1959. The earlier hypothesis, formulated by Mor-

ris [1963], holds that budworms are characterized by two equilibria, one with low density and

one with high density. Disturbances can cause feedback loops which drive low-density popula-

tions to a high-density equilibrium. The second hypothesis, suggested by Royama [1984] after

re-analysis of the Green River data, is that spruce budworm follows a regular oscillatory pattern.

The implications of these two hypotheses are fully explored in section 1.3. Throughout all chap-

ters of this dissertation, I assume that the double-equilibrium theory holds, as this is consistent

with the most recent evidence.

Recent findings have suggested that the Morris hypothesis holds true, although this by no

means represents a consensus [Sturtevant et al., 2015]2. Under the assumption that the double-

equilibrium hypothesis does hold, researchers in New Brunswick developed a new strategy,

2This was also reflected in my conversations with policy planners and entomologists in Canada. Notably, the
former chief entomologist of Ontario shared his concerns about the recent re-appraisals with me.

4



known as the Early Intervention Strategy (EIS), to deal with spruce budworm outbreaks, which

consists of monitoring the landscape, identifying increasing densities of budworms prior to the

realization of full outbreaks and interrupting the feedback loop to prevent epidemics. This strat-

egy has been implemented in other Maritime provinces, such as Newfoundland and Labrador and

Nova Scotia, with varying degrees of success. By comparing treatment programs in different EIS

provinces, we are able to determine the barriers to EIS success.

Two other strategies can be adopted when confronting a spruce budworm outbreak. The

simpler of these strategies is to do nothing. Given the high cost of salvage harvesting and active

budworm monitoring and the under-development of road infrastructure into northern and remote

regions, doing nothing and accepting losses will often be the only available or reasonable op-

tion. The second strategy, which is widely used in Ontario, Quebec, Saskatchewan, Alberta and

British Columbia and was traditionally used in Maritime provinces, is known as Foliage Protec-

tion (FP). This strategy consists of aerially spraying Bacillus thuringiensis var. Kurstaki (Btk)

and tebufenozide in order to suppress defoliation just enough to delay or prevent the death of

trees. Management is explored fully in section 1.5.

Planning for spruce budworm must be done on a long-term horizon, as action plans must

be developed for 25 or 50 year horizons, and in conjunction with planning for other threats to

the forest. While the present dissertation deals only with spruce budworm, certain strategies for

budworm management will have co-benefits. For example, monitoring resources devoted to SBW

may also have value for monitoring other pests, and efforts to diversify the forest inventory and

increase its resilience to SBW will also help prevent against other pest epidemics. Maintenance

of forest integrity can preserve habitat for vulnerable species such as caribou. Managers will

consider these co-benefits when planning activities.

5



In this chapter, I present a comprehensive literature review on the biology, ecology and

management of eastern spruce budworms. I build simplified, generalized models for each facet

of management, and these models can serve as the priors for more focused research. Subsequent

chapters contain their own literature reviews, but these are more specialized, as they present

literature that pertains to the specific management problem at hand.

This chapter is organized as follows. Section 1.2 presents a generalized literature review

with a discussion of other relevant invasive and irruptive endemic pests, highlighting the sim-

ilarities and differences between the two. Section 1.3 focuses on the biology and life cycle of

budworms. Section 1.4 focuses on the ecology of budworms, including their relationship to

forests, their predators and parasites, and the chemical and organic agents that can be used to

treat them. Section 1.5 discusses the economic impact of spruce budworms, the three available

management strategies currently in use, and the history of budworm management. Section 1.6

discusses and concludes.

1.1.1 Motivation

Spruce budworm dynamics have not been extensively studied in economics literature. As

such, most economists, even ones who have knowledge of natural resource and pest dynamics,

are probably unaware of the particularities of spruce budworm management.

This chapter establishes the current state of affairs in spruce budworm literature, and ex-

plores the extant models of budworm and forest dynamics. These models will allow us to to

develop our theories and empirical methods, which are, for the most part, novel. In contrast

to the economics literature, the forestry, dendrochronology and entomology literature on spruce

6



budworm outbreaks is very well developed. This literature contains many parameters which we

will use to calibrate models in subsequent chapters.

The purpose of this chapter is to provide an overview of spruce budworm management that

will allow the uninitiated to quickly understand the context of budworm management and the

state of literature on budworm management. Establishing this baseline will make the rest of this

dissertation easier to understand.

1.2 Invasive and irruptive endemic insects

While the damages caused by invasive species have received extensive, and deserved, at-

tention in natural resource economics literature, less attention has been paid to native species

that display irruptive dynamics. Examples of such species include bark beetles, present in west-

ern North America, cone beetles, present in eastern North America, and the various budworms,

present throughout the northern part of the continent. While many of the dynamics of irruptive

species are similar to those of invasive species, the philosophy underlying their management is

fundamentally different. For example, it is neither optimal nor feasible to eliminate an endemic

irruptive species from its native region. Techniques developed to deal with invasive species can

inform the response to endemic species, but the specifics of fighting any specific endemic species

will be unique to that species. In the following subsections, I discuss relevant insights from other

literature on endemic and invasive species, fast and slow processes, and the economics of tipping

points in ecosystems.

7



1.2.1 The economics of invasive and irruptive species control

The spruce budworm has received significant attention in the ecological and forestry litera-

ture, as covered in sections 1.3 and 1.4. However, the economic literature on spruce budworms is

sparse, especially when compared to other species such as spongy moth, emerald ash borer, jack

pine budworm and mountain pine beetle. Studying the dynamics of other irruptive and invasive

species provides insight as to how best to evaluate the damages caused by spruce budworm, and

work on the mitigation of the economic consequences of other species can be used to design

optimal management strategies for spruce budworm.

1.2.1.1 Invasive pests

Olson and Roy [2005] provide a generalized description of optimized prevention and con-

trol decisions for invasive species. Species are introduced at a rate ω, which can potentially be

reduced through screening in some cases. Planners must minimize the sum of prevention costs,

treatment costs and damages. In some cases, corner solutions are optimal, such that all resources

should be spent on treatment, or on prevention. In other cases, there will be interior solutions

for treatment and prevention, such that resources should be divided between each. The authors

provide five propositions that describe how the initial invasion size, invasion growth rate, intro-

duction rate and planner’s risk attitude affect prevention and control decisions. Certain aspects of

this framework are relevant to the other chapters in this dissertation. Others, such as reductions

in the rate of introduction, are not. While the introduction rate can be observed for an endemic

pest, pathways tend to be natural, and as such planners can only react. Prevention as defined by

Olson and Roy is therefore not possible, and the planner’s decision will be whether to control

8



early, to control later, or to adapt to changing realities.

In Chapter 3, we describe management for a variety of invasive species such as the spongy

moth [Epanchin-Niell et al., 2012], emerald ash borer [Yemshanov et al., 2014] and Asian longhorn

beetle [Yemshanov et al., 2017] that are relevant to the specific context of survey resource allo-

cation. I do not repeat this discussion here, and will instead focus on one additional species that

is not covered in Chapter 3: the invasive brown tree snake in Pacific Island ecosystems. This

species is illustrative as it shows the consequences of improper management.

The damages from invasive pests are often severe, and thus planners must determine the

best course of action prior to and after arrival and be ready to act decisively. Invasive brown

tree snakes (B. irregularis), native to tropical Oceania, have caused extensive damage to wildlife

on Pacific Islands. In Burnett et al. [2008], the authors model optimal search-and-eradication

strategies on Oahu, Hawai‘i. Potential damages are inferred from Guam, where a population

introduced in the 1950s has led to the local extinction of birds, power outages, and human injury.

The authors determine the policies which minimize avoidance expenses, eradication costs and

damages. Optimal policies change according to the status of the invasion. Removal only occurs

at the optimum steady state. Below this steady state, only prevention should occur. Brown tree

snakes are modeled with an Allee effect, whereby at least two snakes are required for population

growth. Damages are linear in the number of snakes, whereas marginal removal cost is decreasing

in the number of snakes. A Weibull function is used to model the introduction rate. If the initial

snake population is above the optimal steady state, a majority of it should be removed as quickly

as possible. This is true even for small snake populations (n = 50). Thus, in the case of invasive

species, full eradication is often the optimal policy if feasible. This is not necessarily the case for

endemic pests, which may play an important role in the ecosystem.

9



1.2.1.2 Endemic pests

Invasive and endemic irruptive species are distinct insofar as invasive species are exotic

to the regions they infest, whereas endemic irruptive species are native to their ecosystems, and

can often be keystone species whose removal would negatively impact their predators. Irruptive

species can, however, become invasive once they reach ecosystems where they had not previously

become established, and this is likely to increasingly occur across North America as climate

change shifts the weather patterns of woodlands. This is the case for mountain pine beetles,

which have drifted east on winds across the Rocky Mountains and now threaten the Boreal forest

of the Prairies [Safranyik et al., 2010]. It is expected that, depending on habitat connectivity,

MPB could spread to Ontario and Quebec by the end of the 21st century. In contrast, eastern

and western spruce budworms are already present throughout North America, being found in all

ten Canadian provinces as well as Yukon and the Northwest Territories. Nonetheless, changing

climate conditions will increase the suitability of northern forests to budworm, and will thus

increase the population density of larvae in these forests through reduced mortality.

The economics of mountain pine beetles have been studied in multiple ways. Corbett et al.

[2016] use a CGE analysis to determine the effects of the MPB infestation on the economy of

British Columbia. Timber contributes 7.8% to provincial GDP in BC, and directly contributes

0.8% to GDP. The authors find that, at a 4% discount rate, provincial GDP would decrease by

1.34%, or 57.4 billion CAD, in current (2009) terms over the period of 2009 to 2054. By cal-

culating compensating variation, the authors predict that total welfare would decrease by $90

billion over this period. The authors note that carbon considerations are not included in these

calculations. Peter and Bogdanski [2010] consider the economics of salvaging forests harmed by

10



mountain pine beetles, and establish the conditions under which salvage of a dead stand is prof-

itable. Whether or not to harvest a stand will depend on the cost to harvest (which depends, for

example, on road access) and on the ability of the stand to regenerate. While some stands will be

profitable to salvage on their own, other motivations such as recreation and fire risk may justify

the salvage of unprofitable stands. The authors emphasize that replanting salvaged areas with

lodgepole pines could potentially set the stage for future MPB pandemics. Replanting decisions

are a key part of any strategy to fight irruptive species, as they will allow forestry managers to

mitigate the damage these species cause in the future. Sims et al. [2010] create a bioeconomic

model to capture the dynamics of mountain pine beetles and the responses of a social planner to

these infestations. This model is then used to compare the outcomes of different management

scenarios. While this bioeconomic model inspires my approach here, one key difference between

the Sims et al. model and the ones I will present is that there are very few effective and economi-

cal pesticide treatments that can combat mountain pine beetles, due to the speed with which they

kill trees. As such, the only option available to many managers is to adapt to the new realities

posed by MPB. In contrast, given that spruce budworm take multiple years to kill their hosts, the

range of options available to managers is greater.

Cone beetles are insects that destroy the seeds of coniferous trees, preventing their repro-

duction. Up to 90% of a seedling crop can be destroyed by these beetles [Kegley, 2006]. Sub-

species include the red pine cone beetle and the white pine cone beetle. While these beetles pose

a threat to forest plantations, control efforts have received very little attention in the literature.

This may be due to the fact that effective controls have been developed, suggested and imple-

mented. Prescribed burns are a popular control method (see Miller [1978], McRae et al. [1994]

and Natural Resources Canada [2013b]). Recently, pheromone traps have also shown promise as

11



a control method [Miller, 2007]. Cone beetles were a major problem in Canada in the 1970s and

1980s, but have since become less prevalent as a threat.

Not all endemic irruptive pests are equally destructive. The forest tent caterpillar is the most

significant endemic pest affecting broadleaf forests in Canada [Cooke, 2022]. However, the forest

tent caterpillar is better described as a nuisance than as a threat. Forest tent caterpillars defoliate

trees, but do not cause these trees to die before they can be harvested [Chang et al., 2011]. The

economic literature on forest tent caterpillar is limited, but this gap in the literature is probably

justifiable, given the lower damages caused by forest tent caterpillar relative to invasive species

such as emerald ash borer and Asian longhorn beetles. The entomological literature on forest tent

caterpillars is well-developed, however. Forest tent caterpillars affect trembling aspen forests,

and their cyclic outbreak-and-decline dynamic has a mean period of about ten years [Roland,

1993]. It is known that habitat fragmentation will increase the duration of forest tent caterpillar

outbreaks [Roland, 1993, Roland and Taylor, 1997]. Habitat fragmentation allows forest tent

caterpillars to "escape" from the threats of predators and parasites, since the forest tent caterpillar

is able to disperse across a fragmented landscape more easily than its natural enemies [Cooke,

2022]. Forest fragmentation will disrupt the natural predator-prey relationship that governs the

oscillation of the forest tent caterpillar population. When it comes to the human relationship with

forest tent caterpillars, familiarity breeds contempt: Chang et al. [2011] found that households in

Saskatchewan were willing to pay for forest tent caterpillar control. The nuisance of defoliation

and habitat degradation is enough to make the public willing to treat forest tent caterpillars, even

if there is no specific benefit to the timber industry.

Spruce budworms are, by far, the most economically significant endemic pest in Eastern

Canada [MacLean et al., 2019]. Extensive literature exists on spruce budworm dynamics, impact

12



and management, and many such articles are cited in the sections below. Economic impact studies

are much more limited, and what studies exist are primarily cost-benefit analyses (see Huff et al.

[1984], Chang et al. [2012a], Chang et al. [2012b] and Liu et al. [2019]). As budworms are

the focus of this dissertation, these studies are discussed further in subsection 1.5.5, with the

exception of Chang et al. [2011], which was calibrated on both spruce budworms and forest tent

caterpillars and which can be applied to other endemic pests.

Chang et al. [2011] presents a unique approach to estimating endemic pest damages. A

contingent valuation approach is used to determine the willingness-to-pay for future budworm

and forest tent caterpillar outbreak prevention of residents of New Brunswick and Saskatchewan.

Generally speaking, respondents supported efforts to combat endemic forest pests (at a rate of

about 80% in each province). Despite the fact that New Brunswick is more economically de-

pendent on forestry than Saskatchewan, respondents in Saskatchewan had a higher willingness-

to-pay for outbreak prevention ($71.44–$104.48) than in New Brunswick ($59.26–$86.19). This

may be explained by the fact that Saskatchewan has a higher median income than New Brunswick.

In New Brunswick, 23.1% of the value of the willingness-to-pay was for recreation and 39.4%

was for ecological considerations, such that total non-market benefits are $53.87 per household

for the households willing to pay $86.19.

The literature on endemic pests allows us to make a few preliminary determinations about

the optimal policies that managers can employ. First, if pest control is prohibitively expensive

or has a low probability of success, then the best managers can do is adapt harvest schedules to

reduce losses and change stand mixes in restocking plantings to reduce susceptibility. Second, a

pest that is easily countered will become part of normal operating costs rather than overwhelming

management efforts. Third, there is high awareness of endemic pests in affected regions. The

13



general public tends to be familiar with these pests and with the effects that they have on the local

economy. As such, active management of endemic pests is likely to have high social acceptability.

1.2.2 Fast and slow processes

Ludwig et al. [1978] developed a mathematical model for insect dynamics that posited the

existence of fast and slow processes, and this analysis was specifically formulated for spruce bud-

worms. This model is cited below, in subsection 1.4.4. Insects have a fast dynamic, while forests

have a slow dynamic. The authors establish a stepwise process. Once fast and slow variables

are established, slow variables are held fixed and the long-term behaviour of fast variables is

analyzed. Equations are scaled to reduce parameters, and parameter values are used to establish

the equilibria for fast variables. The authors describe two stable and one unstable equilibria. The

third step is to hold fast variables fixed and determine the response of slow variables. The fourth

step will be to analyze the long-term behaviour of fast variables given the response from slow

variables. The fifth step is to combine the results and describe the behaviour of the complete sys-

tem. The authors describe transition equations for forests and budworms, as well as the relevant

quantities for these transition equations.

In Ludwig et al. [1979], the authors adapt the Ludwig et al. [1978] model to determine

spatial diffusion. They establish the minimum width of a strip of forest needed to support an

outbreak, as well as the necessary width that a barrier would need in order to prevent outbreaks

from spreading from strip to strip. Unlike in Ludwig et al. [1978], however, the authors do not

consider the dynamics of the slow system, instead holding them fixed.

Vardas and Xepapadeas [2015] consider the generalized problem of renewable resource

14



management when the resource regenerates so slowly that parameters such as carrying capacity

are treated as fixed by agents. Time scale separation results in externalities, because manage-

ment rules will be derived from a misspecified function. The authors model biomass as a fast

process and carrying capacity as a slow process. Carrying capacity will slowly change due to

processes such as climate change (exogenous forcing) or industrial pollution. Cooperative and

non-cooperative solutions are explored. Optimal regulation in a non-cooperative context will

maximize discounted aggregate benefits from harvesting activity net of environmental damages.

This will therefore involve optimization with a damage function. Ignoring this damage function

is likely to lead to overharvesting.

It is appropriate to treat budworms as a stock with fast dynamics and trees as a stock with

slow dynamics. Budworm stocks are affected by rapid changes in external conditions, such as

predation and weather. Trees, meanwhile, are affected over a longer horizon, reacting to climatic

shifts and cumulative years of pest pressure. If a hands-off management framework is employed,

budworms can also be considered as a form of exogenous forcing.

1.2.3 The economics of tipping points

A literature has emerged on the economics of fragile ecosystems whose ecological integrity

can be compromised if they cross a threshold. Crépin [2007] discusses the economics of a fishery

in a fragile coral reef, and develops a generalizable framework. The author’s framework uses a

fast and a slow vector, like Ludwig et al. [1978] and Ludwig et al. [1979], in addition to a

perturbation parameter. There are two concave functions, one of which governs the fast vector

and the other which affects the fast and slow vectors. There is additionally a non-concave function

15



that governs the effect of changes to the fast and slow vectors on the fast vector. The ecosystem

provides ecosystem and harvest values, which are additively separable. The fast vector can be

affected by the social planner. In Crépin’s model, the fast vector is algae and the slow vector is

coral. These compete for sunlight. Harvesting fish will allow algae to thrive, and harm coral.

There are steady states, which are either equilibria or saddle points. Once a low equilibrium has

been reached, it may take a long time to get back to the high equilibrium again, due to non-

convexities. In some cases, a high equilibrium might not be attainable at all. Crépin finds that,

if the fishery is "optimally" managed from the perspective of fish stocks, but without taking the

coral ecosystem into account, this will make the ecosystem much more vulnerable to passing an

irreversible threshold and ending up in a low equilibrium.

Within a single planning cycle, a vulnerable forest can be analogized to the coral reef.

Tree death is irreversible and inevitable once a certain amount of defoliation has been reached.

Outbreaks of spruce budworm, if not contained, will cause massive tree death across a landscape.

In subsection 1.3.2, I discuss the two dominant theories of spruce budworm outbreaks, which are

the oscillatory theory and the double-equilibrium theory. If the double-equilibrium theory holds,

then a "high" equilibrium in terms of budworms will be the root cause of a "low" equilibrium in

terms of healthy trees, and the analogy to Crépin’s model is even more appropriate.

1.3 The biology of spruce budworms

A generation of spruce budworms lives for a year, from summer to summer, before re-

producing itself. In this section, I discuss characteristics of spruce budworm larvae, dynamics

within a year, dispersal, and dynamics over a medium to long-term outlook. Budworm larvae

16



pass through a half-dozen instars before they pupate. Following the pupal stage, they emerge

as moths. Moths then mate and fly, potentially travelling up to 200 km depending on currents.

There are two competing theories on budworm dynamics, and each of these theories has different

implications for management.

1.3.1 The life cycle of spruce budworms

Spruce budworms thrive in the softwood forests of eastern Canada and northern New Eng-

land, where they feed on the nettles of softwoods, preferring spruce and fir. Female and male

moths breed and then fly to new trees to lay eggs on nettles during the summer. These eggs hatch

into larvae in August, and they remain dormant in branches over winter. Caterpillars emerge in

the spring and feed on needles, flowers and buds. Their eating patterns can destroy new shoots

[Balch, 1958]. They pupate for ten to fourteen days in June and July, and emerge as moths

[Talerico, 1983]. Unlike spongy moths, both male and female budworm moths fly, which makes

the use of sex pheromones ineffective to control populations [Régnière et al., 2019].

A generation of spruce budworms lives its entire life from August until July of the following

year, when moths take flight and land on trees, laying the next round of eggs [Talerico, 1983].

Budworms pass through six instars between being laid as eggs and pupation. Eggs, laid in July,

hatch in August, feed, and then form hibernacula as they overwinter. They will emerge from

these shelters as second-instar larvae in April or May. They then molt through four more instar

until they reach their sixth instar, whereupon they consume the greatest percentage of foliage of

any instar. The first five instars will generally eat the nettles and buds of one shoot, while the sixth

instar will eat the foliage of two or more shoots. Finally, in late June or early July, the larvae will

17



pupate into moths over 8 to 12 days, emerging and dispersing to other trees [Talerico, 1983].

Due to predation, pests, weather, the natural defenses of trees and competition for re-

sources, the mortality rate among budworms is high, generally being between 95% and 99%.

When mortality is at the higher end of the spectrum, populations are stable and endemic. When

mortality is low, however, populations can irrupt. This will lead to outbreaks which can quickly

spread across the landscape. This is explored in the following subsection. For a treatment pro-

gram to be effective, it must impose additional mortality, which is to say that the mortality it

imposes must mostly kill budworms which would not otherwise have died.

If mortality from treatment is not additive, then the budworms killed by treatment would,

generally, have been the weakest members of the population, who would otherwise have died of

insufficient resources. This is problematic because it means that the remaining budworms face

less competition for resources. The body weight of survivors would be larger, and females would

be more fecund.

In section 1.5, I lay out the history of budworm treatments. Early budworm treatment

programs involved DDT spraying. Besides the environmental issues involved with DDT’s broad

scope, mistimed application led to massive die-off of budworms, followed by a population bounce-

back shortly after die-off.

1.3.2 Two theories of budworm dynamics

Knowledge about SBW dynamics is evolving, and there is uncertainty about how endemic

populations irrupt into outbreaks [Régnière et al., 2019]. Currently, two theories predominate

about how endemic populations become outbreaks. Both originate from the same observations,

18



taken in Green River, New Brunswick. The first, known as the double-equilibrium theory, holds

that external shocks cause SBW population levels to irrupt above usual levels. The second, known

as oscillatory theory, holds that a periodic predator-prey relationship governs SBW outbreaks. If

the first theory holds, it is possible to reduce, delay or prevent outbreaks through management of

either the underlying forest or spruce budworm populations. If the second theory holds, the best

forestry managers can hope for is to reduce the scale of damages [Régnière et al., 2019].

The double-equilibrium theory was first developed by authors such as Balch [1958] and

Morris [1963]. This occurred in a context where DDT treatments for budworms were first being

developed, and thus where the results of early spray efforts could be observed. Morris produced

life tables for spruce budworm. These life tables lent themselves to analyses such as Ludwig et al.

[1978], as described in section 1.4. Balch determined that outbreaks occurred after several years

of favorable conditions, could be seeded by moth flights, and were self-sustaining once they had

developed. The Ludwig et al. [1978] model specifically identified the low and high equilibria in

a double-equilibrium model.

The oscillatory theory was developed by Royama [1984] after re-examining Morris’s data.

Royama rejected the theory that egg-carrying moths significantly upset a theoretical endemic

equilibrium. Under the oscillatory theory, budworm dynamics do not have equilibrium condi-

tions. Instead, they feature peaks and troughs where the population process has two components:

a primary oscillation around a main trend, and a secondary fluctuation around this primary os-

cillation. Outbreaks are seeded by the local survival of larvae. At most, a moth invasion will

accelerate an outbreak towards a higher peak (Royama describes such invasions as "fertilizer").

The seeming synchrony of outbreaks across landscapes could then be explained by the fact that

density-independent factors such as weather will be correlated across locations. Therefore, what

19



appears to be "spread" is, instead, the simultaneous increase of endemic populations across a

landscape.

The most recent research supports the double-equilibrium theory. Régnière and Nealis

[2019] examined fourteen data sets, including the one used by Royama, and concluded that high

densities were associated with low fecundity and low densities with high fecundity. This implies

that low density plots were migration sinks and high density plots were sources. Régnière and

Nealis reject the Royama hypothesis that migration is a symptom rather than a cause of budworm

outbreaks. They conclude that density-dependent dispersal will offset local population declines,

which will overwhelm small-scale efforts to counter budworms with pesticides. The implication

is that management must be targeted at a landscape scale if they are to be successful.

Despite these findings, there is still controversy concerning which theory is correct [Sturte-

vant et al., 2015]. If, in fact, oscillatory theory is correct, then current early intervention efforts in

New Brunswick are merely correlated with a local trough in budworm populations. This would

imply that future efforts will fail when the underlying outbreak oscillates back towards a peak.

1.3.3 Model: the budworm cycle

All notation in this section is specific to this section, and borrowed from literature sources.

While ecological models can focus on the multiple life stages of budworms in detail, eco-

nomic and policy modeling is easier when the complexities of life stages are distilled down to

single stages. Régnière et al. [2019] describe transitions between egg, larval and adult stages. In

order to get a year-to-year model for larval transitions, I first transcribe the Régnière et al. transi-

tions from one stage to the next, and then simplify these into a single transition equation. These

20



equations treat ecological conditions as exogenous, and therefore can provide a good description

of how budworm populations are expected to evolve in the short-term.

Survival from early-instar larvae to emergent adults is given by the ratio S = A/N , which

is the ratio of emerged adult density to larval density. Based on data derived from four datasets

in Gaspésie, Régnière et al. calculate this ratio empirically, fitting it to a Weibull function. This

is given by:

S =
p0 + p0,S

N
(1− exp{[(p1 + p1|2013 + p1|2014 + p1|S + p2|2012 + p2|2013 + p2|2014)N ]p3}) (1.1)

N is the density of early instar larvae from a collected sample, and A is the density of

emerging adults from a pupal sample. The parameters p0 and p0,S are, collectively, the carry-

ing capacity, with p0 being observed across all datasets and p0,S representing additional carrying

capacity in a dataset that was collected by the SOPFIM and not by the authors. The param-

eters p1, p1|2013, p1|2014, p1|S test for differences in slope between datasets, and the parameters

p2|2012, p2|2013, p2|2014 test for the effectiveness of insecticides. The parameter p3 is a shape pa-

rameter.

This empirical formulation is useful when parameterizing a model; parameter values are,

themselves, presented in Régnière et al. [2019]. In general terms, I rewrite equation (1.1) as:

S =
A

N
=

Ā

N
(1− exp{[(α− τ)N ]η}) (1.2)

This equation thus links larval density to adult density. The next step is to determine how

21



adults relate to eggs. Régnière et al. write this transition3 as:

log(E) = log(FIAI + FYA) (1.3)

The egg density is given by E, FIAI is eggs per shoot from immigrated moths AI due to

fecundity FI , FY is the fecundity of local adults and A is the density of local adults.

To complete the loop, we need the hatching rate of eggs, which will determine the popula-

tion of larvae in the next period. Régnière et al. calculate this as a simple log-linear relationship4,

given by:

log(N) = β0 + β1 log(E) + ε (1.4)

where ε is an error term, β0 is the intercept and β1 is a coefficient that represents successful

hatch-and-survival.

I rewrite equation (1.2) as A = SN , and use this to rewrite equation (1.3) as log(E) =

log(FIAI + FYA) = log(FIAI + FY SN). Finally, by adding time subscripts, I rewrite equation

(1.4) as:

log(Nt+1) = β0 + β1 log(FIAIt + FY StNt) + εt (1.5)

This gives us a simplified transition equation that can be both calculated empirically and

used in a theoretical formulation.

The survival rate St depends on the carrying capacity of the forest, which is considered in

3This is equation (1) in Régnière et al. [2019].
4This is equation (5) in Régnière et al. [2019].

22



section 1.4. As competition for resources increases, the survival rate of larvae to the adult stage

decreases. Insecticide treatment of forest stands will aim to reduce this survival rate.

1.3.4 Parameterization of the budworm cycle model

Parameterization of the budworm cycle is straightforward. Régnière et al. [2019] calculate

values for the parameters in the above model. These parameter values can thus directly inform

our model. Sensitivity analysis in a simulation can then be used to determine how modifications

to the parameters would affect conclusions.

1.4 The ecology of spruce budworms

Spruce budworms are a key part of coniferous North American forests, as they are prey

for birds and invertabrates. In this section, I describe the interactions between budworms, their

forests, and their predators and trace the history of spruce budworm outbreaks across Canada in

the 19th and 20th centuries. I present a basic slow-and-fast process ecological model, adapted

from Ludwig et al. [1978] and Ludwig et al. [1979].

1.4.1 The hosts and predators of spruce budworms

Talerico [1983] provides a summary of spruce budworm predator-prey interactions. As

mentioned in the introduction, eastern spruce budworms prefer balsam fir, white spruce, and

red spruce, and they also eat the nettles of other species such as black spruce, tamarack, eastern

hemlock, and white pine. Eggs tend to be found primarily in the outer perimeter of the tree crown,

but can even be found as deep as the bark. Larvae preferentially feed on staminate flowers. They

23



stay in place until all food is consumed, and then move on. Balsam fir are the most vulnerable

hosts, followed by white spruce, red spruce and black spruce. This preference can be explained

by the timing of bud emergence [Greenbank, 1963]. Mature and overmature trees are the most

susceptible to attack [Jennings and Crawford, 1985].

Trees can defend themselves against budworms. Talerico distinguishes between "qualita-

tive" and "quantitative" defenses. Qualitative defenses include alkaloids, terpenes and cyanide,

which is to say the toxins secreted by trees, and quantitative defenses include foliage toughness

as well as tannins. Talerico acknowledges that the distinction is arbitrary (for example, terpenes

may also be "quantitative"), but largely it comes down to between-species variation in the degree

of defense (i.e. species with more qualitative defenses are more resistant than species with fewer

qualitative defenses) versus within-species variation (i.e., for a given species, a tree with more

quantitative defenses will be better protected than a tree with fewer quantitative defenses).

Food abundance is related to individual budworm size as well as to budworm density: as

the food supply in a forest decreases over the course of an outbreak, larvae will be smaller, with

reduced fecundity [Talerico, 1983].

An understanding of the predators of spruce budworms is critical to integrated pest man-

agement [Jennings and Crawford, 1985]. Different life stages face different predators. Eggs are

eaten or are suspected to be eaten by phalangids, mites, spiders, plant bugs, lacewings, beetles,

ants, and possibly birds such as warblers. Mites are particularly voracious, with each mite eat-

ing, on average, 0.68 budworm eggs a day. When budworms are on trees and in a larval stage,

their predators include coccinellid beetles (i.e. ladybugs), squirrels, and birds such as chickadees,

vireos, sparrows, warblers and nuthatches. Small larvae are not generally considered to be de-

sirable food sources for birds. Some larger budworm larvae will drop to the forest floor to avoid

24



predators. This is an effective survival tactic, but it still leaves them exposed to ants, spiders,

carabid beetles, and insectivorous mammals such as voles, mice and shrews. Pupae are immobile

and thus susceptible to predation, especially by spruce coneworms, which pupate several days

later than budworms, but also by the other arboreal predators of larvae. When moths take flight,

dragonflies, robber flies, and birds such as kinglets, vireos, warblers and chickadees will prey on

them if they can catch them. Female moths are more vulnerable than males due to their heavier

bodies, egg burden, and less rapid flying. Ovipositing and coital moths are also vulnerable to

predation by arboreal predators.

According to the oscillatory theory, described in subsection 1.3.2, predator success rates

determine budworm outbreaks. The double-equilibrium theory focuses on the importance of

local climatic and forest health conditions, and holds that predators are opportunistic and will

seek other prey when budworm levels fall below outbreak levels. Under the double-equilibrium

theory, which I assume holds throughout these essays, predation is one part of the ecosystem’s

response to fluctuating budworm levels, and a determinant of the within-stand larval survival rate

and of the reproduction success rate for adults. It is not, however, the main driver of outbreaks.

1.4.2 Timeline of spruce budworm outbreaks

Spruce budworm outbreaks occur over several generations, and multiple years of sustained

defoliation are required before trees die. Since budworm prefer to eat new foliage rather than

old foliage, old foliage will be preserved in the early stages of an attack, which prevents tree

asphyxiation. The amount of time required for a stand to experience massive death will depend on

stand composition: balsam fir die after 4 to 7 years of defoliation, depending on local conditions,

25



while white and red spruce require one more year to die than balsam. Black spruce tend not to

die until outbreaks are severe and sustained [Talerico, 1983]. Outbreaks tend to begin in stands

where there is an abundant supply of food.

Over the course of the 20th century, the duration of outbreaks was inversely related to their

severity [Navarro et al., 2018]. Once an outbreak is ubiquitous across a landscape and defoliation

has become widespread, collapse will eventually occur due to disease, starvation and emigration

[Régnière et al., 2019]. It stands to reason that an outbreak that exhausts its available resources

faster will also collapse faster. As discussed in subsection 1.4.3, outbreaks have historically

tended to last 30 to 40 years [Sturtevant et al., 2015]. The severe outbreak of 1968-1988 identified

by Navarro et al. [2018] was therefore significantly shorter than a typical outbreak.

Because defoliation takes several years to become severe, because several years of cu-

mulative defoliation are required before death occurs, and because standing dead trees can be

harvested for timber [Liu et al., 2019], the effects of a spruce budworm outbreak on stand yield

will be delayed. Chang et al. [2012b] described a theoretical moderate or severe outbreak in 2012

as having effects that begin to be felt in 2017, and have a maximum harvest impact from 2027 to

2031. This provides different options for SBW treatment: a forest stand can be saved by aerial

spraying of Btk and tebufenozide after it experiences defoliation, but by this point the infestation

will have spread to adjacent stands. For defoliation to be visible through aerial surveys, outbreaks

will have reached sufficient density to spread to neighboring stands: once a defoliation thresh-

old of 25% has been reached in trees, budworms tend to disperse due to competition for food

[Régnière et al., 2019].

The least understood phase of budworm outbreaks is, paradoxically, the most interesting

and important phase. There is very little knowledge about the early dynamics of budworms, and

26



comparatively more knowledge about late-stage dynamics [Régnière et al., 2019]. Modeling the

early dynamics of spruce budworms has proven to be the most challenging part of this disser-

tation. Chapter 3 provides some attempts to model early dynamics. Sensitivity analysis will

account for uncertainty.

Early detection requires intensive, on-the-ground monitoring. Whether it is even feasible

will depend on the density of road networks and the availability of resources, and whether it is

worth pursuing will further then depend on economic, social, political and ecological consid-

erations pertaining to the stand. Early detection is a pre-requisite for any intervention strategy

that could prevent large-scale outbreaks. The question of how to optimally manage outbreaks is

explored in subsection 1.5.2.

1.4.3 A history of Canadian spruce budworm outbreaks

Knowledge of spruce budworm behavior in New Brunswick dates back to the 1770s [Mor-

ris, 1963], and the dendrochronology of budworm habitats in Quebec has been reconstructed to

about 3000 BCE [Morin et al., 2007]. Fossilized droppings from spruce budworms allow a much

longer timeline: fossils have been discovered in Saguenay bogs dating back to 6000 BCE. The

habitats of spruce budworms are relatively young: the spruce-fir forests of Quebec date to about

11,000 years ago, when glaciers retreated at the end of the last great Ice Age.

The first European settlement of what is now Quebec dates to the early 17th century, and

European migration became sustained by the middle of the 17th century5. The intensive, indus-

trialized management and replanting of forests that has occurred since European settlement has

5While Morin et al. characterize the pre-settlement forest as "virgin" (see Fig. 1 in their paper), this could be
seen as an ahistorical characterization [McCann, 1999].

27



led to larger and more intense outbreaks. Three large, well-documented outbreaks occurred over

the course of the 20th century: from 1905 to 1930, from 1935 to 1964, and from 1968 to 1988

[Navarro et al., 2018]. The third of these outbreaks was the most severe. These periods cover

the occurrence of outbreaks over the entire Canadian landscape, as reconstructed through den-

drochronology: in New Brunswick, for example, the worst of the first two outbreaks occurred

from 1912 to 1920 [Balch, 1958] and from 1947 to 1958 [Royama, 1984], while the worst years

for defoliation in New Brunswick during the most recent outbreak were 1975 and 1983 [Chang

et al., 2012a]. There is uncertainty about the effects of climate change will have on the length

of time between future outbreaks, and it is thus possible that the interval between outbreaks will

shorten.

At their maximum extents, the eastern spruce budworm outbreaks of the 20th century led to

annual defoliation totalling 11, 25 and 58 million hectares, successively. During the 1970s-1980s

outbreak, the government of New Brunswick spent $100 million on forest protection programs

and established the most extensive aerial spraying program in the world [Chang et al., 2012a].

This same outbreak affected about 50% of the forested land of Quebec [Navarro et al., 2018]. The

extent of budworms is limited by geography, both to the North and South, and the availability of

food. It is expected that climate change will cause the range of budworms to shift north.

1.4.4 Model: interactions between budworms and forests

As with subsection 1.3.3, all notation is specific to this subsection.

A good model for the interaction between budworms and forests is described in the fast-

and-slow model presented in Ludwig et al. [1978]. Spread dynamics are well described by Lud-

28



wig et al. [1979]. I therefore combine the two to present a model for budworm-forest interactions

in continuous time.

Ludwig et al. [1978] captures budworm population density as a function of the forest’s

carrying capacity and predation. Larval density is given by B, which transitions in continuous

time. Ludwig et al. present6 this as:

dB

dt
= rBB(1− B

KB

)− β
B2

α2 +B2
(1.6)

such that rB is a linear growth parameter representing the growth rate of budworms, KB is

the carrying capacity of the forest, and the term β B2

α2+B2 represents predation by vertebrates (i.e.

birds), where β is a habitat factor and α is a scale factor that determines the saturation of SBW.

This growth rate does not take treatment or diffusion into account. In a steady state, dB
dt

= 0.

Note that the term KB is here held fixed, but will vary according to the slow dynamics of the

forest.

The rate of change dB
dt

is a "fast" process. Predation by vertebrates can vary much more

rapidly than foliage can replace itself, and as such disturbances to the predation parameter will

cause rapid changes to the growth rate of budworms. It is worth noting that this notation implies

a continuous process, such that it needs to be adapted for use in a discrete time context. This is

straightforward and omitted here.

Equilibria will exist when equation (1.6) is equal to zero. This will occur when rBB(1 −

B
KB

) = β B2

α2+B2 . As noted by Ludwig et al. [1978], one such value occurs for B = 0. Since

rBB(1 − B
KB

) is linear and β B2

α2+B2 is quadratic, there are up to three other potential roots, de-

6This is equation (3) in Ludwig et al. [1978].

29



pending on the values of the parameters. Ludwig et al. rewrite7 equation (1.6) as:

R(1− µ

Q
) =

µ

1 + µ2
(1.7)

when at equilibrium, where R = αrB
β

, Q = KB

α
and µ = B

α
. The left hand side is the growth

rate of µ and the right hand side is the death rate of µ, where µ is the scaled density of budworms.

The slow state variable, S, is the total surface area of branches in a stand. It is bounded by

upper limit KS . The health of trees and foliage is summarized in variable E, bounded by upper

limit KE . The transition equation for S is given8 by:

dS

dt
= rSS[1− (

S

KS

× KE

E
)] (1.8)

where rS is the intrinsic branch growth rate. Two equilibria exist: S = 0 and S = KS

KE
E.

Note that due to the sign on S
KS

KE

E
, increases in E and decreases in S will both lead to increases

in dS
dt

.

The transition equation for the health of forests9 follows:

dE

dt
= rEE(1− E

KE

)− P (
B

S
) (1.9)

where P is the rate of energy consumption by budworms. Increases in the density of bud-

worms will cause declines in E, and thus declines in dS
dt

. Ludwig et al. demonstrate numerically

that S is a slow process, approaching its maximum over a 30 year period, whereas B can grow

rapidly from a low initial equilibrium. Once a critical threshold for budworm density is reached,

7This is equation (9) in Ludwig et al. [1978].
8This is equation (21) in Ludwig et al. [1978].
9This is equation (22) in Ludwig et al. [1978].

30



S collapses rapidly to near-zero levels.

The carrying capacity of budworms per acre, KB, relates to the per-branch carrying capac-

ity, K ′ (which is an estimated parameter), the available foliage, S, the health of forests E, and

the threshold for health, TE . Ludwig et al. write this relationship10 as:

KB = K ′S
E2

T 2
E + E2

(1.10)

For large values of E relative to TE , this is approximated by KB = K ′S.

Ludwig et al. [1979] consider a spatial application of the budworm model. They rewrite

function (1.6) in one-dimensional space11 as:

dB

dt
=

σ2

2

∂2B

∂X2
+ rBB(1− B

KB

)− β
B2

α2 +B2
(1.11)

Here, σ2 is the variance of diffusion and X is a rectangular co-ordinate. With equation

(1.11), the "fast" process in the Ludwig et al. [1978] model becomes diffusive, while the "slow"

process remains spatially fixed, and affected by a diffusive stock. As the term σ2

2
∂2B
∂X2 increases due

to increasing spread of budworms from infested to uninfested forests, slow stocks will collapse

across the landscape.

1.4.5 Parameterization of the interaction model

Ludwig et al. [1978] provide empirical parameter estimates for each value in their model.

Additionally, growth functions for different species of trees, based on site indices, are calculated

10This is equation (20) in Ludwig et al. [1978].
11This is equation (6.1) in Ludwig et al. [1979].

31



in Carmean and Hahn [1981]. It is therefore possible to calculate the expected height and surface

area of a tree depending on local conditions, in the absence of pests, and then to estimate how the

above model would predict damages to these trees. We use a similar parameterization method

in Chapter 2 when building our growth-impact model, with some changes based on the specific

objectives of that chapter.

1.5 Managing budworm outbreaks

Budworm outbreaks can be managed through treatment, and different treatment options

exist for managers. In this section, I discuss the economics of spruce budworm outbreaks and

control, the history of budworm management, and the three available treatment strategies.

Careful budworm management can significantly reduce the costs associated with a bud-

worm outbreak. The death of trees occurs after several years of cumulative defoliation. Depend-

ing on objectives, this gives managers time to act: even after defoliation occurs, trees can be saved

or have their deaths delayed for several years. However, outbreak extents cannot be reduced once

they have spread across the landscape.

1.5.1 A history of spruce budworm management in Canada

In the early 20th century, when forest resources in New Brunswick were more abundant

and the pulp and paper industry was in its infancy, insect outbreaks were tolerable. By the 1940s,

depleting forest resources meant that forest stocks had to be carefully managed in a sustainable

way. Following the Second World War, decommissioned military bombers and commercially-

available pesticides made insect population pulverization feasible [Kettela, 1975]. Ontario first

32



sprayed its forests in the 1940s, while New Brunswick launched its first widespread spray pro-

gram in 1952. These programs used DDT. While they were successful in destroying budworm

populations, compensation limited the ability of these spray programs to protect foliage. Further-

more, DDT is not a specific pesticide, and the ecological costs were thus not acceptable. The

timing of treatments was fine-tuned from 1953 onward, and the nerve agent fenitrothion replaced

DDT starting in 1968, as it showed similar effectiveness for budworms and less adverse effects

on other fauna [Kettela, 1975].

Technology, techniques and chemical agents all improved through practice and research.

The bacterial agent Bacillus thuringiensis var. Kurstaki (Btk) was first tested against SBW in

1960. By 1985, better varieties such as the isolate HD-1, better standardization of measurements

and improved spray techniques meant that Btk had become widely used to kill spruce budworm

larvae [von Frankenhuyzen, 1995]. Btk disrupts the feeding of SBW larvae, causing them to

starve to death. Mortality is high but not total. Btk only affects lepidoptera, and therefore will not

kill other forest insects. Thus, Btk has minimal ecological drawbacks. Tebufenozide (RH5992),

which is similarly ecologically benign, began being used against spruce budworms in the late

1990s, after field trials in a balsam fir forest near Longlac, Ontario in 1993. It causes early

moulting and thus interferes with budworm growth. It is harmless to Coleoptera, Orthoptera or

Heteroptera but harmful to Lepidoptera [Cadogan et al., 1997]. In the Longlac study by Cadogan

et al. [1997], mortality without treatment was about 67.5% on average with high variance. De-

pending on treatment, tebufenozide increased mortality to as high as 94%. Defoliation dropped

from 61.6% to 6%. Surviving larvae had less body mass, such that the quality of moths would

be lower. Further studies by Doucet et al. [2007] showed that early instar moulting could also be

disrupted. Modern budworm spraying involves a mix of Btk and tebufenozide.

33



Moth spraying using phosphamidon was attempted in New Brunswick by Forest Protection

Limited [Kettela, 1995]. This program was unsuccessful, since they did not limit egg deposition.

Fortunately, these trials also yielded important insights into moth dispersal patterns. It is now

understood that sea breezes concentrate moth flights, carrying them inland. Since these trials were

unsuccessful, all budworm treatment programs currently in practice focus on larval budworms,

not adults.

Budworm control has grown significantly more efficient and effective over the last few

decades, due to focused research and technological innovation. Nonetheless, knowledge about

how best to protect forests against spruce budworm defoliation is still evolving, and there is

controversy about the degree to which forests can even be protected. This is discussed in the

following subsection.

1.5.2 Early intervention or foliage protection?

If a forestry manager chooses to actively protect a forest from spruce budworm, two strate-

gies can be employed. Traditional spruce budworm management involves foliage protection,

whereas newer techniques have focused on early intervention.

Foliage Protection (FP) is a reactive strategy that involves spraying forests after defoliation

occurs. Under FP, managers aerially spray affected blocks at regular intervals, based on available

resources, in order to prevent tree death due to defoliation. Ideally, enough foliage should be

preserved that trees will survive until shortly before their harvest, minimizing losses from rot.

Some defoliation on treated trees is acceptable. For example, Chang et al. [2012a] describe a

foliage protection program that reduces defoliation from 70% to less than 40%. This will reduce

34



the observed tree death across the landscape and thus limit damages.

A foliage protection strategy will not necessarily treat all defoliated populations. Rather, it

will treat heavily impacted stands, based on prioritization criteria. Kettela [1975] describes these

criteria. A map is made of the trees most likely to suffer tree mortality. Hazard factors include

current defoliation, cumulative defoliation, tree vigor and expected budworm density, and areas

with similar risk are delineated. This map is then used to plan spray operations. The economic

value of stands is considered, since less accessible or less valuable trees might not be worth

the expenditure of treatment efforts. Furthermore, linear spray tracts constrain the geometry of

operations. Some tree death is thus accepted as part of foliage protection. For example, an FP

program in New Brunswick might focus on protecting up to 50% of forested land from budworms

[Chang et al., 2012a]. On-the-ground monitoring is used to complement protective efforts and

guide decision-making, both in the current year and for the next. Foliage protection will slow the

spread of infestations, since suppressed populations will be smaller and will feature physically

weaker moths.

In contrast to FP, the Early Intervention Strategy (EIS) is a proactive strategy. EIS was

developed for use in New Brunswick, and has been applied in other Maritime provinces. It

involves proactive, on-the-ground monitoring of spruce budworm populations in order to detect

increases in growth rates. Once budworm density (which can be defined per shoot or per branch)

exceeds the irruption threshold, managers following an EIS s