p
.-

. IHWM. -

.r.‘i-.1....:.w.flm.:..

:1.

(‘Ivilr’
.:

t
I!

. .1 :1
x?... we“.
.I. V v

a .x
{7 )3) .4 .1
. y .250 \. r

4.. u. 11......

and».

.4“.

at;
.1 u!

43...”...

ll
VA)

53.2111. $1.31

4.25%.

 

 

 

2 LIBRARY
20 a; Michigan State
University

 

 

This is to certify that the
dissertation entitled

OPTIMAL PEST MANAGEMENT IN THE PRESENCE
OF NATURAL PEST CONTROL SERVICES

presented by

Wei Zhang

has been accepted towards fulfillment
of the requirements for the

 

Umbra/g in Agrjzatturai Economics

Major Professor's Signature
”Pa: ~ Q, 2007’

Date

MSU is an affinnative-action, equal-opportunity employer

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

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/07 p:/ClRC/DateDue.indd-p.1

 

 

 

OPTIMAL PEST MANAGEMENT IN THE PRESENCE OF
NATURAL PEST CONTROL SERVICES

By

Wei Zhang

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

2007

ABSTRACT

OPTIMAL PEST MANAGEMENT
IN THE PRESENCE OF NATURAL PEST CONTROL SERVICES

By
Wei Zhang

By integrating natural pest control services into managerial decision-making,
there are new opportunities for improving agricultural pest management in an
economically appealing and socially desirable manner. This research develops dynamic
and spatial bioeconomic models to investigate optimal economic management of an
insect pest in the presence of natural enemies. Of central economic importance are the
opportunity cost of natural enemy mortality due to broad-spectrum insecticides and the
opportunity cost of setting aside land as non-crop habitats for the enhancement of natural
enemy populations. The models are applied to a recent invasive pest of US. soybean, the
soybean aphid, whose management is of both economic and environmental importance to
the North Central region of the United States.

The thesis is divided into three essays. Essay 1 develops a dynamic bioeconomic
model for the insecticide-based management of soybean aphid that explicitly takes into
account both the predation effect of natural enemies on pest density and the nontarget
mortality effect of aphid insecticides on the level of natural predation supplied. The study
develops a natural enemy-adj usted economic threshold that represents the pest population
density at which pesticide control becomes optimal in spite of the opportunity cost of
injury to natural enemies of the target pest.

Essay 2 applies the bioeconomic model developed in Essay 1 for a simulation

experiment on the optimal control of soybean aphid. The study examines the difference in

optimal control choices and associated economic gains with and without consideration of
natural enemies. For instance, the presence of one ladybeetle would justify a change of
optimal control choice from spray to no-spray when the pest density is 20 per plant. The
results highlight the importance of assessing both pest and natural enemy populations in
making insecticide application decisions and accounting for the opportunity cost of
insecticide collateral damage to natural enemies.

The study also estimates the private economic value to farmers of the natural
control services of ladybeetles in suppressing soybean aphid damage. The estimate
constitutes a lower bound for the total economic value of this ecosystem service, because
it omits such benefits as the avoidance of health and environmental risks from insecticide
spraying.

Farmers desiring to rely on natural pest control in lieu of insecticide-based control
can try to manage the habitat for natural enemies. Essay 3 develops a spatial optimization
model to explore economically optimal habitat configurations for the natural enemies of
crop pests. The model is applied to soybean aphid management in representative
conventional and organic farming systems. Results indicate that non-crop habitat
management can potentially be a promising pest management option for organic cropping
systems. However, it tends to reduce farm net returns for conventional farms. Both area
and shape of non-crop habitats affect economic performance, with the greatest value

coming from small, scattered areas of habitat.

Copyright by
WEI ZHANG
2007

To my parents, my husband, and my sister for their love and support, and to those who
still believe in making a difference...

ACKNOWLEDGEMENTS

I feel fortunate to have two wonderful advisors steering me through my doctoral
program.

I would like to thank my major advisor, Richard Horan, for his guidance and
support throughout this process. I am grateful to him for being a great inspiration in so
many ways, for introducing me into the wonderful world of bioeconomic modeling with
his intelligent and effective teaching, for continuing providing constructive comments
and suggestions on my research, even though he was not involved in the dissertation
project, and for contributing greatly to my personal and professional development.

I would like to thank my dissertation research supervisor, Scott M. Swinton, who
has also filled the functions of a major professor since we first worked together. I trust
and respect him as a great advisor, mentor, and friend. I deeply appreciate his kindness,
encouragement, patience, concern for my well being, and for opening the doors to so
many opportunities for me. I am grateful to him for his constant support and outstanding
efficiency in responding to my questions and writings, which made the completion of this
work possible. Not only have I learned from him on research but also on writing,
organizing, critical thinking, and communication, qualities that will benefit me for the
rest of my life.

I would like to express my appreciation to the members of my committee, Sandra
Batie and Douglas Landis, for the valuable contributions they have made to the
improvement of this work and for the support they have given me along the way. I thank
Sandra Batie for being a great role model for female environmental economists and for

her generous help with my professional development. I am grateful to Douglas Landis for

vi

providing collaboration opportunities and crucial data sources for the research, and for
making time teaching me about insect ecology and sharing ideas.

I am grateful to our collaborator, Wopke van der Werf, who traveled trans-
Atlantic to East Lansing to work with us on the habitat management study. I appreciate
his professionalism, his valuable contributions to the development of the research
questions and spatial model, and stimulating ideas and comments that have greatly
improved the work. I enjoy very much his sincerity, humor, and concern for students’
well being.

I also would like to express my gratitude to the support of the Kellogg Biological
Station Long-Term Ecological Research program and the dedication of the members of
the soybean aphid USDA Risk Assessment and Mitigation Program team. I would
especially like to thank Alejandro Costamagna, Mary Gardiner, Chris DiFonzo, Mike
Brewer, and Stuart Gage for their kind help and constructive discussions. I greatly
appreciate their time and efforts. Special thanks to Felix Bianchi for his help on
ecological modeling and Tim Harrigan for taking the time to help me with habitat
establishment cost estimation.

I would like to express my appreciation to the faculty and staff of the Department
of Agricultural Economics for all of their help and support throughout my time here. I
would especially like to thank Robert Myers, Eric Crawford, Zhengfei Guan, John
Hoehn, Debbie Conway, Cynthia Donovan, and Larry Borton.

Many thanks go to fellow graduate students. In particular, I would like to thank
Yanyan Liu, Laila Racevskis, Julius Kirimi Sindi, Zhiying Xu, F eng Song, Lili Gao,

Honglin Wang, Sarma Aralas, Elan Satriawan, Feng Wu, Fang Xie, Catherine Ragasa,

vii

Wolfgang Pejuan, Ricardo Labarta-Chavarri, Laura Donnet, Tomokazu Nagai, and Rohit
Jindal for their friendship and support. A special thank to the memory of Lesiba Eli
Bopape, whose genuine care for others and cheerfiil spirit will always be remembered.

I would like to thank my good friends in the volleyball group who have brought
me so much happiness and support, especially during the most intensive writing stage.

I would like to express my gratitude to my family for their unwavering love and
support. I am grateful to my parents, Lixin Zhang and Shiyun Zhu, for encouraging me to
spread my wings, and for doing everything they could to help me pursue my dreams. I
thank my sister, Ying Zhang, for being my best friend, study (and shopping) buddy, and
most importantly, an inspiring scholar and historian of enormous potential. I reserve my
last words to express my gratitude and love to my husband, Gao Yun, for his faith in me,
constant support, and understanding, and for sharing every ups and downs with me

throughout the process.

viii

TABLE OF CONTENTS

List of Tables ................................................................................................................... xi
List of Figures ................................................................................................................. xii
Introduction ...................................................................................................................... 1

References .............................................................................................................. 5

Essay 1: Bioeconomic Modeling for Natural Enemy-Adjusted Economic Threshold:
An Application to Soybean Aphid

1.1 Introduction ...................................................................................................... 7
1.2 Soybean aphid and its natural enemies ............................................................ 9
1.3 Model of pest management ............................................................................ 'l O
1.4 Bioeconomic model of soybean aphid management ..................................... 13
1.5 Model estimation ........................................................................................... 21
1.6 Illustrative examples ...................................................................................... 27
1.7 Conclusion ..................................................................................................... 29
References ............................................................................................................ 32

Essay 2: Optimal Control of Soybean Aphid in the Presence of Natural Enemies

2.1 Introduction .................................................................................................... 48
2.1 Soybean aphid and its natural enemies .......................................................... 51
2.3 Bioeconomic optimization model .................................................................. 53
2.4 Numerical analysis ......................................................................................... 56
2.5 Sensitivity analysis ......................................................................................... 65
2.6 Conclusion ..................................................................................................... 68
References ............................................................................................................ 71

Essay 3: Spatially Optimal Habitat Management for Enhancing Natural Pest
Control Services

3.1 Introduction .................................................................................................... 83
3.2 Conceptual model .......................................................................................... 87
3.3 Empirical model ............................................................................................. 92
3.4 Numerical analysis ....................................................................................... 100
3.5 Sensitivity analysis ....................................................................................... 107
3.6 Conclusion and future research needs .......................................................... 108
References .......................................................................................................... 1 13

Conclusions ................................................................................................................... 144
References .......................................................................................................... l 47

Appendix A:

MatLab code for the optimal insecticide management model (Essay 2) ....................... 148

ix

Appendix B:

MatLab code for the habitat spatial optimization model (Essay 3) ............................... 153
Appendix C:
Estimated relationship between the pest reduction impact and the proportion of non-crop
habitats in the landscape ................................................................................................ 167
Appendix D:
Proportion of change in variable costs of production due to the establishment of non-crop
habitats (Lambda) .......................................................................................................... 168
Appendix E:
Production costs by farming system and crop ............................................................... 171

Table 1.1:

Table 1.2:

Table 1.3:

Table 1.4:

Table 2.1:

Table 2.2:

Table 3.1:

Table 3.2:

LIST OF TABLES

Parameters for the SBA population model ..................................................... 39
Parameters for the natural enemy population model ...................................... 40
Non-linear least squares estimation results from the reformulated restricted

Cousens rectangular hyperbolic model .......................................................... 41

NEET illustration: population densities of SBA and natural enemies, harvest
yields, and optimal spray decisions chosen for two initial values of S, (40 and
140 aphids/plant) given four values of NE 1 (0-4 NE/plant) (Daily predation
rate=35 aphids/NE, initial maximum yield potential E1[y]=60 bu/ac) ........... 42

Values of parameters from Zhang (Essay l)’s model .................................... 76
Summary of sensitivity analysis results organized by ranges of initial SBA
population density (Initial yield potential=40 bu/ac, daily predation rate=35
aphids/NE) ...................................................................................................... 77

Values of parameters used in the numerical analysis and their sources or
estimations ................................................................................................... l 17

Summary of sensitivity analysis results (Medium pest infestation, Laplace
kernel, and strip NCH) ................................................................................. l 18

xi

LIST OF FIGURES

Images in this thesis/dissertation are presented in color.
Figure 1.1: Illustration of the advancement of biological dynamics within season ......... 43

Figure 1.2: Simulated predation-free daily SBA density (aphids/plant) from
Costamagna et al. (2007b) model .................................................................. 44

Figure 1.3: Composition of ladybeetle species included to quantify natural enemy
presence (Data were provided by Alejandro Costamagna, Department
of Entomology, Michigan State University, at the time the data were
collected) ........................................................................................................ 45

Figure 1.4: Comparison of model prediction of untreated SBA densities during R] to R5
with field data for 2003 and 2005, KBS, Michigan. (Field data were provided
by Alejandro Costamagna, Department of Entomology, Michigan State
University, at the time the data were collected.) ............................................ 46

Figure 1.5: Illustration of how optimal control path is reached for a given combination of
initial values of pest density (S1),, natural enemy density (NE 1),, and maximum
yield potential (E ,[y])k ................................................................................... 47

Figure 2.1: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60 bu/ac
(b) at the mean daily predation rate of 35 aphids per natural enemy ............. 78

Figure 2.2: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60 bu/ac
(b) at the minimum daily predation rate of 17 aphids per natural enemy ...... 79

Figure 2.3: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60 bu/ac
(b) at the maximum daily predation rate of 52 aphids per natural enemy ..... 80

Figure 2.4: Value of producer return at initial yield potential of 40 bu/ac and daily
predation rate of 35 aphids per natural enemy ............................................... 81

Figure 2.5: Value of one natural enemy per plant in stage R1 at daily predation rate of 35
aphids per natural enemy and initial yield potential of 40 bu/ac ................... 82

Figure 3.1: The distribution of land between non-crop habitats, impact zone, and no
impact zone .................................................................................................. l 19

Figure 3.2a: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80X80 grid and with pro_NCH=0.l): Square.. 120

xii

Figure 3.2b: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80XSO grid and with pro_NCH=0.l): Strip ..... 121

Figure 3.2c: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80X80 grid and with pro_NCH=O. l ): Archipelago
...................................................................................................................... 122

Figure 3.33: Illustration of distribution kernels (prepared in 200><200 grid): Cylindrical
kernel (radius=100 m) .................................................................................. 123

Figure 3.3b: Illustration of distribution kernels (prepared in 200><200 grid): Laplace
kernel (a=0.02 m") ...................................................................................... 124

Figure 3.3c: Illustration of distribution kernels (prepared in 200><200 grid): Gaussian
kernel (0:80 m) ............................................................................................ 125

Figure 3.4: The relationship between the NCH area and the average pest reduction impact
(Estimated from Bianchi and van der Werf, 2003) ...................................... 126

Figure 3.5(i)a: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400><400 grid: Cylindrical kernel;
Square ................................................................................................................ 127

Figure 3.5(i)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400><400 grid: Cylindrical kernel;
Strip .................................................................................................................... 128

Figure 3.5(i)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400><400 grid: Cylindrical kernel;
Archipelago ........................................................................................................ 129

Figure 3.5(ii)a: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=O.l in a 400X400 grid: Laplace kernel;
Square .......................................................................................................... 130

Figure 3.5(ii)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with pr0p_NCH=0.l in a 400><400 grid: Laplace kernel;
Strip .............................................................................................................. 131

Figure 3.5(ii)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400 x400 grid: Laplace kernel;
Archipelago .................................................................................................. l 32

Figure 3.5(iii)a: Illustration of distributions of pest control impact (proportion of

reduction), prepared with prop_NCH=O.l in a 400 X400 grid: Gaussian kernel;
Square .......................................................................................................... 133

xiii

Figure 3.5(iii)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCI-I=0.1 in a 400><4OO grid: Gaussian kernel;
Strip .............................................................................................................. 134

Figure 3.5(iii)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400><400 grid: Gaussian kernel;
Archipelago .................................................................................................. 1 35

Figure 3.6a: Illustration of assumed modes of machinery field operation (the number “1”
represents one turn): Square ......................................................................... 136

Figure 3.6b: Illustration of assumed modes of machinery field operation (the number “1”
represents one turn): Strip ............................................................................ 137

Figure 3.6c: Illustration of assumed modes of machinery field operation (the number “1”
represents one turn): Archipelago ................................................................ 138

Figure 3.7: Estimated values of the percentage of change in variable costs of production
for square and strip patterns ......................................................................... 139

Figure 3.8: Estimated values of the percentage of change in variable costs of production
for archipelago pattern ................................................................................. 140

Figure 3.9: Proportion of change in net return to fixed factors (Medium pest infestation,
Laplace kernel) ............................................................................................. 141

Figure 3.10: Proportion of change in net return to fixed factors for a conventional farm
when change in variable costs of production is ignored (Medium pest
infestation, Laplace kernel) .......................................................................... 142

Figure 3.11: The effect of distribution kernels on the relative performance of HM at
medium pest infestation ............................................................................... 143

xiv

Introduction

Daily (1997) defines ecosystem services as the conditions and processes through which
natural ecosystems, and the species that make them up, sustain and fulfill human life.
Agricultural ecosystems are actively managed by humans to optimize provisioning
ecosystem services for food, fiber, and fuel (MA, 2005). To do so, they depend upon a
wide variety of supporting and regulating services such as soil fertility, natural control of
crop pests and pollination as inputs to production (de Groot et al., 2002; MA, 2005; NRC,
2005), which directly translate to the profitability of farming as well as the social and
environmental extemalities to and from agriculture.

The control of pests by their natural enemies represents an important regulating
ecosystem service that maintains the stability of agricultural ecosystems and has the
potential to mitigate pest control costs (Naylor and Ehrlich, 1997; Pimental et al., 1997).
As the limitations and negative extemalities of chemical insecticides have become more
obvious, the value of natural pest control services has increasingly been recognized
(Naylor and Ehrlich, 1997). In addition to the well-documented human health and
environmental risks (Wilson and Tisdell, 2001), insecticide application in agriculture can
damage the functioning of many ecosystem services. For instance, honeybees, which are
vital for the pollination of crops, are affected by most of the insecticides used, causing
agricultural losses due to reduction in insect pollination of crops (Pimentel et al., 1992).

The flow of the natural pest control services critically depends on how
agricultural ecosystems are managed and the diversity, composition, and functioning of

the remaining ecosystems (Tilman, 1999). The functioning and viability of natural

enemies can be damaged by chemically based pest management, which remains the
dominant form of agricultural pest control. Use of broad-spectrum pesticides tends to
severely damage populations of natural enemies, potentially exacerbating existing pest
problems or even triggering the emergence of new pests (Calkins, 1983; Naylor and
Ehrlich, 1997; Krishna et al., 2003). Habitat destruction and intensification of agricultural
systems are destructive of natural pest control services (Naylor and Ehrlich, 1997).
Natural pest control in general is positively correlated to landscape complexity, which is
chiefly characterized by the proportion, size, and spatial arrangement of non-crop habitats
in the landscape (Bianchi et al., 2006; Steffan-Dewenter et al., 2002).

These relationships and interactions can have potentially important economic
implications for farm profitability and the management of this ecosystem service. The
three essays of this dissertation focus on two integral management components: i) to
conserve natural enemies so that they can effectively reduce pest populations, and ii) to
enhance natural enemy populations so that more pest control services are available. The
first component involves optimizing insecticide use to capitalize upon the natural pest
control services—an integration of two alternative pest management mechanisms.
Unfortunately, little attention has been given to the interaction or compatibility of the
different technologies used in pest management (Thomas, 1999). Current chemical
control practices typically don’t take into account the presence of natural enemies.
Untimely application of broad-spectrum insecticides can decimate natural enemy
populations. The non-target mortality effects of chemical insecticides on populations of
natural enemies imply inefficiencies in insecticide use if unaccounted for in the treatment

decision—an “opportunity cost” to producers in terms of foregone natural control

services that would have been provided by existing natural enemies. As a result, farmers
may invest in unwarranted insecticide application, potentially leading to excessive release
of chemical pollutions. To achieve socially optimal insecticide application with natural
enemies efficiently used, key ecological factors and interactions such as the predation
effect of natural enemies on pests, the non-target mortality effect of insecticides on
natural enemies, and the enhancing role of non-crop habitats on natural pest control
services should be incorporated into decision making.

Bioeconomic modeling of the behavior of ecological communities (pests, natural
enemies, and crop plants) has the advantages of quantitatively describing biological
processes and interactions and predicting their response to management decisions (King
et al., 1993). Essay 1 develops a bioeconomic framework for optimal pest management
that explicitly takes into account the population dynamics of natural enemies. The study
develops a natural enemy-adjusted economic threshold that represents the pest population
density threshold at which pesticide control becomes optimal in spite of the opportunity
cost of injury to natural enemies of the target pest, whereas the conventional economic
threshold is generally based on pest abundance and does not address natural enemy
mortality or the impact of natural enemies on pest survival.

Essay 2 applies the bioeconomic model developed in essay 1 for a simulation
experiment on optimal control of soybean aphid, a new invasive pest of soybeans in the
North Central region of the United States, taking into account the contribution of major
natural enemies such as ladybeetles. In particular, the analysis addresses how the optimal
number and timing of insecticide applications would be different if the presence of

natural enemies is accounted for in the decision making. The study also performs

preliminary assessment of the economic value of the natural control services of
ladybeetles in suppressing soybean aphid damage to private producers.

In the long run, effective agroecosystem management will demand more of
managers than simply to reduce the non-target effect of pesticides on natural enemies.
Habitat management that improves landscape complexity can potentially benefit natural
enemies and in most cases result in enhanced biological control of pests (Thies and
Tschamtke, 1999; Wilby and Thomas, 2002; Cardinale et al., 2003; Ostman et al., 2003;
Thies et al., 2003). The second component of the management of natural pest control
services thus moves beyond insecticide use thresholds to develop sustainable agricultural
land use guidelines for explicit management of habitat for the natural enemies of
agricultural pests. Essay 3 develops a spatial optimization model to explore economically
optimal spatial habitat configuration for natural enemies of crop pests. The central
question is to what extent and under what production systems that habitat management
offers private producers the economic incentives for adoption.

Each of the three essays stands alone as individual paper but as a group, they are
designed jointly to contribute to the economic literature on optimal pest management by
incorporating the important ecological function of natural pest control into decision

making.

References

Bianchi, F.J.J.A., C.J.H. Booij, and T. Tschamtke. 2006. “Sustainable pest regulation in
agricultural landscapes: a review on landscape composition, biodiversity and
natural pest control.” Proceedings of the Royal Society of London Series B-
Biological Sciences 273: 1 71 5-1 727.

Calkins, CO. 1983. “Research on exotic pests.” In C.L. Wilson and C.L. Graham, ed.
Exotic Plant Pests and North American Agriculture. New York: Academic Press,
pp. 321-359.

Cardinale, B.J., C.T. Harvey, K. Gross, and AR. Ives. 2003. “Biodiversity and biocontrol:
emergent impacts of a multi-enemy assemblage on pest suppression and crop
yield in an agroecosystem.” Ecology Letters 6: 857-65.

Daily, G. 1997. Nature ’s Services. Washington, DC: Island Press.

Daily, G., and K. Ellison. 2002. The New Economy of Nature--The Quest to Make
Conservation Profitable. Washington, DC: Island Press/Shearwater Books.

de Groot, R.S., M.A. Wilson, and R.M.J. Boumans. 2002. “A typology for the
classification, description and valuation of ecosystem functions, goods and
services.” Ecological Economics 41:393-408.

King, R.P., D.W. Lybecker, A. Regmi, and SM. Swinton. 1993. “Bioeconomic models
of crop production systems: design, development, and use.” Review of
Agricultural Economics. 15(2): 389-401 .

Krishna, V.V., N.G. Byju, and S. Tamizheniyan. 2003. “Integrated pest management in
Indian agriculture: a developing economic perspective.” In E.B. Radcliff and W.D.
Hutchson, ed. [PM World Textbook. St. Paul MN: University of Minnesota.

National Research Council (NRC). 2005. Valuing Ecosystem Services: Toward Better
Environmental Decision-Making. Washington, DC: National Academies Press.

Ostman, 0., B. Ekbom, and J. Bengtsson. 2003. “Yield increase attributable to aphid
predation by ground-living polyphagous natural enemies in spring barley in
Sweden.” Ecological Economics 45: 149-58.

Pimentel, D., H. Acquay, M. Biltonen, P. Rice, M. Silve, J. Nelson, V. Lipner, S.
Giordano, A. Horowitz, and M. D’amore. 1992. “Environmental and human costs
of pesticide use.” Bioscience 42: 750-760.

Pimentel, D., C. Wilson, C. McCullum, R. Huang, P. Dwen, J. Flack, Q. Tran, T. Saltman,
and B. Cliff. 1997. “Economic and environmental benefits of biodiversity.”
BioScience 47(1 1): 47-757.

Steffan-Dewenter, 1., U. Munzenberg, C. Burger, C. Thies, and T. Tschamtke. 2002.
“Scale-dependent effects of landscape context on three pollinator guilds.” Ecology
83(5): 1421-1432.

Thies, C., I. Steffan-Dewenterk, and T. Tschamtke. 2003. “Effects of landscape context
on herbivory and parasitism at different spatial scales.” Oikos 101: 18-25.

Thies, C., and T. Tschamtke. 1999. “Landscape structure and biological control in
agroecosystems.” Science 285(5429): 893-895.

Thomas, MB. 1999. “Ecological approaches and the development of "truly integrated"
pest management.” Proceedings of the National Academy of Sciences of the
United States of America 96(May): 5944-5951.

Tilman, D. 1999. “Global environmental impacts of agricultural expansion: The need for
sustainable and efficient practices.” Proceedings of the National Academy of
Sciences of the United States of America 96(May): 5995-6000.

Wilby, A., and MB. Thomas. 2002. “Natural enemy diversity and pest control: patterns
of pest emergence with agricultural intensification.” Ecology Letters 5: 353-60.

Wilson, C., and C. Tisdell. 2001. “Why farmers continue to use pesticides despite
environmental, health and sustainability costs.” Ecological Economics 39: 449-
462.

Essay 1:
Bioeconomic Modeling for Natural Enemy-Adjusted Economic Threshold: An
Application to Soybean Aphid

1.1 Introduction

The control of pests by their natural enemies represents an important ecosystem service
that maintains the stability of agricultural ecosystems and has the potential to mitigate
pest control costs (Naylor and Ehrlich, 1997; Losey and Vaughan, 2006). In addition to
the well-documented human health and environmental risks of applying broad-spectrum
insecticides (Naylor and Ehrlich, 1997; Thomas, 1999; Heimpel et al., 2004), another
unwanted consequence is the decimation of ambient populations of natural enemies. Loss
of natural enemies can exacerbate existing pest problems or even trigger the emergence
of new pests (Calkins, 1983; Naylor and Ehrlich, 1997; Krishna et al., 2003). Such
unintended effects reduce the cost-effectiveness of insecticides if unaccounted for in the
treatment decision. These create an “opportunity cost” to producers in terms of foregone
natural control services that would have been provided by existing natural enemies'.
Bioeconomic modeling of the behavior of ecological communities has the advantages of
quantitatively describing biological processes and interactions and predicting their
response to management decisions (King et al., 1993). As such, it is an important tool for
addressing such inefficiencies by offering decision rules that integrate natural control

services into decision making.

 

‘ Insecticide resistance of pests constitutes a source of “opportunity cost” experienced directly by
producers. Resistance typically takes multiple seasons to develop and poses less of an immediate
problem for intra-seasonal decision-making as compared to the destruction of natural enemies,
and thus is not addressed by this study.

This study develops an intra-seasonal, dynamic bioeconomic optimization model
to develop a natural enemy-adjusted economic threshold (NEET). The NEET is defined
as the pest population density threshold at which pesticide control becomes optimal in
spite of the opportunity cost of injury to natural enemies of the target pest. Using field
data from Michigan collected under a multi-state soybean aphid USDA Risk Assessment
and Mitigation Program (RAMP) project on “Soybean Aphid in the North Central US:
Implementing 1PM at the Landscape Scale”, the model is applied to the case of soybean
aphid (Aphis glycines, Matsumura) (SBA). While selective insecticides may reduce the
risk on natural enemies, broad-spectrum insecticides have been shown to provide greater
protection from SBA (O’Neal, 2007) and are likely to remain important options for pest
managers. The central question, therefore, is to choose the optimal level of broad-
spectrum insecticide use to conserve natural enemies of SBA to the extent that the
economic benefit to the farmer outweighs the additional cost. While the conservation of
natural enemy insects is likely to confer a wide range of social and environmental
benefits, our model is focused on farrners’ private economic incentives for minimizing
natural enemy mortality via optimizing the number and timing of insecticide applications,
given a pre-determined dose and toxicity level and holding prices constant.

Following this introduction section, we provide background information on the
SBA problem and the role of natural enemies in SBA regulation (section 1.2). We review
existing pest management models in section 1.3, followed by a presentation of our intra-
seasonal, dynamic bioeconomic optimization model in section 1.4. In section 1.5, we
report on parameter estimations and discuss model validation. We then present two

numerical analysis examples in section 1.6 to illustrate how the model works. Finally, we

highlight contributions of the model, identify limitations and suggest future research

needs (section 1.7).

1.2 Soybean aphid and its natural enemies

Soybean aphid is an invasive species that was first discovered in the North Central region
of the United States in 2000. Within four years, it had spread to 21 states and south-
central Canada (Landis et al., 2004). Not only is SBA capable of causing extensive
damage to soybean yield with documented yield loss of up to 40% (DiFonzo and Hines,
2002), SBA outbreaks are also correlated with dramatic increases in virus incidence in
vegetable crops (Alleman et al., 2002; Stevenson and Grau, 2003; Thompson and
German, 2003; Fang et al., 1985; RAMP, 2006). Since its invasion, SBA has prompted
farmers to perform extensive spray of soybean acreage, making it one of the key drivers
of insecticide use in the region (Smith and Pike, 2002). For example, 42% of soybean
acreage in Michigan and 30% in Minnesota were sprayed during the 2005 season,
compared with less than 1% before SBA arrived in 1999 in North Central region states
for which data are available (NASS, 2007).

Existing natural enemy communities play a key role in suppressing SBA
populations (Fox et al., 2004; Aponte and Calvin, 2004; Rutledge et al., 2004; Landis et
al., 2004; Costamagna and Landis, 2006; Berg, 1997). Natural enemies of SBA include
22 predator species (Rutledge et al., 2004), 6 parasitoid species (Kaiser et al., 2007), and
several species of fungi that cause disease in aphids (Nielsen and Hajek, 2005). In
particular, generalist predators (mainly ladybeetles, Coccinellidae) provide strong, season-

long suppression, protecting soybean biomass and yield from SBA damage (Costamagna

et al., 2007a). However, most insect natural enemies are susceptible to the major
insecticides used to treat SBAZ. Evidence from Iowa indicates that insecticides applied in
early season can actually result in greater SBA population later (O’Neal, 2007),
undermining the cost-effectiveness of insecticide investment. Although general
recommendations stress the need for assessing field situation with respect to natural
enemies before spraying (e.g., Smith and Pike, 2002; NSRL, 2002; NCPMC, 2005), the
current extension treatment threshold recommendation relies solely on aphid density
observation, whereas no applicable decision guide has been offered to producers to
conserve and capitalize on the pest regulation services supplied by ambient natural

enemies.

1.3 Models of pest management
The existing models of pest management threshold decision rules have been developed
on two fronts: the economic threshold (ET) model by entomologists and the marginal
analysis model by economists (Mumford and Norton, 1984). Our critique of the literature
necessarily focuses on the economic approach, but also discusses the evolving of the ET
concept in the entomological literature and how the entomologically-based ET model is
linked to (and different from) the economic approach.

Introduced as a crucial component of Integrated Pest Management (1PM) by Stern
et al. (1959) and having since become recognized as an operational decision rule
(Mumford and Norton, 1984), ET in the 1PM literature refers to the pest population

density at which control measures should be initiated to prevent an increasing pest

 

2 Christine DiFonzo, Department of Entomology, Michigan State University, personal
communications, October 4, 2005 and March 2, 2006.

10

population from reaching the economic injury level (Pedigo et al., 1986). With economic
injury level (EIL) defined as the lowest population density that will cause economic
damage and given by the equation EIL=C/VIDK (where C is the cost of chemical control
($/ac), Vthe value of a crop ($/ac), I the injury inflicted by the pest, D the damage
response by the crop to that injury, and K the proportionate reduction in pest attack
conferred by the control action), ET can be derived from EIL by tracking backwards in
time according to the population dynamics of the pest given some lag time needed for
farmers to take action (Pedigo et al., 1986).

Integrating the economic concepts of optimization and marginality, Headley
(I972) redefined the ET as the optimal (net-retum-maximizing) pest population density
where the marginal value product of damage control equals the marginal cost of control.
Hall and Norgaard (1973) improved Headley’s framework by developing a more general
model which considers the optimal timing and quantity of a single pesticide application.
Even though they used time variables in their models, the models are essentially static
because present control decisions do not affect future opportunities (Bor, 1995; Kamien
and Schwartz, 1981). Consideration for multiple treatments later makes it necessary to
design an approach for achieving optimality over time, triggering the incorporation of
dynamic aspects of pest management into ET development (e.g., Talpaz and Borosh,
1974, Zacharias and Grube, 1986, Harper et al., 1994, and Bor, 1995). The suppression
services of natural enemies, as well as the unintended effect of broad-spectrum
insecticides on the population of natural enemies, however, have not been included.

In a single treatment (i.e., static) framework, under certain circumstances (i.e.,

parameters C, V, I, D, and K are independent of pest population, and K is fixed for a

ll

treatment) the entomological concept of ET can potentially achieve optimality in an
economic sense because the EIL is essentially determined by the economically optimal
condition of marginal value produced equal to marginal factor cost. The entomological
model of ET, however, is not capable of providing optimal treatment solutions when
multiple treatments are required during the season.

In the entomological literature, improvements have been made to the current ET
approach that is generally based on pest abundance and does not address natural enemy
mortality or the impact of natural enemies on pest survival (Musser et al., 2006) to
incorporate the dynamic impact of natural enemies on ET (e.g., Brown, 1997, Musser et
al., 2006, Tang et al., 2005). These modeling efforts attempt to address the inefficiency
raised in situations where if pest population grth rates are substantially reduced by
natural enemies, there may be enough population regulation to prevent pests from
reaching the EIL, in which case treatment triggered by ET density would not guarantee
yield benefit equal to the cost of control (Ragsdale et al., 2007). Field observation in
Minnesota shows that this outcome indeed happened in several SBA-infested field trials
in 2005. Musser et al. (2006) propose a framework for the development of dynamic ET
that moves up or down with changes in biological mortality caused by natural enemies in
the period between ET determination and EIL realization, offering potential efficiency
gains from reducing insecticide use. Despite the improvements, these models work with
the same static EIL that is not determined based on the economic method of optimization.
Thus, a dynamic bioeconomic model that models the net-retum-maximizing behavior of

economic agents and explicitly factors in the presence of natural enemies is needed.

12

1.4 Bioeconomic model of soybean aphid management

Our bioeconomic optimization model assumes that a soybean producer maximizes the
returns over variable costs of pest control, subject to three biological constraints: i)
population dynamics of SBA as affected by both chemical control and natural enemy
suppression, ii) population dynamics of natural enemies that is coupled with prey density
and subject to the toxicity of SBA insecticides, and iii) a yield response function that
describes the relationship between pest density and yield potential. A stage-based
dynamic framework similar to that of Harper et al. (1994) is adopted. Specifically, the
biological components evolve over five discrete time periods corresponding to five
growth stages of soybean plant within a growing season (Figure 1.1). The model
incorporates factors such as the contribution of natural enemies to pest regulation, the
positive impact of prey consumption on natural enemy population, and the natural enemy
mortality caused by SBA insecticides, whose economic implications to optimal control
have not been considered in the existing literature. The outcome of the dynamic
optimization model prescribes natural enemy-adjusted optimal number and timing of
insecticide application.

Olson and Badibanga (2005) developed a bioeconomic model to evaluate and
compare the net returns of four potential thresholds (3, 100, 250, and 500 aphids per plant)
to treat SBA and found that the 3 aphids/plant threshold a dominant strategy regardless of
initial infestation date and aphid growth rate. Without accounting for natural enemies of
SBA, the threshold for spraying was 99% below the prevailing North Central states

extension recommendation of 250 aphids per plant (Ragsdale et al., 2007).

I3

The current model differs from Olson and Badibanga (2005)’s model in three
major aspects. First, our model is intended for implementing dynamic optimization
analysis, which prescribes an optimal control path for given initial status of populations
of the pest and natural enemies over a finite planning horizon. In other words, after one
assessment of the infested field, we predict the number and timing of treatments for the
entire season, whereas the decision rule developed by Olson and Badibanga (2005)
requires pest population to be monitored constantly and treatment is triggered whenever
pest population reaches certain threshold. Second, limited by insufficient data, Olson and
Badibanga (2005) adopt a partially developed SBA population growth model.
Specifically, the growth of the aphid population follows an exponential function with
fixed population growth rate and is forced to decline once the population enters a pre-
determined maximum range. F or the population dynamics of SBA, we adopt a daily-
based SBA growth model developed by Costamagna et al. (2007b) that incorporates a
linearly decreasing growth rate into an exponential grth model to account for the
impact of host plant phenology, which has been shown as an important factor affecting
aphid population growth (Rossing et al., 1994; Williams et al., 1999). The model has
been demonstrated to accurately predict SBA population dynamics in soybeans in
Michigan fields, including the population decline towards the end of the season
(Costamagna et al., 2007b). Third, since non-linearity is particularly common in yield
damage functions (Swinton et al., 1994), we adopt the Cousens (I 985) rectangular
hyperbolic functional form for the yield response function and select among alternative

models the one that fits our data best. Most importantly, we include natural control

14

services explicitly in decision making so as to improve the efficiency of insecticide use
by private producers with potential socially desirable outcome.

The system of soybean growth stages divides plant development into vegetative
(V) and reproductive (R) stages (Pedersen, 2004). Our model focuses on the five earlier
reproductive stages, RI through R5 (indexed by discrete t and t=l , 2, 3, 4, 5), during
which period soybeans are most susceptible to SBA damage (Jameson-Jones, 2005). The

following table describes the various stages.

 

 

Vegetative Stages Reproductive Stages
RI (beginning flowering)
VE (emergence) R2 (full flowering)
VC (unrolled unifoliolate leaves) R3 (beginning pod)
V1 (first trifoliolate) R4 (full pod)
V2 (second trifoliolate) R5 (beginning seed)
V3 (third trifoliolate) R6 (full seed)
V(n) (nth trifoliolate) R7 (beginning maturity)
V6 (flowering will soon start) R8 (full maturity)

 

Source: Pedersen, 2004

Farmers tend not to practice variable rate pesticide application due both to
applicator time constraints and label rates being required for manufacturers to guarantee
efficacy. Therefore, we define the control decision in each stage as a binary choice,
denoted by x, (x,=l for spray at fixed label-recommended rates, and x,=0 for no spray at
stage t). We assume that no more than one spray may occur in each stage and that the
predicted yield upon stage R5 is carried through to harvest so that SBA control is only
meaningful during stages R1 to R4. The growth of SBA population over the five
reproductive stages of the soybean plant is given by:
51+] = (St "kS,t ‘xt 'St)+"gt '(St "kS,t ’xt 'St)—P"t (NE, _kNE,t 'xt 'NEt) (I)
(t=1, 2, 3, 4)

where S,. 1 denotes SBA density per plant at stage t+1, NE,denotes density of natural

15

enemies per plant at stage t, k5,, and km, represent mortality rates of SBA and natural
enemies from insecticide application, respectively, ng, denotes net growth rate of SBA
population in the absence of “outside” regulation, and pr, is the aggregate predation rate
per NE unit per time period (stage).

While an abundant number of existing natural enemy communities jointly
contribute to suppressing SBA population in soybeans (Fox and Landis, 2002), the role of
generalist predators (mainly Coccinellidae, or lady beetles) is particularly important
(Costamagna et al., 2007a) due to their high abundance in both number and overall
suppression effectiveness (Costamagna, 2006). We therefore focus on the ladybeetle
family in our quantification of the natural enemy presence by aggregating populations of
major ladybeetle species. The adoption of an aggregate population level is underlined by
the following considerations. First, the major regulating species vary both temporally and
spatially in terms of the suppression services they provide. For instance, in Michigan,
Harmonia axyridis (multi-colored Asian ladybeetle) and Coccinella septempunctata
(seven-spotted ladybeetle) provide sequential pest suppression mid season through
harvest, with seven-spotted ladybeetle dominating the mid season and multi-colored
Asian ladybeetle dominating the late season (McKeown, 2003). Data collected at the
Kellogg Biological Station (KBS) Long-terrn Ecological Research site at Hickory
Comers in Kalamazoo County, Michigan, show that the high populations of seven-
spotted ladybeetle may have aided in delaying SBA colonization of the KBS site
(McKeown, 2003). The spread of SBA later in the season was subsequently further
hindered by the high prevalence of multi-colored Asian ladybeetle (McKeown, 2003). It

is therefore difficult to quantitatively differentiate their individual contributions. Second,

16

detailed data on the biology and ecology of major predator species such as multi-colored
Asian ladybeetle are lacking, limiting our capability to develop reliable population
models for individual species. Ideally, a set of weighting coefficients should be
developed to account for the relative contribution of each included species. In the current
study, however, such information is not available, and we treat each species as equal in
their contribution to the aggregate population level.

We adopt a dynamic Lotka-Volterra predator-prey model (Lotka, 1925; Volterra,
1926) to describe changes in the population density of natural enemies coupled with prey
consumption over discrete time periods. Denoted by NEH], the population density of
natural enemies at stage H] is given by:
NEt+I = (NE, “kit/5,1 -x, 'NEt) +dt '(NEt "kNE,t 'xt 'NEt)

(2)
+bt '(St _kS,t ’xt 'St)'(NEt _kNE,t 'xt ‘NED

(Fl, 2, 3)3
where d, (<0) is the natural net decline rate that NE would suffer in the absence of prey
and b, (>0) is interpreted as the reproduction rate of NE per prey encountered (Sharov,
1996, 1997, 1999).

Farmers often make sequential predictions on achievable yield over the course of
the growing season based on perception of initial yield potential, pest infestation and
other factors such as weather. We offer a conceptual model of yield-pest interaction that

is consistent with the process for updating yield potential described above. We express

 

3 The natural enemy model is estimated for stages R1 to R3 to predict population up to stage R4
(NE... 1..) , which in turn affects SBA population in stage R5—the last stage in which SBA can
cause damage to harvest yield in our model. Therefore, we do not need t=4 for the natural enemy
model.

17

the expected yield potential at stage t+l , denoted by Emjy], as a function of expected

yield potential at stage t (E,[y]) and pest population density at t (S,):

and Elly] = Th. Esly] = yh
where )7}, is maximum (pest-free) potential yield or average historical yield upon which

the season’s first prediction is based, and the actual yield at harvest, yh, is assumed to be
equal to yield potential evaluated at the final reward stage T + 1=6. In a non-linear yield-
pest interaction model such as the Cousens (1985) rectangular hyperbolic model, the
conceptual model can be implemented by replacing the parameter that represents
maximum yield with the fitted value of yield potential obtained in the previous period

(E,[y]) to render the following reformulated Cousens rectangular hyperbolic model:

 

Et+1IYI = Elly] - (1 - ) (4)

1 + 77, - S, / 0,
where n, denotes the proportion of yield lost per unit of pest population and 6, denotes the
maximum proportional yield loss to pest damage (O_<_ 9,31).

We assume that a producer maximizes his/her expected return over variable costs
of pest management (derived by subtracting total SBA control cost from soybean revenue
realized at harvest) over a sequence of control decisions within the growing season,
subject to biological constraints describing pest population, natural enemy population,
and crop yield potential. Denoted by J, the objective function can be written as:

T=5

J = Mgfs [p-yh — Z ctx. >1 (5)
(x, },=_1 t=l

18

subject to equations (1), (2), and (3) with 1,, NE 1, and y, are given. {xt },T:15 represents a

sequence of control actions over the five time periods, p denotes output price, and c(x,)
denotes control cost, including the cost of pest scouting to provide the basis for control
decisions. No discount factor is included for this single-season optimization problem due
to its relatively short duration.

Using the method of dynamic programming (Bellman, 1957), we illustrate some
of the analytical solutions to the dynamic optimization problem. We adopt a general form
for the yield response function because expressions of analytical solution when non-
linearity presents are extremely lengthy and thus tend to hide the intuition we would like
to highlight. Since the return over variable costs of control being maximized does not
realize until the final reward period (T +1=6) and the control variable is binary, we have
dichotomous, as opposed to continuous, optimal value functions that have to be tied to

expected harvest yield, E6[y] or yh. We solve the Bellman’s equation recursively from the
terminal period (T =5), during which time no control is actually necessary (i.e., x; = 0 ), so
the optimal value function that describes the maximum expected reward for taking

action x; = 0 is

V; =P‘EclyI=P'f(E51ylaSS) (6)
Bellman’s equation for t=4 is:

V4 = Max [—c(x4)+V5*] (7)
x4=1 or 0

19

Assuming constant control cost c(x,) = E for each period4, we iterate on Bellman’s

equation to get the first order condition (F 0C) for maximization:

OX4 355 OX4

which gives the following condition:

 

__ 3E 8E
-0 + P736319? ' kNE,4NE4 = P 6.69M ks,4S4(1+ "84) (8)
5

The two terms on the left-hand side (LHS) of (8) indicate the full marginal factor cost
(MF C) of x4 (the sum of control cost and the value of natural SBA suppression lost due to
control action at t=4), whereas the term on the right-hand side (RHS) represents the
marginal value product (MVP) of x4. The optimal solution for x4 is thus determined by the

following conditions:

 

 

 

 

(I If "pmks 4S4(I +ng4) 26-paE6Ly] pr-kNE 4NE4 OI' MVPx 2 MFCx
. as5 ’ as5 ’ 4 4
x4 :4
0 if —paE6[y]kS 484(1+ng4)<E—paE6[y]pr-kNE 4NE4 or MVPx (MFCx
L 6S5 ’ 355 ’ 4 4
(9)

Substituting x; back into the objective function (7) gives two possible optimal value

functions for V4. :

, :1:
It -'c'+p-yh 1fx4=1
V4 = . * (10)
P'J’h If x4 = 0
Consequently, we have two Bellman’s equations for t=3. In the case when x; =1,
V3: Max [-c(x3)-E+V;] (11)

x3=1 or 0

 

4 The assumption is only made for the ease of mathematical exposition in the analytical analysis.

20

and the F 0C for maximization is:

 

 

3]; =_22.-+paE6IJ’I 355 6NE: + aEéIYIaE5[YI§§cr_+ 31361.11] g fl :0 (12)
8173 855 BNE4 3x3 3E5[y] 854 OX3 355 8S4 BX3
where marginal conditionsa—S‘I- 255— _d_S5_ and ENE—4 can be derived from equations

BX3 , 854 , 8NE4 , 81'3
(I) and (2). Analogous to the conditions in (9), it can be shown that x; =1 if the MVP of

control as indicated by the last two terms on the RHS of (1 2) is greater or equal to the

MF C as indicated by the first two terms on the RHS of (l 2), and x; = 0 otherwise.

The analysis illustrates how the inclusion of natural enemies affects the
determination of the optimal control decision rule by raising the MFC to account for the
value of lost natural pest control services that consequently justifies a lower level of pest

control (or a shift from control to no-control for the binary choice case).

1.5 Model estimation

Population of soybean aphid

To estimate the predation-free net growth rate of SBA population ng,, we adopt a meta-
modeling approach by using simulated SBA growth pseudo data generated by a daily-
based SBA growth model developed by Costamagna et al. (2007b). The model describes
population growth under field conditions in the absence of natural suppression, based on
Williams et a1. (1999)’s discrete exponential population growth model. Specifically, SBA

density on day d+1, denoted by ad. 1, is described as:
ad+1=ad -erd (13)

where

21

rd=rmax(l-C-d) (14)
rd is the intrinsic growth rate of SBA that decreases in time (d), and C is the reciprocal of
the time to peak population. Starting at rm (the maximum intrinsic rate of increase)
when d = 0 (where the population is at its peak), rd decreases linearly until rd = 0 when d
= I/C (Costamagna et al., 2007b). Costamagna et al. (2007b) parameterize the model
using data collected from predator exclusion cage experiments conducted in Michigan
soybean fields between 2003 and 2005 and show that the model is robust against
variability within and between experiments. The original model calibrates a maximum
intrinsic grth rate (rm...) of 0.40 for initial infestation occurring around June 23, 2005
(Table 1.1). Since we are interested in the SBA population during soybean reproductive
stages R1 through R5, we adjust the parameter to be 0.28, denoted by rmflgmed, to
account for the time lapse between June 23 and the estimated date when plant enters
stage R1 at KBS (around July 5, 2005) according to equation (14).

We first predict daily SBA population for the period of R1 to R5 using the
Costamagna et al. (2007b) model. Free of predation, the SBA population increases

rapidly and peaks in stage R5 before it starts to crash (Figure 1.2). The simulated pseudo
data are then combined with plant stage data to compute mean population density S, per

stage. We use mean stage duration data from the literature (F ehr and Caviness, 1977)
instead of estimating from our own data, which were collected using a fixed-interval
sampling approach. The net growth rates in the absence of natural suppression are

calculated from:

”St =(‘§t+I/§t)-l (15)

22

The net population growth rate is the highest during R1 at 5.29 and drop to the lowest at
1.13 in R4 (Table 1.1). The calibration is insensitive to initial density, but is sensitive to

length of plant growth stages.

Population of natural enemies

To estimate the stage-specific net decline rate (d,) and the reproduction rate (b,) for the
natural enemy population model, we use two years’ of visual count data collected at KBS
(2003 and 2005) and perform Ordinary Least Squares (OLS) regression analysis with
robust standard errors obtained from the Huber/White estimator (Gould et al., 2006) on

the following equation:

EIAt+1I =dt 'NEt +bt '(St 'NEt)+ 2 goat 'Dummyco (16)

0):]
where E is expectation operator, Am =NE,.; - NE, and Dummy.” denotes a vector of
dummy variables for both year and plots.

The ladybeetle species included in the quantification of natural enemy presence
are Harmonia axyridis adult and larva, Coccinella septempunctata adult and larva,
Coleomegilla maculata adult, C ycloneda munda adult, Cycloneda munda larva, and
Hippodamia convergens adult, the last three of which are in the sample of 2005 but not
2003. Using the total count of each species during the entire sampling period lasting
almost two months, we calculate species composition for each year (Figure 1.3). Among
the species included, Harmonia axyridis was slightly smaller in share than Coccinella
septempunctata in 2003 but became the single predominant species in 2005.

Because SBA was first detected in the United States so recently, few years of

insect data are available and sample sizes are small, making it difficult to estimate stage-

23

specific population growth parameters. As Table 1.2 shows, the reproduction rate is
found significant at the 90% confidence level in stage R3 only, whereas the net decline
rate is significant at the 95% and 99% confidence levels in R2 and R3, respectively.
Estimates of the two parameters d, and b, conform to the theoretical expectation of
negative decline rate and positive reproduction rate. Specifically, in the absence of SBA
prey, the population density of natural enemies will decline from R2 to R3 and from R3
to R4 by 0.90 and 2.13 for each additional natural enemy in stage R2 and R3,
respectively. For each SBA encountered by each additional natural enemy, the population
density of natural enemies will grow from R3 to R4 by the amount of 0.002. The weak
reproduction relationship between SBA and natural enemies is not uncommon because
the population of generalist predators such as ladybeetles tends not to be perfectly

coupled with one particular prey population (Brown, 1997).

Yield response function

Data used to estimate the yield response function were collected from two field trials (the
RAMP project trial and the Michigan State University insecticide timing trial) conducted
at three Michigan sites in 2005 (the Bean and Beet farm in Saginaw County of eastern
Michigan, the KBS site, and a site located in Sandusky in Sanilac County that only
hosted the timing trial)5. We fit the field trial data to the restricted form of the
reformulated Cousens rectangular hyperbolic model as expressed in equation (4) using

Nonlinear Least Squares estimation. The restrictions are imposed on parameter 6, (6, =1

 

5 Data were provided by Christine DiFonzo, Department of Entomology, Michigan State
University.

24

or maximum allowable yield loss = 100%) in each stage to ensure non-negative minimum
yield potential as pest population approaches to infinity.

Table 1.3 reports estimation results from the restricted Cousens model for each
stage. SBA damage significantly affects soybean yield potential in stages R2, R3, and R4.
The proportion of yield lost per unit of pest population (17,) in stage R2 is estimated to be
negative, suggesting a “compensation” yield response relationship between pest injury
and crop yield potential in R2 (Pedigo et al., 1986). Yield potential responds to pest
damage the most in stage R3, with an estimated 0.03% of yield potential lost per SBA per

plant.

Other parameters

Little is known about predation rates of SBA by ladybeetle species. Here we propose an
approximate range for the value of this important parameter. We suggest that scenario
analysis be conducted to account for the uncertainty in the value of the parameter when
applying the model to empirical studies. The biological literature suggests that mean
daily aphid consumption by multi-colored Asian ladybeetle adults typically ranges from
15 to 65 aphids per day (Hu et al., 1989, Hukusima and Kamei, 1970, Lou, 1987, Lucas
et al., 1997), whereas the consumption rate averaged across larval instars is 23 aphids per
day (He et al., 1994) (see review conducted by Kock, 2003). As the bottom figure in
Figure 1.3 (year=2005) shows, 69% of the included ladybeetles are adult, while larvae
account for 31%. Assuming each included ladybeetle species is equally effective
consuming aphids as the multi-colored Asian ladybeetle, we obtain weighted average

number of aphids eaten per ladybeetle per day:

25

Lower bound of the range: 15 *0.69+23 *0.31 =1 7 aphids/day/NE

Upper bound of the range: 65 *0. 69+23 *0.3 1 =52 aphids/day/NE

which gives a mean of 35 aphids/day per ladybeetle. The per stage predation rate pr, is
then computed by multiplying daily predation rate by the number of days in a given stage.

We assume that insecticide will kill 99% of both SBA (kg) and natural enemies
(k~g,,) at each application during the season. This value is considered reasonable given the
high efficiency of current foliar products treating SBA6. The mortality rate for natural
enemies is diflicult to monitor, but current products such as Lambda-cyhalothrin (Warrior
with Zeon Technology®) are highly lethal to natural enemies (O’Neal, 2007).

For price and cost parameters, we use a long-term soybean trend price of $7/bu
and a treatment cost of $12/ac for the RAMP Best Management Practice treatment using
Warrior at 3.2 oz/ac with field scouting provided by Song et a1. (2006). A break-down of
the cost includes $7/ac insecticide cost, $2/ac for scouting, and approximately $3/ac for

spraying (Song et al., 2006).

Validation

The SBA population grth model developed by Costamagna et al. (2007b) has been
validated with experimental data. To see how well the biological model describes the
ladybeetle-SBA predator-prey system, we plot model predictions of untreated SBA
population densities during RI through R5 against field data collected at KBS, Michigan,
which record average initial population densities of Sl=50 aphids/plant and NE1=1 .5/plant

in 2003, and S1=70 aphids/plant and NE ,=2.5/plant in 2005 (Figure 1.4). Model predicted

 

6 Christine DiFonzo, Department of Entomology, Michigan State University, personal
communications, October 4, 2005 and March 2, 2006.

26

SBA densities coincide fairly well with field observations from R1 to R4 for both 2003
and 2005 data. Model predicted SBA density in stage R5, however, deviates from field
observation made in 2005 (data not available for stage R5 in 2003). Field population
reduction around R5 is likely due to worsening plant condition (Costamagna et al., 2007b)
and emigration of winged aphids7. While the natural enemy model is estimated from field
data so that the parameterization may be able to pick up some migration effect, our SBA
model is developed based on simulation model parameterized from experimental data,
which limits the model’s ability to explicitly capture the aphid migration. Fortunately, we
do not expect the deviation in predicted RS-SBA density to significantly affect the
treatment decision rules the model prescribes because according to our estimation

soybean yield is not found to be responsive to SBA density in stage R5 (Table 1.3).

1.6 Illustrative examples

Numerical solutions to the dynamic optimization problem (equation (5)) with respect to
the NEET can be achieved through an optimizing simulation approach analogous to the
algorithm of “DDPSOLVE” computer program developed by Miranda and Fackler
(2002). The approach solves the “complete” solution space for given initial values of SI,
NE 1, and EM. Since there is a finite time horizon, and since we know that it is optimal
to perform no control in the last period R5, we can specify 16 distinct feasible control
paths, each representing a unique sequence of five control choices made over the periods
Rl-RS. We predict producer’s return over variable costs of control for each control path

and choose the one that yields the highest return as the optimal control path (Figure 1.5).

 

7 Christine DiFonzo, Department of Entomology, Michigan State University, personal
communications, June 1, 2006.

27

We use two examples of initial SBA population density in R1 along with various
levels of initial natural enemy density to illustrate how the model works when daily
predation rate is 35 aphids/NE and maximum (pest-free) yield potential is 60 bu/ac. In
example 1, we consider a relatively low initial pest level (81:40 aphids/plant), whereas in
example 2 the initial pest level is relatively high (S,=140 aphids/plant). Table 1.4 reports
how population densities of SBA and natural enemies advance from R1 to R5, harvested
yields, and what difference in the optimal control paths chosen when initial natural
enemy density varies from 0 to 4 NE/plants in R1 (a range that is consistent with
Michigan field data). As the optimal control paths prescribe, the frequency of spray
decreases as the initial presence of natural enemies increases for given initial infestation
level. The NEET is highly sensitive to natural enemy numbers, due to the high SBA
predation value of ladybeetles. For instance, the pest density for spraying once in stage
R1 is 81:40 aphids/plant if NE [SI/plant. But if NE 1 is greater than 1 per plant, there is no
need to spray for the same initial pest density. The NEET for spraying twice at stage RI
and R2 is S1=140 aphids/plant if natural enemies are not present. However, if
NE 121/plant at the same aphid density, the NEET calls for spraying only once in R1.

The illustrative examples demonstrate that at SI=140 aphids/plant, the presence of
only one natural enemy in RI results in an increase of $ l/ac in return to farmers, given
the predation rate and initial yield potential parameters chosen. When combined with
social and environmental benefits of spray frequency reduction, the value of adopting
NEET insecticide management approach goes beyond private economic gains.

In validating performance of the NEET bioeconomic model, one limitation is that

the simulation model finds that spraying twice in both R1 and R2 is the optimal control

28

path for the initial pest density of 140 aphids/plant with no natural enemies present,
whereas farmers and field entomologists wait longer between sprays. One reason may be
that low-level natural control is present in the field, which reduces the need for
insecticide control. But two limitations of the current NEET model may also have
contributed to the result. First, the model does not capture the residual effect of
insecticides, meaning that surviving insect population as modeled can bounce back
immediately, potentially requiring another spray in the following stage to contain the
infestation. Second, the model does not include the emigration of winged aphids, an
important but also rather difficult aspect of the aphid-ladybeetle system to model given

the current monitoring capacity.

1.7 Conclusion
The control of pests by their natural enemies represents an important ecosystem service
that has the potential to mitigate pest control costs both to private producers and to
society. These services, however, are often ignored in pest management threshold
decision rules. Profitability and efficiency of pest management can be improved by
incorporating natural pest control services into pest management decision making.
Focusing on private economic incentives, this study develops an intra-seasonal,
dynamic bioeconomic model that explicitly takes into account the effect of natural pest
control services on pest management and predicts pest control threshold that includes
natural enemies. The model is applied to the case of soybean aphid management in
Michigan. As illustrated by the numerical examples, such natural enemy-adjusted

threshold is likely to lead to fewer recommendations for insecticide use than nai've

29

models that ignore natural enemies, resulting in less insecticide use, while maintaining
profitability for farmers. While the entomological threshold model does not have the right
framework to provide economically optimal control recommendation, the existing
economic models of pest management have lacked populations of natural enemies whose
indirect yield benefit has implications for optimal control levels.

The current model can benefit from improvement in three dimensions. First,
because the species composition of natural enemy communities tends to vary from field
to field, weighting factors should be developed to account for the different suppression
levels associated with different natural enemy species. Second, estimates for certain
biological parameters such as predation rate, net decline rate of natural enemies,
reproduction rate of natural enemies per prey encountered, and mortality rates of both
pests and natural enemies by insecticides need refining and validation. Obtaining better
parameter estimates will require new experimental designs that allow observation of
biological effects by plant growth stage. In addition, the model can be strengthened by
including the residual effect of insecticides and the migration behavior of insects, with
the capacity of such expansion closely depending on improved data and ecological
understanding of the system. Third, given that random effects such as weather play an
important role in driving the underlying biological processes (e.g., insect population
dynamics and crop growth), introducing stochastic processes for Monte Carlo simulation
would enhance the current deterministic model.

By describing biological processes and interactions and predicting their responses
to management decisions, bioeconomic modeling can improve human management of

agroecosystems (King et al., 1993). The multi-stage dynamic optimization model

30

presented here demonstrates how pest suppression by natural enemies can be

incorporated into a natural enemy-adjusted economic threshold for insecticide use that
can maintain or even increase profitability and reduce farmers’ dependence on insecticide.
The model can be used to conduct a wide variety of analyses including i) identifying
dynamically optimal spray strategies and estimating the implied economic value of
natural control services, and ii) developing alternative mechanisms such as habitat
management to enhance natural pest control services and eventually to significantly
reduce the use of chemical insecticides. Furthermore, with the incorporation of cross-
season carry-over factors, such as overwintering of pests and natural enemies, the current
model can contribute to building multi-year models for studying long-term pest

management problems.

31

References

Alleman, R.J., C.R. Grau, and DB. Hogg. 2002. “Soybean aphid host range and virus
transmission efficiency.” Paper presented at Wisconsin Fertilizer, Aglime, and
Pest Management Conference, Madison WI. http://www.soils.wisc.edu/
nextension/FAPM/ fertaglime02.htm

Aponte, W., and D. Calvin. 2004. “Entomological notes: soybean aphid.” Department of
Entomology, Pennsylvania State University, http://www.ento.psuedu/extension/
factsheets/sovbeanAphid.htm

 

Bellman, R. 1957. Dynamic Programming. Princeton NJ: Princeton University Press.

Berg, H. van den, D. Ankasah, A. Muhammad, R. Rusli, H.A. Widayanto, H.B. Wirasto,
and I. Yully. 1997. “Evaluating the role of predation in population fluctuations of

the soybean aphid Aphis glycines in farmers’ field in Indonesia.” Journal of
Applied Ecology 34(4): 971 -984.

Bor, Y.J. 1995. “Optimal pest management and economic threshold.” Agricultural
Systems 49: 113-133.

Calkins, CO. 1983. “Research on exotic pests.” In C.L. Wilson and C.L. Graham, ed.
Exotic Plant Pests and North American Agriculture. New York: Academic Press,
pp. 321-359.

Costamagna, A.C. 2006. “Do varying natural enemy assemblages impact Aphis glycines
population dynamics?” PhD Dissertation, Michigan State University, East
Lansing, MI.

Costamagna, A.C., and DA. Landis. 2006. “Predators exert top-down control of soybean

aphid across a gradient of agricultural management systems.” Ecological
Applications 16(4): 1 61 9-1628.

Costamagna, A.C., D.A. Landis, and CD. DiFonzo. 2007a. “Suppression of soybean
aphid by generalist predators results in a trophic cascade in soybeans.” Ecological
Applications 17(2):441—45 1 .

Costamagna, A.C., W. van der Werf, F .J.J .A. Bianchi, and DA. Landis. 2007b. “An
exponential growth model with decreasing r captures bottom-up effects on the
population grth of Aphis glycines Matsumura (Hemiptera: Aphididae).”
Agricultural and Forest Entomology 9:1—9.

Cousens, R. 1985. “A simple model relating yield loss to weed density.” Annals of
Applied Biology 107: 239-252.

32

DiFonzo, CD, and R. Hines. 2002. “Soybean aphid in Michigan: update from the 2001
season.” Michigan State University Extension Bulletin E-2748, East Lansing, MI.

Fang, H.S., H.H. Nee, and T.G. Chou. 1985. “Comparative ability of seventeen aphid
species to transmit tobacco vein-banding mosaic virus.” Bulletin of Taiwan
Tobacco Research Institute 22: 41 -46.

Fehr, W.R., and CE. Caviness. 1977. “Stages of soybean development.” Iowa State
University Special Report 80: 1-12, Ames, IA.

Fox, T.B. 2002. “Biological control of the soybean aphid, Aphis glycines Matsumura
(Homoptera: Aphididae).” MS Thesis, Michigan State University, East Lansing,
MI.

Fox, T.B., and DA. Landis. 2002. “Impact of habitat management on generalist predators
of the soybean aphid, Aphis glycines Matsumura.” Paper presented at the First
lntemational Symposium on Biological Control of Arthropods, Honolulu H1, 13-
18 January.

Fox, T.B., D.A. Landis, F.F. Cardoso, and CD. DiFonzo. 2004. “Predators suppress
Aphis glycines Matsumura population growth in soybean.” Environmental
Entomology 33(3): 608-618.

Gould, W., J. Pitblado, and W. Sribney. 2006. “Chapter 1: theory and practice.” In
Maximum Likelihood Estimation with Stata, 3rd Edition. College Station TX: Stata
Press.

Hall, DO, and LI. Moffitt. 1985. “Application of the economic threshold for
interseasonal pest control.” Western Journal of A gricultural Economics 10(2):
223-229.

Hall, DC, and RB. Norgaard. 1973. “On the timing and application of pesticides.”
American Journal of Agricultural Economics 55: 198-201.

Harper, J.K., J.W. Mjelde, M.E. Rister, M.O. Way, and BM. Drees. 1994. “Developing
flexible economic thresholds for pest management using dynamic programming.”
Journal of Agricultural and Applied Economics 26(1): 134-147.

He, J .L., E.P. Ma, Y.C. Shen, W.L. Chen, and X.Q. Sun. 1994. “Observations of the
biological characteristics of Harmonia axyridis (Pallas) (Coleoptera:
Coccinellidae).” Journal of the Shanghai Agricultural College 12:1 19—124.

Headley, J .C. 1972. “Defining the economic threshold.” In Pest Control Strategies for the
Future. Washington DC: National Academy of Sciences, pp. 100-108.

33

Heimpel, G.E., D.W. Ragsdale, R.Venette, K.R. Hopper, R.J. O'Neil, C.E. Rutledge, and
Z. Wu. 2004. “Prospects for importation biological control of the soybean aphid:

anticipating potential costs and benefits.” Annals of the Entomological Society of
America 97(2): 249-258.

Hu, Y.S., Z.M. Wang, C.L. Ning, Z.Q. Pi, and G.Q. Gao. 1989. “The functional response
of Harmonia (Leis) axyridis to their prey of Cinara sp.” Natural Enemies of
Insects 11:164—168.

Hukusima, S., and M. Kamei. 1970. “Effects of various species of aphids as food on
development, fecundity and longevity of Harmonia axyridis Pallas (Coleoptera:
Coccinellidae).” Research Bulletin of the Faculty of Agriculture, Gifu University
29:53—66.

Jameson-Jones, S. 2005. “Insect and insect management: soybean aphid.” University of
Minnesota Extension, http://www.soybeans.umn.edu/crop/insects/aphid/aphid.
ht_m. Accessed May 25, 2005.

Kaiser, M.E., T. Noma, M.J. Brewer, K.S. Pike, J.R. Vockeroth, and SD. Gaimari. 2007.
“Hymenopteran parasitoids and dipteran predators found using soybean aphid

after its midwestem United States invasion.” Annals of the Entomological Society
of America 1 00(2): 196-205.

Kamien, M.I,. and N.L. Schwartz. 1981. Dynamic Optimization: The Calculus of

Variations Optimal Control in Economics and Management. New York: North-
Holland.

Koch, R.L. 2003. “The multicolored Asian lady beetle, Harmonia axyridis: a review of its
biology, uses in biological control, and nontarget impacts.” Journal of Insect
Science 3:32-47.

King, R.P., D.W. Lybecker, A. Regmi, and SM. Swinton. 1993. “Bioeconomic models
of crop production systems: design, development, and use.” Review of
Agricultural Economics 15(2):389-401 .

Krishna, V.V., N.G., Byju, and S., Tamizheniyan. 2003. “Integrated pest management in
Indian agriculture: a developing economic perspective.” In E.B. Radcliff and W.D.
Hutchson, ed. [PM World Textbook. St. Paul MN: University of Minnesota.

Landis, D.A., T.B. Fox, and A.C. Costamagna. 2004. “Impact of multicolored Asian
Lady Beetle as a biological control agent.” American Entomologist 50(3):153-154.

Lotka, A.J. 1925. Elements of physical biology. Baltimore MD: Williams & Wilkins Co.

Losey, J.E., and M. Vaughan. 2006. “The economic value of ecological services provided
by insects.” Bioscience 56(4): 331-323.

34

Lou, H.H. 1987. “Functional response of Harmonia axyridis to the density of
Rhopalosiphum prunifoiae.” Natural Enemies of Insects 9:84—87.

Lucas, E, D. Coderre, and C.Vincent. 1997. “Voracity and feeding preferences of two
aphidophagous coccinellids on Aphis citricola and Tetranychus urticae.”
Entomologia Experimentalis et Applicata 85:151—159.

McKeown, CH. 2003. “Quantifying the roles of competition and niche separation in
native and exotic Coccinellids, and the changes in the community in response to
an exotic prey species.” MS Thesis, Michigan State University, East Lansing, MI.

Miranda, M.J., and PL. Fackler. 2002. “CompEcon Toolbox for Matlab.” Matlab library
functions developed to accompany M.J. Miranda and PL. Fackler. 2002. Applied
Computational Economics and Finance. Cambridge MA: MIT Press.
http://www4.ncsu. edu/~_pfackler/compecon/toolbox.html

Moffitt, L.J., D.C. Hall, and CD. Osteen. 1984. “Economic thresholds under uncertainty
with application to corn nematode management.” Southern Journal of
Agricultural Economics 16(2): 1 51-157.

Morgan, P.H., L.P. Mercer, and NW. F lodin. 1975. “General model for nutritional
responses of higher organisms.” Proceedings of the National Academy of Sciences
of the USA 72: 4327-4331.

Mumford, J. D., and G.A. Norton. 1984. “Economics of decision making in pest
management.” Annual Review of Entomology 29: 157-74.

Musser, F.R., J.P. Nyrop, and A.M. Shelton.2006. “Integrating biological and chemical
controls in decision making: European corn borer (Lepidoptera: Crambidae)
control in sweet corn as an example.” Journal of Economic Entomology 99(5):
1538-1549.

National Soybean Research Laboratory (N SRL). 2002. “Illinois soybean pathology and
entomology research: soybean aphid.” University of Illinois NSRL Factsheet #4.
http://www.nsrl.uiuc.edu/

National Agricultural Statistics Service (NASS). 2007. “Agricultural Chemical Usage
Database.” US. Department of Agriculture. httpJ/wwwpestmanagcmcnt.info/
nass/

Naylor, R., and P. Ehrlich. 1997. “Natural pest control services and agriculture.” In G.

Daily, ed. Nature's Services: Societal Dependence on Natural Ecosystems.
Washington DC: Island Press, pp. 151-74.

35

Nielsen, C., and A.E., Hajek. 2005. “Control of invasive soybean aphid, Aphis glycines
(Hemiptera: Aphididae), population by existing natural enemies in New York

State, with emphasis on entomophathogenic fungi.” Environmental Entomology
34(5): 1036-1047.

North Central Pest Management Center (N CPMC). 2005. “National pest alert: soybean
aphid.” US. Department of Agriculture. http://wwwncpmc.org/alerts/soybean

aphidcfm

North Central Soybean Research Program (N CSRP). 2004. “Soybean aphid research
update.” North Central Soybean Research Program. http://ww.planthealth.info

Olson, K., and T. Badibanga. 2005. “A bioeconomic model of the soybean aphid
treatment decision in soybeans.” Paper presented at American Agricultural
Economics Association Annual Meeting, Providence RI, 24-27 July.
http://agecon.lib.umn.edu/cgi-bin/pdf_view.plC’paperid=l 6358&ftype=.pdf

O’Neal, M. 2007. “Practices to conserve and use natural enemies in soybean aphid 1PM.
Managing soybean aphids in 2007: how will biological control contribute?”
Distance education short course, North Central Soybean Research Program,
March 6, 2007.

Pedersen, P. 2004. “Soybean growth and development.” Iowa State University Extension
publication PM 1945, Ames, IA.

Pedigo, L.P., S.H. Hutchins, and LG. Higley. 1986. “Economic injury levels in theory
and practice.” Annual Review of Entomology 31: 341-68.

Ragsdale, D.W., B.P. McComack, R.C. Venette, B.D. Potter, I.V. MacRae, E.W.
Hodgson, M.E. O’Neal, K.D. Johnson, R.J. O’Neil, C.D. DiFonzo, T.E. Hunt, P.A.
Glogoza, and E. M. Cullen. 2007. “Economic threshold for soybean aphid
(Hemiptera: Aphididae).” Journal of Economic Entomology 100(4): 1258-1267.

Risk Avoidance and Mitigation Program project on “Soybean Aphid in the North Central
US: Implementing IPM at the Landscape Scale” (RAMP). 2006. Project Update
Vol. 2-2 (June). http://www.soybeans.umn.edu/cropiinsects/aphid/aphid_ramj;
ht_m

Rossing, W.A.H., R.A. Daamen, and M.J.W. Jansen. 1994. “Uncertainty analysis applied
to supervised control of aphids and brown rust in winter-wheat .1. Quantification
of uncertainty in cost-benefit calculations.” Agricultural Systems 44: 419-448.

Rutledge, C.E., R.J. O'Neil, T.B. Fox, and DA. Landis. 2004. “Soybean aphid predators

and their use in 1PM.” Annals of the Entomological Society of America 97:240-
248.

36

Sharov, AA. 1996, I997, 1999. Quantitative Population Ecology On-line Lectures. Vol.
2006, Virginia Tech University. http://www.gvpsymoth.ento.vt.edu/~sharov/
PopEcol/popecol.html

 

Smith, GS, and D. Pike. 2002. “Soybean pest management strategic plan.” US.
Department of Agriculture North Central Region Pest Management Center and
United Soybean Board.

Song, F., S.M. Swinton, C. DiFonzo, M. O'Neal, and D.W. Ragsdale. 2006. “Profitability
analysis of soybean aphid control treatments in three north-central states.”
Department of Agricultural Economics Staff Paper No. 2006-24, Michigan State

University, East Lansing, MI. http://ageconiibumn.edu/cgibin/pdf_view.pl?
paperid=23574&ftvpe =gpdf

Stevenson, W.R., and CR. Grau. 2003. “Virus resistance: a possible solution to snap
bean loss.” Paper presented at Wisconsin Fertilizer, Aglime, and Pest
Management Conference, Madison WI. http://www.soils.wisc.edu/nextension/
F APM/ fertaglime02.htm

 

Swinton, S.M., and CR Lyford. 1996. “A test for choice between hyperbolic and
sigmoidal models of crop yield response to weed density.” Journal of Agricultural,
Biological, and Environmental Statistics 1(1): 97-106.

Swinton, S.M., J. Stems, K. Renner, and J. Kells. 1994. “Estimating weed-crop
interference parameters for weed management models.” Michigan Agricultural
Experiment Station Research Report 538, East Lansing, MI.

Tang, 8., Y. Xiao, L. Chen, and R.A. Cheke. 2005. “Integrated pest management models
and their dynamic behavior.” Bulletin of Mathematical Biology 67: 115-135.

Thomas, MB. 1999. “Ecological approaches and the development of ‘truly integrated’
pest management.” Proceedings of the National Academy of Sciences of the USA
96(May): 5944-5951 .

Thompson, A., and T. German. 2003. “Soybean aphid and virus incidence in snap beans.”
Paper presented at Wisconsin Fertilizer, Aglime, and Pest Management
Conference, Madison, WI. http://www.soils.wisc.edu/nextension/FAPM/
fertaglimeO2.htm

 

Volterra, V. 1926. “Variazioni e fluttuazioni del numero d'individui in specie animali
conviventi.” Mem. R. Accad. Naz. dei Lincei. Ser. VI, 2:31-113.

Williams, I.S., W. van der Werf, A.M. Dewar, and A.F.G. Dixon. 1999. “Factors

affecting the relative abundance of two coexisting aphid species on sugar beet.”
Agricultural and Forest Entomology l: 1 19-125.

37

Young, D.L., and H.H. Haantuba. 1998. “An economic threshold for tick control
considering multiple damages and probability-based damage functions.” Journal
of Agricultural and Resource Economics 23(2): 483-493.

38

Table 1.1: Parameters for the SBA population model
Value of parameters

rmw, (Initial infestation: June 23, 2005)an 0.40 :l: 0.03
Cb 0.02 :t 0.001
rm_adj,,s,ed (Soybean plants reach R1: July 5, 2005) 0.28
fig] 5.29
ngz 5.15
ng3 2.35
ng., I. I 3

 

“’1’ Parameters (mean :t SE) estimated by Costamagna et al. (2007b).

39

Table 1.2: Parameters for the natural enemy population model

 

Plant growth stage

 

 

R1 R2 R3
Net decline rate of NE (d,) -O.59 -0.90*** -2.13**
(0.38) (0.28) (0.86)
Reproduction rate of NE per prey encountered (b,) 0.002 -0.0001 0.002“
(0.003) (0.0005) (0.001)
Number of Observations 28 28 30
R2 0.31 0.55 0.51

 

Robust standard errors in parentheses

* Significant at 90%; ** significant at 95%; *** significant at 99%.

Data: Kellogg Biological Station, Hickory Comers, Michigan, 2003 and 2005; provided
by Alejandro Costamagna, Department of Entomology, Michigan State University at the
time of the data collection.

40

Table 1.3: Non-linear least squares estimation results from the reformulated
restricted Cousens rectangular hyperbolic model

 

 

R1 R2 R3 R4 R5
E,[y] 37.22***
(1.95)
27, 0.0002 -0.001** 0.0003* 0.0001* 0.0002
(0.001) (0.001) (0.0002) (0.00004) (0.001)
6, 1 1 1 1 1
Obs 43 43 43 43 43
Adj. R2 0.92 0.93 0.93 0.94 0.94

 

Standard errors in parentheses.

* Significant at 90%; ** significant at 95%; *** significant at 99%.

Data: multiple sites in Michigan, 2005; provided by Christine DiFonzo, Department of
Entomology, Michigan State University

41

Table 1.4: N EET illustration: population densities of SBA and natural enemies,
harvest yields, and optimal spray decisions chosen for two initial values of S, (40
and 140 aphids/plant) given four values of NE 1 (0-4 NE/plant) (Daily predation
rate=35 aphids/NE, initial maximum yield potential E Ayl=60 bu/ac)

 

 

 

Pest density (aphids/plant) Return OVCF
NE density at variable costs
R1 yharvest of control Optimal control
(NE/plant) R1 R2 R3 R4 R5 (bu/ac) ($/ac) path
0 40 2.5 15.5 51.9 110.6 59.4 398 Spray in R1
1 40 1.5 5.5 18.2 38.8 59.8 401 Spray in R1
2 40 41.6 0 0 0 60 415 No Spray
3 40 0 0 0 0 60 415 No Spray
4 40 0 0 O 0 60 415 No Spray
0 140 8.8 0.5 1.8 3.9 60 390 Spray in R1 & R2
1 140 7.8 44.2 147.8 315.3 58.4 391 Spray in R1
2 140 6.7 34.2 114.1 243.5 58.7 394 Spray in R1
3 140 5.7 24.3 80.4 171.6 59.1 396 Spray in R1
4 140 4.6 14.3 46.7 99.7 59.5 399 Spray in R1

 

42

Plant R1 R2 R3 R4 R5 Harvest

 

 

 

stages (t=1) (i=2) (t=3) (t=4) (i=5) (7+1)
Natural
enemies NE1T—’§E2r\—-’ §E3r\-\——>‘NE4\_\
' ’I . II I I, .\

Control Spray? '\,” Spray? X" Spray? 1‘," Spray? '\.
decisions C I \.\[: I \.\C I \.\- \\

x 'x x 'x x 'x '24
Yield E A E """"""" _.A E ' A E A E A
potential ’M—’ 234—» 3M —-> 4l.VI—-* 5M ——9 ynarvest

..... , Reproduction of NE due to SBA consumption
—--.+ Predation of NE on SBA
................ , Yield damage by SBA
_p Mortality by insecticides
Figure 1.1: Illustration of the advancement of biological dynamics within season

43

R1 R2 R3 R4 R5

W W
j/

 

 

 

25000

 

20000

1

10000 I;

5000 If
04M.

7/5/05 7/12/05 7/19/05 7/26/05 8/2/05 8/9/05 8/16/05

 

Aphid density

 

 

 

 

 

 

 

 

 

liliirtrrrfirT r1

+ Model predicted daily population + Mean population of stage

Figure 1.2: Simulated predation-free daily SBA density (aphids/plant) from
Costamagna et al. (2007b) model

44

 

Year=2003

 

 

I Harmonia axyridis larvae

I Harmonia axyridis adult

I: Coleomegilla rmculata adult

1: Coccinella septerrpunctata larvae .

I Coccinella septerrpunctata adult ‘

 

 

 

Year=2005

51%

 

 

 

 

I Harmonia axyridis adult

I Harmonia axyridis larvae

D Coccinella septen'punctata adult
I: Coccinella septempunctata larvae
I Cycloneda rrunda adult

I cycloneda rmnda larvae

I Hippodam'a convergens adult

I: Coleomegilla rmculata adult

 

 

Figure 1.3: Composition of ladybeetle species included to quantify natural enemy
presence (Data were provided by Alejandro Costamagna, Department of
Entomology, Michigan State University, at the time the data were collected)

45

 

 

Aphid density

 

R4 R5

R1 R2 R3
+ KBS data 2003 (S1=50,NE1=1.5) +Model prediction (S1=50,NE1=1.5)
+ KBS data 2005 (S1=70,NE1=2.5) -—)lt— Model prediction (S1=70,NE1=2.5)

Figure 1.4: Comparison of model prediction of untreated SBA densities during R1
to R5 with field data for 2003 and 2005, KBS, Michigan. (Field data were provided
by Alejandro Costamagna, Department of Entomology, Michigan State University,

at the time the data were collected.)

46

Starting Control Yields Returns over variable

 

 

 

 

 

 

 

 

 

 

 

 

 

 

values paths (CP) resulted costs of control (NR)
CPI (Vharvest)ijk iCPI NR1
CPZ (,VharvesOijk iCPZ NR2
Pest density (S 1), + .
NE density (NE 1)‘ —- . =* a . Optimal control path=
Max. yield ’ , ' , ary maXINerNRre}
P0terltial (E1 [.ka
CPI” O’harvest)ijk ICPle NR1“

 

 

 

 

 

Figure 1.5: Illustration of how optimal control path is reached for a given
combination of initial values of pest density (51),, natural enemy density (NE 1),, and
maximum yield potential (E 1M),

47

Essay 2:
Optimal Control of Soybean Aphid in the Presence of Natural Enemies

2.1 Introduction

Natural enemies provide an important ecosystem service of pest population suppression
that maintains the stability of agricultural systems and potentially mitigates producers’
pest control costs (Naylor and Ehrlich, 1997; Losey and Vaughan, 2006). While the
various approaches to biological control, including importation (or classical biological
control), augmentation and conservation, all directly and purposefully use the natural
control services (Barbosa and Braxton, 1993), integrating available natural control
services into the decision-making of chemical control offers an important approach to
improving the economic efficiency of insecticide use with potentially socially desirable
outcomes. Focusing on the management of soybean aphid (Aphis glycines, Matsumura)
(SBA), a new pest of soybeans in the North Central region of the United States, this study
assesses how predation by natural enemies of SBA (mainly ladybeetles, Coccinellidae)
contributes to optimal insecticide strategies. In the process, it also provides a lower bound
estimate of the value of natural pest control services.

Current chemical pest control practices typically do not take into account the
presence of natural enemies. Untimely application of broad-spectrum insecticides can
decimate natural enemy populations, potentially exacerbating existing pest problems or
even triggering the emergence of new pests (Calkins, 1983; Naylor and Ehrlich, I997;
Krishna et al., 2003). Such unintended effects imply inefficiencies in insecticide use if

unaccounted for in the treatment decision—an “opportunity cost” to producers in terms of

48

foregone natural control services that would have been provided by existing natural
enemies.

Economic threshold (ET) refers to the optimal (net-retum-maximizing) pest
population density where the marginal value product of damage control equals the
marginal cost of control (Headley, 1972). The current ET concept is generally based on
pest abundance and does not address natural enemy mortality or the impact of natural
enemies on pest survival (Musser et al., 2006). Zhang (Essay 1) develops an intra-
seasonal, dynamic bioeconomic optimization model that explicitly includes the predation
effect of natural enemies on the target pest and demonstrates that the incorporation of
natural pest control services into pest management threshold decision rules can
potentially lead to reduction in insecticide use. This study applies the bioeconomic
optimization model developed in Zhang (Essay 1) to i) identify optimal insecticide
strategies for the control of SBA, taking into account the presence of natural enemies, and
ii) provide preliminary assessment of the economic value of the SBA biological control
services to private producers. The results suggest optimal SBA density as observed upon
the initial decision point for pest control over the course of pest management, at which
the prescribed control strategy is optimal despite the opportunity cost of natural enemy
mortality due to insecticides. The estimated values are conservative, because they take
into account only farmers’ private profitability benefits from optimizing the number and
timing of broad-spectrum insecticide applications in the presence of natural enemies. A
full accounting of the natural pest control services would also include potential social and

environmental benefits (such as averted human health risks and environmental pollution

49

due to pesticides), which are likely to justify further reduced levels of insecticide use and
higher economic value of natural pest control services.

There have been two general types of valuation studies that assess the benefits of
natural control services: 1) ex post impact assessment of classical biological control
projects that look at the economic benefit of artificial introduction or massive release of
natural enemies (Hill and Greathead, 2000), and ii) calculation of the aggregate annual
monetary value of averted crop losses as a result of pest population suppression by extant
natural enemies (e.g., Losey and Vaughan, 2006; Pimentel et al., 1997). This study
focuses on the natural pest control services supplied by existing natural enemies. To
calculate the aggregate annual monetary value of natural pest control services, existing
studies typically start by estimating the total cost of pest damage resulted from all pest
control mechanisms and then attribute a fraction of the total pest control benefit to natural
enemies. For instance, Pimentel et al. (1997) estimated that natural enemies provide
approximately $100 billion worth of pest control worldwide per year (about 60% of $156
billion total averted pest control cost a year), whereas Losey and Vaughan (2006)
estimated the value of natural control to be $4.5 billion annually for the US. While these
aggregate values provide snapshots on the possible magnitude of the benefit from natural
enemies of crop pests humans enjoy, they ignore local context (e.g., pest species, pest
pressure, existing natural enemy level, the value of protected yield, cost, effectiveness,
and availability of alternative pest control mechanisms), and thus are rather
uninforrnative for the producer-level management of this ecosystem service.

Natural pest control services as regulating ecosystem services (MA, 2005) can be

valued indirectly via their contribution as inputs to the biological production of marketed

50

products. Thus, their partial economic value can be inferred from the price of marketed
products (Swinton and Zhang, 2005). In this study, model results will compare producer
returns over variable costs of insecticide management with and without accounting for
the presence of natural enemies. The results will be used to make a preliminary estimate
of the incremental return over variable costs of control resulting from an additional
natural enemy in the system given a set of economic and biological conditions.
Following this introduction section, we provide background information on the
SBA problem and the role of natural enemies in its regulation in section 2.2. We then
briefly introduce the bioeconomic optimization model adopted in section 2.3. In section
2.4, we present numerical results from the dynamic optimization analysis for single
season SBA management and the estimated economic value of natural enemies that
attack SBA. Section 2.5 reports findings from a sensitivity analysis of key parameters.
Finally, we highlight main findings, identify applications for the effects of natural enemy

populations on optimal SBA control, and suggest future research directions (section 2.6).

2.2 Soybean aphid and its natural enemies

Soybean aphid is an invasive species that was first discovered in the North Central region
of the United States in 2000. Within four years, it had spread to 21 states and south-
central Canada (Landis et al., 2004). Not only is SBA capable of causing extensive
damage to soybean yield with documented yield loss of up to 40% (DiFonzo and Hines,
2002), SBA outbreaks are also correlated with dramatic increases in virus incidence in
vegetable crops (Alleman et al., 2002; Stevenson and Grau, 2003; Thompson and

German, 2003; Fang et al., 1985; RAMP, 2006). Since its invasion, SBA has prompted

51

extensive spray of soybean acreage, which had previously required negligible insecticide
use in the region (Smith and Pike, 2002). For example, 42% of soybean acreage in
Michigan and 30% in Minnesota were sprayed during the 2005 season, compared with
less than 1% before SBA arrived in 1999 in North Central region states for which data are
available (NASS, 2007).

Existing natural enemy communities play a key role in suppressing SBA
populations (Fox et al., 2004; Aponte and Calvin, 2004; Rutledge et al., 2004; Landis et
al., 2004; Costamagna and Landis, 2006; Berg, 1997). Natural enemies of SBA include
22 predator species (Rutledge et al., 2004), 6 parasitoid species (Kaiser et al., 2007), and
several species of fungi that cause disease in aphids (Nielsen and Hajek, 2005). In
particular, generalist predators (mainly ladybeetles, Coccinellidae) provide strong, season-
long suppression, protecting soybean biomass and yield from SBA damage (Costamagna
et al., 2007). However, most insect natural enemies are susceptible to the major
insecticides used to treat SBA1 . Evidence from Iowa indicates that insecticides applied in
early season can actually result in greater SBA population later (O’Neal, 2007),
undermining the cost-effectiveness of insecticide investment. Although general
recommendations stress the need for assessing the field situation with respect to natural
enemies before spraying (e.g., Smith and Pike, 2002; NSRL, 2002; NCPMC, 2005), the
current extension treatment threshold recommendation relies solely on aphid density
observation. However, it was developed from field data where natural enemies were

probably present, so their effect is likely to be implicit in the threshold recommendation.

 

' Christine DiFonzo, Department of Entomology, Michigan State University, personal
communications, October 4, 2005 and March 2, 2006.

52

Up to now, producers have not been offered decision rule that explicitly accounts for the

pest regulation services supplied by ambient natural enemies.

2.3 Bioeconomic optimization model

Using field trail data from Michigan collected during 2003 and 2005 under a multi-state
soybean aphid USDA Risk Assessment and Mitigation Program (RAMP) project on
“Soybean Aphid in the North Central US: Implementing [PM at the Landscape Scale”,
Zhang (Essay 1) develops an intra-seasonal, dynamic bioeconomic optimization model
for SBA management over five time periods that correspond to the five reproductive
stages of soybean plant growth, R1 through R5, during which soybeans are most
susceptible to SBA damage (Jameson-Jones, 2005). The model assumes that a producer
chooses the optimal control action (spray or no spray) at each decision point (t) to
maximize end-of-season return over variable costs of control, subject to biological
constraints describing the dynamics of pest population (5,), natural enemy population
(NE,), and expected crop yield potential (E,[y]). Denoted by J, the objective function over

the finite time horizon covering stages R1 to R5 can be written as:

T=5
J= M455 [p-yh—thxm (1)
{xt}t=-I [=1
subject to
. 77t'St
E =E - 1————— 2
1) t+lIJ’I ,[y] ( 1+771'Sr/9z) ( )

and E][y] = y'h,E6[y] = yh, t=l, 2, 3, 4, 5

10S”, =(1+ng.)-(S.—ks,-x.-S.>—pr.(Na-km-x.-NE.>.2=I.2. 3.4 (3)

53

iii) NE,+1 = (1 +d,)-(NE, —kNE,, ~x, - NE,)+b, (3, —k5,, -x, .s,)-(NE, —kNE,, -x, ~NE,)

i=1, 2, 32 (4)
iv) S1, NE], and Elfy] are given
where
p = output price
x, = binary choice for control. x,=l for spray at fixed label-recommended rates at stage t,
and x,=0 for no spray
c(x,) = control cost at stage t, including the cost of pest scouting to provide the basis for
control decisions
S, = population density of SBA per plant at stage t
NE, = population density of natural enemies per plant at stage t
k5,, = mortality rate of SBA from insecticide application
km, = mortality rate of natural enemies from insecticide application
d, = natural net decline rate natural enemies would suffer in the absence of prey
b, = the reproduction rate of natural enemies per prey encountered
ng, = net growth rate of SBA population in the absence of “outside” regulation
pr, = predation rate per natural enemy unit per stage
E,[y] = expected yield potential at stage t
n, = proportion of yield lost per unit of pest population
6, = maximum proportional yield loss to pest damage (056, El)

y, = pest-free yield potential or average historical yield upon which the season’s first

prediction is based

 

2 The model predicts population of natural enemies up to stage R4, which in turn affects SBA
population in stage R5, the last stage when SBA can cause yield damage.

54

y), = actual yield at harvest (assumed to be equal to yield potential evaluated at stage
T+ 1=6)

Table 2.1 reports the values of parameters from Zhang (Essay 1)’s model. A few
key points deserve note. First, the model assumes that no more than one spray may occur
in each stage and that the predicted yield upon stage R5 is carried through to harvest so
that SBA control is only meaningful during stages R1 to R4. Second, the quantification of
the natural enemy presence is focused on major generalist predator species of the
ladybeetle family, due to their high abundance in both number and overall suppression
effectiveness (Costamagna, 2006). Populations of major ladybeetle species are
aggregated, including Harmonia axyridis (multi-colored Asian ladybeetle) adult and larva,
Coccinella septempunctata adult and larva, Coleomegilla maculata adult, C ycloneda
munda adult, Cycloneda munda larva, and Hippodamia convergens adult. Third, based on
findings from the biological literature and field observation of species composition, the
model proposes an approximate range for the weighted average predation rate of SBA by
ladybeetles: 17 to 52 aphids eaten per ladybeetle per day, which gives a mean
consumption rate of 35 aphids/day per ladybeetle. The per stage predation rate pr, is then
computed by multiplying daily predation rate by the number of days in a given stage
(Table 2.1). Fourth, for price and cost parameters, we use a long-term soybean trend price
of $6.9/bu and a treatment cost of $12.2/ac for the RAMP Best Management Practice
treatment using pesticide Lambda-cyhalothrin (Warrior with Zeon Technology®) at 3.2
oz/ac (Song etal., 2006). A break-down of the cost includes $7/ac insecticide cost, $2/ac

for scouting, and approximately $3.2/ac for spraying (Song et al., 2006). Finally, it is

55

assumed that insecticide will kill 99% of both SBA and natural enemies at each
application during the season.

Estimated values of parameters in Zhang (Essay 1) that are statistically significant
are used directly in the numerical optimization analysis of this study with the exception
of ”2, the proportion of yield lost per unit of pest population in stage R2, which is
estimated to be negative, suggesting a “compensation” yield response relationship
between pest injury and crop yield potential in R2 (Pedigo et al., 1986). While this
estimation is theoretically possible (Pedigo et al., 1986; Tammes, 1961; Fenemore, 1982),
field observations in Michigan do not show evidence of such compensation3. Thus, we
assume that yield potential in stage R2 is not responsive to pest injury (i.e., n2=0) in the
numerical exercise. For parameters that are found insignificant in their respective models,

we use zeros instead of the estimated values in the numerical optimization analysis.

2.4 Numerical analysis

The Optimizing simulation approach

We adopt an optimizing simulation approach to solving the dynamic optimization
problem numerically, within a solution space that is relevant to field observations made
in Michigan soybean fields (see MatLab code in Appendix A). The approach is
essentially an integration of two components: 1) a simulation routine to predict the
economic outcome of each scenario, and ii) a selection routine to choose the control
strategy (i.e., control path) that yields the best economic outcome. The algorithm of the

approach is analogous to that of “DDPSOLVE”, a dynamic programming computer

 

3 Christine DiFonzo, Department of Entomology, Michigan State University, personal
communication, July 6, 2007.

56

program developed by Miranda and F ackler (2002) but with two major improvements: i)
it allows the biological transition equations to contain stage-specific parameters, and ii) it
significantly reduces computational expenses and thus enables us to use smaller and more
accurate value intervals and wider ranges of possible initial values for the biological state
variables. Specifically, the optimization is carried out as following:

0 Define space matrices for initial values of state variables S, and NE,: i) 31 possible
values for S1 (0:5: I 50) (meaning a range of 0 to 150 aphids on average per plant
with an interval of 5 in R1), and ii) 9 possible values for NE 1 (0:0.5z4). These
ranges are chosen to reflect field observations of population densities of SBA and
natural enemies in stage R1 in field trials in Michigan“.

0 Consider 11 scenarios for maximum (pest-free) yield potential (E1[y]) that are
consistent with common Michigan yield levels (40:2:60) (MSU Field Crops AOE
Team, 2002) and 3 scenarios for daily ladybeetle predation rate (pr,) (minimum,
mean, and maximum of 17, 35, and 52 aphids per ladybeetle per day, respectively)
to account for uncertainties in these parameter values.

0 Specify 16 distinct possible control paths, each representing a unique sequence of
five control choices made over the periods R1-R5 with the optimal control action
in the last period R5 always being “no control” (i.e., x5 =0 known).

For each of the 33 maximum yield potential-predation rate scenarios (3*1 l=33 scenarios),
we compare the predicted returns over variable costs of control from the 16 control paths
for each of the 279 combinations of initial values of population densities of SBA and

natural enemies (31*9=279). The total number of simulations to run therefore amounts to

 

4 Michigan field data for 2003 and 2005 provided by Christine DiFonzo and Alejandro
Costamagna, Department of Entomology, Michigan State University.

57

147,312 (33*279*l6=147,312). In each simulation, the control path that yields the
highest value of return over variable costs is designated the optimal control path.

By defining relevant ranges for the initial values of population densities of SBA
and natural enemies and scenarios for maximum yield potential and predation rate, we
delimit a relevant sub-space within the full optimization solution space, effectively
reducing the computational expense. Certainly, the smaller the intervals are, the more
accurate are the predictions. The analysis covers sufficiently wide ranges of relevant

initial values of biological state variables with reasonably small intervals.

Numerical results

For this deterministic, discrete and finite time horizon problem, the dynamic optimization
model predicts the sequence of control actions that would be optimal for the entire season
given initial values of the population densities of SBA and its natural enemies. Because
the model is deterministic, its results follow from field scouting information once in the
initial period of stage R1.

To illustrate key results fiom the optimization analysis, we plot predicted optimal
control paths against values of population densities of SBA (SI) and natural enemies (NE 1)
in stage R1 for given daily predation rates and initial yield potentials in Figures 2.1-2.3.
Figures 2.1a, 2.2a, and 2.3a correspond to results associated with a lower initial yield
potential of 40 bu/ac, whereas Figures 2. l b, 2.2b, and 2.3b correspond to results for a
higher initial yield potential of 60 bu/ac. The figures are not normal phase planes in the
sense that the x-axis represents all possible values of S], y-axis represents all possible

values of NE 1, and each x-y coordinate in the optimal control space corresponds to an

58

optimal control path (not just a control action at a decision point) determinedjointly by S,
and NE 1. For instance, at a daily predation rate of 3S aphids/NE and an initial yield
potential (ED/1]) of 60 bu/ac, the optimal control path is to control in both R1 and R2 and
do nothing from R3 to R5 when S1=125 aphids/plant and NE1=0/plant (Figure 2.1b).

We organize our presentation of the key results in the following five aspects:

I ) Optimal control paths
A total of three distinct optimal control paths emerge given the parameters used: (i) no
control in all stages (“No spray”), (ii) control in stage R1 only (“Spray RI”), and iii)
control in both R1 and R2 (“Spray R1+R2”). Note that since we have incorporated the
population dynamics of natural enemies, any control action prescribed by the model
remains optimal in spite of the opportunity cost of injury to natural enemies. While it is
obvious that no insecticide spray is necessary during the last stage (R5), stages R3 and R4
are found to be too late to take any control action in any circumstances with respect to the
values of S1 and NE 1. “No spray” and “Spray RI” strategies prevail in all circumstances,
whereas “Spray R1+R2” has to be justified by relatively heavy infestation, low natural
enemy population (or low predation rate), and high initial yield potential. Figures 2.1-2.3
show that, in the absence of natural suppression (i.e., NE 1=0), “Spray R1+R2” is never
optimal when Ejyl] is as low as 40 bu/ac but becomes desirable in more heavily infested
situations (512125) at a higher initial yield potential such as 60 bu/ac.

Our results show that for a pest that is capable of rapid reproduction like SBA,
early treatment actions are preferred over late actions, which is consistent with the current

extension recommendation for managing SBA (NCPMC, 2005). The simulation model

59

finds that spraying twice in both R1 and R2 is the optimal control path for initial pest
density exceeding 120 aphids/plant with no natural enemies present, whereas farmers and
field entomologists wait longer between sprays. As Zhang (Essay 1) points out, the actual
presence of natural enemies in the field, which reduces the need for insecticide control,
along with two limitations of the model (i.e., omitting the residual effect of insecticides

and the emigration of winged aphids) may have potentially contributed to the result.

2) The eflect of natural enemies on optimal control threshold
In the absence of natural enemies as shown in the bottom rows of Figures 2.1-2.3,
chemical control is cost-effective for initial pest density as low as 5 aphids/plant. This
zero-natural enemy scenario exemplifies the assumption by many soybean farmers who
ignore natural control services. Empirical observation shows that producers often do not
hesitate to spray the fields, because of the relatively low cost of spray. The 3 aphids/plant
action threshold suggested by Olson and Badibanga (2005) (the pest density at which
action should be initiated to ensure spray is carried out by the 7th day from the
observation of the density) is largely consistent with our result of treating SBA at 5
aphids/plant threshold only if the population of natural enemies is zeros. As Figure 2.1
shows, with just one natural enemy per plant, the optimal threshold is sharply increased
to 30 aphids/plant—IO times of the level suggested by Olson and Badibanga (2005).
Spraying a second time in R2 after the first treatment (i.e., optimal control path

“Spray R1+R2”) would not be needed except when high pest pressure accompanies little

 

5 Among the four potential SBA treatment thresholds (3, 100, 250, and 500 aphids per plant)
included in Olson and Badibanga (2005)’s analysis, 3 aphids/plant is the lowest threshold
considered. It is expected that their model may suggest even smaller threshold if such scenario is
included.

60

presence of natural enemies. For instance, at daily predation rate of 35 aphids/NE and
initial yield potential of 60 bu/ac, the fields need to be sprayed twice in both R1 and R2
stages when initial infestation level is 125 aphids/plant and when there are no natural
enemies (Figure 2.1b). The same SBA population density only needs one spray in R1 if
natural enemy is just l/plant (Figure 2.1b). Although this finding is specific to the current
model parameters, it demonstrates that wise insecticide strategy can conserve natural
enemies, allowing them continue suppressing pest populations and avoiding excessive

use of insecticides.

3) Eflect of variation in predation rate

Predation rate plays an important role in determining the optimal control decisions. The
effect is best illustrated by the shrinkage of the region for optimal control path “Spray
R1” (or equivalently, the expansion of the region for “No spray”) in Figures 2.1-2.3 as
the daily predation rate changes from 17 aphids/NE to the mean and maximum levels of
35 and 53 aphids/NE/day, respectively. A higher daily predation rate increases the
threshold for insecticide use, implying that i) the same natural enemy density can now
sustain a higher control threshold, or ii) fewer natural enemies are needed to sustain a
given threshold density. For instance, Figure 2.2a suggests an optimal control threshold
of 15 aphids/plant at NE 1=1/plant when daily predation rate is 17 aphids/NE, whereas the
threshold becomes 30 and 45 aphids/plant for daily predation rate of 35 and 52 aphids/NE,
respectively, holding the same initial yield potential of 40 bu/ac (Figures 2.1a and 2.3a).

Predation rate is not a variable under farmer control. However, populations of species

61

that are particularly effective suppressing SBA may be targeted to improve predation rate

through habitat management that provides compatible conditions favoring certain species.

4) Effect of variation in initial yield potential (or equivalently, historical yield level)
The effect of initial yield potential on the choice of optimal control path is not obvious
for moderately infested fields, i.e., Sl<125 aphids/plant. Provided that on average over
125 aphids per plant are scouted in stage R1, the same population densities of SBA and
natural enemies may require more insecticides being used (i.e., optimal control path
changes from “Spray R1” to “Spray R1+R2”) for fields with high initial yield potentials.
“Spray R1+R2” would never be needed when the initial yield potential is at the low end
of 40 bu/ac, regardless of the daily predation rate (Figures 2.1 to 2.3). The result
conforms to the general expectation that more productive fields justify more insecticide

use than the less productive ones at given output price and control cost.

5) Values of returns to producers over variable costs of control
We plot the values of return over variable costs of control against initial SBA densities
for two levels of initial natural enemy density in Figure 2.4. The initial yield potential is
set at 40 bu/ac and the daily predation rate is 35 aphids/NE. The first curve (from the left)
is associated with NE 1=0/plant, whereas the second one is associated with NE 1=l/plant.
For NE 1=0, the return to producers from optimal SBA management over variable
costs of control is a monotonically decreasing function of initial pest density (Figure 2.4).
Starting at the maximum level of $276/ac when pest density equals zero (S,=0), the

values of return steadily decline to $254/ac at the maximum SBA density level of

62

ISO/plant (corresponding to optimal control paths depicted in Figure 2.1a). For NE ,=1 ,
the predicted values of return show a plateau at the $276/ac level for S, between 0 and 25
aphids/plant, drop to $264/ac at S,=30/plant, and maintain the declining trend throughout
the rest range of S ,. At a daily predation rate of 35 aphids/NE and initial yield potential of
40 bu/ac, as a field becomes more infested, the capability of a given level of natural
enemies to maintain the maximum achievable return of $276/ac declines, although higher
NE, naturally leads to larger return for given initial SBA density as compared to lower
NE ,. At a higher daily predation rate such as 52 aphids/NE, however, an initial density of
4 natural enemies per plant is able to maintain the maximum achievable return ($276/ac),

even in the most SBA infested fields (not shown in the figure).

6) Economic value of natural pest control services

These numerical results can be used to make a preliminary estimate of the value of the
natural pest control ecosystem service. The value is calculated from the increase in return
to producers over variable costs of control as a result of an increased initial population of
natural enemies so the estimate constitutes a lower bound for the total economic value of
this ecosystem service because it omits such benefits as the avoidance of health and
environmental risks from insecticide spraying.

The value is context-dependent, because the marginal value of an additional unit
of natural enemy population not only depends on the predation rate, initial yield potential
and pest population, but also the existing natural enemy population and prices. To
illustrate, we plot in Figure 2.5 values of an initial natural enemy density of l per plant as

compared to the baseline of zero natural enemies per plant for various initial pest

63

densities for an initial yield potential-daily predation rate scenario defined in Figure 2.4.
At a daily predation rate of 35 aphids/NE and initial yield potential of 40 bu/ac, the
presence of one natural enemy per plant in R1 (as compared to none) implies a sequence
of minimum values associated with given initial pest populations: for instance, $12.50/ac
at S,= 5/plant (corresponding to optimal control path changing from “Spray Rl” to “No
spray” in Figure 2.13), and $13.90/ac at S,= 25/plant (corresponding to optimal control
path changing form “Spray Rl” to “No spray” in Figure 2.1a), from where the value
declines as S, increases. That the value at S,= 25/plant is higher than that at S,= 5/plant is
because higher SBA density is capable of causing more yield loss.

Figure 2.5 also indicates that there is always a positive gain in return to producers
(at the minimum $1 .70/ac when S,=150 aphids/plant and initial yield potential is 40 bu/ac)
due to the presence of one natural enemy per plant as compared to the NE ,=0 baseline, so
long as the field is infested with SBA (i.e., S,>0). The minimum gain is lower, at
$0.03/ac when S,=150 aphids/plant, if the initial yield potential is increased from 40
bu/ac to 60 bu/ac (not shown in the figure), implying a relative advantage of using natural
enemies to control pests on less productive land. When existing natural enemies are
already at a relatively high density, such as 3/plant, one more natural enemy does not
convey any economic value unless the field is infested with more than 75 aphids/plant in
R1.

Aggregating these results for the value of natural enemies for the broad region is
difficult. The reason is that we cannot observe the correct area where insecticide
treatment could have been averted because natural enemies adequately suppressed SBA

numbers. The problem is that in the real world we do not observe the counterfactual cases

64

of (3) acres that never reached threshold because of natural enemies, and (b) acres that
were treated but did not need it because natural enemies would have contained SBA

damage.

2.5 Sensitivity analysis

To assess the effect of uncertainty associated with the economic and biological
parameters used in the dynamic optimization analysis, we perform a sensitivity analysis
on selected, key parameters by changing parameters one at a time holding the rest
constant and comparing the results with the baseline which is based on parameters
reported in Table 2.1. For a case in which daily predation rate is 35 aphids/NE and initial
yield potential is 40 bu/ac, a total of 18 scenarios are examined (Table 2.2). Parameters
estimated from field data are increased and/or decreased by one standard deviation,
whereas parameters that are assumed or derived from other studies are increased and/or
decreased by 5%, respectively, except for the two economic parameters, output price and
control cost, whose values are varied by 20% and 50%, respectively". Table 2.2
summarizes the major results from the sensitivity analysis. Specifically, we look at two
aspects of changes from baseline resulted from varying parameters: choice of optimal

control path and values of return over variable costs of control.

1) Choice of optimal control path
Varying the values of most of the parameters does not alter the selection of optimal

control paths in most scenarios with the exception of reducing the mortality rate of SBA

 

6 We also ran scenarios for 5% of change in the values of output price and control cost and found
no impact on the model results when varying control cost and only 5% of gain (or loss) when
price is increased (or decreased) by 5%.

65

to insecticide (k5,) by 5% and varying control cost by 50% (Table 2.2). Lower insecticide
efficacy rate means that SBA population is more likely to rapidly rebound after spraying
so that delaying spray when there is reasonable amount of natural enemies present can
become attractive. As a result, at a daily predation rate of 35 aphids/NE and initial yield
potential of 40 bu/ac, a 5% decrease in kg, leads to the selection of optimal control path
“Spray R2” over “Spray Rl” when low-medium SBA population (30-70 aphids/plant) is
combined with relatively abundant natural enemies (1-2 NE/plant). On the one hand, too
low of a SBA population (below 30 aphids/plant) does notjustify any spray unless no
natural enemies are present. On the other hand, given low-medium SBA population,
“Spray R1+R2” would be preferred over “Spray Rl” if natural enemy population is
relatively low (no greater than 2 NE/plant) or no spray would be needed otherwise (i.e.,
higher than 2 NE/plant). When SBA population is relatively high (between 70 and 110
aphids/plant), however, 5% reduction in kg, results in the choice of “Spray R1+R2” over
“Spray RI”, unless the natural enemy population is high enough to warrant “No spray”.
For SBA population above 110 aphids/plant, spray twice in both R1 and R2 would be
needed, regardless of natural enemy population. The analysis also shows that a 5%
increase in the survival rate of natural enemies is not large enough to induce any change
to the choice of optimal control path, given the daily predation rate and initial yield
potential considered in this case.

Given the low initial yield potential (40 bu/ac) considered in the current analysis,
20% change in soybean price does not have a significant impact on the choice of optimal
control path (Table 2.2). Varying control cost by 50% does result in limited changes from

the baseline. Specifically, increasing control cost by 50% only slightly scales down the

66

incentive for spraying in RI as opposed to “No spray” at medium SBA population,
reconfirming the relative cost-effectiveness of current practice of insecticide application,
especially when natural enemies are less than abundant in the field. This finding is
reinforced by the scenario of reducing control cost by 50%, which calls for more frequent
sprays (i.e., “Spray R1+R2” over “Spray R1”) for relatively high SBA population when

there is limited presence of natural enemies.

2) Values of return over variable costs of control
While varying the output price by 20% does not affect the choice of optimal control path,
output price variation has the greatest impact on producer’s return over variable costs of
control, followed by scenarios reducing the mortality rate of SBA to insecticide by 5%.
Specifically, varying output price by 20% leads to roughly proportional change in the
value of return. Reducing the mortality rate of SBA to insecticide by 5% results in losses
in return ranging from 2 to 5%, with impacts rising with SBA density. Reducing the
mortality rate of natural enemies to insecticide by 5% slightly improves the returns over
variable costs by up to 2.5%. Varying control cost by 50% has disproportionately small
financial effects in terms of change in return over variable costs of control (ranging from
0 to 4%). This result demonstrates again the high payoff to insecticide application even
for land with initial yield potential as low as 40 bu/ac.

In the two price sensitivity scenarios, the impact on model results grows as initial
pest population rises, while the initial natural enemy level tends to muffle the effects. In
the two insect mortality rate scenarios, impact also grows as initial pest population rises

but relatively low (or high) natural enemy populations accompanying a relatively low (or

67

high) SBA population are responsible for greater effects. The remaining sensitivity

analysis scenarios have negligible impacts on returns above central costs.

2.6 Conclusion
The control of pests by their natural enemies represents an important ecosystem service
that has the potential to mitigate pest control costs both to private producers and to
society. This important ecosystem service, as well as the unintended effect of broad-
spectrum insecticides on the populations of natural enemies, however, have not been
included in the existing economic models of optimal pest management (e.g., Talpaz and
Borosh, 1974; Zacharias and Grube, 1986; Harper et al., 1994; Bor, 1995), nor has any
applicable decision guide been offered to crop farmers to conserve and capitalize on the
pest regulation services supplied by ambient natural enemies.

The current North Central states extension recommendation of action threshold of
250 aphids per plant given a 7-day window between the observation of the pest density
and actual insecticide application (Ragsdale et al., 2007) has been introduced as an
Integrated Pest Management alternative to prophylactic SBA control. The
recommendation is based on a static approach that does not account for the dynamic
effects of insecticide application on natural enemies and consequently the population of
the pest, especially when multiple treatments are needed. Moreover, the recommendation
does not provide specific guidance on the timing of applying this threshold nor does it
offer any applicable guide on how to incorporate natural enemies into pest management
decision-making. Olson and Badibanga (2005)’s model implies that even the smallest

population density of SBA can justify insecticide treatment, regardless of aphid growth

68

rate. Their conclusion is only consistent with findings from this study in the absence of
natural enemies.

Using a simulation experiment developed for the soybean aphid and ladybeetle
prey-predator system, this study examines the difference in optimal control actions
chosen with and without the consideration of natural enemies and how that difference is
translated into economic gain. The results highlight the importance of assessing both pest
and natural enemy populations in making pest management decisions and accounting for
the opportunity cost of insecticide collateral damage to natural enemies. However, it is
important to recognize that the current model is limited by some simplifications. For
instance, the absence of the insecticide residual effect and insect migration behavior from
the model can potentially lead to overestimation of the urgency and frequency of sprays,
which has likely contributed to the lower control threshold suggested by the model than
the extension recommendation, regardless of our account of the natural enemy levels.
With the further incorporation of practical issues such as stochastic environmental and
weather factors, time lag needed by farmers to prepare for insecticide application after the
control decision is made, and the development of applicable measures of natural enemy
population density, the current simple framework can potentially be developed into a
decision aid model.

Based on the results from the dynamic optimization analysis, this study provides
preliminary estimates of the economic value of natural pest control ecosystem service in
the management of soybean aphid. These values reflect the economic benefit from an
increase in the natural enemy population as inferred from the output value of the

marketed soybean product, given that control decisions already take into account natural

69

pest control services (i.e., decisions that are optimal in spite of the opportunity cost of
injury to natural enemies by broad-spectrum insecticides). While caution should be paid
to the extrapolation of the estimated values due to their context dependence, they offer
instrumental insights on the magnitude of the economic value of natural enemy
population management to private producers. In the long run, effective agroecosystem
management will demand more of managers than simply to reduce the non-target effect
of pesticides on natural enemies. Habitat management that improves landscape
complexity can potentially benefit natural enemies and in most cases result in enhanced
biological control of pests (Thies and Tschamtke, 1999; Wilby and Thomas, 2002;
Cardinale et al., 2003; Ostman et al., 2003; Thies et al., 2003). Future research should
move beyond insecticide use thresholds to develop landscape-scale guidelines for explicit

management of habitat for the natural enemies of agricultural pests.

70

References

Alleman, R.J., C.R. Grau, and DB. Hogg. 2002. “Soybean aphid host range and virus
transmission efficiency.” Paper presented at Wisconsin Fertilizer, Aglime, and
Pest Management Conference, Madison WI. http://www.soils.wisc.edu/
nextension/FAPM/ fertaglime02.htm

Aponte, W., and D. Calvin. 2004. “Entomological notes: soybean aphid.” Department of
Entomology, Pennsylvania State University. http://www.ento.psu.edu/extension/
factsheets/soybeanAphid.htm

Barbosa, P., and S. Braxton. 1993. “A proposed definition of biological control and its
relationship to related control approaches.” In R.D. Lumsden and J.L. Vaughn, ed.
Pest Management: Biologically Based Technologies(Proceedings of Beltsville
Symposium XVIII, Agricultural Research Services, USDA. Beltsville MD, 2-6 May,
1993). Washington, DC: American Chemical Society.

Berg, H. van den, D. Ankasah, A. Muhammad, R. Rusli, H.A. Widayanto, H.B. Wirasto,
and I. Yully. 1997. “Evaluating the role of predation in population fluctuations of
the soybean aphid Aphis glycines in farmers’ field in Indonesia.” Journal of
Applied Ecology 34(4): 971-984.

Calkins, CO. 1983. “Research on exotic pests.” In C.L. Wilson and C.L. Graham, ed.
Exotic Plant Pests and North American Agriculture. New York: Academic Press,
pp. 321-359.

Cardinale, B.J., C.T. Harvey, K. Gross, A.R. Ives. 2003. “Biodiversity and biocontrol:
emergent impacts of a multi-enemy assemblage on pest suppression and crop
yield in an agroecosystem.” Ecology Letters 6: 857-65.

Costamagna, A.C. 2006. “Do varying natural enemy assemblages impact Aphis glycines
population dynamics?” PhD Dissertation, Michigan State University, East
Lansing, MI.

Costamagna, A.C., and DA. Landis. 2006. “Predators exert top-down control of soybean
aphid across a gradient of agricultural management systems.” Ecological
Applications 16(4): 161 9-1 628.

Costamagna, A.C., D.A. Landis, and CD. DiFonzo. 2007. “Suppression of soybean aphid
by generalist predators results in a trophic cascade in soybeans.” Ecological
Applications 17(2):441—451 .

DiFonzo, CD, and R. Hines. 2002. “Soybean aphid in Michigan: update from the 2001.
season.” Michigan State University Extension Bulletin E-2748, East Lansing, MI.

71

Fang, H.S., H.H. Nee, and T.G. Chou. 1985. “Comparative ability of seventeen aphid
species to transmit tobacco vein-banding mosaic virus.” Bulletin of Taiwan
Tobacco Research Institute 22: 41-46.

F enemore, PG. 1982. Plant Pests and Their Control. Wellington, New Zealand:
Butterworths.

Fox, T.B., D.A. Landis, F .F. Cardoso, and CD. Difonzo. 2004. “Predators Suppress
Aphis glycines Matsumura Population Growth in Soybean.” Environmental
Entomology 33(3): 608-618.

Harper, J.K., J .W. Mjelde, M.E. Rister, M.O. Way, and BM. Drees. 1994. “Developing
flexible economic thresholds for pest management using dynamic programming.”
Journal of Agricultural and Applied Economics 26(1): 134-147.

Headley, J .C. 1972. “Defining the economic threshold.” In Pest Control Strategies for the
Future. Washington DC: National Academy of Sciences, pp. 100-108.

Hill, G., and D. Greathead. 2000. “Economic evaluation in classical biological control.”
In C. Perrings, M.H. Williamson, and S. Dalmazzone, ed. The Economics of
Biological Invasions. Northampton MA: Edward Elgar: pp. 208-226.

Jameson-Jones, S. 2005. “Insect and insect management: soybean aphid.” University of
Minnesota Extension. by;://www.soybeans.umn.edu/crg)/insects/aphid/gajgghid.
ht_m. Accessed May 25, 2005.

Kaiser, M.E., T. Noma, M.J. Brewer, K.S. Pike, J.R. Vockeroth, and SD. Gaimari. 2007.
“Hymenopteran parasitoids and dipteran predators found using soybean aphid
after its midwestem United States invasion.” Annals of the Entomological Society
of America 100(2): 196-205.

Krishna, V.V., N.G., Byju, and S., Tamizheniyan. 2003. “Integrated pest management in
Indian agriculture: a developing economic perspective.” In E.B. Radcliff and W.D.
Hutchson, ed. [PM World Textbook. St. Paul MN: University of Minnesota.

Landis, D.A., T.B. Fox, and A.C. Costamagna. 2004. “Impact of multicolored Asian
Lady Beetle as a biological control agent.” American Entomologist 50(3): 1 53-1 54.

Losey, J.E., and M. Vaughan. 2006. “The economic value of ecological services provided
by insects.” Bioscience 56(4): 331-323.

Millennium Ecosystem Assessment (MA). 2005. Ecosystems and Human Well-being:
Synthesis. Washington, DC: Island Press.

72

Miranda, M.J., and PL. Fackler. 2002. “CompEcon Toolbox for MatLab.” MatLab
library functions developed to accompany M.J. Miranda and PL. F ackler. 2002.
Applied Computational Economics and Finance. Cambridge MA: MIT Press.
httg//www4.ncsu.edu/~pfackler/cormaecon/toolbox.html

 

MSU Field Crops AOE Team. 2002. “Determining Best Management Practices for
control of the soybean aphid in Michigan.” Michigan State University, East
Lansing, MI. http://fieldcropmsu.edu/documents/02039%20Controlling%
2OSoybean%20 aphidpdf

 

Musser, F.R., J .P. Nyrop, and A.M. Shelton.2006. “Integrating biological and chemical
controls in decision making: European corn borer (Lepidoptera: Crambidae)

control in sweet corn as an example.” Journal of Economic Entomology 99(5):
1538-1549.

National Soybean Research Laboratory (N SRL). 2002. “Illinois soybean pathology and
entomology research: soybean aphid.” University of Illinois NSRL Factsheet #4.
http://www.nsrl.uiuc.edu/.

 

National Agricultural Statistics Service (NASS). 2007. “Agricultural Chemical Usage
Database.” US. Department of Agriculture. mzflwwwpestmanagement.info/
nass/

Naylor, R., and P. Ehrlich. 1997. “Natural pest control services and agriculture.” In G.

Daily, ed. Nature ’s Services: Societal Dependence on Natural Ecosystems.
Washington DC: Island Press, pp. 151-74.

Nielsen, C., and A.E., Hajek. 2005. “Control of invasive soybean aphid, Aphis glycines
(Hemiptera: Aphididae), population by existing natural enemies in New York
State, with emphasis on entomophathogenic fungi.” Environmental Entomology
34(5): 1036-1047.

North Central Pest Management Center (N CPMC). 2005. “National pest alert: soybean
aphid.” US. Department of Agriculture. http://www.ncpmc.org/alerts/soybcan

aphidcfm

Olson, K., and T. Badibanga. 2005. “A bioeconomic model of the soybean aphid
treatment decision in soybeans.” Paper presented at American Agricultural
Economics Association Annual Meeting, Providence RI, 24-27 July.
http://agecon.lib.umn.edu/cgi-bin/pdf_view.pl?paperid= l 6358&fivpe=.pdf

O’Neal, M. 2007. “Practices to conserve and use natural enemies in soybean aphid 1PM.
Managing soybean aphids in 2007: how will biological control contribute?”
Distance education short course, North Central Soybean Research Program,
March 6, 2007.

73

Ostman, O., B. Ekbom, and J. Bengtsson. 2003. “Yield increase attributable to aphid
predation by ground-living polyphagous natural enemies in spring barley in
Sweden.” Ecological Economics 45: 149-58.

Pedigo, L.P., S.H. Hutchins, and LG. Higley. 1986. “Economic injury levels in theory
and practice.” Annual Review of Entomology 31: 341-68.

Pimentel, D., C. Wilson, C. McCullum, R. Huang, P. Dwen, J. Flack, Q. Tran, T. Saltman,
and B. Cliff. 1997. “Economic and environmental benefits of biodiversity.”
BioScience 47(1 1): 47-757.

Ragsdale, D.W., B.P. McComack, R.C. Venette, B.D. Potter, I.V. MacRae, E.W.
Hodgson, M.E. O’Neal, K.D. Johnson, R.J. O’Neil, C.D. DiFonzo, T.E. Hunt, P.A.
Glogoza, and E. M. Cullen. 2007. “Economic threshold for soybean aphid
(Hemiptera: Aphididae).” Journal of Economic Entomology 100(4): 1258-1267.

Risk Avoidance and Mitigation Program project on “Soybean Aphid in the North Central
US: Implementing 1PM at the Landscape Scale” (RAMP). 2006. Project Update
Vol. 2-2 (June). http://www.soybeans.umn.edu/crop/insects/aphid/aphid_ramg
ht_m

Rutledge, C.E., R.J. O'Neil, T.B. Fox, and D.A. Landis. 2004. “Soybean aphid predators
and their use in 1PM.” Annals of the Entomological Society of America 97:240-
248.

Smith, GS, and D. Pike. 2002. “Soybean pest management strategic plan.” US.
Department of Agriculture North Central Region Pest Management Center and
United Soybean Board.

Song, F., S.M. Swinton, C. DiFonzo, M. O'Neal, and D.W. Ragsdale. 2006. “Profitability
analysis of soybean aphid control treatments in three north-central states.”
Department of Agricultural Economics Staff Paper No. 2006-24, Michigan State
University, East Lansing, MI. http://agecon.lib.umn.edu/cgibin/pdf_view.pl?
pgperid=23574&ftype =.pdf

Stevenson, W.R., and OR. Grau. 2003. “Virus resistance: a possible solution to snap
bean loss.” Paper presented at Wisconsin Fertilizer, Aglime, and Pest
Management Conference, Madison WI. http://www.soils.wisc.edu/nextension/
FAPM/ fertaglime02.htm

 

Swinton, S.M., and W. Zhang. 2005. “Rethinking ecosystem services from an
intermediate product perspective.” Paper presented at American Agricultural
Economics Association Annual Meeting, Providence RI, 24-27 July.
http://agecon.lib.umn.edu/cgi-bin/pdf_view.pl?_paperid=l 6238&ftype=.pdf

74

Tammes, P.M.L. 1961. “Studies of yield losses. II. Injury as a limiting factor of yield.”
Tijdschr. Plantenziekten 67: 257-63.

Thies, C., and T. Tschamtke. 1999. “Landscape structure and biological control in
agroecosystems.” Science 285(5429): 893-895.

Thies, C., I. Steffan-Dewenter, and T. Tschamtke. 2003. “Effects of landscape context on
herbivory and parasitism at different spatial scales.” Oikos 101: 18-25.

Thomas, MB. 1999. “Ecological approaches and the development of ‘truly integrated’
pest management.” Proceedings of the National Academy of Sciences of the USA
96(May): 5944-5951 .

Thompson, A., and T. German. 2003. “Soybean aphid and virus incidence in snap beans.”
Paper presented at Wisconsin Fertilizer, Aglime, and Pest Management
Conference, Madison, WI. http://www.soils.wisc.edu/nextension/FAPM/
fertaglime02.htm

 

Wilby, A., and MB. Thomas. 2002. “Natural enemy diversity and pest control: patterns
of pest emergence with agricultural intensification.” Ecology Letters 5: 353-60.

Zacharias, TR, and AH. Grube. 1986. “Integrated Pest Management strategies for
approximately optimal control of corn rootworm and soybean cyst nematode.”
American Journal of A gricultural Economics 68(3): 704-715.

Zhang, W. Essay 1. “Bioeconomic modeling for natural enemy-adjusted economic
threshold: an application to soybean aphid.” PhD dissertation, Michigan State
University, East Lansing, MI.

75

Table 2.1: Values of parameters from Zhang (Essay Q’s model

 

 

Parameters R1 R2 R3 R4 R5
Duration of plant growth stage (day) 3 10 9 9 IS
Mortality rate of SBA from insecticides (k5,) 0.99 0.99 0.99 0.99 0.99
Mortality rate of natural enemies from
insecticides (kNm) 0.99 0.99 0.99 0.99 0.99
Natural enemies
Net decline rate of NE (61,) -0.59 -0.90*** -2.13**
Reproduction rate of NE per prey
encountered (b,) 0.002 -0.0001 0002*
Soybean aphid

Net growth rate of SBA population (ng,) 5.29 5.15 2.35 1.13
Predation rate per natural enemy per stage
(Prr)

daily predation rate=l7/NE 51 170 153 153

daily predation rate=35/NE 105 350 315 315

daily predation rate=52/NE 156 520 468 468

Soybean yield
Proportion of yield lost per unit of pest
population (’lt) 0.0002 -0.001** 0.0003* 0.0001* 0.0002
Maximum proportional yield loss to pest
damage (19,) 1 1 1 1 1
Economic parameters

Output price (p) $6.9/bu
Control cost (c(x,)) $12.2/ac

 

* significant at 90%; ** significant at 95%; *** significant at 99%.

Source: Zhang (Essay 1)

76

Table 2.2: Summary of sensitivity analysis results organized by ranges of initial SBA
densities (Initial yield potential=40 bu/ac, daily predation rate=35 aphids/NE)

 

Changs from baseline model results'

 

Returns to producers over variable

 

Scenarios Optimal control paths costs of control
2055,540 40<S,580 80<S ,5] 20 20551540 40<S,58O 80<S,512O
ng, up 5% - - - - - -
"gr down 5% ' ' " ' ' '
"Splray R1+R2" "Spray "Spray
rep aces "Spray R1+R2" R1+R2"
R1"if S,=40, becomes replaces I 2_4% for I 3-5% iii-2:31)"
k5,, down 5% NEFO; "Spray needed "Spray R1" 1 NE for low levels of
R2" replaces when NE, except when ow 1 NE, NE
"Spray RI " if is relatively ifS,=100, I
S,=40, NE,=1 low NE,=4
T 51.5% o
kNEJ down 5% - - - - EC; A175; WEISSE
t73 up I s.d. - - - 151% 151%
773 down I s.d. - - - T 51% 151%
714 up 1 s.d. - - - 151%
774 down 1 s.d. - - - 151%
b3 up 1 s.d. - - - - - -
b3 down 1 s.d. - - - - - -
T 1% for
612 up 1 s.d. - - - - S,=80, -
NE 1 :3
d2 down 1 s.d. - - - - - -
(13 up 1 s.d. - - - - - -
(13 down 1 s.d. - - - - - -
p up 20% - - - T 20-21% T 20-21% T 20-22%
p down 20% - - - I 20-21% I 20-21% I 20-21%
“No spray”
replaces
“Spray R1”
c(x,) up 50% - for medium - 1 0-2% 1 0-2% 1 0-2%
S] and
relatively
“Spray
R1+R2”
replaces
c(x,) down 50% - - ffrp'ay R1 102% 10-2% (0-4%
relatively
high S, and
low NE,

 

6‘ 99

represents change of 0.5% or smaller.

8‘The baseline model is based on parameters reported in Table 2.1, and initial yield potential=40
bu/ac and daily predation rate=35 aphids/NE.

77

0 9009-996 90

O 99.0.... o.

o o o 9

Natural enemies per plant

 

0 10 20 30 40 60 0 100110120130140150

50 70 80 9
Soybean aphids per plant

. No control in all stages a Control only in R1

(3)

o o- o 0.. .00
o 90 o 9.9 -00

o. o o 0.

Natural enemies per plant

 

010 20 30 40

50 60 70 80 90 100110120130140150
Soybean aphids per plant

. No control in all stages 0 Control only in R1 . Control in R1 & R2

(b)
Figure 2.1: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60
bu/ac (b) at the mean daily predation rate of 35 aphids per natural enemy

78

Natural enemies per plant

 

0 10 20 30 40 0 60 70 8O 90 100110120130140150

5
Soybean aphids per plant

. No control in all stages 0 Control only in R1

(8)

Natural enemies per plant

 

010 20 30 40

50 60 70 80 90100
Soybean aphids per plant

. No control in all stages a Control only in R1 . Control in R1 & R2

0))
Figure 2.2: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60
bu/ac (b) at the minimum daily predation rate of 17 aphids per natural enemy

79

000.

.90.

Natural enemies per plant

010 20 30 40

000

-0-

60

O

0

900009

.00.--

o o.

 

50 7O _80 90 100110120130140150
Soybean aphids per plant

. No control in all stages 0 Control only in R1

0000

O.-.

9

Natural enemies per plant

010 20 30 40

O O-
O 90

O

50 60

70 0 90 1
Soybean aphids per plant

9

O

(a)

ooooooooooooooo

O

O

o

 

8 00110120130140150

. No control in all stages 0 Control only in R1 . Control in R1 & R2

0))

Figure 2.3: Optimal control paths for initial yield potentials of 40 bu/ac (a) and 60
bu/ac (b) at the maximum daily predation rate of 52 aphids per natural enemy

80

Predation rate=35 aphids/day; Initial yield potential=40 bu/ac

 

280 4

275 -

 
    

Diffe nce = Value of control

270- provided by 1 NE

Return over control cost ($/ac)

 

 

 

265-
260-
255~
I I I I I I I I I If H fl Th If 7 F
0 10 20 30 40 50 60 70 _80 90 10011012013014015
Soybean aphids per plant

—0— NE1=0 —l— NE1=1

Figure 2.4: Value of producer return at initial yield potential of 40 bu/ac and daily
predation rate of 35 aphids per natural enemy

81

i: [r/TI
10 j
l
l

 

 

 

 

 

$Iac
co

 

.11
:1

0 V I I I I I I I I I

0 10 20 30 40 50 60 7O 8O 90 100110120130140150
Soybean aphids per plant

 

 

 

 

 

 

I I E I I I I I I I T I I I I T I f I

+Change in retum when NE1 increases from 0 to 1/plant

Figure 2.5: Value of one natural enemy per plant in stage R1 at daily predation rate
of 35 aphids per natural enemy and initial yield potential of 40 bu/ac

82

Essay 3:
Spatially Optimal Habitat Management for Enhancing Natural Pest Control
Services

3.1 Introduction

The control of pests by their natural enemies represents an important ecosystem service
that maintains the stability of agroecosystems and has the potential to mitigate pest
control costs both to private producers and to society (N aylor and Ehrlich, 1997; Losey
and Vaughan, 2006). To perform this function effectively, natural enemies depend on
resources such as food for adults, alternative prey or hosts, hibernation site and shelter
from adverse conditions (Landis et al., 2000). These factors can be supplied by crop and
non-crop habitats at spatial scales compatible with the resource requirements and the
dispersal capabilities of insects (Landis et al., 2005). How agricultural ecosystems are
managed at the site scale and the diversity, composition and functioning of the
surrounding landscape can have great influence on the availability of these resources
(Tilman, 1999), underlying the potential role of agricultural land use choices in
enhancing natural pest control services.

Habitat management (HM), a form of conservation biological control, aims to
create a suitable ecological infrastructure within the agricultural landscape to provide
needed habitat resources and functions (Landis et al., 2000). The potential mechanisms of
HM are broadly divided into two categories: manipulation of crop systems (e.g.,
interplanting, cover crop, polyculture and rotation) and establishment of non-crop
habitats (Landis et al., 2005). As the limitations and social costs of chemical control have

been increasingly recognized (Naylor and Ehrlich, 1997), there has been growing interest

83

among ecologists in HM as a potential alternative to achieve sustainable pest
management (Barbosa, 1998). Relatively undisturbed non-crop habitats (NCH) such as
hedgerows and woodlots in agricultural landscapes typically support a higher degree of
functional biodiversity than crop systems (Bianchi et al., 2006) and usually persist at the
same place for a long time so that the occurrence of their resources is more stable and
predictable (Bianchi et al., 2007). Empirical evidence from recent ecological research
shows that pest suppression is positively correlated with the proportion of NCH in the
landscape (Thies and Tschamtke, 1999; Thies et al., 2003). Using a spatially explicit
simulation model, Bianchi and van der Werf (2003) find the shape, area, and
fragmentation of NCH elements can have important effects on the control of aphids by
generalist predator Coccinella septempunctata. In particular, they find that pest control is
achieved the best in landscapes with a substantial area of NCH and where these habitats
are evenly distributed over the landscape. No prior studies, however, have investigated
economically optimal spatial habitat configuration for natural enemies of crop pests. The
question remains whether the “ecologically optimal” choice is the most economically
desirable to private producers, especially when accounting for the increase in production
cost due to farming fragmented fields.

In studying the impacts of specific HM practices in field trials, some
entomologists have gone further to conduct budgetary analyses to assess the economic
impact of field-level HM practices such as the establishment of vegetative strips (Barbosa,
1998). While these empirically-based studies provide useful insights on the economic
feasibility of specific practices, a modeling exercise has the advantage of allowing more

space to explore the economics of spatially optimal management of NCH at larger scales

84

(such as farm and landscape) under various economic conditions and production systems.
Key spatial, ecological, and economic characteristics affect how optimal HM is carried
out on the farm and across the landscape. For instance, spatial distribution pattern
determines how ecological services are dispersed into surrounding crop fields. In addition
to output prices, economic factors such as production costs associated with habitat
establishment also play a role in driving the final outcome with regard to economically
optimal spatial configuration. This study develops a spatial optimization model to explore
spatial manipulation of NCH in a simulated landscape so as to optimize net returns to
fixed factors of production under both i) a conventional farming system (where chemical
pesticides are used to treat pests), and ii) an organic farming system (where chemical
pesticides are not allowed). The results provide insights on the potential economic
incentive (or the lack of it) for private producers to adopt the HM practice of establishing
NCH for natural enemies of crop pests.

Spatial optimization of wildlife habitats has become an important approach in
population management and conservation in the past few decades (Turner et al., 1995). A
body of literature has developed on “reserve site selection” for maximum species
conservation, given constraints on budget or on the number of sties allowed (see review
in Nalle et al., 2004). The approach has relatively few applications in economics, but has
included forestry harvest scheduling (e.g., Hof and Bevers, 1998), land use allocation
among various choices such as agriculture, industry, and recreation (e.g., Aerts et al.,
2005; Seppelt and Voinov, 2002), spatial exploitation of a fishery (e.g., Sanchirico and
Wilen, 2000), and the more recent efforts that combine both economic objectives (e.g.,

production of marketed commodity) and ecological objectives (e.g., species conservation)

85

(e.g., Hof and Joyce, I992; Nalle et al., 2004; Polasky et al., 2005). For instance, Nalle et
al. (2004) examine the joint production of wildlife and timber in a dynamic and spatial
analysis to evaluate land use and land management decisions. Polasky et al. (2005) focus
on species conservation in a working landscape by making spatially optimal land use
choices that serve both biological and economic objectives. However, spatial dimension
has rarely been considered in economic studies of pest management. Brown et al. (2002)
examine a spatially dependent insect-transmitted plant disease and optimize social
welfare over the width and the effectiveness of vegetative barriers. In this study, we
develop a spatial optimization model to explore spatial manipulation of NCH to
maximize private producers’ economic outcome of crop production. Specifically, the
study attempts to address three questions:

i) What is the optimal proportion and spatial configuration of NCH in the landscape?
ii) How do the outcomes differ between conventional and organic farming systems?

iii) What factors determine optimal size and configuration of NCH?

Following this introduction section, we introduce a simple conceptual model to
gain insights on the economic theory guiding the spatially optimal management of NCH
(section 3.2). In section 3.3, we present an illustrative empirical model based on the
natural control of soybean aphid by ladybeetles. The model is comprised of an ecological
module for the distribution of natural pest control services and an economic module for
the optimization of net returns to fixed factors of crop production. We then report and
discuss the results of the numerical analysis (section 3.4), followed by a sensitivity

analysis that addresses parameter uncertainties in section 3.5. We conclude in section 3.6

86

by highlighting main findings, identifying limitations and applications of the model, and

suggesting future research directions.

3.2 Conceptual model

This section uses a simple spatially explicit conceptual model to examine i) some general
economic conditions under which spatial land use pattern optimizes the natural pest
control benefits of NCH over associated variable costs, and ii) how key ecological and
economic factors may affect the economic outcome. In this simple model, NCH acts as
the source origin of natural enemies from which pest regulation services are dispersed
into surrounding crop fields according to a spatial distribution kernel (which can be
imagined as a probability density function in space), resulting in spatially linked crop
yield damage protection at each point in the affected crop fields. Using a grid map of N
by M dimension (i = l, 2, ..., N, and j = 1, 2, ..., M), we define a field that is divided into
N XM homogeneous cells (indexed by (i,/)) that can be either used to grow a crop or set
aside as habitat to provide pest control services (Figure 3.1). Mathematically, we write
the farmer’s problem as one that maximizes total net return (NR) to fixed factors over a
binary choice of land use in each cell (ka):

NMK

Max NR: ZZzy-k-xy, (1)
xijk i j k
where
0 .
l—DI —1+/l VC fk=l
”0k: WI ()1 ( ) I. (2)
0 fik=0

and k indexes land use option (k = l for crop and k = 0 for NCH), x0, = k if cell (i,j) is

assigned to land use k, In}, is net return received from cell (i,j) when land use option k is

87

applied to (ij), p is output price of crop ($/ton), yo denotes maximum (pest-free) yield
potential (ton/cell), I is pest density in the crop fields (pests/plant), D(I) represents the
damage function for the proportion of crop yield lost to pest density 1, and VC denotes the
variable costs of production ($/cell), which is subject to change by the proportion of A, a
coefficient measuring the average change in VC per crop cell due to change in field
configuration caused by the establishment of NCH that sometimes requires adjustments

in machinery fieldwork load (}.=0 if k=l , Vi, j ). By optimizing land use choice for each

individual cell, ka, a spatially linked land use pattern that satisfies optimization criteria of
spatial configuration concerning area, shape, and location of NCH elements (each
element referring to a cluster of spatially adjacent NCH cells) can be obtained for the
landscape. Thus, the total area of NCH or the total number of cells assigned to NCH is

N M H
given by ANCH = zzxijJ<=0 = 2 Ah (where h indexes NCH elements, h=l , 2, ..., H,

i j h

and Ah denotes the area of element h), and the total number of land cells is the sum of

NCH cells and crop cells, Am, = Total area = N - M = Acmp + ANCH
N M

= Zszyk-l + ANCH . Note that although A m, is defined as the area of NCH, it
i 1'

contains spatial information regarding the configuration of the NCH cells (for instance,
location indicated by the value of cell indices i and 1).

In order to show the key relationships analytically, we consider a simple problem
where a farmer chooses the size of an individual NCH element (h=l) such that HM is
economically superior to insecticide-based pest control from the private management

perspective. We use the model to solve for analytical conditions for the optimal area of

88

NCH. Under the pesticide control method, crops are grown in all cells (i.e.,

xij,k=1 =1,Vi, j) and receive pesticide treatment to reduce pest density from 10 by the

proportion of cache", at the expense of c per cell, where cache," denotes the efficacy rate of
insecticide and c is control cost per cell]. The total net return from chemical control

(NRchem) is then derived from aggregating net return from each individual cell ache”, :

NRaem =NM era... =NM-1py°(I—Da.m)-c-VC1 (3)
where Dchem = D[(l — wchemfloj = D0 —ADchem , D0 = D(Io) , and ADC/mm is the decline
in the proportion of yield damage due to chemical control. Defining

7:0 = py°(1— D0)— VC (4)

as the baseline net return per cell evaluated at untreated pest density 10, we rewrite (3) as:
NRchem = NM - no + NM - [pyOADchem — c] (5)

The sign of the second term on the RHS of (5) reveals the condition for a positive gain in

total net return resulted from pesticide control as compared to the no-control baseline, i.e.,

the value of the protected yield is greater than the cost of control ( pyOADchem - c > 0 ).

Under HM, the farmer is assumed to rely on NCH for pest management. For the
ease of exposition, we assume natural pest control services are evenly distributed to each
point within a radius of r, meaning that each cell within the “impact zone” enjoys the
same amount of pest reduction. The total net return under HM (NRNCH) is expressed as
the sum of net retums from NCH cells, crop cells within the impact zone, and crop cells

outside the impact zone:

 

' For an organic farm, cache", =0, c=0.

89

NRNCH = 0 - Am, + IZ-tpy°<1— DNCH)- VC(1+ 4)1+ NIZ-[pyOU - Do) - VC(1+ 4)]
(6)
where DNCH = D[(1— (UNCH )IO] = D0 + ADNCH , IZ denotes the area of the “impact
zone” (i.e., the number of cells within radius r), NIZ (“no-impact zone”) denotes the area
of the crop fields that receives no impact, and ADM.” represents the decline in the
proportion of yield damage due to NCH. Substituting equation (4) into (6) and
rearranging terms, we can rewrite (6) as:
NRNCH = NM-no — ANCH x0 —,1- VC(NM — ANCH)+ IZ - pyOADNCH (7)
The RHS of equation (7) indicates two sources of cost due to designating ANCH cells of
land as habitats: i) forgone income from NCH cells (AMHrtO ), and ii) change in variable
costs of production on all crop cells (zl- VC (NM — AM.” ) ). The last term represents a gain

in the output value of the crop harvested in the impact zone. The distribution of the
benefits and costs of the management approach shows a clear spatial distinction.
Assuming there exists a non-trivial interior solution, the first-order condition (FOC) for

the maximization of equation (7) with respect to A NCH is

 

 

m=A-VC—VC- 8’1 (NM—ANCH)—fl0+pyO-IZ-aiD—&H—
NCH aANCH aANCH (8)
0 BIZ
+Py 'ADNCH ' aANCH =

Rearranging terms of equation (8), we have

py0[IZ'%—DM+ADNCH' aIZ 1:7[0-A'VC'I'VC' all

BANCH aANCH ANCH

 

 

(NM “Awe/1) (9)

Equation (9) renders the classic optimal condition for the choice of land use type that

balances the marginal factor cost (MFC) of setting aside an additional crop cell (the RHS

90

of the equation) with the marginal value product (MVP) of the action in terms of
improved output value due to pest regulation (the LHS of the equation). The MFC

includes the opportunity cost of potential net return from a crop cell (no — xl- VC) as well
as a potential increase in variable costs by the amount of BA/BAMW that applies to all crop

cells.

In addition to condition (9), the following relationship has to hold in order for a
HM approach to be economically preferable over insecticide control:
NRNCH > NRchem. (10)
Substituting equations (3) and (7) into (10), we derive
IZ ' PyoADNCH > ANCH '”0 + 4' VC (NM — ANCH)+ NM '[PyOADchem ‘6] (1 I)
The expression suggests that the size of the NCH element ANCH must be chosen in a way
that the benefit of yield saving collected in the impact zone is greater than the sum of
three terms: i) the opportunity cost of setting aside an area of ANCH for NCH purpose, ii)
the increased production cost due to field fragmentation caused by NCH, and iii) the
output value of the yield saving resulted from pesticide control less the cost of control
aggregated over the entire crop field.

The spatially explicit impacts of ANC,, on ecological factors such as [Z and ADM.”

and economic factor variable costs change (2.) are not easy to show analytically using

mathematical notations. However, generally speaking, 132/ BA m, >0 if longer machinery

field time is needed to farm the fragmented field as a result of changing ANCH. While it is

intuitive that ANCH tends to positively affect 12, its impact on ADM .H is somewhat mixed.

In the current problem where there is only one NCH element and change in Axon only

91

affects the area of the element, BAD,“ /8A <0 is possible if i) a negative scale

N('H
dependence relationship presents between the density of pest control agents and the size
of individual NCH element (Hambaeck and Englund, 2005), so that an increase in the
size of NCH element may actually lead to lower pest control services, and ii) the increase
in the area of impact zone due to change in Ave” is disproportionately higher than the
increase in pest control services available as ANCH increases, so that on average each cell
received less pest reduction impact. In cases where a unit of increase in ANCH is
associated with the establishment of an additional NCH element, it is conceivable that the

new element generates its own impact zone but .12 and ADM.” of existing elements are not

affected so long as there is no overlap in impact zones and each NCH element is an
independent source of ecological benefits. Finally, as more realistic distribution functions
are adopted to describe the dispersal of pest control services into surrounding fields,

ADM.” is expected to change nonlinearly with distance from the source of the services.

While the current model looks at a simple static problem, it is worth noting that
some economic aspects of non-temporary NCH are inherently dynamic. In a soybean-
com rotation, for instance, the opportunity cost of setting aside land to provide pest
control services for soybean carries on into the production of the rotating crop corn,
making NCH more expensive, especially if corn production does not benefit from the

NCH.

3.3 Empirical model
First discovered in 2000, soybean aphid (Aphis glycines, Matsumura) is a new invasive

pest of soybeans in the North Central region of the United States that is capable of

92

causing extensive damage to soybean yield (DiFonzo and Hines, 2002). Existing natural
enemy communities, especially generalist predator ladybeetles (Coccinellidae) play a key
role in suppressing soybean aphid populations (Costamagna et al., 2007a; Fox et al.,
2004; Rutledge et al., 2004) and are believed to have contributed to the observed two-
year cycle of aphid population where aphid outbreaks occur every two yearsz. The
development of insights to enhance and capitalize on the pest control services supplied by
ladybeetles through HM, therefore, is of interest not only to private producers but also to
the general public with respect to protecting a major commodity crop without large scale
spraying of chemical insecticide.

Using the soybean aphid-ladybeetle example, we develop an empirical model that
combines i) an ecological module for calculating the distribution of pest control services
given the distribution of NCH in the landscape and a distribution kernel that represents
the spatial probability distribution of pest control services around a source origin", and ii)
an economic module for evaluating the net return to fixed factors of crop production,
given a land use pattern (see MatLab code in Appendix B). The two models are coupled
with an optimization method that finds the land use patterns that are most economically
desirable among the patterns considered given parameters assumed. By focusing on
selected patterns, we effectively delimit a relevant sub-space within the full optimization
solution space. The approach is chosen over performing a global search over all possible
land use patterns to find an optimal solution to the problem, whose computational cost

can be exceedingly high (Polasky et al., 2005).

 

2 Douglas A. Landis, Department of Entomology, Michigan State University, personal
communication, September 27, 2005.

3 Wopke van der Werf, Department of Plant Sciences, Wageningen University, personal
communications, October 2006 to December 2006. Dr. van der Werf is also a contributor to the
simulation model code.

93

To illustrate our approach we apply the model to a simple agricultural landscape
composed of 1600 ha (4,000 m><4,000 m) square cells or land parcels, arranged in a 800
X 800 grid (n=800) with each cell being 25 m2 in size (Figures 3.2a to 3.20). For
simplicity, we assume that there is no existing natural habitat in the landscape. The
hypothetical landscape is arbitrarily divided into four square, homogenous full-time
soybean-com farms each with the size of 400 ha (or about 988 acres)4, arranged in a 2X2
checkboard (Figures 3.2a to 3.2c). We assume the economic agents are rational and thus
consider only a selected set of options regarding the shape and location of NCH elements.
Specifically, since pest control services are dispersed around a source origin within a
certain range, private producers would choose to place the NCH elements in the center of
the farm so that the farm enjoys as much the services as possibles. For practical
consideration, we eliminate irregularly shaped NCH elements and consider three shape
options: squares, strips, and archipelago. In the square distribution (Figure 3.2a), there is
a square ofs by s NCH cells in the centre of each farm. In the strip configuration (Figure
3.2b), a strip of width w (counted in cells) runs through the axis of each farm. Finally, a
landscape is introduced with random allocation of cells to either NCH (with probability
equal to the proportion of NCH in the landscape, denoted by prop_NCH) or crop (with
probability l-prop_NCH). Figure 3.2c gives a result for prob_NCH = 0.1. The use of
selected configuration options effectively simplifies the optimization problem, making it
possible to focus the optimization on the area of NCH (or prob_NCH) and choice among

three shapes of NCH elements.

 

4 According to a national survey, the typical sizes of small, mid-size, and large commercial farms
in the United States are 160, 605 and 2180 acres, respectively (USDA, 2000).
5 In the current analysis, we don’t consider the spillover of NCH benefits.

94

Ecological module for the distribution of pest control services

Relationships between a parameter or a variable and spatial scale are often called scale
dependencies (Hambaeck and Englund, 2005). Empirical research has shown that animal
densities may both increase and decrease with habitat patch size (Hambaeck and Englund,
2005), a scale dependence effect that may conceivably apply to the relationship between
the pest control impact of insect natural enemies and the size of individual habitat patches
(i.e., NCH elements). The resource concentration hypothesis (Root, 1973) predicts that
specialist herbivores should achieve higher densities in large patches. Hambaeck and
Englund (2005) propose a power relationship to model theoretical scaling relationships
and use the model predictions to explain variability in density-area relations from
published studies on herbivorous insect-dominated systems. However, quantitative
measures of the relationship between insect predator density (and consequently the
services they provide) and habitat size are not available. In the following numerical
analysis, we assume predator density (or the services provided) does not depend on the
size of NCH element (i.e., no scale dependence). We discuss implications of a positive
relationship for pest management in the last section of the paper6.

Assuming there is one unit of the density of pest control services (“impact”) for
each area unit of NCH, the amount of services per NCH cell is proportional to the area of
a cell and the amount of services in an NCH element is proportional to the area of the
element. Specifically,

Services per NCH element = (Density of pest control services) * (Area of NC H element)

 

6 Given the absence of scale dependence and the homogeneous farm assumptions, solving the
landscape problem is essentially the same as solving four individual farm problems and then
aggregating them for the entire landscape. We keep the multiple-farrn landscape model rather
than focusing on farrn-level problem to allow for future exploration of landscape-scale
coordination possibilities.

95

The services stored in each NCH element are dispersed into surrounding crop area
according to a distribution kernel, which describes the probability distribution of landing
locations of services around the source origin in a two-dimensional plane (Skelsey et al.,
2005). The positions x and y are distances from the source, and K(x,y) is the probability
density at location (xy) (Skelsey et al., 2005). We consider 3 options of distribution
kernels (Figures 3.3a to 3.3c): i) vertical cylinder (Figure 3.3a) with a probability density

equal to MIT) within a radius r from the source, and 0 elsewhere

War2 for (Ix2+y2 5r
0 for (Ix2+y2 >r

ii) rotated exponential (Laplace) kernel (Figure 3.3b)

2
K(x.y)=“— _a,.2.,2 (13)

e
27:

K(x,y)= (12)

where a is the slope of the decline of allocated services with distance, and iii) two-
dimensional normal (Gaussian) kernel (Figure 3.3c)

_:2+_yz
1 202
K(x.y)= , e (14)
27r6

 

where 6 represents the standard deviation. The mean dispersal distance in the plane is r

for a cylindrical kernel, 2/01 for a Laplace kernel, and 6H for a Gaussian kernel. The
Laplace kernel has a stronger peak and more rapid decay as compared to the Gaussian
kernel, whereas the cylindrical kernel has a flat top near the center rather than a sharp
peak. The Laplace kernel has been used in the ecological literature to model the dispersal

of ladybeetles (e.g., Bianchi and van der Werf, 2003; Bianchi et al., 2007). The other two

96

kernels are included in order to investigate the sensitivity of model outcomes to
differently shaped kernels.

Allocated actual control impact measured in terms of the percentage of reduction
in pest density per unit area of crop area is proportional to the “impact” per unit area of
NCH and depends on the proportion of NCH in the landscape which corresponds to an
overall pest reduction magnitude across crop fields. We estimate the relationship between
the average percentage of reduction in pest density across crop fields and the proportion
of NCH in the landscape using simulation results from Bianchi and van der Werf (2003)
(Appendix C) for the interaction between aphids in wheat and Coccinella septempunctata,
a major aphid predator in the ladybeetle family that has been identified as a major
contributor to the natural suppression of soybean aphids (McKeown, 2003; Costamagna,
2006) (Figure 3.4)7. Although the scale of the landscape simulated in Bianchi and van der
Werf (2003) is smaller than the one defined in our model, which may potentially lead to
over-estimation of the pest control impact of NCH, their model provides the best
available quantitative information on the relationship between aphid density and the
proportion of NCH in the landscape as a result of C occinella septempunctata predation.
Other potential sources of secondary data, including the empirical studies by Thies and
Tschamtke (I 999) and Thies et al. (2003) are not suitable because they look at the
parasitoid category of natural enemies, which is likely to have different pest-natural
enemy interaction and require different resources from habitats as compared to predators.

Figures 3.5(i)a to 3.5(i)c, 3.5(ii)a to 3.5(ii)c, and 3.5(iii)a to 3.5(iii)c render graphical

 

7 To find values at intermediate points, we use the “interpl” command in MatLab that performs
linear interpolation between data points (The MathWorks Inc., 1994-2007).

97

illustrations of the distribution of pest control services from various shapes of NCH,

given 10% of landscape area devoted to NCH.

Economic module for the evaluation of land use decisions

Practice of pest management varies with farming systems, which has important
implications for the economic performance of HM on private producers. We consider two
types of farming systems, a conventional system and an organic systems. In the baseline,
we assume that the application of chemical insecticides is triggered by the occurrence of
the new soybean pest in a conventional farm, whereas synthetic insecticides are not
allowed in an organic farm so that the pest goes untreated9. Under HM, both farming
systems rely on NCH to control soybean aphid. We define net returns to fixed factors (NR)

for a soybean-com rotation (one crop at a time) as following:

Baseline: NRbase = NRbase__ soy + NRbase_ com (15)
HM: NRNCH = NRNCH _ soy + NRNCH _corn (16)
where

NRbase _soy = [Psoy 'ybase_ soy - VC soy — T C051 sprayI' Areatotal (17)

gives the baseline net return for soybean, which is derived by multiplying the total land
area (represented by total number of cells), Area,,,,,,,, by the net return per cell. p5,,y is the

price of soybean output ($/ton), VC,,,y denotes variable costs of production, and TC ostspmy

 

8 To ensure a healthy system, certified organic farms are often required to include one and
sometimes two other crops rotated with soybean and corn (Delate, 2003). Our loosely defined
organic farm, however, only includes two rotating crops, soybean and com. This simplification
makes direct comparison between conventional and organic systems easier without affecting the
implications we draw from the analysis.

9 Many organic farms use non-synthetic insecticides such as biological insecticides, but usually
on higher value crops than soybean and com.

98

represents the cost of soybean aphid control (T Cost,,,,,,y=Costspmy *Number__of_sprays).
Both VC,,,, and T Costspmy are scaled to a per-cell base ($/cell). The baseline yield

(ton/cell), ybasejoy is described by a Cousens hyperbolic yield function (Cousens, 1985):

 

77 [(1 _ Eflicacy spray )p es’initial I ] (1 8)

ybase_ soy = y 50)“ _ max I — 1 + n[(l - Eflicacyspmy )PeStinitial I / r“

where ysoyJw is the maximum (pest-free) yield potential, Eflicacy,,,,,,y is the efficacy rate
of soybean aphid insecticides, pest,,,,,,,,, is the untreated average pest density, n denotes the
proportion of yield lost per unit of pest population, and ,1 denotes the maximum
proportional yield loss to pest damage (05 ,u 51). Assuming equal efficacy rate across

crop cells, ybase_,0y is a scalar. Similarly, the baseline net return for corn is given by:
N Rbase _corn = Ipcorn 'ybase_ corn " VCcorn] ' Ar eatotal (1 9)

The net return for soybean under HM is:

Areasoy
NRNCH _ soy = E [Hwy 'yNCH _ soy,l — (l + 4): V C soy] (20)
where 2, determined by NCH configuration, measures the average change in variable
costs of production per crop cell due to change in field configuration caused by NCH, and
AreaNCH denotes the area of NCH (represented by the number of NCH cells). The
summation operator is necessary because the amount of pest control services allocated to
each crop cell (and consequently crop yield) is spatially variant rather than uniform

across crop cells as in equation (18). Soybean yield in crop cell 1 (ton/cell), yN(7H_soy.r, thus

is described by the Cousens hyperbolic yield function (Cousens, I985):

_ nrtl—anpestim-aal ) (21)
1 + 77[(1 - at )pestmmar 1/ #

.VNCH_soy,l = J’soy_max [1

99

where a), represents allocated pest control services (the proportion of reduction in pest

density) in crop cell 1. Finally, the net return for corn under HM is given by:
NRNCH _corn = Ipcorn 'ybase_corn — (1 + 2') ° VCcornI ' (Areatotal — AreaNCH) (22)

which indicates that variable costs of corn production, VCcom, are also affected by the
establishment of NCH by a factor of 1+}. because the non-temporary nature of the NCH.
For each cell assigned to NCH that is not available for corn production, there is an
opportunity cost of foregone income.

The above expressions (equations (15)-(22)) apply to both farming systems with
Eflicacyspmy=0 and C ostspmy=0 for the organic system and Efficacyspmpo and C ostspmy>0
for the conventional system.

To assess the land use patterns under HM, we refer to relative economic
performance of HM as compared to the baseline for each farming system. We define the

proportion of change in net return to fixed factors from the baseline (nr) as:

____ NRNCH — NRbase : (NRNCH _soy + NRNCH _corn ) — (NRbase_soy + NRbase _corn)
N Rbase (NRbase _ soy + N Rbase_ corn )

 

nr (23)

Thus, the economic objective of the farmer is to choose the area and shape of NCH to

maximize equation (23).

3.4 Numerical analysis

Parameters

Table 3.1 summarizes parameters used in the numerical analysis along with their sources,
including literature, estimations from field data, estimations from secondary data, and

assumptions. We use the simulation model developed by Costamagna et al. (2007b) to

100

predict three levels of average predation-free soybean aphid population density
(aphids/plant) for the period of soybean plant growth stage R1 (reproductive stage one) to
R5, corresponding to three levels of initial pest density as starting values for running the
simulation model (30, 47 and 73 aphids/plant at the beginning of stage RI) taken from
Michigan field data, assuming stage Rl begins on July 510. We assume the number of
sprays needed is one for low and medium infestation levels (5000 and 8000 aphids/plant
on average during R1 -R5, respectively) and two for high infestation level (12000
aphids/plant). The assumption is made based on results from Zhang (Essay 2), which
suggests that, in the absence of predators, soybeans be sprayed twice for mean aphid
density in stage R1 equal to or greater than 120 per plant, and once otherwise. This study
rounds that value to 100, which corresponds to average density of 12000 aphids/plant for
the period of stage R1 to R5.

To measure how the variable costs of production change as the crop fields are re-
configured to establish NCH, we focus on the change in machinery field time spent on
turning. Turns are an important part of machinery field efficiency with turning time
typically ranging from 12% to 15% of the total field time (Bowers, 1992). Assuming a
width of 5 meters for crop strip (approximately 6 rows or 15 feet wide) and following
operation modes as illustrated in Figures 3.6a to 36¢, we first count the approximate
number of turns needed with and without NCH for all shapes and values of prop_NCH

considered (Appendix D)1 1. We assume that 15% of the machinery field time is spent on

 

1° Data were provided in 2005 and 2006 by Alejandro Costamagna and Christine DiFonzo,
Department of Entomology, Michigan State University.

” With archipelago, land cells are randomly assigned to either crop or NCH so that actual
locations of NCH cells are not predictable given prop_NCH. We therefore assume the NCH cells
are evenly distributed across the landscape and estimate the approximate number of turns that
might be needed to operate on such fields.

101

turning in the baseline (no NCH), based on which any change in the number of turns
made to accommodate NCH can be converted to change in the percentage of machinery
time spent on turning. We then combine production cost data (UIUC, 2003) to estimate
the amount of change in variable costs of production (3.) due to change in machinery field
time for soybean and corn separately under both conventional and organic systems with
cost savings on seed in NCH accounted for. The cost composition varies with types of
farming system and with crop grown: the percentage of machinery cost (including repair,
fuel, and hire) is highest for organic soybean (63%), followed by organic com (40%)
(UIUC, 2003) (Appendix B). As Figures 3.7 and 3.8 show, field re-configuration can
induce both positive and negative changes in the variable costs of production, depending
on the shape and proportion of NCH. The overall magnitude of such changes remains
small for the square and strip shapes (within the range of -4% to +4%), but can be

remarkably high for the archipelago shape.

Numerical results

In the baseline, pesticide control proves to be cost-effective for conventional farms,
saving 95% to 91% of the pest-free level of net return to fixed factors for the soybean-
com rotation. By contrast, organic farms suffer significant loss to the new soybean pest
ranging from 38% to 50% reduction in net returns, depending on the level of pest
infestation that goes without any control as well as the distribution kernels used. As
expected, the organic farms have a much higher stake than the conventional farms in
considering HM as a potential pest control mechanism in the face of the new soybean

pest. This conclusion is not only because of the difference in the baseline pest

102

management approaches, but also the considerable variability in the initial (pre-soybean
aphid) net returns to fixed factors given the economic parameters assumed. Specifically,
organic systems earn almost twice the level of net return conventional systems earn,
mainly attributed to the price premium of organic products as well as a small variable
costs advantage in producing organic com. This advantage exists in spite of the existence
of yield disadvantages associated with both organic soybean and corn (Table 3.1).

Our presentation of key results is focused on the medium infestation level and
Laplace distribution kernel, followed by a discussion of the effects of pest pressure and
differently shaped distribution kernels. Overall, 1% of NCH (prop_NCH=0.01) arranged
in archipelago is found the optimal solution for HM approach to controlling soybean
aphid among all configuration options considered. The land use pattern leads to an
increase in net return by 59% from the no-control baseline under the organic system. For
conventional farms, reliance on HM in lieu of insecticide-based aphid control reduces net
returns in all simulations. However, NCH has the least negative effect at 1%, configured
in an archipelago pattern, which results in a decrease by a mere 4% from the insecticide-
based control baseline under the conventional system (Figure 3.8).

The negative slope of the curves associated with archipelago after peaking at
prop_NCH=0.01 implies a decreasing returns to scale effect of the area of NCH in the
landscape, compounded by the opportunity cost of land use change and increased
production cost due to farming a fragmented field (Figure 3.9). Due to the rapid rise in
the estimated change in variable costs of production for archipelago as prop_NCH
increases, the relative advantage of archipelago over square and strip at any given

prop_NCH declines sharply once passing the peak at prop_NCH=0.01. In addition, the

103

performance of archipelago after the peak point declines at a much faster rate under the
organic system than the conventional system as prop_NCH increases, partly because the
estimated changes in variable costs of production under the organic system are about
three times of those under the conventional system for the archipelago pattern. The effect
of the variable costs change becomes more obvious in Figure 3.10 when such change is
ignored (i.e., i=0), in which case the archipelago is preferred over the square and strip
configurations at any given positive area of NCH within the relevant range.

Between square and strip patterns, our results indicate that the strip pattern
consistently shows better economic performance in both systems, although its
comparative advantage is small under the conventional system (Figure 3.9). Specifically,
9% of NCH arranged in strips leads to the smallest reduction by 32% in net return under
the conventional system, 0.2% smaller than the best achievable level that the square
pattern can offer at prop_NCH=0. 1 6. Under the organic system, over 27% of
improvement in net return can be expected at prop_NCH=0.05 for strip, 5% higher than
the best achievable level by square at pr0p_NCH=0. l 5.

Overall, the adoption of HM by a conventional system makes the farm worse off,
which in the best scenario amounts to 4% reduction in net return as compared to the
insecticide-based control baseline when NCH is established in archipelago pattern and
accounts for 1% of total land area (Figure 3.9). The figure also shows that a conventional
farm would be 54% worse off under the “doing nothing” scenario (i.e., prop_NCH=0)
than applying insecticide to control the pest. In sharp contrast, the organic system gains
significantly in economic performance after establishing NCH. Specifically, an organic

farm would be better off than doing nothing by setting aside any positive amount of land

104

in strips or squares as habitats or 1-3% of land in an archipelago pattern to provide pest
control services. With 1% of NCH arranged in an archipelago, the increase in net return
reaches the highest level of 59%, more than twice the largest improvement the strip
configuration can achieve with 5% of land devoted to NCH.

While pest infestation level does not significantly influence the optimal choices
with regard to the shape and area of NCH, it does play a role in determining the
performance of HM relative to the baseline management. For instance, under the
conventional system (and assuming a Laplace distribution kernel), the reductions in net
return are 5% and 4% for low and medium infestation levels, respectively, given the
optimal solution of 1% of NCH arranged in an archipelago pattern. At high infestation
level, however, the same land use pattern leads to a slight increase in net return by 0.3%.
This can be attributed to both the higher insecticide control cost under the high infestation
scenario (when two applications of insecticides would be needed as compared to only one
for low to medium pest levels) and the relatively lower return to insecticide control in the
baseline as the number of pests escaped from the control tends to be higher when there is
high infestation. Under the organic system, infestation levels have a more visible impact
on the relative performance of HM. Specifically, the increases in net returns from the
baseline are 41%, 59%, and 77% for low, medium, and high infestation levels,
respectively, resulted from the same optimal configuration of NCH (i.e., 1% of NCH
arranged in an archipelago).

For square and strip patterns, higher pest pressure always corresponds to greater
disadvantage (under the conventional system) or advantage (under the organic system) of

HM relative to the baselines. For archipelago, however, there exists a threshold level of

105

NCH area (prop_NCH=0.l3), below which the gap between HM and chemical control
gets smaller as infestation level increases under the conventional system, meaning that
the higher the pest level is, the smaller the disadvantage of HM is as compared to the
insecticide-based control baseline. Likewise, under the organic system, the higher the
pest level, the better HM performs relative to the baseline for prop_NCH below 0.09. The
result reflects the fact that archipelago contrasts with square and square patterns with
respect to its superior ecological benefit and extraordinarily high production cost. When
prop_NCH is relatively small (below the threshold levels), the farm benefits more from
the ecological benefit associated with archipelago than suffering from increased
production cost, including foregone yield. Higher pest levels simply exaggerate this
effect.

Given the parameters assumed, our results show that model outcomes are
sensitive to the differently shaped distribution kernels used to describe the dispersal of
natural pest control services around the NCH for square and strip patterns but remain
robust to the choice of distribution kernel for archipelago. Given equal mean dispersal
distance of 100 meters, the Laplace kernel is responsible for the best relative performance
of HM as compared to the baseline (i.e., the most increase in net return under the organic
system or the least reduction in net return under the conventional system), followed by
Gaussian and cylindrical kernels for square and strip patterns (Figure 3.11). From the
economic perspective, this result can be interpreted as “efficiency” difference between
various dispersal modes of natural enemies or their services”. Coverage appears to be

more important than intensity of control. When the landscape is mapped in a way that

 

'2 Note that the distribution kernel is not a choice variable. Our analysis demonstrates that the
distribution kernel implemented in the simulation model can have an impact on the economic
outcomes, highlighting the need for better understanding of this important ecological factor.

106

each unit of land (i.e., cell) is sufficiently small as approached in this study, small patches
of habitat as characterized by archipelago collectively deliver the same amount of control
services across landscape, regardless of the dispersal patterns of natural enemies (Figure
3.1 I). This possibly raises another tradeoff relationship between the increase in
production cost associated with field fragmentation and the robustness of overall

ecological impact of habitats to natural enemy dispersal behavior.

3.5 Sensitivity analysis

To investigate the effects of variations in a set of key spatial, ecological, and economic
parameters, we perform sensitivity analyses on a specific case where infestation level is
set at medium, natural pest control services are distributed according to a Laplace kernel,
and the shape of NCH is strip. We look at how the relative performance of HM changes
as values of these parameters are varied by 5% in both directions (except for the price of
soybean, pm, which is varied by 10% in both directions).

We report in Table 3.2 the percentage changes of the relative performance of HM
from model outcomes based on parameters reported in Table 3.1 as a result of varying
parameter values. Overall, model results are robust to parameter variations for the
conventional system, except for efficacy rate of soybean aphid insecticides and natural
enemy mean dispersal distance. Specifically, when decreasing Eflicacy,,,,,,y by 5% (no
increase scenario is included because the baseline value is already 0.99), the advantage of
chemical control relative to HM reduces by 18.4%. Extending (or reducing) the mean
dispersal distance of natural enemies by 5 meters results in the advantage of chemical

control over HM decreasing (or increasing) by 3.4%. The impacts of parameter variations

107

on model results under the organic system are generally stronger than those on the
conventional system, because of the differentiated levels of yield potential and economic
coefficients. In particular, model outcomes are most sensitive to variations in the mean
dispersal distance and soybean price, followed by maximum soybean yield potential and

the yield loss coefficient.

3.6 Conclusion and future research needs

Natural enemies provide important ecosystem services to agriculture by suppressing pest
damage to crop yield and also, less visibly, by maintaining an ecological equilibrium that
prevents herbivore insects from reaching pest status. Enhancing this service by providing
essential resources and compatible environment to natural enemies constitutes a potential
alternative to the current insecticide-based pest management approach, which, in recent
decades, has increased the frequency of pesticide resistance, pest outbreak and resurgence.
The result is to make chemical control more costly and unreliable, and to produce
unintended negative health outcomes for nontarget organisms, including humans
(Thomas, 1999).

This study explores economically optimal spatial habitat configuration for natural
enemies of crop pests. The model developed here focuses on the simple function of non-
crop habitats as sources of natural pest control services and evaluates the economic
tradeoffs associated with land use choices between farming and setting aside land as
natural enemy habitats. Not only is there an opportunity cost of forgone income from

setting aside land, but the economic outcome is also highly dependent on the spatial

108

configuration of the non-crop habitats as well as the spatial distribution of natural control
services into the surrounding crop fields. Our three main findings follow:

First, non-crop habitat management is a promising pest management option for
organic systems, not only because of their relatively high profitability, but also because
of the constrained options in the pest management toolbox as compared to conventional
systems. While any positive amount of habitat in square and strip shapes would guarantee
an improvement in net return level from the no-control baseline, small area of habitat in
archipelago results in the best outcome. Moreover, the higher the pest pressure is under
an organic system, the greater the advantage of habitat management over the no-control
management baseline, except when a relatively large area of habitat is arranged in high-
cost archipelago shape.

The adoption of habitat management in a conventional soybean-com system,
however, tends to reduce farm net returns, highlighting the need for reducing the private
cost of habitat management. In addition, it is important to note that the full economic
value of the services from non-crop habitats is likely to be higher than that estimated
from the private producer perspective in this study. Besides the social and environmental
benefits from reducing the use of chemical insecticides, diversely structured agricultural
landscapes tend to be positively related to other socially desirable ecological benefits
such as habitats for beneficial insects and wildlife. Non-crop habitats could become
attractive if policy were to reward all the ecosystem services due to their positive
extemalities.

Second, the shape and area of habitats are important factors in spatially optimal

land use decisions. Land use patterns that devote a small amount of land to archipelago

109

habitat patches show the best economic performance in both systems. However, the
benefit of fragmentation disappears rapidly as the area of habitat increases, leaving it
inferior to strip and square patterns. While Bianchi and van der Werf (2003) find that
better pest control is achieved in landscapes with a substantial area of non-crop habitats
and where these habitats are distributed in small patches over the landscape, our analysis
highlights the tradeoff between economic and ecological performance associated with the
area and patchiness of habitat. From a private producer perspective, patchiness is only
desirable when the total habitat area and configuration yield pest control benefits that
balance the opportunity cost of land use change and increased production cost caused by
field fragmentation.

Third, the spatial distribution of natural control services to crop fields is an
important factor determining the economic performance of habitat management. The
simulation experiment in this study considers a simplified case in which natural pest
control services are dispersed around a source origin into the crop fields within a certain
range. The more complicated interactions associated with re-distribution and crowding of
insect populations are ignored. Given equal mean dispersal distance assumed, we find
positive association between the coverage (or spatial extent) of natural pest control
services (as opposed to intensity of control) and the relative performance of habitat
management for square and strip configurations. For archipelago, however, the use of
different distribution kernels in the simulation model made no difference on the relative
performance of habitat management. In practice, optimal habitat configuration is likely to
be species specific, highlighting the need to rely on solid ecological knowledge in

building models for management decision support. Economic parameters such as prices

110

of organic products and biological parameters such as the pest mortality rate due to
insecticides also have important impact on the model results.

Several issues deserve future attention. First, while not considered in the current
study, species scale dependence may have important implications for spatially explicit
models involving land use choices. If natural enemy density increases exponentially with
area of contiguous habitat, the aggregation of patchy habitats may become desirable and
coordinated action among multiple land managers may become socially desirable. Future
research into habitat management may also benefit from enhanced capability to link
actual natural enemy population density with the size of non-crop habitats. Such linkage
would allow us to explore more species-targeted management practices as well as
integrated approaches that combine natural control with chemical control.

Second, obtaining improved parameter estimates (such as the efficacy rate of
insecticides and species spatial distribution scale parameters) represents an important
direction to strengthen such interdisciplinary research. The relationship between the area
and spatial configuration of non-crop habitats in the landscape and the density of natural
enemies remains a highly relevant ecological question to be explored. F urtherrnore, the
estimation of the pest regulation effect of non-crop habitats could greatly benefit from the
use of empirical data.

Finally, given the spatial nature of the dispersal of natural enemies and their
services, issues of extemalities and spillovers will arise, which may influence the design
of socially optimal policy incentives. While the model developed here is capable of
investigating such issues at the landscape scale, it is beyond the scope of the current

analysis. Future research may also look into potential opportunities for bundling habitat

III

management policies with other policy incentives that address issues such as water
pollution and soil conservation. Two factors are particularly important when thinking
about socially optimal land use choices: the distribution of natural enemies in space and
the scale dependence effect. The latter offers a potential gain in total control services
generated from a larger contiguous non-crop habitat if species population increases
disproportionately with habitat size, whereas a longer dispersal distance as described by
the Laplace kernel ensures that the services reach more crop fields. For instance, strip
habitats near farm borders may produce better collective outcomes than individual farms
establishing their own habitats of equal area. Parkhurst et al. (2002) conduct an
experiment to explore a voluntary incentive mechanism, the agglomeration bonus,
designed to protect endangered species and biodiversity by reuniting fragmented habitat
across private land. The mechanism provides incentives for non-cooperative landowners
to voluntarily create a contiguous reserve across their common border (Parkhurst et al.,
2002). Such policy mechanisms may be useful when models like the one developed here

show coordination benefits to optimal spatial configuration of non-crop habitats.

112

References

Aerts, J .C.J .H., M. van Herwijnen, R. Janssen, and T.J. Stewart. 2005. “Evaluating spatial
design techniques for solving land-use allocation problems.” Journal of
Environmental Planning and Management 48(1): 121-142.

Barbosa, P. 1998. Conservation Biological Control. San Diego CA: Academic Press.

Bianchi, F.J.J.A., C.J.H. Booij, and T. Tschamtke. 2006. “Sustainable pest regulation in
agricultural landscapes: a review on landscape composition, biodiversity and
natural pest control.” Proceedings of the Royal Society of London Series B-
Biological Sciences 273 : l 71 5-1 727.

Bianchi, F .J .J .A., A. Honek, and W. van der Werf. 2007. In press. “Linking land use
patterns to population viability: implications for conservation biological control.”
Landscape Ecology.

Bianchi, F.J.J.A., and W. van der Werf. 2003. “The effect of the area and configuration of
hibernation sites on the control of aphids by Coccinella septempunctata
(Coleoptera: Coccinellidae) in agricultural landscapes: a simulation study.”
Environmental Entomology 32(6): 1290-1304.

Brown, C., L. Lynch, and D. Zilberrnan. 2002. “The economics of controlling insect-
transmitted plant diseases.” American Journal of Agricultural Economics 84: 279-
291.

Bowers, W. 1992. Machinery Management. Moline IL: Deere & Company.

Costamagna, A.C. 2006. “Do varying natural enemy assemblages impact Aphis glycines
population dynamics?” PhD Dissertation, Michigan State University, East
Lansing, MI.

Costamagna, A.C., D.A. Landis, and CD. DiFonzo. 2007a. “Suppression of soybean
aphid by generalist predators results in a trophic cascade in soybeans.” Ecological
Applications 17(2):441—45 1 .

Costamagna, A.C., W. van der Werf, F .J.J.A. Bianchi, and D.A. Landis. 2007b. “An
exponential growth model with decreasing r captures bottom-up effects on the
population growth of Aphis glycines Matsumura (Hemiptera: Aphididae).”
Agricultural and Forest Entomology 9: 1—9.

Cousens, R. 1985. “A simple model relating yield loss to weed density.” Annals of
Applied Biology 107: 239-252.

113

DiFonzo, CD, and R. Hines. 2002. “Soybean aphid in Michigan: update from the 2001
season.” Michigan State University Extension Bulletin E-2748, East Lansing, MI.

Fox, T.B., D.A. Landis, F.F. Cardoso, and CD. DiFonzo. 2004. “Predators suppress
Aphis glycines Matsumura population growth in soybean.” Environmental
Entomology 33(3): 608-618.

Hambaeck, RA, and G. Englund. 2005. “Patch area, population density and the scaling
of migration rates: the resource concentration hypothesis revisited.” Ecology
Letters 8: 1057-1065.

Hof, J ., and M. Bevers. 1998. Spatial Optimization for Managed Ecosystems. New York:
Columbia University Press.

Hof, J .G., M. Bevers, and B. Kent. 1997. ”An optimization approach to area-based fest
pest management over time and space.” Forest Science 43(1): 121-128.

Hof, J .G., and LA. Joyce. 1992. “Spatial optimization for wildlife and timber in managed
forest ecosystems.” Forest Science 38(3): 489-508.

Landis, D.A., S.D. Wratten, and GM. Gurr. 2000. “Habitat management to conserve

natural enemies of arthropod pests in agriculture.” Annual Review of Entomology
45: 175-201.

Landis, D.A., F.D. Menalled, A.C. Costamagna, and T.K. Wilkinson. 2005.
“Manipulating plant resources to enhance beneficial arthropods in agricultural
landscapes.” Weed Science 53: 902-908.

Losey, J .E., and M. Vaughan. 2006. “The economic value of ecological services provided
by insects.” Bioscience 56(4): 331-323.

McKeown, CH. 2003. “Quantifying the roles of competition and niche separation in
native and exotic Coccinellids, and the changes in the community in response to
an exotic prey species.” MS Thesis, Michigan State University, East Lansing, MI.

Nalle, D.J., CA. Montgomery, J.L. Arthur, S. Polasky, and NH. Schumaker. 2004.
“Modeling joint production of wildlife and timber.” Journal of Environmental
Economics and Management 48: 997-1017.

Naylor, R., and P. Ehrlich. 1997. “Natural pest control services and agriculture.” In G.
Daily, ed. Nature 's Services: Societal Dependence on Natural Ecosystems.
Washington DC: Island Press, pp. 151 -74.

Parkhurst, G.M., J.F. Shogren, C. Bastian, P. Kivi, J. Donner, and R.B.W. Smith. 2002.

“Agglomeration bonus: an incentive mechanism to reunite fragmented habitat for
biodiversity conservation.” Ecological Economics 41: 305-328.

114

Polasky, S., E. Nelson, E. Lonsdorf, P.L. Fackler, and A. Starfield. 2005. “Conserving
species in a working landscape: land use with biological and economic

objectives.” Ecological Applications 15(4): 1387-1401.

Root, RB. 1973. “Organization of a plant-arthropod association in simple and diverse
habitats: the fauna of collards (Brassica oleracea).” Ecological Monographs 43:
95-124.

Rutledge, C.E., R.J. O'Neil, T.B. Fox, and D.A. Landis. 2004. “Soybean aphid predators
and their use in 1PM.” Annals of the Entomological Society of America 97:240-
248.

Sanchirico, IN, and J .E. Wilen. 2000. “Dynamics of spatial exploitation: a
metapopulation approach.” Resources for the Future Discussion Paper 00-25-
REV, Washington, DC.

Seppelt, R., and A. Voinov. 2002. “Optimization methodology for land use patterns using
spatially explicit landscape models.” Ecological Modeling 151: 125-142.

Skelsey, P., W.A.H. Rossing, G.J.T. Kessel, J. Powell, and W. van der Werf. 2005.
“Influence of host diversity on development of epidemics: an evaluation and
elaboration of mixture theory.” Phytopathology 95(4): 328-338.

The MathWorks Inc. 1994-2007. MatLab Function Reference. Natick, MA.

Thies, C., I. Steffan-Dewenter, and T. Tschamtke. 2003. “Effects of landscape context on
herbivory and parasitism at different spatial scales.” Oikos 101: 18-25.

Thies, C., and T. Tschamtke. 1999. “Landscape structure and biological control in
agroecosystems.” Science 285(5429): 893-895.

Thomas, MB. 1999. “Ecological approaches and the development of ‘truly integrated’
pest management.” Proceedings of the National Academy of Sciences of the USA
96: 5944-5951.

Tilman, D. 1999. “Global environmental impacts of agricultural expansion: the need for
sustainable and efficient practices.” Proceedings of the National Academy of
Sciences of the United States of America 96(May): 5995-6000.

Turner, M.G., G.J. Arthaud, R.T. Engstrom, S.J. Hejl, J. Liu, S. Loeb, and K. McKelvey.
1995. “Usefulness of spatially explicit population models in land management.”
Ecological Applications 5(1 ): 12-16.

University of Illinois at Urbana-Champaign (UIUC). 2003. “Illinois specialty farm
products.” Department of Agricultural and Consumer Economics.
http://webacesuiuc.edu/value/factsheets

 

115

US. Department of Agriculture (USDA). 2000. “2000 Agricultural Resource
Management Survey.” Washington DC. http://www.ncrlc.com/GR-campaign-
webpages/US-farm-stats.html

 

Welland, R., and D. Smith, 2007. “Metric conversions.” Ag Decision Maker, File C6-80.
Iowa State University, University Extension, Ames, IA. http://www.extension.
iastate.edu/AGDM/wholefarm/pdf/C6-80g)_df

Zhang, W. Essay 2. “Optimal Control of Soybean Aphid in the Presence of Natural
Enemies.” PhD dissertation, Michigan State University, East Lansing, MI.

116

Table 3.1: Values of parameters used in the numerical analysis and their sources or

 

 

estimations

Parameters Values Sources

n: proportion of yield lost per unit 0.00026 Estimated from Michigan field data

of pest population for 2005 provided by Christine
DiFonzo

,u: maximum allowable yield loss 1 Model restriction

pmy conventional $247.9/tonl3 UIUC (2003) Food-Grade

pm, organic $518/ton UIUC (2003) Food-Grade

pm", conventional $85.1/ton UIUC (2003) Regular hybrid

pcom organic $133.2/ton UIUC (2003), Feed grade

ym_,oy conventional 3.08 ton/ha UIUC (2003) Food-Grade

ymax ,0, organic 2.45 ton/ha UIUC (2003) Food-Grade

ym_c,,,,, conventional 10.85 ton/ha UIUC (2003) Regular hybrid

ymax can, organic 9.45 ton/ha UIUC (2003) Feed grade

VCsoy conventional $260/ha UIUC (2003) Food-Grade

VCW organic $260/ha UIUC (2003) F ood-Grade

VCcom conventional $490/ha UIUC (2003) Regular hybrid

VCm, organic $472.5/ha UIUC (2003) Feed grade

pest,,,,~,,-,,,: control-free pest 5000 (low), 8000 Predicted from Costamagna et al.

infestation level (avg soybean (medium), and (2007b) model with starting values

aphid density during soybean 12000 (high) taken from Michigan field data

plant stages R1 through R5) aphids/plant

Cost,,,,,,y: cost of spray per $30.5/ha Song et al. (2006)

application
Number_of_sprays

Eflicacyspmy: efficacy rate of
soybean aphid insecticides

r: radius of cylindrical kernel

a: slope of the decline of allocated
services with distance for Laplace
kernel

6: standard deviation of Gaussian
kernel

Avg. percentage of reduction in
pest density responding to the
percentage of NCH in landscape

2.: Proportion of change in
variable costs due to the
establishment of NCH

1 for low, medium
infestation; 2 for
high infestation
0.99

100 m

0.02 m'1

80 m

See Figure 3.4

See Figure 3.7-3.8

Adapted from results in essay 2

Assumed

Assumed
Assumed

Assumed

Estimated from simulation results
from Bianchi and van der Werf
(2003)

Estimated using cost data from
UIUC (2003) and estimate of the
amount of machinery field time
spent on turning (Bowers, 1992)
(Appendix D)

 

 

'3 1 metric ton = 36.74 (37) bushels soybeans (60 pound bu) and 1 bushel/acre = 0.0673 (0.07)
metric tons/hectare (Weiland and Smith, 2007). 1 hectare = 2.471 (2.5) acres

117

Table 3.2: Summary of sensitivity analysis results (Medium pest infestation, Laplace
kernel, and strip NCH)
Changes in outcomes (nr associated with optimal
prop NCH) from baseline“

 

 

Parameters Conventional Organic
n: proportion of yield lost per unit of pest T5%: I 1.4% T5%: T 3.3%
population I5%: T 1.5% I5%: I 3.3%
pm, T10%: I 2.3% T10%: T 6.8%

I10%: T 2.7% I10%: I 7.2%
ymaxgw, T5%: I 1.2% T5%: T 3.5%

I5%: T 1.3% I5%: I 3.5%
VCmy T5%: I 1.1 % T5%: T 1.7%

I5%: T 1% I5%: I 1.6%
Cost,,,,,,.: cost of spray per application T5%: T 0.4 %

I5%: I 0.4%
Efiicacyspmy: efiicacy rate of soybean aphid I5%: T 18.4%

insecticides

Mean dispersal distance (2/a) T5%: T 3.4% T5%: T 5.2%
I5%: I 3.4% I5%: I 5.1%

Avg. percentage of reduction in pest density T5%: T 0.5% T5%: T 0.7%

responding to the percentage of NCH in I5%: I 0.5 % I5%: I 0.8 %

landscape

 

* The baseline refers to model outcomes based on parameters given in Table 3.1.

118

 

i=I,...,N

Figure 3.1: The distribution of land between non-crop habitats, impact zone, and no
impact zone

119

 

-1500 -1000 -500 O 500 1000 1500 2000

Figure 3.2a: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80X80 grid and with pro_NCH=0.l): Square

120

 

-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.2b: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80X80 grid and with pro_NCH=0.l): Strip

121

 

-2000 ' '
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.2c: Illustration of landscape configuration with four farms and three NCH
configurations (prepared in 80X80 grid and with pro_NCH=0.l): Archipelago

122

0.02.........._...

0,01 _q

 

 

 

 

 

 

 

 

 

 

4000

Figure 3.3a: Illustration of distribution kernels (prepared in 200x200 grid):
Cylindrical kernel (radius=100 m)

123

0.02.. --------- " .......

 

 

 

 

 

 

 

 

 

600

 

4000 -1000

Figure 3.3b: Illustration of distribution kernels (prepared in 200x200 grid): Laplace
kernel (a=0.02 m")

124

0,02,. ........... " ..........

0015 .. .............................

0.01 m

 

 

 

 

 

 

 

 

 

~1000

 

4000 4000

Figure 3.3c: Illustration of distribution kernels (prepared in 200x200 grid):
Gaussian kernel (0=80 m)

125

 

80%

 

 

60% //
40%

 

 

Reduction of pest density (%)

 

20% /
0%

 

 

T fi T l I T T I I 1 T fl T I 1 T

0% 2% 4% 6% 8% 10% 12% 14% 16%
NCH area (%)

Figure 3.4: The relationship between the NCH area and the average pest reduction
impact (Estimated from Bianchi and van der Werf, 2003)

126

2000

1 500

1 000

500

O

-500

 

 

-1000

-1500

 

-2000
-2000 —1500 -1000 —500 O 500 1000 1500 2000

Figure 3.5(i)a: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400x400 grid: Cylindrical kernel;
Square

127

1500 ‘03
r 1 0.8

1000.
.0]
500 05
0 f 0.5
_500 04

-1000

 

 

-1500

      

-2000 -
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.5(i)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400x400 grid: Cylindrical kernel;
Strip

128

2000

1 500

1000

500

-500

 

 

-1000

-1500

  

-2000
-2000 —1500 —1000 -500 0 500 1000 1500 2000

Figure 3.5(i)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400x400 grid: Cylindrical kernel;
Archipelago

129

2000

1500 "0'9
-0.8
1000
. 0.7
500 ; 0.6
o 0.5
_500 0.4
-1000

 

 

-1500

   

-2000
-2000 -1500 -1000 -500 O 500 1000 1500 2000

Figure 3.5(ii)a: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.1 in a 400x400 grid: Laplace kernel; Square

130

2000

1500 '09
-00
1000
-0]
500 05
o 05
_500 0A
-1000

 

 

-1500

   

-2000
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.5(ii)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400x400 grid: Laplace kernel; Strip

131

2000

4 0.3
1 500
1000 “ 0-25
500 0'2
0
0.1 5
-500

 

 

-1000

-1500

      

-2000 ,
-2000 -1500 —1000 -500 0 500 1000 1500 2000

Figure 3.5(ii)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400x400 grid: Laplace kernel;
Archipelago

132

2000

1500 " 0'9
: 0.8
1000
- 0.7
50° ' 0.6
o 0.5
_500 0.4
-1000

 

 

-1500

   

-2000
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.5(iii)a: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400X400 grid: Gaussian kernel;
Square

133

 

 

 

1500 ‘0'9
“0.8
1000}
-o.7
soo , 0.6
o f 0.5
_500 0.4
0.3
4000
r 0.2
-1500 0.1
-2000 o

A
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.5(iii)b: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400X400 grid: Gaussian kernel; Strip

134

2000 _— 0.35
150° . 0.3
1000

. 0.25
500
02
0
0.15
-500 '
-1000

 

 

-1500

    

-2000
-2000 -1500 -1000 -500 0 500 1000 1500 2000

Figure 3.5(iii)c: Illustration of distributions of pest control impact (proportion of
reduction), prepared with prop_NCH=0.l in a 400x400 grid: Gaussian kernel;
Archipelago

135

 

 

JV

 

 

 

«((t:<<<<¢¢<(<z¢¢<(«(¢«¢(

mwwww H HmHmwwwwwwwww

 

 

 

 

 

 

 

 

 

A

 

 

V
Figure 3.6a: Illustration of assumed modes of machinery field operation (the

Square

number “1” represents one turn)

136

 

 

A

 

 

 

 

 

 

 

)nrp)>))»»>3):3»)>)>»»u»y»)»»)))
(..(«t(tti¢(((t((««41((((««(ii:tt

 

 

 

 

 

 

 

 

 

 

A

 

 

(the

10!]

Illustration of assumed modes of machinery field operat

Figure 3.6b

Strip

number “1” represents one turn)

137

 

 

 

 

S ’
C
0 ’
(
) )
¢
’ )
V
> }
(
) )
(
) 0
1
I }
T
i 3
(
) 0
(
i )
¢
1‘ L

 

 

 

 

 

 

 

 

 

 

 

 

G c ( ( < ( ¢ 4 1
b D b ) i so ) I > D t j
( C ( V 8 ( ( t ( ( (
’ , ) ’ ’ ) ’ i F . ’ )
.1 t C v a. 0 t 1 ( 1
i 0 ) ) \. .r ) t s. s. ) .2
d c ( ¢ ( c (.1 (

lago
l 3 8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

1

 

 

 

 

Arch

Figure 3.6c: Illustration of assumed modes of machinery field operation (the
ipe

number “1” represents one turn)

2%

A O

33 m

'8’ 0%

U

5

§ 4%

2

° 4%
-5%

 

 

 

 

 

”xx-M
9x
‘u.—‘-,~ 7‘. Ff ,7 j’ f r I T - ‘ J~

 

 

 

 

 

 

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%11%12%13%14%15%16%

Percentage of NCH

-—+— conv_com_squane —s— conv_soy_square - + — org_com_square —-><——-— org_soy_square

- - x - - conv_com_strip —o——conv_soy_strip - - -+« - - org_com_stn'p

 

org_soy__strip

Figure 3.7: Estimated values of the percentage of change in variable costs of
production for square and strip patterns

139

 

 

 

 

 

Change in variable cost (%)

    

j,

1 1

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%11%12%13%14%15%16%

Percentage of NCH
+ conv_com + conv_soy + org_com + org_soy

Figure 3.8: Estimated values of the percentage of change in variable costs of
production for archipelago pattern

140

 

 

 

 

 

 

 

 

 

 

Proportion of change in nr from baseline

 

 

 

 

. l
-2 "‘ -.
I .
‘I
-2.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Proportion of NCH
+ Square (conv) —9—-— Strip (conv) — - s - - Archipelago (conv)
—-—+—— Square (organic) —0— Strip (organic) - - -e- - - Archipelago (organic)

Figure 3.9: Proportion of change in net return to fixed factors (Medium pest
infestation, Laplace kernel)

141

0.1

 

 

 

 

T.“I-_..‘
I ‘-‘__‘
O r] r ‘1 a j Wi f r r r r r T r fl
~-..‘ .

1 ~.._‘
' "“s

-01 ' ""r

43......“

e I “.1
1

-0.2 .L

 

 

 

 

 

 

Proportion of change in nr from baseline

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Proportion of NCH
—e— Square (conv) —<;~— Strip (conv) — - s - — Archipelago (conv)

Figure 3.10: Proportion of change in net return to fixed factors for a conventional
farm when change in variable costs of production is ignored (Medium pest
infestation, Laplace kernel)

142

Square

+ Cylindrical
(COM)

—0— Laplace
(00ml)

- 1 - - Gaussian
(60M
—.— Cylindrical '

(organic)
—6— Laplace
..—I—-c-—I--'l'—O""""'.'""" (organic)

Proportion 01 change in nr from
baseline

. —I- - I - -I-'
----- -- Gaussian
(organic)

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Proportion of NCH

Strip

+ Cylindrical
(00M

—0— Laplace

(60PM

— -- - - Gaussian
(coma

baseline

—s——Cylindrical
(weenie)

r —0— Laplace
(orsariC)

-~-I- -- Gaussian

as - -__ ._ -_ -2 , - (organic)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

ProportionofNCH

Proportion of change in nr tram

 

 

Archipelago

+ Conventional
1 —0— Organic

Proportion of change in nr from
baseline

 

1
o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Proportion of NCH
Figure 3.11: The effect of distribution kernels on the relative performance of HM at
medium pest infestation

143

Conclusions

The three essays of this dissertation explore two approaches to managing natural pest
control ecosystem services in order to achieve improved pest management in agricultural
systems. Essays 1 and 2 focus on integrating natural pest control into insecticide
decision-making so that natural enemies of crop pests are conserved and efficiently used
to the extent that the marginal factor cost of insecticide application (including the
opportunity cost of natural enemy mortality from insecticides) balances the marginal
value of the yield benefit. Essay 3 moves beyond insecticide-based pest management to
look at optimal spatial land use decisions for the management of habitats of natural
enemies.

By conserving (or better utilizing) and enhancing the natural pest control services,
there are new opportunities for improving pest management in an economically appealing
and socially desirable manner. To promote such opportunities would require not only a
tremendous increase in scientific understanding of ecosystems, but also major
innovations to our economic and social institutions to capture this value and incorporate
it into day-to-day decision-making (Daily and Ellison, 2002). The approach presented
here offers a useful framework for the management of other supporting and regulating
ecosystem services that serve as inputs to biological production of marketed agricultural
products.

The three essays employ bioeconomic modeling and optimization analysis to
explore the economic consequences of these opportunities on private producers.
According to these experiments, there are clearly economic gains from incorporating

natural enemies into insecticide decisions, which effectively delays and reduces the need

144

for insecticide spraying. The economic advantage of establishing non-crop habitats in
agricultural landscape, however, depends on the alternative pest management practices
available. For instance, relying on non-crop habitats of natural enemies for the
management of pests may not be economically viable if chemical control remains a cost-
effective option, as under a conventional farming system. The relevant policy question,
therefore, is how to develop policy instruments 1) to promote the adoption of natural
enemy-incorporated insecticide strategies that have the potential to improve economic
returns to private producers, and ii) to provide private producers with needed economic
incentives to adopt sustainable pest management approaches, such as habitat management,
that enhance the natural pest control services. In the second case, values of ecological and
environmental benefits from the establishment of non-crop habitats (e.g., enhanced
ecosystem services provided by beneficial pollinator insects) may be of interest because
they help justify the social incentives for supporting such practices. Results from Essay 3
show the magnitude of reduction in private net returns to fixed factors of production as a
result of habitat management. Such estimates may serve as a lower bound for the
financial support needed for conventional farmers to adopt habitat management
voluntarily.

At the landscape scale, coordination issues are also relevant to the management of
natural pest control services when spillovers exist for the distribution of natural control
benefits and the costs due to nontarget natural enemy mortality from insecticides. The
spillover of natural control benefits may reduce private incentives for voluntary adoption
due to the free-rider problem. Because of the nontarget natural enemy mortality from

insecticides, even if some farmers decide to adopt biological pest control strategies, they

145

could be harmed by pesticide use on neighboring farms (Wilson and Tisdell, 2001). Such
spillover effects would require individual farmers to coordinate action in adopting
sustainable management approaches if economic losses are to be avoided (Wilson and
Tisdell, 2001). Finally, scale matters for natural enemy habitats that may affect socially
optimal spatial land use choices. If natural enemy density increases disproportionately
with size of habitat, the aggregation of patchy habitats through coordinated action may

become socially desirable.

146

References
Daily, G.C., and K. Ellison. 2002. The New Economy of Nature-The Quest to Make
Conservation Profitable. Washington DC: Island Press/Shearwater Books.
Wilson, C., and C. Tisdell. 2001. “Why farmers continue to use pesticides despite

environmental, health and sustainability costs.” Ecological Economics 39: 449-
462.

147

 

Appendix A:
MatLab code for the optimal insecticide management model (Essay 2)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Single-season optimizing simulation model: Interaction between
soybean aphid, natural enemies, and soybean yield
Author: Wei Zhang, 2007

%
%
g
%
% Soybean aphid population growth module developed by Felix Bianchi,

% Alejandro Costamagna, and Wopke van der Werf, May 2005 (Costamagna et
% al., 2007), and modified by Wei Zhang

%

%

%

%

%

%

%

Reference:

Costamagna, A.C., W. van der Werf, F.J.J.A. Bianchi, and D.A. Landis.
2007. “An exponential growth model with decreasing r captures bottom-
up effects on the population growth of Aphis glycines Matsumura
Hemiptera: Aphididae)." Agricultural and Forest Entomology 9:1—9.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc

% PARAMETERS

% SIMULATION TIME STEP

DELT=1;

% SBA DAILY POPULATION GROWTH FITTED BY WILLIAMS MODEL: Estimated
from the generalized model

RGRMAX = 0.3978; % corresponds to the first infestation date at KBS
in 2005, which is approximately 6/23/05

C = 0.0240;

% Kill rate of insecticides

KI = 0.99;

KN = 0.99;

% Death rate of natural enemy

D1 = 0;

D2 = -O.9;

D3 = -2.l3;

% Birth rate of natural enemy due to consumption of SBA
B1 =0;

BZ =0;

B3 = 0.002;

% Percentage of yield loss due to 1 unit of SBA
YDl = 0;

YD2 = 0;

YD3 = 0.0003;

YD4 = 0.0001;-

YDS = 0;

% Percentage of maximum yield loss
YMl = 1; % restricted to be one

YM2 = l;
YM3 = 1;
YM4 = l;
YM5 - 1‘

% CONTROL COST

148

COST =12.18;
% OUTPUT PRICE
PRICE =6.91;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SBA population density for each stage in the absence of predation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fid = fopen('SBA_no_predation_26JulO7.txt','w');
% PLANT GROWTH STAGE
% At KBS in 2005, R1 approximately began on July 5
% Mean R-stage length data from literature: 3,10,9,9,15 days

DATEOR1_KBS = datenum('7/5/2005');
DATE1R1_KBS = datenum('7/7/2005');
DATEOR2_KBS = datenum('7/8/2005');
DATE1R2_KBS = datenum('7/l7/2005');
DATEOR3_KBS = datenum('7/18/2005');
DATE1R3_KBS = datenum('7/26/2005');
DATEOR4_KBS = datenum('7/27/2005');
DATE1R4_KBS = datenum('8/4/2005');
DATEOR5_KBS = datenum('8/5/2005');
DATE1R5_KBS = datenum('8/19/2005');

R1_KBS = DATE1R1_KBS-DATEOR1_KBS+1; % Number of days during R1
R2_KBS = DATE1R2_KBS~DATEOR2_KBS+1;
R3_KBS = DATE1R3_KBS—DATEOR3_KBS+1;
R4_KBS = DATE1R4_KBS-DATEOR4_KBS+1;
R5_KBS = DATE1R5_KBS-DATEOR5_KBS+1;

L_KBS = R1_KBS+R2_KBS+R3_KBS+R4_KBS+R5_KBS;

% Initial conditions (SBA/plant)
I=73.45; % KBS, mean of multiple plots, 7/5/05

TIME=O;

% R1 Time Loop: FINISH TIME or SIMULATION (DAY)
TIME_KBS =L_KBS;

while TIME<TIME_KBS

% SBA population model

DATE_INFESTATION = datenum ('6/23/2005'); % This is the day when
SBA population has a maximum intrinsic growth rate (RGRMAX)

BEFORE_R1 = DATEOR1_KBS-DATE_INFESTATION;

RGRMAX_ADJUST = RGRMAX * (1-C * BEFORE_R1); % derive the "RGRMAX"
for the first day of R1

RGR = RGRMAX_ADJUST * (l - C * TIME); % Relative Growth Rate

RA = I*(exp(RGR) - 1); % SBA population Growth Rate (SBA/day)

% Output
output=[TIME; I; RA; RGR];
fprintf(fid, '%12.0f %12.6f %12.6f %12.6f\n', output);

% Integration

149

% Time integration
TIME=TIME+DELT;
% Integration of aphid population
I=I+RA;
end
I=I;

fclose(fid)
load SBA_no_predation_26Jun07.txt;

SBA_R1_NP=mean(SBA_no_predation_26Jun07((1:R1_KBS),2))r % obtain
average density of SBA population
SBA_R2_NP=mean(SBA_no_predation_26Jun07(((R1_KBS+1):(R1_KBS+R2_KBS)),2)
);
SBA_R3_NP=mean(SBA_no_predation_26Jun07(((R1_KBS+R2_KBS+1):(R1_KBS+R2_K
BS+R3_KBS)),2));
SBA_R4_NP=mean(SBA_no_predation_26Jun07(((R1_KBS+R2_KBS+R3_KBS+1):(R1_K
BS+R2_KBS+R3_KBS+R4_KBS)),2))i
SBA_R5_NP=mean(SBA_no_predation_26JunO7(((R1_KBS+R2_KBS+R3_KBS+R4_KBS+1
):(R1_KBS+R2_KBS+R3_KBS+R4_KBS+R5_KBS)),2));

SBA_KBS_NP = zeros(4,1);
SBA_KBS_NP=[SBA_R1_NP SBA_R2_NP SBA_R3_NP SBA_R4_NP SBA_RS_NP];

% Calculate net growth rate of SBA density
NG1=(SBA_R2_NP/SBA_R1_NP)-1;
NG2=(SBA;R3_NP/SBA_R2_NP)-1;
NG3=(SBA_R4_NP/SBA_R3_NP)-1;
NG4=(SBA_R5_NP/SBA_R4_NP)—1;

NG=[NG1 NG2 NG3 NG4];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Simulation over ranges of daily predation rate, initial yield

% potential, all possible control paths, and initial values of SBA and
% NE densities in R1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fid = fopen('output_AugO7.txt','w');

for j = 35 % mean predation rate (SBA/day/NE)
PR = j;

for g = 40:2:60 % range and interval of initial yield potential
Y1 = 9;

% define control path: X=1 if control, X=0 if no control
X1=[0 1]';

X2=[O 1]';

X3=[0 1]';

X4=[0 1]';

X=gridmake(X1, X2, X3, X4);

150

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Stage R1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Simulate initial values of SBA_Rl and NE_R1
for k =0:5:150 % range and interval of initial values of SBA_Rl
SBA_Rl = k;

for h = 0:.5:4 % range and interval of initial values of NE_R1
NE R1 =h;

for i=1:16 % A total of 16 possible control paths
X1 = X(i,l);
X2 = X(i.2);
X3 X(i,3);
X4 X(i,4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Stage R2

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PR_R1 = PR * R1_KBS;

SBA_R2=max(0, (SBA_Rl-KI*X1*SBA_R1)+ NG1*(SBA_Rl—KI*X1*SBA_R1)-
PR_R1*(NE_R1-KN*X1*NE_R1));

NE_R2=max(O, (NE_R1-KN*X1*NE_R1)+ D1*(NE_R1-KN*X1*NE_R1)+B1*(SBA_Rl-
KI*X1*SBA_R1)*(NE_R1-KN*X1*NE_R1));

Y2 = Y1*(1-(YD1*SBA_Rl)/(1+(YD1*SBA_R1/YM1)));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Stage R3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PR_R2 = PR * R2_KBS;

SBA_R3=max(0, (SBA_RZ—KI*X2*SBA_R2)+ NGZ*(SBA_RZ-KI*X2*SBA_R2)-
PR_R2*(NE_R2-KN*X2*NE_R2));

NE_R3=max(0, (NE_R2-KN*X2*NE_R2)+ D2*(NE_R2-KN*X2*NE_R2)+B2*(SBA_R2-
KI*X2*SBA_R2)*(NE_R2-KN*X2*NE_R2));

Y3 = Y2*(l—(YD2*SBA_R2)/(1+(YD2*SBA_R2/YM2)));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Stage R4

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PRfiRB = PR * R3_KBS;

SBA_R4=max(0, (SBA_R3-KI*X3*SBA_R3)+ NG3*(SBA_R3-KI*X3*SBA_R3)-
PR_R3*(NE_R3-KN*X3*NE_R3));

NE_R4=max(0, (NE_R3-KN*X3*NE_R3)+ D3*(NE_R3-KN*X3*NE_R3)+B3*(SBA_RB-
KI*X3*SBA_R3)*(NE_R3-KN*X3*NE_R3))i

Y4 = Y3*(1-(YD3*SBA_R3)/(1+(YD3*SBA_R3/YM3)));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Stage R5

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PR_R4 = PR * R4_KBS;

SBA_RS=max(0, (SBA_R4-KI*X4*SBA_R4)+ NG4*(SBA_R4-KI*X4*SBA_R4)—
PR_R4*(NE_R4-KN*X4*NE_R4));

%NE_R5=max(O, (NE_R4-KN*X4*NE_R4)+ D4*(NE_R4-KN*X4*NE_R4)+B4*(SBA_R4-
KI*X4*SBA_R4)*(NE_R4-KN*X4*NE_R4));

Y5 = Y4*(1—(YD4*SBA_R4)/(l+(YD4*SBA_R4/YM4)));

151

SBA =
NE =

[SBA;R1 SBA_R2 SBA_R3 SBA_R4 SBA_RS];
[NE_R1 NE_R2 NE_R3 NE_R4];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% HARVEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Harvest yield

YH = Y5*(1-(YD5*SBA_R5)/(1+(YD5*SBA_R5/YMS)));
% Net return from pest management

QR = PRICE*YH—(X1+X2+X3+X4)*COST;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Optimization: find optimal control paths
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of all possible control paths

output=[PR; PR_Rl; PR_R2; PR_R3; PR_R4; Y1; Y2; Y3; Y4; Y5; YH; QR; X1;
x2; x3; X4; SBA_Rl; SBA_RZ; SBA_R3; SBA_R4; SBA_RS; NE_R1; NE_R2; NE_R3;
NE R4 ];

fprintf(fid,'%12.0f %12.0f %12.0f %12.0f %12.0f %12.0f %12.4f %12.4f
%12.4f %12.4f %12.4f %12.4f %12.0f %12.0f %12.0f %12.0f %12.4f %12.4f

%12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f\n', output);
end
end

end

end

end

fid = fopenl'maxqr_Aug07.txt','w');
load output_AugO7.txt;
for i=1:16:49089
[MAXQR INDEX] =

% Calculating max net return

max(output_Aug07((i:(i+l6-1)),12));
output=[MAXQR; INDEX];

fprintf(fid,'%12.4f %12.0f\n', output);

end

load maxqr_AugO7.txt;

MAXQR = maxqr_Aug07(:,l);
INDEX = maxqr_AugO7(:,2);
fid = fopen('ocp_AugO7.txt','w');

load output_AugO7.txt;
for i=1:1:3069 % (49104/16)
A = output_AugO7([((i-1)*16+1)
ocp = A((INDEX(i,1)),:);
ocpl = horzcat (ocp, INDEX(i,1));
output=[ocp1]:

:(i*16)]I:);

fprintf(fid,'%12.0f %12.0f %12.0f
%12.4f %12.4f %12.4f %12.4f %12.4f %12.0f
%12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
output);

end

152

%12.0f %12.0f %12.0f %12.4f
%12.0f %12.0f %12.0f %12.4f
%12.4f %12.4f %12.0f\n',

Appendix B:
MatLab code for the habitat spatial optimization model (Essay 3)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Spatially Optimal Non-crop Habitats (NCH) for Natural Pest Control

% Services at the Landscape Scale

% Author: Wei Zhang and Wopke van der Werf (Oct 2006-Nov 2007)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Conventional farming systems %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear;
fid =

fopen('HM_11Nov07_conv_SeedSaving_SameMeanDispersalDis_n800.txt','w');

% Setup of a square space, representing a landscape

n = 800; % Number of divisions along x-axis for landscape
nx = n; % number of cell divisions along x—axis

ny = n; % number of cell divisions along y-axis

size = 4000; % total landscape measures "size" by "size" m
dx = size/n; % cell width in x-direction (m)

dy = size/n; % cell width in y-direction (m)

x = dx * [-nx/2:1:nx/2-1]; % calculation of x-coordinates in m
y = dy * [-ny/2:1:ny/2—1]; % calculation of y-coordinates in m
[X,Y] = meshgrid(x,y); % setting up the matrix of (x,y) coordinates

% Initial pest population density per plant in soybeans

pest0_l = 5000; % low infestation
pest0_m = 8000; % medium infestation
pest0_h = 12000; % high infestation
n_spray = 0; % Number of sprays in a season
pesto = 0;
for j = 1:3
if j==1
pesto = pest0_l
n_spray = l

elseif j==2
pesto = pest0_m
n_spray = 1
elseif j==
pesto = pest0_h
n_spray = 2

end

% Yield damage function (Cousens, 1985)

d1 = 0.00026; % proportion of yield loss due to 1 unit of pest density
per plant

153

d2 = 1; % Proportion of maximum yield loss

% Assuming efficacy rate of insecticides is 99%

dm = (d1 * (pesto * 0.01))./(1 + (d1 * (pesto * 0.01) / d2 )); %
proportion of yield loss due to pest density pesto

% Assume homogeneous farms, Soybean—corn rotation
farmingsystem = 'conventional';

farmingsystem = 2;

% Conventional soybean production (pesticide control)

price_s = 6.7; % Price of conventional Food-Grade, Clear Hilum
Soybeans (UIUC 2003)

ymax_s = 44; % Yield of conventional Food-Grade, Clear Hilum
Soybeans (UIUC 2003) (bu/ac)

pcost_s = 104; % Variable production cost of Food-Grade, Clear Hilum

Soybeans (UIUC 2003) ($/ac)
ccost_s = 12.18; % Cost of pesticide control (S/ac) (Song et al. 2006)
tccost_s = n_spray * ccost_s; %Total pesticide control cost

% Conventional corn production

price_c = 2.3; % Price of conventional regular hybrid corn ($/bu)
(UIUC 2003)

ymax_c = 155; % Yield of conventional regular hybrid corn (bu/ac)
(UIUC 2003)

pcost_c = 196; % Variable production cost of regular hybrid corn

(UIUC 2003)($/ac)

landscape = zeros(n)

% Defining farms - the landscape has four farms, arranged in a 2x2
checkerboard
farml = [ones(ny/2) zeros(ny/Z); zeros(nx/2,nx)]

farm2 = farm1(:,nx:-l:1)
farm3 = farm1(ny:-1:1,:)
farm4 = farm1(ny:-1:1,nx:-1:1)

farm = zeros (n/2)

% Maximum (pest-free) profit per cell from soybean-corn rotation (no
pest for soybean)

spi_max_cell = 2.4710439 .* (ymax_s * price_s -pcost_s)* (dx * dy
/10000); % Maximum (pest-free) profit per cell from soybean
cpi_max_cell = 2.4710439 .* (ymax_c * price_c -pcost_c)* (dx * dy
/10000); % Profit per cell from corn

rotpi_max_cell = spi_max_cell + cpi_max_cell;

rotpi_max_farm = (farm * (—l) + 1) .* rotpi_max_cell;
tpi_max_farm = sum(sum(rotpi_max_farm)); % Maximum (pest—free)

profit per farm

tpi_max_ls = 4 * tpi_max_farm; % Maximum (pest—free) profit for
landscape

154

%%%%%%%%% Baseline: Conventional farml with soybean infested with
"pestO"; control with insecticides %%%%%%%%%%%%%

y0_s = (farm * (-1) + 1) .* (ymax_s * (1 — dm)); % Actual soybean
yield given pesto (bu/ac)

y0_c = (farm * (-1) + l) .* ymax_c; % Corn yield

% Proft per cell

spi0_cell = 2.4710439 .* (y0_s * price_s — pcost_s - tccost_s)* (dx *
dy /10000);

cpi0_cell = 2.4710439 .* (y0_c * price_c - pcost_c)* (dx * dy /10000);
rotpi0_cell = spi0_cell + cpi0_cell;

tpiO_farm = sum(sum(rotpi0_cell)); % Baseline profit level per farm

tpiO_ls = 4 * tpiO_farm; % Baseline profit level for the whole
landscape

pp=[0 4 9 16]; % NCH area (percentage of total landscape area)
reduc_data = [0 26 67 100]; % pest reduction (%) corresponding to
NCH area (%). Parameters estimated from Bianchi and van der Werf (2003)
simulation results for C7 and aphid

ncadist = 1 % Define shape of NCH

xp dx * [—(nx/2)/2:1:(nx/2)/2] % x—coordinates for plotting
yp = dy * [-(ny/2)/2:1:(ny/2)/2] % y-coordinates for plotting
[xplot,yplot] = meshgrid(xp,yp) % setting up the matrix of (x,y)
coordinates for plotting

% Kernel parameters (mean dispersal distance = 100 meters)
% Radius of cylindrical distribution K of impact

radius = 100 % m

% Standard deviation of Guassian distribution K of impact
sigma = 80 % m

% Range parameter of Laplace Distribution K of impact
range = 50 % m

% Distribution of pest control impact in space

% Cylindrical distribution kernel (K) for impact of natural enemies
x = dx * [-nx/2/2:1:nx/2/2-1]; % calculation of x-coordinates in m
y = dy * [—ny/2/2:1:ny/2/2-1]; % calculation of y-coordinates in m
[X,Y] = meshgrid(x,y); % setting up the matrix of (x,y) coordinates

K1 = (sqrt(X.‘2 + Y.‘2) < radius)
integral = sum(sum(K1))

K1 = Kl/integral

le = fft2(K1)

% Laplace distribution kernel (K) for impact of natural enemies
K2 = exp(-(sqrt(X.‘2 + Y.‘2))/range)

integral = sum(sum(K2))

K2 = K2/integral

155

fKZ = fftZ (K2)

% Gaussian distribution kernel (K) for impact of natural enemies
K3 = exp(-(X.‘2 + Y.‘2)/(2 * sigma‘2))

integral = sum(sum(K3))

K3 = K3/integral

fK3 = fft2(K3)

%%%% Proportion of NCH = 0 --> no pest control, no control cost %%%%%%%
for ncadist=1:3

for p = 0 % NCH area (percentage of total landscape area)

reduc 0 % pest reduction (%) corresponding to p

shape farm

r1 = 0 % Proportion of pest reduction (i.e. measurable actual
impact)
r2 =
r3 = 0

O

cp_s = 0 % Proportion of change in variable cost of production for
soybean due to establishing NCH under conventional system

cp_c = 0 % Proportion of change in variable cost of production for
soybean due to establishing NCH under conventional system

pestl = pesto * (1 - r1)
pest2 = pesto * (1 - r2)
pest3 = pesto * (1 - r3)

dml = (d1 * pestl)./(1 + (d1 * pestl / d2 ))
dm2 (d1 * pest2)./(1 + (d1 * pest2 / d2 ))
dm3 = (d1 * pest3)./(1 + (d1 * pest3 / d2 ))

y1_s1 = (shape * (~1) + 1) .* (ymax_s * (1 - dm1)) % Actual
soybean yield (bu/ac)

y1_s2 = (shape * (—1) + 1) .* (ymax_s * (1 - dm2))

y1_s3 = (shape * (-1) + 1) .* (ymax_s * (l - dm3))

spi1_celll = (shape * (-1) + 1) .* 2.4710439 .* (y1_sl * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000) % Soybean profit per CELL

spi1_ce112 = (shape * (—1) + 1) .* 2.4710439 .* (y1_sZ * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

spi1_cell3 = (shape * (-1) + 1) .* 2.4710439 .* (y1_s3 * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

cpil_cell = (shape * (—1) + 1) .* 2.4710439 .* (y0_c * price_c -
pcost_c * (1 + cp~C)) * (dx * dy /10000) % Corn profit given NCH taken
out of production

rotpi1_celll
rotation

rotpil_cell2

rotpi1_ce113

spi1_celll + cpi1_cell % Profit per soybean-corn

spil_ce112 + cpilficell
spi1_cell3 + cpi1_cell

tpil_farml = sum(sum(rotpi1_celll)) % profit per rotation per farm
tpil_farmz = sum(sum(rotpi1_ce112))
tpil_farm3 = sum(sum(rotpi1_ce113))

156

tpil_lsl 4* tpil_farml % profit for landscape
tpil_lsz 4* tpil_farm2
tpil_ls3 = 4* tpil_farm3

% Change in soybean profit at the farm scale from baseline

change_farm_sl = ( (sum(sum(spi1_celll))) - (sum(sum(spio_cell))) )
/ (sum(sum(spi0_cell)))

change_farm_sz = ( (sum(sum(spi1_ce112))) - (sum(sum(spio_cell))) )
/ (sum(sum(spio_cell)))

change_farm_sB = ( (sum(sum(spi1_cell3))) - (sum(sum(spi0_cell))) )

/ (sum(sum(spi0_cell)))
% Change in rotation profit at the farm scale from baseline

change_farml = (tpil_farml - tpiO_farm) / tpiO_farm
change_farm2 = (tpil_farm2 — tpiO_farm) / tpiO_farm
change_farm3 = (tpil_farm3 - tpiO_farm) / tpiO_farm

% Change in rotation profit at the landscape scale from baseline
change_lsl (tpil_lsl - tpiO_ls) / tpiO_ls
change_ls2 (tpil_lsZ - tpiO_ls) / tpiO_ls
change_lsB (tpil_ls3 - tpiO_ls) / tpiO_ls

checkl = change_lsl - change_farml

check2 = change_lsz — change_farm2

check3 = change_ls3 - change_farm3
% Output

output=[farmingsystem; n; pesto; n_spray; p; reduc; alpha; beta; cp_s;
cp_c; ncadist; change_farm_sl; change_farm_sz; change_farm_s3;
change_farml; change_farm2; change_farm3;change_ls1; change_lsz;
change_lsB];

fprintf(fid,'%12.0f %12.0f %12.0f %12.0f %12.2f %12.2f %12.2f %12.2f
%12.4f %12.4f %12.0f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f\n', output);

end
end

%%%%%%%%%% Square %%%%%%%%%%%%%%%%%%%%%%%%%%%
for ncadist = 1 % Landscapes with square NCH
for p = 1:1:16

if p == 1
cp_s = 0.001
cp_c = 0
elseif p == 2
cp_s = 0.001
cp_c = —0.001
elseif p == 3
cp_s = 0
cp_c = -0.002
elseif p == 4
cp_s = -0.001
cp_c = -0.003
elseif p == 5
cp_s = -0.002
cp_c = -0.004

157

reduc=i
to p

elseif p == 6

cp_s = -0.004
cp_c = -0.005
elseif p == 7
cp_s = -0.005
cp_c = -0.007
elseif p == 8
cp_s = -0.006

cp_c = -0.008
elseif p == 9

cp_s = —0.007
cp_c = -0.010
elseif p == 10
cp_s = -0.009
cp_c = -0.011
elseif p == 11
cp_s = -0.010
cp_c = -0.013
elseif p == 12
cp_s = -0.011
cp_c = —0.014
elseif p == 13
cp_s = -0.013
cp_c = -0.015
elseif p == 14
cp_s = -0.014
cp_c = -0.017
elseif p == 15
cp_s = -0.016
cp_c = -0.018
elseif p == 16
cp_s = -0.017
cp_c = -0.020
end

nterp1(pp, reduc_data, p) % pest reduction (%) corresponding

s = round(sqrt (n*2*(p/100)/4)/2) * 2 % Define size of the NCH

squares
square

= [zeros(n/4-s/2,n/2); zeros(s,n/4-s/2) ones(s) zeros(s,n/4-

s/2); zeros(n/4—s/2,n/2)]

size_of
source
shape =

_square = 5‘2 * dx * dy

= square * dx * dy * a1pha*(size_of_square)‘beta
square

totalsource = sum(sum(source))

fsource

impactl
impact2
impact3

= fft2(source)

= max(0, real(fftshift(ifft2(fK1 .* fsource))))
= real(fftshift(ifft2(fK2 .* fsource)))
= real(fftshift(ifft2(fK3 .* fsource)))

% Balance check: total impact must be equal before and after

distributi
afterl
after2

on over the landscape
= sum(sum(impact1))
= sum(sum(impact2))

158

after3 = sum(sum(impact3))

before = sum(sum(source))

relerrl = (afterl — before)/before
relerr2 (after2 - before)/before
relerr3 = (after3 - before)/before
relimpactl = impactl/totalsource
relimpact2 impact2/totalsource
relimpact3 impact3/totalsource

ic = sum(sum(shape *(-1) + 1))
crop_impactl = (shape * (-1) + 1)
crop_impact2 = (shape * (-1) + 1) .* impact2
crop_impact3 = (shape * (-1) + 1) .* impact3
tcrop_impactl sum(sum(crop_impact1))
tcrop_impact2 sum(sum(crop_impact2))
tcrop_impact3 sum(sum(crop_impact3))

.* impactl

 

r1 = min(1, (reduc * ic / tcrop_impactl) .* crop_impactl )

r2 = min(1, (reduc * ic / tcrop_impact2) .* crop_impact2 )

r3 = min(1, (reduc * ic / tcrop_impact3) .* crop_impact3 )

pestl = pesto * (1 - r1)

pest2 = pesto * (l — r2)

pest3 = pesto * (1 - r3)

dml = (d1 * pestl)./(1 + (d1 * pestl / d2 ))

dm2 = (d1 * pest2)./(1 + (d1 * pest2 / d2 ))

dm3 = (d1 * pest3)./(1 + (d1 * pest3 / d2 ))

y1_sl = (shape * (—1) + 1) .* (ymax_s * (1 — dm1)) % Actual soybean
yield (bu/ac)

y1_52 = (shape * (-1) + 1) .* (ymax_s * (1 - dm2))

y1_s3 = (shape * {-1) + 1) .* (ymax_s * (1 - dm3))

spi1_celll = (shape * (-1) + 1) .* 2.4710439 .* (y1_sl * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000) % Soybean profit per CELL

spi1_ce112 = (shape * (-1) + 1) .* 2.4710439 .* (y1_sz * price_s —
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

spilficellB = (shape * (—1) + 1) .* 2.4710439 .* (y1_s3 * price_s -

pcost_s * (1 + cp_s)) * (dx * dy / 10000)

cpi1_cell = (shape *
pcost_c * (1 + cp_c)) *
out of production

(—1) + 1) .* 2.4710439 .* (y0_c * price_c -
(dx * dy /10000) % Corn profit given NCH taken

rotpi1_ce111
rotation

rotpi1_ce112

rotpi1_ce113

spi1_celll + cpi1_cell % Profit per soybean-corn

spi1_ce112 +
spi1_cell3 +

cpi1_cell
cpi1_cell

tpil_farml =
tpil_farm2 =
tpil_farm3 =

sum(sum(rotpi1_celll))
sum(sum(rotpi1_ce112))
sum(sum(rotpi1_ce113))

% profit per rotation per farm

tpil_lsl
tpil_lsz
tpil_ls3

4* tpil_farml % profit for landscape
4* tpil_farm2

4* tpil_farm3

159

% Change in soybean profit at the farm scale from baseline

change_farm_sl = ( (sum(sum(spi1_celll))) - (sum(sum(spi0_cell))) )
/ (sum(sum(spi0_cell)))

change_farm_sZ = ( (sum(sum(spi1_ce112))) - (sum(sum(spi0_cell))) )
/ (sum(sum(spi0_cell)))

change_farm_s3 = ( (sum(sum(spi1_ce113))) - (sum(sum(spi0_cell))) )

/ (sum(sum(spi0_cell)))
% Change in rotation profit at the farm scale from baseline
change_farml = (tpil_farml — tpiO_farm) / tpiO_farm
change_farm2 (tpil_farm2 - tpiO_farm) / tpiO_farm
change_farm3 = (tpil_farm3 - tpiO_farm) / tpiO_farm
% Change in rotation profit at the landscape scale from baseline
change_lsl = (tpil_lsl - tpiO_ls) / tpiO_ls

change_lsz = (tpil_lsZ - tpiO_ls) / tpiO_ls
change_lsB = (tpil_ls3 — tpiO_ls) / tpiO_ls
checkl = change_lsl - change_farml

check2 = change_lsZ - change_farm2
check3 = change_ls3 - change_farm3
% Output

output=[farmingsystem; n; pesto; n_spray; p; reduc; alpha; beta; cp_s;
cp_c; ncadist; change_farm_sl; change_farm_sz; change_farm_sB;
change_farml; change_farm2; change_farm3;change_lsl; change_lsZ;
change_lsB];

fprintf(fid,'%12.0f %12.0f %12.0f %12.0f %12.2f %12.2f %12.2f %12.2f
%12.4f %12.4f %12.0f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f\n', output);

end
end

%%%%%%%%%% Strip %%%%%%%%%%%%%%%%%%%%%%%%%%%
for ncadist = 2 % Landscapes with strip NCH
for p = 1:1:16

if p == 1
cp_s = —0.002
cp_c = —0.002
elseif p == 2
cp_s = -0.004
cp_c = -0.004
elseif p == 3
cp_s = -0.006
cp_c = —0.006
elseif p == 4
cp_s = -0.009
cp_c = -0.008
elseif p == 5
cp_s = —0.011
cp_c = -0.010
elseif p == 6
cp_s = -0.013
cp_c = -0.012
elseif p == 7

160

cp_s = -0.015

cp_c = —0.014
elseif p == 8
cp_s = -0.017
cp_c = -0.016
elseif p == 9
cp_s = -0.019
cp_c = —0.018
elseif p == 10
cp_s = ~0.021
cp_c = -0.020
elseif p == 11
cp_s = -0.023
cp_c = -0.022
elseif p == 12
cp_s = -0.026
cp_c = -0.024
elseif p == 13
cp_s = -0.028
cp_c = -0.026
elseif p == 14
cp_s = -0.030
cp_c = -0.028
elseif p == 15
cp_s = -0.032
cp_c = -0.030
elseif p == 16
cp_s = —0.034
cp_c = ~0.032
end

reduc=interp1(pp, reduc_data, p) % pest reduction (%) corresponding
to p

w = max(round((n‘2 * (p/lOO)/4)/(n/2)),1) % Define width of the
strips
strip = [zeros(n/4-round(w/2),n/2);ones(w,n/2);zeros(n/2—w-(n/4-

round(w/2)),n/2)]
size_of_strip = w * n/2 * dx * dy
source = strip * dx * dy * alpha*(size_of_strip)‘beta
shape = strip

totalsource = sum(sum(source))

fsource = fft2(source)

impactl = max(0, real(fftshift(ifft2(fK1 .* fsource))))
impact2 = real(fftshift(ifft2(fK2 .* fsource)))
impact3 = real(fftshift(ifft2(fK3 .* fsource)))

% Balance check: total impact must be equal before and after
distribution over the landscape

afterl = sum(sum(impact1))

after2 = sum(sum(impact2))

after3 = sum(sum(impact3))
before = sum(sum(source))
relerrl = (afterl - before)/before
relerr2 = (after2 — before)/before

161

relerr3 (after3 - before)/before

relimpactl = impactl/totalsource
relimpact2 = impact2/totalsource
relimpact3 = impact3/totalsource

ic sum(sum(shape *(-1)
crop_impactl
crop_impact2
crop_impact3
tcrop_impactl
tcrop_impact2
tcrop_impact3

+ 1))

(shape * (-1) + 1)
(shape * (-1) + 1)
(shape * (-1) + 1)
sum(sum(crop_impact1))
sum(sum(crop_impact2))
sum(sum(crop_impact3))

.* impactl
.* impact2
.* impact3

r1 = min(1, (reduc * ic / tcrop_impactl) .* crop_impactl )

r2 = min(1, (reduc * ic / tcrop_impact2) .* crop_impact2 )

r3 = min(1, (reduc * ic / tcrop_impact3) .* crop_impact3 )

pestl = pesto * (1 - r1)

pest2 = pesto * (1 — r2)

pest3 = pesto * (1 - r3)

dml = (d1 * pestl)./(1 + (d1 * pestl / d2 ))

dm2 = (d1 * pest2)./(1 + (d1 * pest2 / d2 ))

dm3 = (d1 * pest3)./(1 + (d1 * pest3 / d2 ))

y1_sl = (shape * (-1) + 1) .* (ymax_s * (1 - dm1)) % Actual
soybean yield (bu/ac)

y1_52 = (shape * (-1) + 1) .* (ymax_s * (1 - dm2))

y1_83 = (shape * (-1) + 1) .* (ymax_s * (1 - dm3))

spi1_ce111 = (shape * (-1) + 1) .* 2.4710439 .* (y1_sl * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000) % Soybean profit per CELL

spi1_ce112 = (shape * (-1) + 1) .* 2.4710439 .* (y1_s2 * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

spi1_cell3 = (shape * (—1) + 1) .* 2.4710439 .* (y1_s3 * price_s -

pcost_s * (1 + cp_s)) * (dx * dy / 10000)

cpi1_cell (-1) + 1)
pcost_c * (1 + cp_c))

out of production

(shape *

*

rotpi1_celll
rotation

rotpi1_ce112

rotpi1_ce113

spi1_celll + cpi1_cell

spi1_ce112 +
spi1_cell3 +

cpi1_cell
cpil_cell

tpil_farml = sum(sum(rotpi1_celll))
tpil_farm2 = sum(sum(rotpi1_ce112))
tpil_farm3 = sum(sum(rotpil_ce113))
tpil_lsl = 4* tpil_farml

tpil_lsz = 4* tpil_farm2

tpil_lsB = 4* tpil_farm3

% Change

162

.* 2.4710439
(dx * dy /10000) % Corn profit given NCH taken

.* (y0_c * price_c -

% Profit per soybean-corn

% profit per rotation per farm

% profit for landscape

in soybean profit at the farm scale from baseline

change_farm_sl = ( (sum(sum(spi1_celll))) (sum(sum(spi0_cell))) )
/ (sum(sum(spi0_cell)))

change_farm_sz = ( (
/ (sum(sum(spi0_cell)))

change_farm_s3 = ( (sum(sum(spil_ce113)))
/ (sum(sum(spi0_cell)))

% Change in rotation profit at the farm scale from baseline

change_farml = (tpil_farml - tpiO_farm) / tpiO_farm

change_farm2 (tpil_farm2 - tpiO_farm) / tpiO_farm

change_farm3 = (tpil_farm3 - tpiO_farm) / tpiO_farm

% Change in rotation profit at the landscape scale from baseline

sum(sum(spil_ce112))) - (sum(sum(spi0_cell))) )

(sum(sum(spi0_cell))) )

change_lsl = (tpil_lsl — tpiO_ls) / tpiO_ls
change_ls2 = (tpil_lsZ — tpiO_ls) / tpiO_ls
change_ls3 = (tpil_ls3 - tpiO_ls) / tpiO_ls

checkl = change_lsl - change_farml

check2 = change_lsZ ~ change_farm2
check3 = change_ls3 - change_farm3
% Output

output=[farmingsystem; n; pesto; n_spray; p; reduc; alpha; beta; cp_s;
cp’c; ncadist; change_farm_sl; change_farm_sz; change_farm_s3;
change_farml; change_farm2; change_farm3;change_lsl; change_ls2;
change_lsB];

fprintf(fid,'%12.0f %12.0f %12.0f %12.0f %12.2f %12.2f %12.2f %12.2f
%12.4f %12.4f %12.0f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f\n', output);

end
end

%%%%%%%%%% Archipelago %%%%%%%%%%%%%%%%%%%%%%%%%%%
for ncadist = 3 % Landscapes with archipelago NCH

for p = 1:1:16
if p == 1
cp_s = 0.12
cp c = 0.084
elseif p == 2
Cp 8 = 0.239
cp_c = 0.168
elseif p == 3
cp_s = 0.359
cp_c = 0.252
elseif p == 4 %
cp_s = 0.479
cp_c = 0.337
elseif p == 5
cp_s = 0.598
cp_c = 0.421
elseif p == 6
cp_s = 0.718
cp_c = 0.505
elseif p == 7
cpfls = 0.837
cp_c = 0.589

163

reduc=interp1(pp, reduc_data, p) %

to p

for i=1

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

elseif p
cp_s
cp_c

end

:(n/2)

for j=1:(n/2)

end
end

totalsource

fsource

impactl
impact2
impact3

% Balan
distributi

archip(i,j)=(rand(1)<

archip
source
shape

CE
on

max(0,
real(fftshift(ifft2(fK2
real(fftshift(ifft2(fK3

= 8
0.957
0.673
9
1.077
0.757
10
1.196
0.841
11
1.316
0.926
12
1.436
1.010
13
1.555
1.094
14
1.675
1.178
15
1.794
1.262
16
1.914
1.346

pest reduction (%) corresponding

(p/100));

archip * dx * dy * alpha*(dx*dy)‘beta

archip

sum(sum(source))

fft2(source)

real(fftshift(ifft2(fK1 .* fsource))))
.* fsource)))
.* fsource)))

check: total impact must be equal before and after
over the landscape

afterl = sum(sum(impact1))

after2
after3
before
relerrl
relerr2

sum(sum(impact2))
sum(sum(impact3))
sum(sum(source))
(afterl - before)/before
(after2

- before)/before

164

relerr3 = (after3 - before)/before

relimpactl = impactl/totalsource
relimpact2 = impact2/totalsource
relimpact3 = impact3/totalsource

ic = sum(sum(shape *(-1) + 1))

crop_impactl = (shape * (—1) + 1) .* impactl
crop_impact2 = (shape * (-1) + 1) .* impact2
crop_impact3 = (shape * (-1) + 1) .* impact3

tcrop_impactl
tcrop_impact2
tcrop_impact3

sum(sum(crop_impact1))
sum(sum(crop_impact2))
sum(sum(crop_impact3))

r1 = min(1, (reduc * ic / tcrop_impactl) .* crop_impactl )
r2 = min(1, (reduc * ic / tcrop_impact2) .* crop_impact2 )
r3 = min(1, (reduc * ic / tcrop_impact3) .* crop_impact3 )
pestl = pesto * (1 - r1)
pest2 = pesto * (1 - r2)
pest3 = pesto * (1 - r3)
dml = (d1 * pestl)./(1 + (d1 * pestl / d2 ))
dm2 = (d1 * pest2)./(1 + (d1 * pest2 / d2 ))

/( ))

dm3 = (d1 * pest3). 1 + (d1 * pest3 / d2

y1_sl = (shape * (-1) + 1) .* (ymax_s * (l - dm1)) % Actual
soybean yield (bu/ac)

y1_s2 = (shape * (-1) + 1) .* (ymax_s * (1 - dm2))

y1_s3 = (shape * (-1) + 1) .* (ymax_s * (1 - dm3))

spil_celll = (shape * (-1) + 1) .* 2.4710439 .* (y1_sl * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000) % Soybean profit per CELL

spil_cellz = (shape * (-1) + 1) .* 2.4710439 .* (y1_sZ * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

spi1_ce113 = (shape * (-1) + 1) .* 2.4710439 .* (y1_s3 * price_s -
pcost_s * (1 + cp_s)) * (dx * dy / 10000)

cpil_cell = (shape * (—1) + 1) .* 2.4710439 .* (y0_c * price_c -
pcost_c * (1 + cp_c)) * (dx * dy /10000) % Corn profit given NCH taken
out of production

rotpi1_celll
rotation

rotpi1_ce112

rotpi1_ce113

spil_celll + cpi1_cell % Profit per soybean-corn

spi1_ce112 + cpi1_cell
spi1_ce113 + cpil_cell

tpil_farml sum(sum(rotpi1_celll)) % profit per rotation per farm
tpil_farm2 = sum(sum(rotpi1_ce112))
tpil_farm3 = sum(sum(rotpi1_ce113))

tpil_lsl = 4* tpil_farml % profit for landscape
tpil_lsZ = 4* tpil_farm2
tpil_lsB = 4* tpil_farm3

% Change in soybean profit at the farm scale from baseline

165

change_farm_sl = ( (sum(sum(spi1_celll))) — (sum(sum(spi0_cell))) )
/ (sum(sum(spi0_cell)))

change_farm_sZ = ( (sum(sum(spi1_ce112))) - (sum(sum(spi0_cell))) )
/ (sum(sum(spi0_cell)))
change_farm_s3 = ( (sum(sum(spi1_ce113))) - (sum(sum(spi0_cell))) )

/ (sum(sum(spi0_cell)))
% Change in rotation profit at the farm scale from baseline
change_farml = (tpil_farml — tpiO_farm) / tpiO_farm
change_farm2 (tpil_farm2 - tpiO_farm) / tpiO_farm
change_farm3 - (tpil_farm3 - tpiO_farm) / tpiO_farm
% Change in rotation profit at the landscape scale from baseline
change_lsl = (tpil_lsl - tpiO_ls) / tpiO_ls

change_lsz = (tpil_lsz - tpiO_ls) / tpiO_ls
change_ls3 = (tpil_ls3 - tpiO_ls) / tpiO_ls
checkl = change_lsl - change_farml
check2 = change_ls2 - change_farm2
check3 = change_ls3 — change_farm3

% Output

output=[farmingsystem; n; pesto; n_spray; p; reduc; alpha; beta; cp_s;
cp_c; ncadist; change_farm_sl; change_farm_sz; change_farm_s3;
change_farml; change_farm2; change_farm3;change_lsl; change_lsz;
change_ls3];

fprintf(fid,'%12.0f %12.0f %12.0f %12.0f %12.2f %12.2f %12.2f %12.2f
%12.4f %12.4f %12.0f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f %12.4f
%12.4f %12.4f\n', output);

end

end

end

166

Appendix C:
Estimated relationship between the pest reduction impact and the proportion of
non-crop habitats in the landscape

 

Proportion of reduction in aphid
density as compared to the case
Aphid density Proportion of non-crop habitats when the proportion of non-crop

 

Japhids/mz)a in landscape habitats in landscape is 0.01b
4600 0.01 O
3400 0.04 0.26
l 533 0.09 0.67
0 0.16 l

 

a Aphid density in wheat at the time of harvest (Julian date 230). Data source: Bianchi
and van der Werf, 2003
b Calculated by author.

167

Appendix D:

Proportion of change in variable costs of production due to the establishment of

 

 

 

non-crop habitats (Lambda)
Square
# of # of
strips strips proportion coef of Lambda Lambda Lambda Lambda
prop_ in outside # of of total machinery (organic (conv (organic (conv
NCH NCH NCH turns field time cost com) com) soy) soy)

0 0 400 399 0.15 1 0.00 0.00 0.00 0.00
0.01 40 360 439 0.17 1.02 0.00 0.00 0.01 0.00
0.02 57 343 456 0.17 1.02 0.01 0.00 0.01 0.00
0.03 69 331 468 0.18 1.03 0.01 0.00 0.01 0.00
0.04 80 320 479 0.18 1.03 0.01 0.00 0.01 0.00
0.05 89 31 1 488 0.18 1.03 0.01 0.00 0.01 0.00
0.06 98 302 497 0.19 1.04 0.01 -0.01 0.01 0.00
0.07 106 294 505 0.19 1.04 0.00 -0.01 0.01 0.00
0.08 1 13 287 512 0.19 1.04 0.00 -0.01 0.01 -0.01
0.09 120 280 519 0.20 1.05 0.00 -0.01 0.01 -0.01

0.1 126 274 525 0.20 1.05 0.00 -0.01 0.01 -0.01
0.1 1 133 267 532 0.20 1.05 0.00 -0.01 0.01 -0.01
0.12 139 261 538 0.20 1.05 0.00 -0.01 0.01 -0.01
0.13 144 256 543 0.20 1.05 0.00 -0.02 0.01 -0.01
0.14 150 250 549 0.21 1.06 0.00 -0.02 0.01 -0.01
0.15 155 245 554 0.21 1.06 0.00 -0.02 0.01 -0.02
0.16 160 240 559 0.21 1.06 0.00 -0.02 0.01 -0.02

 

168

Appendix D (cont’d):
Proportion of change in variable costs of production due to the establishment of

non-crop habitats (Lambda)

 

 

 

Strip
# of # of
strips strips proportion coef of Lambda Lambda Lambda Lambda
prop_ in outside # of of total machinery (organic (conv (organic (conv
NCH NCH NCH turns field time cost comL corn) sgy) soy)

0 0 400 399 0.15 1 0.00 0.00 0.00 0.00
0.01 4 396 395 0.15 1 0.00 0.00 0.00 0.00
0.02 8 392 391 0.15 1 0.00 0.00 -0.01 0.00
0.03 12 388 387 0.15 1 -0.01 -0.01 -0.01 -0.01
0.04 16 384 383 0.14 0.99 -0.01 -0.01 -0.01 -0.01
0.05 20 380 379 0.14 0.99 -0.01 -0.01 -0.01 -0.01
0.06 24 376 375 0.14 0.99 -0.01 -0.01 -0.02 -0.01
0.07 28 372 371 0.14 0.99 -0.02 -0.01 -0.02 -0.01
0.08 32 368 367 0.14 0.99 -0.02 -0.02 -0.02 -0.02
0.09 36 364 363 0.14 0.99 -0.02 -0.02 -0.02 -0.02

0.1 40 360 359 0.13 0.98 -0.02 -0.02 -0.03 -0.02
0.1 l 44 356 355 0.13 0.98 -0.02 -0.02 -0.03 -0.02
0.12 48 352 351 0.13 0.98 -0.03 -0.02 -0.03 -0.03
0.13 52 348 347 0.13 0.98 -0.03 -0.03 -0.04 -0.03
0.14 56 344 343 0.13 0.98 -0.03 -0.03 -0.04 -0.03
0.15 60 340 339 0.13 0.98 -0.03 -0.03 -0.04 -0.03
0.16 64 336 335 0.13 0.98 -0.03 -0.03 -0.04 -0.03

 

169

_ Appendix D (cont’d):
Proportion of change in variable costs of production due to the establishment of

non-crop habitats (Lambda)

 

 

 

Archipelago
proportion coef of Lambda Lambda Lambda
prop_ number of Number of total machinery (organic (conv (organic Lambda
NC H NCH cells of tums field time cost com) com) soy) Aconv soy)
0 0 399 0.15 1 0.00 0.00 0.00 0.00
0.01 1600 1999 0.75 1.60 0.24 0.08 0.37 0.12
0.02 3200 3599 1.35 2.20 0.47 0.17 0.75 0.24
0.03 4800 5199 1.95 2.80 0.71 0.25 1.12 0.36
0.04 6400 6799 2.56 3.41 0.95 0.34 1.50 0.48
0.05 8000 8399 3.16 4.01 1.19 0.42 1.87 0.60
0.06 9600 9999 3.76 4.61 1.42 0.50 2.24 0.72
0.07 11200 11599 4.36 5.21 1.66 0.59 2.62 0.84
0.08 12800 13199 4.96 5.81 1.90 0.67 2.99 0.96
0.09 14400 14799 5.56 6.41 2.13 0.76 3.37 1.08
0.1 16000 16399 6.17 7.02 2.37 0.84 3.74 1.20
0.1 1 17600 17999 6.77 7.62 2.61 0.93 4.12 1.32
0.12 19200 19599 7.37 8.22 2.85 1.01 4.49 1.44
0.13 20800 21199 7.97 8.82 3.08 1.09 4.86 1.56
0.14 22400 22799 8.57 9.42 3.32 1.18 5 .24 1.67
0.15 24000 24399 9.17 10.02 3.56 1.26 5.61 1.79
0.16 25600 25999 9.77 10.62 3.79 1.35 5.99 1.91

 

170

Appendix E:
Production costs by farming system and crop

 

 

 

 

 

 

Soybean
Proportion of
Machinery (repair, Seed machinery cost in Proportion of
fuel and hire) ($/ha) A8/ha) VC (S/ha) VC seed cost in VC
Organic 162.5 47.5 260 0.63 0.18
Conv 52.5 47.5 260 0.20 0.18
Corn
Proportion of
Machinery (repair, Seed machinery cost in Proportion of
fuel and hire) ($/ha) (S/ha) VC (s/th VC seed cost in VC
Organic 187.5 75 472.5 0.40 O. 16
Conv 70 87.5 490 0.14 0.18

 

Source: UIUC, 2003.

171

   

uTTTTTITTTTTTIT):