EPA/600/R-XX/XXX | October 2010 | www.epa.gov/nrmrl



# Risk Assessment of the Evolution of Resistance in European Corn Borer( Ostrinia nubilalis Hubner) and Southwestern Corn Borer( Diatraea grandiosella ) to Smartstax ® 

# corn

Letter Report

Sustainable Technology Division, Cincinnati, OH 45268 National Risk Management Research Laboratory Office of Research and DevelopmentEPA/600/R-XX/XXX October 2010



# Risk Assessment of the Evolution of Resistance in European Corn Borer( Ostrinia nubilalis Hubner) and Southwestern Corn Borer( Diatraea grandiosella ) to Smartstax ® 

# corn

Letter Report

October 2010

Michael Caprio 1 

### , John A. Glaser 2

1 Mississippi State University, Department of Entomology and Plant Pathology, Mississippi State, MS 39762-9775
2 US Environmental Protection Agency, Na tional Risk Management Research Laboratory, Sustainable Technology Divis ion, Cincinnati, OH 45268



### Sustainable Environments Branch

Sustainable technology Division National Risk Management Research Laboratory Office of Research and Development Cincinnati, Ohio 45258

U.S. Environmental Protection Agency Office of Research and Development Washington, DC 20460

## Notice

The U.S. Environmental Protection Agency thr ough its Office of Research and Development funded and managed the research described here. It has been subjected to the Agency=s peer and administrative review and has been approv ed for publication as an EPA document. Mention of trade names or commercial products does not constitute endorsement or recommendation for

use

. The information provided in this paper is not intended for determining compliance with state or federal regulations for Plant Iincorporated Pesticide resistance management. For these purposes, information should be obtained from the appropriate local, state and federal regulatory agencies, the Federal Insecticide Fungicide and Rodentic ide Act, the United States Code, the Code of Federal Regulations, the Federal Register and other sources.

## Abstract

Genetically-Modified(GM) crops containing pes ticidal traits are valued as environmental

assets since they directly replace broad spec trum chemical pesticides having detrimental

environmental and human health effects. As pa rt of the risk assessment for each new GM

crop registration requires an evaluation of the sustainable lifetime for each new GM crop

variety. Models employing principles of popul ation genetics have been used to simulate field

conditions where the development of insect pest re sistance to the control tr aits of the crop is

encountered. The Monsanto Company’s submission of the Superstax ® corn event for control

of the European corn borer( Ostrinia nubilalis Hubner) and the Southwestern Corn Borer

( Diatraea grandiosella ) has been evaluated for the development of insect pest resistance

using the EPA developed deterministic two locu s simulation model POPGEN D2L. The design

of research is presented wit h the interpreted results.

## Foreword

The U. S. Environmental Protection Agency (USEPA) is charged by Congress with protecting the Nation's land, air, and water resources. Under a mandate of national environmental laws, the Agency strives to formulate and implement actions leading to a compatible balance between human activities and the ability of natural systems to support and nurture life. To meet this mandate, USEPA’s re search program is providing data and technical support for solving environmental problems today and building a science knowledge base necessary to manage our ecological resources wisely, understand how pollutants affect our health, and prevent or reduce env ironmental risks in the future.

The National Risk Management Research Laboratory (NRMRL) is the Agency's center for investigation of technological and management approaches for preventing and reducing risks from pollution that threaten human health and the environment. The focus of the Laboratory's research program is on methods and their cost-effectiveness for prevention and control of pollution to air, land, water, and subsurface resource s; protection of water quality in public water systems; remediation of contaminated sites, sedi ments and ground water; prevention and control of indoor air pollution; and restoration of ec osystems. NRMRL collaborates with both public and private sector partners to foster technologies that reduce the cost of compliance and to anticipate emerging problems. NRMRL's research provides solutions to environmental problems by: developing and promoting technologies that protect and improve the environment; advancing scientific and engineering information to support regulatory and policy decisions; and providing the technical support and information transfer to ensure implementation of environmental regulations and strategies at the national, state, and community levels.

This publication has been produced as part of the Laboratory's strategic long-term research plan. It is published and made av ailable by USEPA's Office of Research and Development to assist the user community and to link researchers with their clients.

Sally Gutierrez, Director National Risk Management Research Laboratory

## Contents

Notice.............

............................................................................................................ ...... Abstract.......................................................................................................

................ ..... Foreword.......................................................................................................................

... Contents........................................................................................................

............... ..... List of Figures................

.................. ............... ................ ................ ................ ............... ..... List of Tables..........

...................... .................. ................ ................ ................ ............... ...... Terminology............

........................................................................................................ CHAPTER 1 Introduction............................................................................... 1.1 Background.................................................................................. 1.2 Purpose....................................................................................... CHAPTER 2 Study design............................................................................ 2.1 RM Models 2.2 Parameters 2.3 Methods and materials 2.4 Results CHAPTER 3 Discussion and Conclusions References......................................................................................................

............... .. Appendix 1 Resistance Manage ment Models Used for this Analysi s................

................ Appendix 2 Deterministic Parameter Description.................

.................. ............... ............ Appendix 3 European CornBorer Sensitivity Analysis Appendix 4 Southwestern Corn Borer Sensitivity Analysis

## List of Figures

Figure 1: Schematic of the deterministic frequency based m odel for both seed-blend and block refuge deployments

## List of Tables

Table 1: PERT parameters for the variables in the structured and larval movement simulations of European corn Borer

Table 2: PERT parameters for the variables in the structured and larval movement simulations of Southwestern corn Borer

Table 3: The fitnesses and dominance values draw n in this example of fitness calculations

Table 4a: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was SS

Table 4b: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was RS

Table 4c: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was RR

# Risk Assessment of the Evolution of Resistance in European Corn Borer( Ostrinia nubilalis Hubner) and Southwestern Corn Borer( Diatraea grandiosella ) to Smartstax ® 

# corn

Letter Report

October 29, 2010

Michael Caprio 1 

### , John A. Glaser 2

1 Misssissippi State University, Department of Entomology and Plant Pathology, Mississippi State, MS 39762-9775
2 US Environmental Protection Agency, Na tional Risk Management Research Laboratory, Sustainable Technology Divis ion, Cincinnati, OH 45268

Keywords: PIP corn variety, PIP crop registration, re sistance management, simulation modeling, refuge in bag



### CHAPTER 1 Introduction

The USEPA, under its administrat ion of the Federal Insectic ide Fungicide and Rodenticide

Act (FIFRA), requires the registration of all pe sticides and pesticidal materials. The GM or

Plant Incorporated Protectant (P IP) crops containing pesticidal traits are subject to FIFRA

registration requirements. Concerns relating to future environmental effects of these crops

can be investigated only using simu lation models. Model application in this instance offers an

analysis of the useful lifetime for the pesticida l traits. USEPA has clearly supported the use of

these traits as replacements of broad spectrum pesticides that have significant environmental

footprints.

1.1 Background

Resistance management (RM) simulation models are designed as analytical methodologies

to provide realistic assessment of the risk of re sistance evolution given the allele frequencies

used as initial conditions. New concepts of PIP crop deployment such as new trait structuresand refuge-in-the-bag require a detailed evaluation to ensure the claims associated with each

concept offer the sustainable protection of the crop. Simulation m odels offer a means to

evaluate the threat of crop lo ss through the development of resistance in the near future.

1.2 Purpose

This research effort was designed to evaluat e the relative merit of resistance management

concepts as submitted by Monsanto Company relative to the Superstax ® corn registration.

This research specifically analy zed the relative risks related to the control of western corn

rootworm in seed mixture scenarios



### CHAPTER 2 Study Design

To understand the relative risks related to the evolution of resistance in western corn

rootworm for the Superstax ® corn variety as submitted by Monsanto Company, a two locus

frequency-based deterministic model was deve loped and evaluated to simulate the

development of insect pest resistance..

2.1 RM Models

POPGEN-D2L

The deterministic model POPGEN-D2L is a modifi cation of a previously developed simple

frequency-based model that incorporates noncom pliance, non-random mating in compliant

fields and larval movement. This dual locu s simulation model designed to evaluate the

population dynamics of crop pest insects relating to the devel opment of resistance to

pesticidal controls installed in the crop. The model includes a switch to evaluate a blockrefuge design and a seed-mixture design. Biologic al parameters were primarily derived fromthat model with the except ion of mortality rates, block size , dispersal rates and spatial aspects

of refuge placement and movement.

2.2 Materials and Methods

The same deterministic risk assessment mo del was used for these simulations as was

used for the western corn rootworm simulations (though all three loci were used). An excerpt

from previous research is also included at t he end of this report that more fully presents

details of the deterministic model (Caprio &G laser 2010a&b). Paramete rs were adjusted for

the unique biology of these insects and the impa cts of the three toxins on each species (see

Tables 1 and 2). Some specif ic adjustments included an increas e in the effective refuge size

because these insects are more mobile and a more even deposition of eggs across the field

would be expected (see Caprio & Glaser 2010a& b). The base larval and asymmetrical

movement rates were both in creased. The proportion of consistent non-compliance was

maintained at the same level as the corn r ootworm simulations, reflecting a concern over

areas of concentrated non-compliance, but the amount of mixing between these fields and

other fields was increased to reflect the greater overwintering dispersal of the two corn borer

species.

The greatest difficulty in simulating the time to resistance based on the submitted data

is partitioning the non-multiplicative interactions between the loci. If the mortality caused by

each toxin were independent of the mortality c aused by the other toxi ns, one would expect

the overall mortality of the produc t to be the product of the survivor ship to each toxin. If two

toxins each kill 95% of the population, then one w ould expect the second toxin to kill 95% of

the 5% of the population that survived the first toxin and the joint survivorship should be

0.25%. These simulations can estimate this non-multiplicative interaction by comparing theoverall survivorship drawn from our PERT dist ribution with product of the individual toxin

mortalities based on the draws from their respec tive PERT distributi ons. In a two locus

simulation, there is only one interaction, and all of the interaction can be attributed to that pair

of loci. In three locus simulations as used with Superstax ® , there are three interactions

(Cry1A.105<->Cry2Ab2, Cry1A.105<->Cry1F, Cr y2Ab2<->Cry1F), and it is impossible to

accurately distribute the interactions without addi tional data on the two locus interactions. In

the absence of data the mortality effects of pairs of toxins, the attempt was made to distribute

the interactions evenly between the three pairs of loci. Note that we assumed if an insect is

resistant to two loci, then the mortality rates fo r the remaining locus are the same as if that

toxin were used alone. The mortality of W [SS][RR][RR] is therefor estimated as W [SS] . The

overall survivorship is given by W [SS][SS][SS] . The fitnesses that are difficult to determine based

on the submitted data are: W [SS][SS][RR] , W [RR][SS][SS ] and W [SS][RR][SS] . Our approach was to

estimate the individual interact ions by taking the cube root of the total non-multiplicative

interaction ( INI , measured as Overallsurvivorship/(W [SS][RR][RR] * W [RR][SS][RR] * W [RR][RR][SS] ). The

fitness of W [SS][SS][RR] was then W [SS][RR][RR] * W [RR][SS][RR] * INI

.

nonAdditiveInteraction = OverallSurvi vorship/(fit1[0] * fit2[0] *fit3[0]);

nonAdditiveInteraction2L = Math.e xp(Math.log(nonAdditiveInteraction)/3);

Survivorships[0][0][ 0] = OverallSurvivorship;

Survivorships[2][0][0] = fit1[0] * fit2[0] * no nAdditiveInteraction2L;

In this code fit1[0] is W [SS][RR][RR] and fit2[0] is W [RR][SS][RR] . There were several additional

constraints on the new fitness. The fitness of the double susceptible genotype had to be less

than or equal to either of the component single susceptible genotypes. This ensures that thefitness of a genotype does not decrease as additional resistance alleles are added.

if (Survivorships[2][0][0 ] > Math.min(fit2[0],fit3[0]))

{ Survivorships[2][0 ][0] = Math.min(fit2[0],fit3[0]); }

Finally, the new fitness of the double susceptible genotype could not be less than the overall

fitness. Note that the overall survivorship was already constrained to be at least as low as the

lowest single toxin fitness.

if(Survivorships[2][0][0 ] < OverallSurvivorship) {

Survivorships[2][0][0 ] = OverallSurvivorship; }

This process was repeated for all three doubl e susceptible genotypes. The remaining

fitnesses involving heterozygous genotypes could then be calculated based on dominance

values and fitness values already estimated. The relevant code is (hl1, hl2 and hl3 are the

dominance values drawn for dominance of t he Cry1A.105, Cry2Ab2 and Cry1F resistance

loci):

Survivorships[0][2][2] = fit1 [0]; //This is the equivalent of W [SS][RR][RR]
Survivorships[1][2][2] = (1 .0 - fit1[0]) * hl1 + fit2[0];

Survivorships[2][2][2] = 1.0;

Survivorships[2][0][2] = fit2[0];

Survivorships[2][1][2] = (1 .0 - fit2[0]) * hl2 + fit2[0];

Survivorships[2][2][0] = fit3[0];Survivorships[2][2][1] = (1 .0 - fit3[0]) * hl3 + fit3[0];

Survivorships[0][1][2] = (Survivorshi ps[0][2][2] - Survivorsh ips[0][0][2]) * hl2 +

Survivorships[0][0][2];

Survivorships[1][0][2]= (Survivorshi ps[2][0][2] - Survivorsh ips[0][0][2]) * hl1 +

Survivorships[0][0][2];

Survivorships[2][1][0] = (Survivorshi ps[2][2][0] - Survivorsh ips[2][0][0]) * hl2 +

Survivorships[2][0][0];

Survivorships[2][0][1] = (Survivorshi ps[2][0][2] - Survivorsh ips[2][0][0]) * hl3 +

Survivorships[2][0][0];

Survivorships[0][1][0] = (Survivorships[0 ][2][0] - OverallSurvi vorship) * hl2 +

OverallSurvivorship;

Survivorships[1][2][0] = (Survivorshi ps[2][2][0] - Survivorsh ips[0][2][0]) * hl2 +

Survivorships[0][2][0];

Survivorships[1][0][0] = (Survivorships[2 ][0][0] - OverallSurvi vorship) * hl1 +

OverallSurvivorship;

Survivorships[2][2][1] = (1.0 - Survivorships[2][2][0]) * hl3 + Survivorships[2][2][0];

Survivorships[2][1][1] = (Survivorshi ps[2][1][2] - Survivorsh ips[2][1][0]) * hl3 +

Survivorships[2][1][0];

Survivorships[1][0][1] = (Survivorshi ps[1][0][2] - Survivorsh ips[1][0][0]) * hl3 +

Survivorships[1][0][0];

Survivorships[0][0][1] = (Survivorships[0 ][0][2] - OverallSurvi vorship) * hl3 +

OverallSurvivorship;Survivorships[0][2][1] = (Survivorshi ps[0][2][2] - Survivorsh ips[0][2][0]) * hl3 +

Survivorships[0][2][0];

Survivorships[1][2][1] = (Survivorshi ps[1][2][2] - Survivorsh ips[1][2][0]) * hl3 +

Survivorships[1][2][0];

Survivorships[0][1][0] = (Survivorships[0 ][2][0] - OverallSurvi vorship) * hl2 +

OverallSurvivorship;

Survivorships[0][1][1] = (Survivorshi ps[0][1][2] - Survivorsh ips[0][1][0]) * hl3 +

Survivorships[0][1][0];

Survivorships[1][1][0] = (Survivorships[2][1][0] - Surviv orships[0][1][0])*(hl1+hl2)/2 +

Survivorships[0][1][0];

Survivorships[1][1][1] = (Survivorships[2][1][1] - Surviv orships[0][1][1])*(hl1+hl2)/2 +

Survivorships[0][1][1];

Survivorships[1][1][2] = (Survivorships[2][1][2] - Surviv orships[0][1][2])*(hl1+hl2)/2 +

Survivorships[0][1][2];

As noted in the CRW modeling report, there can be multiple ways to estimate double

heterozygotes (Caprio & Glaser, 2010c ). For example, the fitness W [RS][RS][RR] could be

calculated as (W [RR][RS][RR] – W [SS][RS][RR] ) * hl1 + W [SS][RS][RR] , or it could be calculated as

(W [RS][RR][RR] – W [RS][SS][RR] ) * hl2 + W [RS][SS][RR] . Another alternative is to use a mean

dominance for double heterozygotes. Other opti ons certainly exist. For example, the

minimum, mean or maximum of the two calculated heterozy gotes fitnesses could be used

depending on the degree of conserva tism one desires. The options became clearer as the

modeling research progressed, and we were not entirely consistent in their use. Testing thetwo options suggested the model was insensitive to each option, and given the short time

frame we chose to proceed with the calculations as shown.

All simulations were extended for at least 10 00 generations. Assuming that each gene should

ideally last at least 15 year s, the target time horizon fo r a three gene product would be 45

years. Conservatively assuming that there ar e 3 generations per year for both species, this

gives a target time goal of 135 generations. Fo r both species, at least 1000 simulations were

conducted for both the structur ed refuge and seed-blend options.



### 2.3 Results

The European corn borer simulations did not show any cases of resistance prior to the

time goal of 135 generations. The seed-blend opt ion was less durable, but the shortest time

taken for resistance to evolve in any single si mulation was 158 generations. The shortest

time for the structured refuge option was lon ger than 1000 generations (see Appendix 3). The

risk of resistance was somewhat greater with Southwestern corn borer than with European

corn borer. The seed-blend option was less durable and 4.5% of the simulations resulted in

resistance evolving in less than 135 generations (c a. 45 years). For the structured refuge

option, the shortest time to resistance wa s 118 generations and 0.2% of the simulations

resulted in the evolution of resistance in less than 135 generati ons (see Appendix 4).



### Chapter 3 - Discussion

The results presented here sugge st that there is a low risk of resistance evolving within

45 years to SmartStax corn in either specie s (<5%). These may be considered somewhat

conservative estimates as potential fitness cost s were not included in the simulations. Giventhe long time frames observed for the evolution of resistance, it is likely that fitness costs

could have a significant impact in further delay ing resistance. The genetics and interactions

between fitness costs to different toxins ar e, however, unknown and would add considerably

to the uncertainty of the result s. Given the time frames alr eady observed, the inclusion of

fitness costs seemed superfluous.

The inclusion of three loci significantly incr eased the complexity of these simulations.

The non-multiplicative interactions between loci were impossible to accurately partition given

the information submitted. To the degree possible, inclusion of data on two locus interactions

in future submissions would help to more accurately evaluate the data. The solutions to the

problems of three locus simulations present ed here are merely a first attempt and will

hopefully provide a basis for further improv ement in methods and data needs to understand

how resistance evolves in these complex systems.



### References

Caprio, M. A. and D. Sumerford. 2007. Evaluating transgenic plan ts for suitability in pest and resistance management programs, 2nd edition. L. Lacey & H. Kaya [eds]. Field Manual of Techniques for the Application and Evaluation of Entomopathogens.

Caprio, M.A. and J.A. Glaser 2010a, The Use of Simulation Models to Evaluate Pest Resistance Development to Refuge in the B ag Concepts related to Pioneer Submission: Letter Report, January 2010, US EPA Natio nal Risk Management Research Laboratory, Cincinnati, OH.

Caprio, M.A. and J.A. Glaser 2010b, The Use of Simulation Models to Evaluate Pest Resistance Development to Refuge in the B ag Concepts related to Pioneer Submission: Letter Report Addendum, April 2010, US EPA National Risk Management Research Laboratory, Cincinnati, OH.

Caprio, M.A. and J.A. Glaser 2010c, Risk Assessment of the Evol ution of Resistance in Western corn rootworm ( Diabrotica virgifera virgifera LeConte) to Smartstax ® corn, Letter Report, October 2010, US EPA National Risk Management Research Laboratory, Cincinnati, OH.Hibbard, BE, MI Higdon, DP Duran, YM Schweikert, and MR Ellersieck. 2004. Role of egg density on establishment and pl ant-to-plant m7(3): 871-882

Hibbard, BE, TT Vaughn, IO Oyediran, TL Clark , MR Ellersieck. 2005. Effect of Cry3Bb1 expressing transgenic corn on plant-to-plant mo vement by western corn rootworm larvae (Coleoptera Chrysomeldiae). J. Econ. Entomol. 98(4): 1126-1138

Vose, 2000. Risk Analysis: A quantit ative guide. Wiley, New York.Variable Min Mode Max Comments Cry1A.105 0.00001 0.001 0.005 Cry2Ab2 0.00001 0.001 0.01 Cry1F 0.001 0.005 0.01 Overall Survivorship 0.00001 0.001 0.005This will always be as low as lowest of the three loci Dominance 0.01 0.05 0.2Drawn independently for both loci Initial frequency 0.001 0.005 0.02

These are variables specific to spatial refuges Refuge size 0.025 0.04 0.06Always set to 0.05 if seed-mix Non-compliance 0 0.3 0.6 Always set to 0 for seed-mix Non-compliance mixing 0.8 0.9 1 Non-random mating 0.2 0.5 0.7Always set to 0 for seed-mix

These are v ariables specific to seed-mixes Base larval movement 0.3 0.5 0.7Always set to 0 for spatial refuges Days of larval selection 5 10 15 Asymmetrical larval movement 0.8 0.9 0.95Always set to 0 for spatial refuges

Table 15: PERT parameters for the variables in th e structured and larval movement simulations of E uro p ean corn Bore r

Variable Min Mode Max Comments Cry1A.105 0.001 0.05 0.08 Cry2Ab2 0.001 0.05 0.1 Cry1F 0.001 0.005 0.01 Overall Survivorship 0.00001 0.005 0.008This will always be as low as lowest of the three loci Dominance 0.01 0.05 0.2Drawn independently for both loci Initial frequency 0.0005 0.001 0.002

These are variables specific to spatial refuges Refuge size 0.025 0.04 0.06Always set to 0.05 if seed-mix Non-compliance 0 0.3 0.6 Always set to 0 for seed-mix Non-compliance mixing 0.8 0.9 1 Non-random mating 0.05 0.3 0.5Always set to 0 for seed-mix

These are v ariables specific to seed-mixes Base larval movement 0.3 0.5 0.7Always set to 0 for spatial refuges Days of larval selection 5 10 15 Asymmetrical larval movement 0.8 0.9 0.95Always set to 0 for spatial refuges

Table 26: PERT parameters for the variables in th e structured and larval movement simulations of Southwestern corn Bore rSurvivorship of homozygous susceptibles Dominance

Cry1A.105 0.00275 0.11500 Cry2Ab2 0.00190 0.09976 Cry1F 0.00502 0.03600 Overallsurvivorship 0.00140 N/A
Table 3: The fitnesses and dominance values drawn in this example of fitness calculations

Cry1A.105

SS RS RR Cry2Ab2 SS 0.00140 0.00140 0.00140

RS 0.00140 0.00144 0.00176

RR 0.00140 0.00176 0.00502
Table 4a: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was SS

Cry1A.105

SS RS RR Cry2Ab2 SS 0.00140 0.00140 0.00142

RS 0.00140 0.00182 0.00535

RR 0.00145 0.00593 0.04084
Table 4b: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was RS

Cry1A.105

SS RS RR Cry2Ab2 SS 0.00140 0.00146 0.00190

RS 0.00153 0.01228 0.10148

RR 0.00275 0.11764 1.0
Table 4c: The fitness values calculated for Cry1A.105 and Cry2Ab2 genotypes when the Cry1F genotype was RRFigure 12: Schematic of the deterministic frequency based model for both seed-blend and block refuge deployments.

### Appendix 1 - Resistance Management Model Used for this Analysis

The deterministic model is a relatively simp le frequency-based model that incorporates noncompliance, non-random mating in compliant fields and larval movement. It includes a switch

to vary between a block-refuge design and a seed-mixture design. Appendix 2 includes

descriptions of the different parameters. The pr imary difference between t he Bt population in

the non-compliant population an d the Bt-population in the non-random mating population is

that no refuge was planted for the non-compliant fields. Non-compliant populations reduce

both non-random mating and refuge size. (Caprio & Glaser, 2010a&b).

While this may overestimate move ment of refuges by growers, th is was incorporated into the

model by defining the refuge size not as the physical area devoted to the refuge, but rather

the proportion of the eggs in a field that st art out underneath the new refuge. This is the

effective refuge size to distinguish it from physical refuge size (the proportion of an area

planted to a refuge). These small refuge size s are independent of non-compliance and result

from growers moving their refuge to areas of the field were few eggs were deposited the

previous year. To estimate this important parame ter, we used the stochastic model to estimate

egg densities at the start of a year across our f our different field sizes. In each case, we

estimated a best and worst scenario. For the bes t case scenario, the grower moved their

refuge to the opposite side of t he field, next to where the re fuge would have been planted in

the neighboring field the previous year (these simulations were run with all gr owers planting

refuges to the same sides of their fields and swapping them every y ear). The worst case

scenario was based on planting the refuge in t he area of the field w here the egg density was

the lowest. Because the egg density distribution ac ross fields has never been measured, it is

unlikely that growers could accomplish this, but it does represent and theoretical lower bound

for effective refuge size. The worst case effectiv e refuge sizes for the four different field sizeswere (from smallest to larges t field size): 15%, 11 %, 3% and 0.055%. Few insects were noted

to be moving into the center of large fields as re flected by the effective refuge size of 0.055%

for 144 ha fields. Other estimates for dispersa l are higher and may depend on the region of

the country. To test the effect of higher di spersal rates we doubled the vector of daily

movement (to 29m/day) and repeated t he large field size simulation In this case the density

of eggs in the center of the field was fifty ti mes greater under the wors t case scenario and the

effective refuge size was 1%. Most fields in the corn belt, however, are smaller, in the range of

30-50 ha, and we decided to use a lower limit of 1% for this parameter.

Asymmetrical movement was included in the model, though the amount movement of

susceptible larvae from transgenic corn is uncer tain (Hibbard et al 2004, Hibbard et al 2005).

Asymmetrical movement was defined as the probability that larvae that have survived

exposure on a Bt-plant will move. When la rvae move, they move onto plant genotypes

according to the ratio of those genotypes in the field. In this case, a larva leaving a transgenic

plant had a 95% probability of moving onto another transgenic plant. As with other rates in the

model, this movement rate is converted into a daily rate (depending on the days of larval

movement parameter).

### Appendix 2 - Deterministic Parameter Description

Wss – The fitness of homozygous susceptible genotypes on the transgenic plants. Without

better knowledge of field tests it's difficult to develop a range, but a spec ific factor over and

under was used to deve;op our estimate. One question to be asked might be what is the

lowest/highest performance under field conditions. Instead of 98.75% mortality, could it be

95% (as an example)?

Dominance – The relative fitness of heteroz ygotes. The traditional population genetics

equation was employed:

Wrs = (Wrr – Wss) * h + Wss

where h is the dominance and Wrr = 1.0. Our distribution is derived from an estimate of

h=0.05, but that seems low compared to many estimates based on LC50s. LC50s, however,

are based on a log scale, however this research has used a linear scale. In general, for

products with lower effectiveness, dominance t ends to be higher ( Caprio et al 2007).

IRF – The initial resistance allele frequency. My impression from deal ing with CRW folks is

that this value has tended to be higher in empirical estimates than we have seen for other

insects.

Block refuge model parameterization:

Values cited above are shared wi th the larval movement model and changes in would effect

both the block and larval movement models to a similar degree.Refuge proportion – Initially set this to 20%. However, it can be viewed as the proportion of

eggs in a compliant field that end up being in a refuge (perhaps after being moved), and the

non-random oviposition patterns can be addressed usi ng this parameter. If more individuals

survive in refuges, and they tend to lay eggs near that area, then the number of eggs in the

soil to start the new growing s eason will be greatest near the refuge from the previous year. If

the refuge is moved, it stands to reason that the new refuge, even if it covers 20% of the area,

will receive less than 20% of the eggs ovipos ited in the field. Based on this modeling

research, this fact and the likelihood that refuges are moved are identified as key

assumptions of previous modeling efforts. Unfo rtunately, there is little empirical data on the

non-random oviposition patterns of CRW.

Non-compliance – This is the proportion of fields that are planted without a refuge.

Individuals emerging from this ar ea mate as a separate population. The most likely value is a

literature value (CSPI). This parameter should be based on a field by field basis and

incorporate some estimate of amount of non-comp liance. A person planting a 3% refuge in a

field is not the same as someone not planting any re fuge. Alternatively, it shouldn't measure if

a field is compliant (as yes./no answer), but how compliant a non-compliant field is. General

comments have been encountered which indicated t hat 30% non-compliance was too low. It

is not obvious how non-compliance was estima ted. This parameter may be important

because it determines how much Bt-c orn is planted without any refuge.

Non-compliance mixing – This determines how much movement there is between compliant

and non-compliant fields. If non-co mpliant growers are accidentally non-compliant (i.e. they

never got around to planting the refuge because of weather), then they will generally becompliant in the next year, and this parameter s hould be close to 1.0. On the other hand, if

non-compliant growers are growers who purposefully don't plant refuges and continue this

practice year-by-year, then this paramete r should be low. How low would depend on how

much movement naturally occurs between non-comp liant and compliant fiel ds. Inevitably this

leads to discussion of the cluste ring of non-compliant fields.

Non-random mating – This parameter addresses the proportion of the population in the Btportion of compliant fields that is far enough away from the refuges that they do not mate at

random. These differ from non-compliant fields in that refuge is plant ed, but it was too far

away. The non-random oviposition that result s from this non-random mating (and limited

dispersal capability) is covered by the reductions in refuge size discussed above.

Larval movement model parameters

The refuge proportion is fixed at 0.05 in the larval movement model.

Base larval movement – This is the amount of movement that might occur in a non-transgenic

field with populations low enough so that significant density-dependent dispersal is not a

factor. In the stochastic m odels, population decline is found to be a greater problem than

density-dependent factors such as mortality or dispersal. The model does include

asymmetrical movement, with the movement of individuals on Bt plants increased by an

amount related to their daily mortality rate s. Susceptibles ther efore move more than

heterozygotes, and resistant homozygotes would only move at the base larval movement

rate. Of course, an individual leaving a transgenic plant only has a 5% change of moving

onto a non-Bt plant. Various estimates of la rval dispersal rates have been encountered butmostly on the low side. Generally, this research assumes that populations will be low in seedmix fields and there will be little to no density- dependent larval dispersal. This could be an

area of concern since the selectio n of alternate values is relatively unimportant compared to

other parameters and a precise estimate would be a misapplication of resources.

Days of larval movement – Movement and larval development are assumed to occur over this

period of days. Movement occurs once per day . Daily survivorship is constant and is

determined as the rate that raised to the days power results in the overall fitness listed for the

genotype in the original table. In a previous ca se, that was 0.0125 for susceptible larvae. If

the days of larval movement is 10, then the daily survivorship rate is 0.645. This means that

on day 1, 36.5% of the SS larvae on Bt die (assu me conservatively that mortality occurs

before dispersal) , and of t he remaining 64.5%, 36.5% will di sperse (see above). Of these

dispersants, only 5% will move onto non-Bt plants, increasing the refuge size from 5% to ca.

6%. If the base larval movement is low (remem ber it is spread over days as well), then this

process can lead to an increase in the refuge population and actually de crease the rate of

resistance evolution. This featur e was inserted in the model to s ee what effect it might have.

The value was varied between 5, 10 and 15 and it had very little effect on the results.

### Appendix 3 – European Corn Borer Sensitivity Analysis **Structured Refuge** > numSummary(ECBStruct2[,"time"], statistics=c("mean", "sd", "quantiles"),

+ quantiles=c(0,.05,.1,.25,.5))

mean sd 0% 5% 10% 25% 50% n

48653.23 39796.83 1125 3055.7 4259.8 9187.5 37657 1099

Call:

lm(formula = log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance +

non.compliance.mixing + non.random.mating + Overall + Refuge +

w3dominance + w3ss + wss, data = ECBStruct2)

Residuals:

Min 1Q Median 3Q Max

-2.42872 -0.58097 0.09332 0.55130 2.42397

Coefficients:
Estimate Std. Error t value Pr(>|t|)

(Intercept) 12.04053 0.67677 17.791 < 2e-16 ***

dominance -4.65073 0.71820 -6.476 1.43e-10 ***

IRF -106.55591 8.46078 -12.594 < 2e-16 ***

l2dom -7.28007 0.73243 -9.940 < 2e-16 ***

l2wss -436.50924 17.99658 -24.255 < 2e-16 ***

Non.compliance -0.69809 0.22527 -3.099 0.00199 **

non.compliance.mixing 0.04642 0.69378 0.067 0.94666non.random.mating 0.31598 0.28462 1.110 0.26717

Overall 2290.92934 83.97219 27.282 < 2e-16 ***

Refuge 21.30089 3.90634 5.453 6.13e-08 ***

w3dominance -0.82344 0.75083 -1.097 0.27301

w3ss -252.49117 13.89056 -18.177 < 2e-16 ***

wss -362.84562 31.62867 -11.472 < 2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7681 on 1086 degrees of freedom

Multiple R-squared: 0.6285, Adjusted R-squared: 0.6244

F-statistic: 153.1 on 12 and 1086 DF, p-value: < 2.2e-16

Stepwise regression

> stepwise(RegModel.1, direction='backward/forward', criterion='BIC')

Direction: backward/forward

Criterion: BIC

Start: AIC=-501.85

log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance +

non.compliance.mixing + non.random.mating + Overall + Refuge +

w3dominance + w3ss + wss...

Step: AIC=-520.22

log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance +

Overall + Refuge + w3ss + wss

Df Sum of Sq RSS AIC

<none> 642.32 -520.22

- Non.compliance 1 6.11 648.43 -516.82

+ non.random.mating 1 0.82 641.49 -514.63

+ w3dominance 1 0.81 641.51 -514.60

+ non.compliance.mixing 1 0.01 642.31 -513.23

- Refuge 1 17.66 659.98 -497.41

- dominance 1 25.13 667.44 -485.05

- l2dom 1 58.46 700.77 -431.50

- wss 1 79.09 721.41 -399.60

- IRF 1 93.99 736.30 -377.15

- w3ss 1 195.15 837.47 -235.66

- l2wss 1 347.86 990.17 -51.58

- Overall 1 442.41 1084.73 48.66

Call:

lm(formula = log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance + Overall + Refuge + w3ss + wss, data = ECBStruct2)Coefficients:

(Intercept) dominance IRF l2dom l2wss

12.186 -4.684 -106.721 -7.289 -436.892

Non.compliance Overall Refuge w3ss

wss

-0.723 2296.728 21.362 -252.181 -365.391

Standardized regression coefficients

> lm.beta(RegModel.1)

dominance IRF l2dom

-0.120300126 -0.234139159 -0.184230039

l2wss Non.compliance non.compliance.mixing

-0.467551121 -0.057654482 0.001239275

non.random.mating Overall Refuge

0.020643543 0.571578932 0.101041557

w3dominance w3ss wss

-0.020441152 -0.338343358 -0.232784395

Bayesian Model AnalysisCall:

iBMA.bicreg.matrix(x = as.matrix(ECBStruct2[, 1:12]), Y = log(ECBStruct2$time))

completed 1 iteration

number of iterations in last call = 100

variables selected = 1 2 3 4 5 6 7 8 11

statistics for variables examined so far

variable status max Probne0 n times in model

1 w3ss selected 100 1

2 Overall selected 100 1

3 l2wss selected 100 1

4 IRF selected 100 1

5 l2dom selected 100 1

6 dominance selected 100 1

7 Refuge selected 100 1

8 Non.compliance selected 86.1 1

9 w3dominance dropped 4.6 1

10 non.random.mating dropped 4.7 1

11 wss selected 100 1

12 non.compliance.mixing dropped 0 1

Results of running BMA on final set of selected variables:Call:

bicreg(x = currentX, y = cs$Y, wt = cs$wt, maxCol = cs$maxNvar + 1)

2 models were selected

Best 2 models (cumulative posterior probability = 1 ):

p!=0 EV SD model 1 model 2

Intercept 100.0 12.1517 0.2214 12.186 11.962

w3ss 100.0 -252.3820 13.8802 -252.181 -253.497

Overall 100.0 2295.0778 83.9948 2296.728 2285.936

l2wss 100.0 -436.8656 18.0020 -436.892 -436.719

IRF 100.0 -106.7926 8.4613 -106.721 -107.188

l2dom 100.0 -7.2734 0.7334 -7.289 -7.188

dominance 100.0 -4.6883 0.7181 -4.684 -4.714

Refuge 100.0 21.3890 3.9066 21.362 21.541

Non.compliance 84.7 -0.6125 0.3323 -0.723 .

wss 100.0 -364.6580 31.6159 -365.391 -360.598

nVar 9 8

r2 0.628 0.624

BIC -1022.529 -1019.104

post prob 0.847 0.153**Seed-blend**

> numSummary(ECBLM3CBLM[,"time"], statistics=c("mean", "sd", "quantiles"),

+ quantiles=c(0,.05,.1,.25,.5))

mean sd 0% 5% 10% 25% 50% n

22687.02 30770.43 158 451.6 638 1303.5 7752 1000

Call:

lm(formula = log(time) ~ AsymmMove + BaseLarvalMovement + dominance +

IRF + Overall + SelectionDays + w2dominance + w2ss + w3dominance

+

w3ss + wss, data = ECBLM3CBLM)

Residuals:

Min 1Q Median 3Q Max

-5.5379 -0.8099 0.1515 0.8006 3.0982

Coefficients:
Estimate Std. Error t value Pr(>|t|)

(Intercept) 12.85794 1.23390 10.421 < 2e-16 ***

AsymmMove 0.10445 1.32983 0.079 0.937408

BaseLarvalMovement -1.65905 0.52120 -3.183 0.001502 **

dominance -3.69039 1.05205 -3.508 0.000472 ***

IRF -137.61374 12.70775 -10.829 < 2e-16 ***Overall 4142.36059 116.90224 35.434 < 2e-16 ***

SelectionDays -0.04638 0.01979 -2.344 0.019294 *

w2dominance -10.82444 1.06005 -10.211 < 2e-16 ***

w2ss -457.19541 27.30907 -16.742 < 2e-16 ***

w3dominance -1.99457 1.04612 -1.907 0.056857 .

w3ss -308.19289 19.43282 -15.859 < 2e-16 ***

wss -474.23244 40.24046 -11.785 < 2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.059 on 988 degrees of freedom

Multiple R-squared: 0.6505, Adjusted R-squared: 0.6466

F-statistic: 167.2 on 11 and 988 DF, p-value: < 2.2e-16

Stepwise regression:

> stepwise(RegModel.2, direction='backward/forward', criterion='BIC')

Direction: backward/forward

Criterion: BIC

Start: AIC=185.72

log(time) ~ AsymmMove + BaseLarvalMovement + dominance + IRF +Overall + SelectionDays + w2dominance + w2ss + w3dominance +

w3ss + wss

...

Step: AIC=173.63

log(time) ~ BaseLarvalMovement + dominance + IRF + Overall +

w2dominance + w2ss + w3ss + wss

Df Sum of Sq RSS AIC

<none> 1117.9 173.63

+ SelectionDays 1 5.52 1112.4 175.58

- BaseLarvalMovement 1 10.36 1128.3 175.94

+ w3dominance 1 3.44 1114.5 177.45

- dominance 1 13.50 1131.4 178.72

+ AsymmMove 1 0.00 1117.9 180.53

- w2dominance 1 115.59 1233.5 265.11

- IRF 1 131.72 1249.6 278.11

- wss 1 154.28 1272.2 296.00

- w3ss 1 283.43 1401.3 392.69

- w2ss 1 320.52 1438.4 418.81

- Overall 1 1412.28 2530.2 983.56

Call:

lm(formula = log(time) ~ BaseLarvalMovement + dominance + IRF + Overall + w2dominance + w2ss + w3ss + wss, data = ECBLM3CBLM)Coefficients:

(Intercept) BaseLarvalMovement dominance
IRF

12.306 -1.579 -3.645 -137.652

Overall w2dominance w2ss w3ss

4143.697 -10.758 -460.466 -308.774

wss

-471.161

Standardized regression coefficients:

> lm.beta(RegModel.2)

AsymmMove BaseLarvalMovement dominance
IRF

0.001483205 -0.060187208 -0.066242028 - 0.204426528

Overall SelectionDays w2dominance w2ss

0.746663470 -0.044292524 -0.192556319 - 0.334520193

w3dominance w3ss wss

-0.036173282 -0.298782467 -0.236638839

Bayesian Model Analysis:Call:

iBMA.bicreg.matrix(x = as.matrix(ECBLM3CBLM[, 1:11]), Y = log(ECBLM3CBLM$time))

completed 1 iteration

number of iterations in last call = 100

variables selected = 1 2 3 4 5 6 7 8 9 10

statistics for variables examined so far

variable status max Probne0 n times in model

1 Overall selected 100 1

2 w3ss selected 100 1

3 IRF selected 100 1

4 w2dominance selected 100 1

5 w2ss selected 100 1

6 dominance selected 96.3 1

7 SelectionDays selected 26.6 1

8 BaseLarvalMovement selected 79.9 1

9 wss selected 100 1

10 w3dominance selected 10.5 1

11 AsymmMove dropped 0 1

Results of running BMA on final set of selected variables:Call:

bicreg(x = currentX, y = cs$Y, wt = cs$wt, maxCol = cs$maxNvar + 1)

7 models were selected

Best 5 models (cumulative posterior probability = 0.9276 ):

p!=0 EV SD model 1 model 2

Intercept 100.0 12.26600 0.50899 12.30648 12.74934

Overall 100.0 4144.30464 117.20047 4143.69684 4140.57938

w3ss 100.0 -308.15724 19.50628 -308.77437 - 307.98185

IRF 100.0 -137.45800 12.74766 -137.65239 - 137.50792

w2dominance 100.0 -10.75447 1.06398 -10.75756 - 10.80279

w2ss 100.0 -459.87983 27.36956 -460.46560 - 460.75032

dominance 96.3 -3.47898 1.24143 -3.64453 - 3.59952

SelectionDays 26.6 -0.01172 0.02197 . - 0.04378

BaseLarvalMovement 79.9 -1.26788 0.78852 -1.57893 - 1.58982

wss 100.0 -472.20715 40.34886 -471.16082 - 474.89833w3dominance 10.5 -0.19824 0.67056 . .

nVar 8 9

r2 0.648 0.649

BIC -987.47098 - 985.51176

post prob 0.477 0.179

model 3 model 4 model 5

Intercept 11.48683 12.46686 11.91835

Overall 4147.57545 4145.13265 4144.52495

w3ss -306.74836 -309.03770 -305.95236

IRF -137.05360 -137.78116 -136.90694

w2dominance -10.69724 -10.77550 -10.74147

w2ss -458.31118 -457.23042 -458.57754

dominance -3.50910 -3.72975 -3.46375

SelectionDays . . -0.04321

BaseLarvalMovement . -1.64049 .

wss -471.46061 -470.24516 -475.15152

w3dominance . -1.82763 .

nVar 7 9 8

r2 0.644 0.649 0.646

BIC -985.14465 -983.63185 -983.02685

post prob 0.149 0.070 0.052

### Appendix 4 – Southwestern Corn Borer Sensitivity Analysis

**Structured refuge** > numSummary(SWCBStruct2[,"time"], statistics=c("mean", "sd", "quantiles"),

+ quantiles=c(0,.05,.1,.25,.5))

mean sd 0% 5% 10% 25% 50% n

8944.133 26217.33 118 207.8 262.9 389 677 1000

Call:

lm(formula = log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance +

non.compliance.mixing + non.random.mating + Overall + Refuge +

w3dominance + w3ss + wss, data = SWCBStruct2)

Residuals:

Min 1Q Median 3Q Max

-1.5722 -0.6733 -0.2550 0.3588 3.5677

Coefficients:
Estimate Std. Error t value Pr(>|t|)

(Intercept) 11.7292 0.9155 12.812 < 2e-16 ***

dominance 0.4475 0.9895 0.452 0.65121

IRF -299.8843 128.9619 -2.325 0.02025 *

l2dom -1.1349 0.9816 -1.156 0.24788

l2wss -35.8689 1.3597 -26.380 < 2e-16 ***

Non.compliance -1.5360 0.4908 -3.130 0.00180 **non.compliance.mixing -3.0610 0.9301 -3.291 0.00103 **

non.random.mating 0.2468 0.4251 0.581 0.56168

Overall 187.2322 18.7328 9.995 < 2e-16 ***

Refuge 22.6041 5.3726 4.207 2.82e-05 ***

w3dominance -8.7198 0.9968 -8.748 < 2e-16 ***

w3ss 111.9971 18.7953 5.959 3.53e-09 ***

wss -39.2748 1.5177 -25.878 < 2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9758 on 987 degrees of freedom

Multiple R-squared: 0.6329, Adjusted R-squared: 0.6285

F-statistic: 141.8 on 12 and 987 DF, p-value: < 2.2e-16

Stepwise regression

> stepwise(RegModel.4, direction='backward/forward', criterion='BIC')

Direction: backward/forward

Criterion: BIC

Start: AIC=27.75

log(time) ~ dominance + IRF + l2dom + l2wss + Non.compliance +

non.compliance.mixing + non.random.mating + Overall + Refuge +

w3dominance + w3ss + wss

...Step: AIC=7.38

log(time) ~ l2wss + Non.compliance + non.compliance.mixing +

Overall + Refuge + w3dominance + w3ss + wss

Df Sum of Sq RSS AIC

<none> 946.68 7.38

+ IRF 1 5.11 941.57 8.88

- Non.compliance 1 9.38 956.06 10.33

- non.compliance.mixing 1 10.31 956.99 11.30

+ l2dom 1 1.23 945.45 12.99

+ non.random.mating 1 0.28 946.40 13.99

+ dominance 1 0.15 946.53 14.13

- Refuge 1 17.42 964.10 18.70

- w3ss 1 33.82 980.51 35.58

- w3dominance 1 73.28 1019.96 75.03

- Overall 1 98.33 1045.01 99.29

- wss 1 632.35 1579.03 512.07

- l2wss 1 660.31 1607.00 529.63

Call:

lm(formula = log(time) ~ l2wss + Non.compliance + non.compliance.mixing + Overall + Refuge + w3dominance + w3ss + wss, data = SWCBStruct2)Coefficients:

(Intercept) l2wss Non.compliance

11.407 -35.632 -1.540

non.compliance.mixing Overall Refuge

-3.057 189.786 22.918

w3dominance w3ss wss

-8.738 111.878 -38.956

Standardized regression coefficients

> lm.beta(RegModel.4)

dominance IRF l2dom

0.008746106 -0.045226973 -0.022345949

l2wss Non.compliance non.compliance.mixing

-0.512162511 -0.060586663 -0.063649039

non.random.mating Overall Refuge

0.011247447 0.201656003 0.081445809

w3dominance w3ss wss

-0.169883903 0.119719428 -0.501846586

Bayesian Model Analysis

Call:

iBMA.bicreg.matrix(x = as.matrix(SWCBStruct2[, 1:12]), Y =log(SWCBStruct2$time))

completed 1 iteration

number of iterations in last call = 100

variables selected = 1 2 3 4 5 6 7 8 12

statistics for variables examined so far

variable status max Probne0 n times in model

1 wss selected 100 1

2 l2wss selected 100 1

3 Overall selected 100 1

4 w3ss selected 100 1

5 w3dominance selected 100 1

6 Refuge selected 100 1

7 non.compliance.mixing selected 90.4 1

8 Non.compliance selected 84.1 1

9 l2dom dropped 2.9 1

10 non.random.mating dropped 0 1

11 dominance dropped 0 1

12 IRF selected 30.4 1

Results of running BMA on final set of selected variables:

Call:bicreg(x = currentX, y = cs$Y, wt = cs$wt, maxCol = cs$maxNvar + 1)

6 models were selected

Best 5 models (cumulative posterior probability = 0.9712 ):

p!=0 EV SD model 1 model 2 model 3

Intercept 100.0 11.208 1.1935 11.407 11.789 11.136

wss 100.0 -39.061 1.5229 -38.956 -39.243 -39.077

l2wss 100.0 -35.676 1.3609 -35.632 -35.826 -35.492

Overall 100.0 189.387 18.7835 189.786 187.077 191.507

w3ss 100.0 111.649 18.8479 111.878 112.972 108.950

w3dominance 100.0 -8.709 0.9999 -8.738 -8.761 -8.616

Refuge 100.0 22.612 5.3836 22.918 22.294 22.340

non.compliance.mixing 90.1 -2.766 1.2733 -3.057 -3.089 -3.073

Non.compliance 83.6 -1.292 0.7272 -1.540 -1.553

.

IRF 31.3 -93.059 155.6262 . -298.641

.nVar 8 9 7

r2 0.630 0.632 0.627

BIC -939.693 -938.182 -936.751

post prob 0.502 0.236 0.115

model 4 model 5

Intercept 8.648 11.509

wss -38.915 -39.360

l2wss -35.692 -35.682

Overall 191.424 188.857

w3ss 110.980 110.001

w3dominance -8.576 -8.638

Refuge 22.754 21.721

non.compliance.mixing . -3.104

Non.compliance -1.548 .

IRF . -293.772

nVar 7 8

r2 0.626 0.629

BIC -935.760 -935.025

post prob 0.070 0.049**Seed-blend**

> numSummary(SWCBLM3CBLM[,"time"], statistics=c("mean", "sd", "quantiles"),

+ quantiles=c(0,.05,.1,.25,.5))

mean sd 0% 5% 10% 25% 50% n

8171.048 25354.55 73 138.85 158.9 214.75 346 1000

p <135 generations = 4.5%

Call:

lm(formula = log(time) ~ AsymmMove + BaseLarvalMovement + dominance +

IRF + Overall + SelectionDays + w2dominance + w2ss + w3dominance

+

w3ss + wss, data = SWCBLM3CBLM)

Residuals:

Min 1Q Median 3Q Max

-2.0351 -0.7045 -0.2690 0.3404 3.7590

Coefficients:
Estimate Std. Error t value Pr(>|t|)

(Intercept) 9.69785 1.31742 7.361 3.83e-13 ***

AsymmMove -0.87515 1.41242 -0.620 0.535657

BaseLarvalMovement -1.02658 0.50214 -2.044 0.041176 *

dominance -3.39043 1.07559 -3.152 0.001670 **IRF -20.01400 142.62874 -0.140 0.888434

Overall 359.61183 20.70324 17.370 < 2e-16 ***

SelectionDays 0.02491 0.02060 1.209 0.226800

w2dominance 0.90340 1.05706 0.855 0.392960

w2ss -32.76668 1.43105 -22.897 < 2e-16 ***

w3dominance -9.37930 1.04545 -8.972 < 2e-16 ***

w3ss 74.75041 20.93917 3.570 0.000374 ***

wss -39.69144 1.70834 -23.234 < 2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.073 on 988 degrees of freedom

Multiple R-squared: 0.6186, Adjusted R-squared: 0.6144

F-statistic: 145.7 on 11 and 988 DF, p-value: < 2.2e-16

Stepwise regression:

stepwise(RegModel.1, direction='backward/forward', criterion='BIC')

Direction: backward/forward

Criterion: BIC

Start: AIC=211.72

log(time) ~ AsymmMove + BaseLarvalMovement + dominance + IRF +Overall + SelectionDays + w2dominance + w2ss + w3dominance +

w3ss + wss

...

Step: AIC=183.99

log(time) ~ dominance + Overall + w2ss + w3dominance + w3ss +

wss

Df Sum of Sq RSS AIC

<none> 1145.3 183.99

+ BaseLarvalMovement 1 4.77 1140.5 186.73

- dominance 1 11.46 1156.7 187.04

+ SelectionDays 1 1.67 1143.6 189.44

+ w2dominance 1 0.79 1144.5 190.21

- w3ss 1 15.25 1160.5 190.31

+ AsymmMove 1 0.48 1144.8 190.47

+ IRF 1 0.03 1145.2 190.87

- w3dominance 1 97.10 1242.4 258.46

- Overall 1 346.01 1491.3 441.07

- w2ss 1 608.00 1753.3 602.93

- wss 1 624.28 1769.5 612.17

Call:

lm(formula = log(time) ~ dominance + Overall + w2ss + w3dominance + w3ss + wss, data = SWCBLM3CBLM)Coefficients:

(Intercept) dominance Overall w2ss w3dominance w3ss

8.710 -3.391 358.116 -32.853 -9.551 76.011

wss

-39.669

Standardized regression coefficients

> lm.beta(RegModel.1)

AsymmMove BaseLarvalMovement dominance
IRF

-0.012216973 -0.040440872 -0.062078028 - 0.002765404

Overall SelectionDays w2dominance w2ss

0.351883583 0.023826750 0.016814413 - 0.451905952

w3dominance w3ss wss

-0.177519991 0.072209652 -0.459232630

Bayesian Model Analysis

Call:

iBMA.bicreg.matrix(x = as.matrix(SWCBLM3CBLM[, 1:11]), Y = log(SWCBLM3CBLM$time))completed 1 iteration

number of iterations in last call = 100

variables selected = 1 2 3 4 5 6 7

statistics for variables examined so far

variable status max Probne0 n times in model

1 w2ss selected 100 1

2 wss selected 100 1

3 Overall selected 100 1

4 w3dominance selected 100 1

5 w3ss selected 100 1

6 dominance selected 83 1

7 BaseLarvalMovement selected 19.3 1

8 w2dominance dropped 0 1

9 IRF dropped 0 1

10 AsymmMove dropped 0 1

11 SelectionDays dropped 4.1 1

Results of running BMA on final set of selected variables:

Call:

bicreg(x = currentX, y = cs$Y, wt = cs$wt, maxCol = cs$maxNvar + 1)4 models were selected

Best 4 models (cumulative posterior probability = 1 ):

p!=0 EV SD model 1 model 2 model 3

Intercept 100.0 8.7703 0.2905 8.710 9.202 8.491

w2ss 100.0 -32.8635 1.4329 -32.853 -32.780 - 32.995

wss 100.0 -39.6477 1.7068 -39.669 -39.546 - 39.689

Overall 100.0 358.1576 20.7353 358.116 360.542 355.602

w3dominance 100.0 -9.5344 1.0452 -9.551 -9.375 - 9.657

w3ss 100.0 75.7921 20.9239 76.011 74.450 76.545

dominance 82.3 -2.7928 1.6221 -3.391 -3.405

.

BaseLarvalMovement 20.1 -0.2052 0.4667 . -1.021

.

nVar 6 7 5

r2 0.616 0.618 0.612

BIC -915.692 -912.960 - 912.649

post prob 0.656 0.1670.143

model 4

Intercept 8.977

w2ss -32.923

wss -39.568

Overall 357.995

w3dominance -9.484

w3ss 75.002

dominance .

BaseLarvalMovement -1.012

nVar 6

r2 0.614

BIC -909.772

post prob 0.034