SIMULATION MODELING OF THE PINK BOLLWORM

ERADICATION PROGRAM IN ARIZONA

July 28, 2006

Information prepared by Bruce Tabashnik

Simulations run by Mark Sisterson

Contents 

Summary 

Table 1. Parameter values for simulation model 

Table 2. Simulation outcomes 

Simulation objectives, approach, scenarios, time horizon, and criteria 

(June 23, 2006 email to Sharlene Matten) 

Appendix I: Reprint of Sisterson et al. (2004) describing simulation
model 

Appendix II: Reprint of Tabashnik et al. (2005) summarizing bioassay
monitoring data 

SUMMARY 

SIMULATION MODELING OF THE PINK BOLLWORM 

ERADICATION PROGRAM IN ARIZONA as of July 28, 2006 

Methods 

We used a computer model to simulate potential effects of the Arizona
pink bollworm 

eradication program on resistance to Bt cotton and population
suppression. Details of our 

objectives, approach, scenarios, time horizon, and criteria were emailed
to Sharlene Matten on June 23, 2006 (see attached). Briefly, we used a
model of pink bollworm in Arizona that has been described in detail in a
research publication (Sisterson et al. 2004, attached), with minor
modifications including the release of sterile moths. 

We began by simulating the eradication program with the best estimates
available for all 

parameters, based as much as possible on published data (Table 1). These
values are referred to as “default values,” because they are used
unless noted otherwise. We systematically examined alternatives to the
default values that were more pessimistic, i.e., more likely to result
in resistance. A region with 4096 cotton fields was modeled for 4 years.
In preliminary results to date, we have examined 12 sets of assumptions,
each of them simulated 5-16 times, for a total of 128 simulation runs. 

Results 

In 11 of 12 sets of assumptions examined so far, the simulated
eradication program eliminated the pink bollworm from the 4096 fields
modeled in two years or less without causing a resistance problem (Table
2). The only set of assumptions examined that did not yield loss of pink
bollworm from the region included no release of sterile moths in Bt
cotton fields. After 4 years in this exceptional case, population
density declined by 98% and the resistance allele frequency increased
from 0.01 to 0.02. Note that in all simulations, sterile moths were
released in non-Bt cotton fields at the default rate of 500 moths per ha
in each release with one release per three days. 

The 12 sets of simulations include the default values (best estimates
for all parameters) and 11 other sets in which assumptions were
purposely more pessimistic to increase the chances of resistance
evolution. In particular, the default assumption was an initial
resistance allele frequency (r) of 0.001 based on extensive bioassays
(Tabashnik et al. 2005, attached) and DNA screening (Tabashnik et al.,
unpublished data). In the 11 sets with more pessimistic assumptions, r
was 0.01, ten times higher. 

The additional pessimistic assumptions that resulted in loss of pink
bollworm from the region in 2 years included dominant (rather than
recessive) inheritance of resistance, 90% Bt cotton and 10% non-Bt
cotton refuges (rather than 100% Bt cotton), no fitness cost of
resistance (rather than a 10% fitness cost in homozygous resistant
insects), and release rates of 1, 2, 3, 4, 5, 10, or 15 sterile moths
per ha in Bt cotton fields (rather than 75 sterile moths per ha). 

With no steriles released in Bt cotton fields, 90% Bt cotton, and r =
0.01, pink bollworm 

persisted in the region for the 4 years of the eradication program in
all 5 replicate simulations. From the 5 replicate simulations, the means
were 0.02 for the final value of r, and 460 larvae per field surviving
overwintering. The final resistance allele frequency represents a
doubling over 4 years from the initial value, but is well below the 0.50
value typically used as a criterion for a resistance problem. With
recessive resistance (as seen in pink bollworm) and r = 0.02, the
frequency of phenotypically resistant individuals (rr) capable of
survival on Bt cotton would be 4 in 10,000 (0.0004). The mean final
population density of 460 overwintering larvae per field is less than 2%
of the starting population density in the simulations (29,000
overwintering larvae per field). In sum, with no steriles released in Bt
cotton fields, 98% population suppression occurred without a major
resistance problem. 

Discussion 

Preliminary results from simulations suggest that it is likely that the
eradication program in Arizona will suppress pink bollworm without
creating a problem with resistance to Bt cotton. The preliminary
simulation results suggest that best estimates for parameters and some
more pessimistic assumptions do not yield rapid evolution of resistance
under the conditions of the pink bollworm eradication program in
Arizona. We plan to analyze results in greater detail to test their
robustness. We will also explore additional pessimistic assumptions to
determine which conditions might cause severe resistance problems. The
simulation results suggest that release of sterile moths in Bt cotton is
important for driving pink bollworm population densities to extremely
low levels. 

References Cited 

Sisterson, M. S. L. Antilla, Y. Carrière, C. Ellers-Kirk and B. E.
Tabashnik. 2004. Effects of insect population size on evolution of
resistance to transgenic crops. J. Econ. Entomol. 97: 1413-1424. 

Tabashnik, B. E., T. J. Dennehy, and Y. Carrière. 2005. Delayed
resistance to transgenic cotton in pink bollworm. Proc. Nat’l. Acad.
Sci. U.S.A. 102: 15389-15393. 



Page 1 of 2 for Table 1 REVISED July 28, 2006

Table 1. Parameter values for eradication model (revised from Sisterson
et al. 2004).

Default values, which are used unless noted otherwise for parameters
with more than one value, are indicated by an asterisk.

________________________________________________________________________

Parameter 							Values__________________

Adults 

Mean % of adults that leave their natal field 			10, 55*, 75 

Number of eggs per female per day in Bt cotton fields 	10 

Number of eggs per female per day in non-Bt cotton fields 	10 

Mean % of adults that die each day 				10 

Egg-pupae 

Mutation rate (from S to R per allele) 			5 x 10-5

Mean % of SS and RS killed in non-Bt cotton fields 	79.2

Mean % of RR killed in non-Bt cotton fields 		79.2, 81.3*(10% fitness
cost)

Mean % of SS and RS killed in Bt cotton fields 		99.8a, 100*

Mean % of RR killed in Bt cotton fields 			79.2, 83.2*(incomplete R=0.9)

Development time (degree days) 				433

Mean % of larvae that die during overwintering 		95

Region

Initial R allele frequency 					0.0001, 0.001*, 0.01

Number of fields 						4096 (64 X 64 square)

Size of fields 							15 hectares

Percentage of Bt fields 					80, 85, 90, 95, 100*

Percentage of Bt plants in Bt fields 				99a, 100*

Distribution of fields 						Random

Carrying capacity per field 					4,200,000

Initial overwintering larvae per field 				2900, 29,000*, 290,000

a 99.8% mortality of RS and SS simulates 100% Bt fields that have 99% Bt
cotton plants and 1% non-Bt

cotton plants (contaminants); 100% die on the Bt plants, 79.2% die on
the non-Bt plants

(0.99 X 100% + 0.01 X 79.2% = 99.8%) 

Page 2 of 2 for Table 1 

Steriles 

Release period 

Frequency of releases in each field 

Sex ratio of steriles 

Steriles per ha per release in Bt cotton fields 

Steriles per ha per release in non-Bt cotton fields 

Pheromone ropes only in non-Bt cotton fields 

All non-Bt fields treated once early in season 

May 1-Oct 15 (1st bloom to defoliation) 

1 per 3 days per field 

1 female: 1 male 

0, 1, 2, 3, 4, 5, 10, 15, 75* 

0, 100, 500*, 1000 

May 17-June 20 (6-leaf stage) 

Daily % reduction in fecundity caused by pheromone ropes 20, 40*, 60
for 30 days 

Insecticide & pheromone sprays only in non-Bt cotton fields 

Spray threshold 					>60 no spray

(check sterile male:native male ratio weekly)	30-59 spray pheromone

							0-29 spray pheromone + insecticide

Daily reduction in fecundity caused by pheromone sprays 	20, 40*, 60 for
14 days

Mean % of adults killed daily by insecticide			37 per day for 5 days

Larvae are not killed by sprays				95 per day for 5 days



Table 2. Simulation outcomes: effects of pessimistic assumptions on
simulated outcomes of the pink bollworm eradication program in Arizona.
In all cases except the default case, the initial resistance allele
frequency (r) was 0.01, which is ten times higher than the default value
of 0.001.  In all cases, 500 sterile moths per ha were released in
non-Bt cotton fields, with one release per three days. 

Parameter values different from default values 			Outcome* 

None (all parameters at default values) 				Loss in 1 year 

Initial resistance allele frequency (r) = 0.01 				Loss in 2 years 

No fitness cost, r = 0.01 						Loss in 2 years 

Dominant resistance to Bt cotton, r = 0.01 				Loss in 2 years 

90% Bt cotton, r = 0.01, Loss in 2 years 

Steriles released in Bt cotton fields 

at 1, 2, 3, 4, 5, 10, or 15 steriles per ha 

90% Bt cotton, r = 0.01 						averages after 4 years 

No steriles released in Bt cotton fields 				r = 0.02 

460 larvae per field 

(overwintering survivors) 

*loss means that no pink bollworm were present in any of the 4096 cotton
fields modeled 



June 23, 2006

Dear Sharlene,

We are in the early stages with modeling. We’d like to optimize the
contribution of the

modeling to EPA’s evaluation of the proposed pink bollworm (PBW)
eradication program in AZ.  So, this is a good time to begin discussing
with you the objectives, approach and scenarios to be modeled.

A draft of parameter values is attached. As this is research in
progress, we ask you to protect its confidentiality as much as possible.
We understand that the results of the simulations will be provided to
EPA for analysis and public comment as part of the SAP process.

Your input is welcome.

Best wishes,

Bruce

Objectives 

1) Simulate scenarios to aid EPA evaluation of resistance risk vs.
population suppression associated with the proposed pink bollworm (PBW)
eradication program in AZ 

2) Produce a manuscript suitable for publication that describes the
results of simulations and their relevance to the PBW eradication
program. 

Approach 

We will use as our core model the PBW model described in detail by
Sisterson et al. (2004)  (attached). We will make relatively minor
modifications to the core model to simulate various scenarios relevant
to the AZ PBW eradication program. 

This approach has several advantages. By using an established model, we
can produce results in a timely fashion. We know the model works. It has
been tested thoroughly and scrutinized by the peer review process. Its
assumptions are published. The model contains sufficient spatial and
temporal detail to realistically address key issues of population
suppression and resistance risk for PBW in AZ. 

The simulations will examine population suppression (number of pink
bollworm per ha) and risk of resistance to Bt cotton (rate of increase
of resistance allele frequency). We will use realistic assumptions that
incorporate the best and most recent data available for pink bollworm on
the genetic basis of resistance to Bt cotton, the frequency of
resistance alleles in field populations, population sizes, population
dynamics, and movement. As much as possible, we will rely on published
data for parameter estimates. 

We will describe qualitative patterns and quantitative effects of
various parameters on population size and resistance allele frequency.
Because the model is stochastic, we will replicate runs to determine
variation among runs and record the proportion of runs with various
outcomes. 

Scenarios 

We will analyze a variety of scenarios, including those based on the
best estimates for all parameters, as well as more optimistic and more
pessimistic scenarios. We will accomplish this by using sensitivity
analyses that systematically vary parameters that are naturally variable
(e.g., movement) or for which there is uncertainty (e.g., resistance
allele frequency). The modeling will also explore the impact on
population suppression and resistance risk of alternative management
options (e.g., variable refuge size and release rates of sterile moths).


Time Horizon and Criteria 

Simulations will be run for 4 years to match the statutory limit for the
AZ program, with overwintering larvae from the 4th year checked to
assess the following criteria: 

Resistance will occur if the resistance allele frequency exceeds 0.50. 

Population recovery will occur if the final population size is equal to
or greater than the initial population size (29,000 overwintering larvae
per field is the default value). 

Population suppression will occur if the mean PBW density in the region
is equal to or less than 0.1 overwintering larvae per 15 ha field (=
0.0067 larvae per ha). 

Regional loss will occur if all fields in the region modeled have 0 PBW.


Reference 

Sisterson, M. S. L. Antilla, Y. Carrière, C. Ellers-Kirk and B. E.
Tabashnik. 2004. Effects of insect population size on evolution of
resistance to transgenic crops. J. Econ. Entomol. 97: 1413-1424. 

VOLUME 5

DOCUMENT 1

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