Managing Resistance
Evolution with Refugia
Livingston, Carlson
and Fackler
Presented by Ben
Crost
The Setting
Cotton production in the midsouth
 Two pests: budworm and bollworm
 Two pest-control technologies: Btcotton and pyrethroids
 Evolution of resistance to pestcontrol is a major problem

The Setting (2)
Resistance-free pests are a public
good
 The EPA tries to control resistance
by mandating refugia
 Farmers have two options:
 1.) leave 5% of their cotton-crop
non-Bt and unsprayed
 2.) leave 20% non-Bt but sprayed

The Question
 What
is the optimal size of
refugia?
 Combine biological, economic
and regulatory model
Biological Model
2-locus by 2-allele model
 Locus: The specific place on a
chromosome where a gene is
located
 Allele: A variant of the DNA
sequence at a given locus

Biological Model (2)
2 Loci: Bt-resistance, Pyrethroid
resistance
 2 Alleles: resistant, non-resistant
 This setup gives rise to 9 different
genotypes (since each individual has
2 sets of chromosomes)

Biological Model (3)
5 non-overlapping generations
 Genes get transmitted between
generations by random mating
 (Calculate frequencies of all 4
possible gametes and then
frequencies of all 9 possible
combinations)

Biological Model (4)
Genotypes can be confronted with 4
possible environments (Bt/non-Bt by
sprayed/unsprayed)
 Each genotype has a survivalprobability in each environment
 Given the environments, we know
what will happen to the pestpopulation

Economic Model
Representative producer maximizes
profits, s.t. pest-population and
regulatory constraints
 Size of pest-population maps into
Bt-use, Pyrethroid-use and profits
 Bt-use and Pyrethroid-use feed back
into biological model

Regulatory Model
Regulators want to choose refuge
constraints that maximize the
representative producers discounted
profits
 2 Scenarios: Static and dynamic

Estimation
Lots of parameters from a variety of
sources (lab-studies, econometric
estimation from observed data,
educated guesses from observed
data)
 Grid search over possible refugia
sizes

Results
Current refugia mandates are too
large (optimal would be 2%
unsprayed or 16% sprayed)
 Results are very sensitive to
heterozygous Bt-resistance
parameter (up to 74% sprayed
refugia with still realistic
parameters)

Remarks
It seems that the authors were
aiming for a low value of refugia:
 They chose a short time-horizon and
no bequest value
 Their values for heterozygous
resistance are lower than lab-studies
suggest

Improvements?
Get better estimates of model
parameters
 Calibrate model to observed data
 Bayesian Model Averaging
