Managing Resistance Evolution with Refugia

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Managing Resistance Evolution with Refugia

• Livingston, Carlson and Fackler
• Presented by Ben Crost

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The Setting

• Cotton production in the midsouth
• Two pests budworm and bollworm
• Two pest-control technologies Bt-cotton and
  pyrethroids
• Evolution of resistance to pest-control is a
  major problem

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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

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The Question

• What is the optimal size of refugia?
• Combine biological, economic and regulatory model

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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

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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)

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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)

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Biological Model (4)

• Genotypes can be confronted with 4 possible
  environments (Bt/non-Bt by sprayed/unsprayed)
• Each genotype has a survival-probability in each
  environment
• Given the environments, we know what will happen
  to the pest-population

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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

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Regulatory Model

• Regulators want to choose refuge constraints that
  maximize the representative producers discounted
  profits
• 2 Scenarios Static and dynamic

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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

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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)

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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

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Improvements?

• Get better estimates of model parameters
• Calibrate model to observed data
• Bayesian Model Averaging