1. [25%] Consider selection in a predator-prey model. Assume two haploid organisms. In the predator organism we consider a locus with alleles A and a; in the prey organism, we consider a locus with alleles B and b. Assume allele A provides the predator an advantage to hunt prey with genotype B. Plentiful prey of genotype B give A-predators a selective advantage. Then wA = 1 + fB s − t, where s and t are selection coefficients.
(A) [10%] Calculate the change in allele frequencies in the predator per generation. Simplify your equations.
(B) [10%] Assume now that allele B in the prey is disadvantaged if allele A is common in thepredator. ThuswB =1−fAs + t,wheres and tareselectioncoefficients. Calculatethe change in the allele frequencies in the prey in one generation. Simplify your equations.
(C) [5%] Is there a non-trivial equilibrium for fA and fB such that ∆fA = 0 and ∆fB = 0? By non-trivial, we mean when neither A nor B has frequency 0 or 1. If a non-trivial equilibrium exists, then characterize it?

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