Homework 3 Solutions Wayne Lawton Department of Mathematics S , Theme for Semester I, 2008/09 : The Logic of Evolution, Mathematical Models of Adaptation from Darwin to Dawkins

Ridley page 136 problem 6 Genotype Observed Frequency HW Freq. Ratio Fitness Selection Coefficient

Ridley page 136 problem 7 freq. ofin population 1, 2 migration rate = fraction of population 2 who are first generation immigrants from pop. 1 next generation

Ridley page 136 problem 8 a The effect of assortive mating on a locus with 2 alleles A, a with A dominant  2 intermating populations, genotypes freq p(n) of A and q(n) of in gen n in satisfies populations converge to {AA} and {aa}

Ridley page 136 problem 8 b The effect of assortive mating on a locus with 2 alleles A, a with 3 phenotypes  3 intermating populations, genotypes Half of the offspring of {Aa} split off each generation so the 3 populations converge to the 2 populations

Ridley page 136 problem 8 c Assortive mating where females mate only with i. dominant phenotype fix A (its freq  1) ii. recessive phenotype fix a (its freq  1)

Ridley page 136 problem 9 Genotype Generation n Baby Frequency Generation n Adult Frequency (selection against dominant A) Adult Gene Frequency Under the assumption of random mating these generation n adult gene frequencies will equal the generation (n+1) baby gene frequencies

Ridley page 136 problem 10 We assume that the mutation rate m for a recessive allele a is small and that the selection (with coefficient s) works against the allele a Letdenote the equilibrium frequency for allele a The frequency p(n) in the n-th generation satisfies

Question 11 Assume that for a two allele locus that genotype AA has fitness 1-s, genotype Aa has fitness 1, and genotype aa has fitness 1-t and that random mating occurs. Let p = baby freq. of gene A and q = baby freq. of gene a. Derive formuli for the next baby freq. p’ and q’.

Answer Question 11 Genotype Generation n Baby Frequency Generation n Adult Frequency (selection against homozygytes) Adult Gene Frequencies

Question 12 Assume that in a two allele locus all genotypes have fitness = 1 but that each genotype mates only with the same genotype. Derive equations for the evolution of gene frequencies. Remark Same genotype evolution as in problem 8a gene frequencies are constant