problem set 8 2009 key

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3. Consider a Levene model of a random-mating population that is completely randomly dispersed every generation across three environments such that the relative fitnesses for the genotypes determined by an autosomal locus with 2 alleles are: Env. Genotype AA Aa Aa 1 1 1 0.8 2 0.8 1 1.1 3 1.05 1 1 Which of the following niche outputs under a soft selection model will protect the polymorphism loss (show the conditions that leads to your conclusion): a). c 1=0.2, c 2=0.2, c 3=0.6 b). c 1=0.1, c 2=0.5, c 3=0.4 c). c 1=0.1, c 2=0.8, c 3=0.1 Use the conditions: i 1 ∑ ci vi
6. A large population consists of only AA individuals at an autosomal locus with random mating such that the population is stable in size and the number of progeny is given by a Poisson distribution. A new mutation occurs, a, such that Aa individuals have an average of 1.05 offspring and a variance of 2 in the number of offspring. a) What is the probability of a surviving in this large population? Use equation 14.20 (2 pts). First calculate s=0.05 (1 pt). Second, note that the variance in 2 offspring number = 2 =1+s+σ s (1 pt), so the probability of survival = 0.1/2 = 0.05 (1 pt) b) Assume now that Aa individuals also have a Poisson number of progeny, but still with a mean of 1.05. What is the probability of a surviving in this population now? First calculate s=0.05 (1 pt). Second, note that the variance in offspring number =1+s = 1.05 (2 pts), so the probability of survival = 0.1/1.05 = 0.095 (1 pt). 7. A recessive allele, a, is associated with two different life history phenotypes in a population with overlapping generations such that: AA & Aa aa x l x m xb x l x m xb x 0 0.8 0 0.5 0 1 0.7 0.5 0.4 4 2 0.6 1 0.3 3 3 0.2 1 0.2 1 4 0.1 0.2 0.1 0 Calculate the fitness of both phenotypes using a) the net reproductive rate, and b) the Malthusian parameter (use an approximation). Use equations 15.1 (1 pt) and 15.10 (1 pt). AA & Aa aa x l x m xb x l xm xb x xl xm xb x l x m xb x l xm xb x xl xm xb x 0 0.8 0 0 0 0.5 0 0 0 1 0.7 0.5 0.35 0.35 0.4 4 1.6 1.6 2 0.6 1 0.6 1.2 0.3 3 0.9 1.8 3 0.2 1 0.2 0.6 0.2 1 0.2 0.6 4 0.1 0.2 0.02 0.08 0.1 0 0 0 R 0= 1.17 2.23 R 0= 2.7 4 r= 0.076233184 r= 0.425 1 pt for R 0, 1 pt for r 1 pt for R 0, 1 pt for r
Page 1: Problem Set 8, Bio 4181: Due Dec. 3

problem set 8 2009 key

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