Lab 5: Selection

Relative fitness(ω)  Average number of surviving progeny of one genotype compared to a competitive genotype.  Survival rate = “N” after selection/ “N” before selection.  Genotype with highest survival rate has ω=1.  Assumes equal fecundity for all genotypes. GenotypeA1A1A1A2A2A2 Nbefore 100 Nafter Survival rate Rel. fitness (ω) /0.8 = /0.8 = 0.5

Mean Fitness(ω) and Genotype frequency after selection ω = (100/300)(1) + (100/300)(0.7) + (100/300)(0.5) = P’ = {(100/300)(1)}/ = GenotypeSum A1A1A1A2A2A2 Relative fitnessω 11 ω 12 ω 22 Genotype frequency before selection P =p 2 H = 2pqQ = q 2 1 Genotype frequency  Relative fitness P(ω 11 )H(ω 12 )Q(ω 22 )ω Genotype frequency after selection P(ω 11 )/ω = (P’) H(ω 12 )/ ω = (H’) Q(ω 22 )/ ω = (Q’) 1

Fitness in terms of ‘s’ and ‘h’ Genotype A1A1A1A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s and h 11 – hs1 – s

Change in allele frequency after selection

Heterozygous Effect h = 0, A 1 dominant, A 2 recessive h = 1, A 2 dominant, A 1 recessive 0 < h < 1, incomplete dominance h = 0.5, additivity h < 0, overdominance h > 1, underdominance

Problem 1. A complete census of a population of a cold-intolerant plant revealed the following numbers for genotypes A1A1, A1A2, and A2A2 before and after a severe spring frost (but before sexual reproduction):( 20 minutes) a. Calculate the relative fitness for each of the three genotypes. b. What is the mean fitness of this population? How do you expect it to change in response to selection? c. Based on the values calculated in a), calculate the values of h and s. What type of selection has occurred? d. If the surviving individuals mate at random, what will be the genotype frequencies in the next generation (i.e., assuming no other evolutionary forces intervene)? e. Calculate the change in the frequency of allele A2 as a result of the frost: i. Based on the genotype frequencies calculated in d). ii. Using the formula for ∆q as a function of p, q, h, and s. f. What are the assumptions of the calculation in e)? What is your biological interpretation of this result? Genotype A1A1A1A2A2A2 Number before selection Number after selection

Problem 2. Assume that a population has two alleles A1 and A2, with frequencies of p = 0.8 and q = 0.2, respectively. Using the general equations for changes in allele frequencies, explore the relative effects of dominance and the selection coefficient by calculating Δp and Δq and the fitness of each genotype. You should perform the calculations for at least 5 different scenarios, using a range of values of each parameter. a.) What do you think is going to happen with the frequencies of A1 and A2 in each of these cases in the long term? b.) Rank the cases from greatest to smallest allele frequency change and explain what determines the different magnitudes of change. Be sure to include an evaluation of the relative importance of dominance and the selection coefficient. c.) What are the implications of the relative effects of h and s from an evolutionary standpoint? In your answer, consider that most mutations that afffect fitness usually have deleterious effects, and few are fully dominant. Casehs

Populus Simulation program that can be used as a ‘time machine’ for prediction of evolutionary and demographic aspects of population dynamics. Example: Use Populus to evaluate the changes of allele frequencies, genotype frequencies, and mean fitness after 10 generations of selection in a population with the p=0.7 and q= 0.3, but with h = 0.3 and s = 0.05.

Populus

Problem 3. Use Populus to determine the allele frequencies for A1 and A2 for all 5 cases from Problem 2 after 50 generations. Include the values of the final allele frequencies and a graph for the change of p over time in your report, but also look at the graphs showing the changes of genotype frequencies over time and the graphs showing ∆p and for different values of p. a.) Which cases show the fastest change in allele and genotype frequencies, and why? b.) What is the general trend for and why?

Heterozygote advantage (Overdominance) Genotype A1A1A1A2A2A2 Fitnessω 11 ω 12 ω 22 Fitness in terms of s and h 1 – s 1 11 – s 2 Where, s 1 and s 2 are the selection disadvantages of A1A1 and A2A2 with respect to A1A2.

Heterozygote advantage (Overdominance)

Problem 4:(25 minutes) a)If p = 0.65, q = 0.35, s 1 = 0.13, and s 2 = 0.19, calculate the equilibrium frequency of A2. b)Use Populus to verify the result of (a). Does q eq depend on the initial allele frequencies p and q? How do you explain this result? c)When will the population reach its maximum mean fitness? How might a population be perturbed from this state? What would cause the population to return to maximum mean fitness? d)GRAD STUDENTS ONLY: Is this equilibrium stable or unstable and why? What causes a population to reach a stable equilibrium? Provide a specific example of a trait and selection regime that would result in a stable equilibrium.