Recall the haploid model of evolution by natural selection from the Week 12 Prac. For a gene with two alleles (an A allele with frequency p and fitness wa, and an a allele with frequency q = 1 -p and fitness wa), the allele frequency in the next generation will be: PWA P' = - pwAt (1 - p)wa Question 4. Imagine that you work in a lab that has recently carried out an evolution experiment in which there is a rapid increase in the frequency of an allele that they believe is beneficial in their study system (the study system is a microbial population of haploid individuals). Over a span of 25 generations, the allele has increased from an initial frequency of 0.05 to a final frequency of 0.95. Members of the lab wish to estimate the fitness advantage of individuals with the beneficial allele relative to the fitness of individuals without the allele (i.e., they wish to estimate wa/Wa, where wA is the fitness of individuals with the beneficial allele and we is the fitness of individuals with the alternative allele). Use the allele frequency data and the haploid model to estimate the fitness advantage of individuals with the beneficial allele. [1 point] Scoring: Full credit for providing the correct answer and showing how the answer was obtained (e.g., submit the R code and relevant simulation output to justify the answer OR present a detailed mathematical solution to the question). Question 5. Now consider a population in which the fitness advantage of the beneficial allele is 50% (i.e., WA/Wa = 1.5). Suppose the beneficial allele starts out as a single copy within a population of 100,000 individuals (its initially frequency would, therefore, be 10-5). Assuming that the advantage of the allele remains constant over time, how many generations will it take for it to reach a frequency of 0.5? How long would it take to reach a frequency of 0.99? [1 point]