4. Consider two populations of the plant Fumaria. The number of individuals with

Question

4. Consider two populations of the plant Fumaria. The number of individuals with each genotype is genotype: # indiv in western pop: AiAi AiA2 AiA3 A2A2 A2A3 A3A3 7 #indiv in Eastern pop: 700 900 300 800 400 200 (a) (2 points) In which population of Fumaria, Western or Eastern, is the frequency of Ay more likely to be larger in the next generation? Explain your logic. You may ignore mutation and migration, and this is a neutral loc Suppose that a single Fumaria seed is blown away to a distant island. This seed is able to found a large new Island population after it germinates because the plant can self-fertilize. In the next two parts, you will provide the probability that the founding seed does not carry allele A3, so that the only alleles in the Island population are Ai and A2. (b) (1 point) What is this probability of As being lost if the founder came from the Western population? Show your work. (c) (I point) What is this probability of Aj being lost if the founder came from the Eastern population? Show your work. (d) (3 points) The scenario in the two previous parts shows the loss of an allele through the founder effect which is one source of genetic drift. How does population size affect drift specifically in this scenario? Your answer should compare the values from (b) and (c), and it should mention the population sizes of the Western, Eastern, and Island populations.

Explanation / Answer

(a) In a population with small size, even a small change in the genetypic population will result in great change in allele frequency. But if the population size is huge, then the change does not cause major impact and the allele frequency almost remains the same.

In this case the A3 allele frequency in Western population = [3+4+(2*2)]/2*(7+9+3+8+4+2)] = 11/66 = 0.1667

A3 allele frequency in Estern population =[300+400+(2*200)]/2*(700+900+300+800+400+200)]=1100/6600=0.1667

Note that both frequencies are same. But if one individual having A3 A3 genotype is lost in both population, then the number of individuals in western population is 1 and the number of individuals in eastern population is 199 .So the frequecies are:

A3 allele frequency in Western population = [3+4+(2*1)]/2*(7+9+3+8+4+1)] = 9/64 = 0.1401

A3 allele frequency in Estern population=[300+400+(2*199)]/2*(700+900+300+800+400+199)]=1098/6598= 0.1666

Note that the allele frequency of Western population changes significantly than that of the Eastern population. Additionaly, the allele frequency of A1 and A2 are 0.39 and 0.439 respectively for both the population, making the A3 allele rare. So there is a great chance to lose the A3 allele in the next generation.

Considering everything, the allele frequency of A3 will be larger in the Eastern population.

(b) Probability of A3 being lost if the founder comes from Western population:

Probability of A3 being lost = Number of individuals without A3 in Western population / Number of individuals without A3 in both population = (7+9+8)/(7+9+8)+(700+900+800) = 24/2424= 0.0099

Probability of A3 being lost if the founder comes from Western population = 0.0099

(c) Probability of A3 being lost if the founder comes from Eastern population:

Probability of A3 being lost = Number of individuals without A3 in Eastern population / Number of individuals without A3 in both population = (700+900+800)/(7+9+8)+(700+900+800) = 2400/2424

  Probability of A3 being lost if the founder comes from Eastern population = 0.9901

(d) As you can see, the probability of A3 being lost is higher if the founder comes from the Eastern population. Because Eastern population is higher than the Western population. So there is increased chance for the Eastern population individual to spread when compared to Western population, resulting in higher A3 being lost.

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