Assume the migration rate between two populations Pop1 and P

Assume the migration rate between two populations (Pop1 and Pop2) is 0.3 and that the initial requencies of allele A1 in each population 0.0 (Pop1) and 1 (Pop2). a. What are the new allele frequencies for each population after one generation? (4 pts) b. What is the equilibrium frequency for A1 ifgene flow is the only force acting? (2pts) I c. Will this equilibrium frequency be the same if the gene flow rate is not the same between the two populations (Pop1 to Pop2 is not as Pop2 to Pop1). Briefly explain. (2pts)

Solution

Let the migration rate between the two populations be m.; m= 0.3

Let the Allele frequency of population 1(PoP1) = p_{x =} 0.0.    

Let the Allele frequency of population 2 (PoP2)= p_y= 1

a) Change in allele frequency after one generation = dP= -m(p_x -py) = -0.3(0.0-0-1) =-0.3(-1) = 0.3 .  

Hence, new allele frequency ,new p_x = 0.0-0.3= 0.3 = new allele frequency of PoP1   

                                                 new p_{y =} 1-0.3= 0.7 = new allele frequency of PoP2 .

b) Allele frequency reaches equilibrium when change in allele frequency =0.

dP=(p_x - p_y )= 0. There fore ; p_x = p_{y .} (allele frequencies of the two populations will get closer till they become rqual in order to reach equilibrium) .

c) According to the equation dP= -m(p_x -p_y) ; the change in allle frequency depends on migration rate . Hence, migration rate is propotional to allele frequency. So, the equilibrium frequency will not be the same if the gene flow rate is not the same between the two populations.