Population genetics—second cousins: This is a continuation of Exercise 5 and Exercise 6. Second cousins are individuals each of whom has one parent who is a first cousin to a parent of the other...

Population genetics—second cousins: This is a continuation of Exercise 5 and Exercise 6. Second cousins are individuals each of whom has one parent who is a first cousin to a parent of the other individual. For matings between second cousins, the proportions of the genotypes of the children can be accounted for in terms of the previous three generations. In this case, λ1 is still the solution to an polynomial equation for λ. But here the powers of λ1 indicate decrease in deviation from an equilibrium genetic structure rather than decrease in the heterozygous population. If λ1 = 0.75, for example, the deviation from equilibrium genetic structure decreases by 25% each generation. The equation is

a. Find all solutions to the quartic equation above and identify which is λ1.

b. How many solutions did you expect to the quartic equation?

c. After 5 generations how close will the population be to its equilibrium structure?

d. After 20 generations how close will the population be to its equilibrium structure?