Consider two genes A and a in a population, where A is a dominant gene and a is a recessive gene controlling the same genetic trait. (That is, A and a belong to the same locus.) Suppose that, initially, 80% of the genes are A and 20% are a. Suppose that, in each generation, .003% of gene A mutate to gene a.
(a) Find the difference equation for yn, the percentage of gene a after n generations. [The percentage of gene A = 100 - (the percentage of gene a).]
(b) Solve the difference equation from part (a).
(c) Use the solution from part (b) to calculate the percentage of gene a after 1800 generations?