Question

Accounting for linkage, derive the three equations for the frequencies of A1B2, A2B1, and A2B2 gametes after one round of mating.

Answer 1

The combination of two gene pairs, A and B, each with two alleles are shown in the classical two-by-two table, where r, s, t, and u are the observed gamete frequencies of the gametes AB, Ab, aB and ab,

         gene A   gene B       B              b            frequency  

                 --------- ---------------------------------------

                   A               |         r=p(A)*p(B)+D s=p(A)*q(b)-D |   p(A)                

                   a                |         t=q(a)*p(B)-D   u=q(a)*q(b)+D |   q(a)

                         -----------------------------------------------

                Frequency |      p(B)                      q(b)               |    1

Gene frequencies can be calculated by means of the gene counting method. The expected frequency of a gamete is the product of the border distributions which is equal to p(A) = r + s = p(A)*p(B) + D + p(A)*q(b) - D = p(A)[p(B) + q(b)] = p(A).