Question

At a biallelic locus, suppose that genotypes A1A1, A1A2, and A2A2 have relative fitnesses 1, 1.02, and 1.03 and that the frequency of A1 is p = 0.1. (a) What is the population’s mean relative fitness? (b) What are the “marginal” or allele-specific relative fitnesses of A1 and A2? (c) What is the expected frequency of A1 in the following generation?

Answer 1

a) To calculate the population's mean relative fitness first we dive the most fitness genotype:

A2A2/A2A2 = 1.03/1.03 = 1.00

A2A2 has a population’s mean relative fitness of 1.00

The followings fitness calculation are based on the most fitness genotype:

A1A1/A2A2 = 1/1.03 = 0.97

A1A1 has a population’s mean relative fitness of 0.97

A1A2/A2A2 = 1.02/1.03 = 0.99

A1A2 has a population’s mean relative fitness of 0.99

b)

To calculate the "marginal" fitness we use the following formulas:

A1 = (p)(A1A1) + (1 - p)(A1A2)

A1 = (0.1)(0.99) + (1 - 0.1)(0.99)

A1 = 0.099 + 0.891 = 0.99

and

A2 = (p)(A1A2) + (1 - p)(A2A2)

A2 = (0.1)(0.99) + (1 - 0.1)(1)

A2 = 0.099 + 0.9

A2 = 0.999