Solutions For An Introduction to Genetic Analysis Chapter 18 Problem 33P

A colony on an island consists of 50 men and 50 women. The frequency of a recessive trait after 50 generations, if its previous frequency on the mainland was 1/500, can be calculated as follows:

The frequency of the recessive trait is 1/500 or 0.002. This is equal to q². Then the value of q is 0.045. The inbreeding frequency after 50 generations can be calculated as:

…… (1)

Substitute the values in equation (1):

If the allele frequency remains constant, the new frequency of a/a homozygotes after 50 generations would be as follows:

Hence, one or two members would express the recessive trait after 50 generations.

The above calculation applies only if the frequency of the alleles did not change. Since the recessive allele has no effect on fitness, changes in allelic frequency would be due to genetic drift. Being a small population, genetic drift is much more than in large populations. There is a 0.045 chance of the ultimate fixation of the recessive allele or 1-0.045 chance that it will be lost from the population. This would be 0.955.