Question

10. Researchers observe a large population of birds on a remote island. Birds in the population are found to have either red crest feathers or white crest feathers on their heads. Genetic analysis indicates that the allele for red crest feathers is dominant over the allele for white crest feathers. In a survey of the population, the researchers determine the frequencies of the crest-feather phenotypes. The results of the survey are shown in the table below.
PHENOTYPE FREQUENCIES IN AN ISOLATED BIRD POPULATION
Phenotype
Number of Individuals
Red crest feathers - 11,088
White crest feathers - 1,759

Assuming that the bird population is in Hardy-Weinberg equilibrium, what proportion of future populations is expected to be heterozygous controlling crest feather color? Give your answer as a value between 0 and 1, rounded to two decimal places.

Answer 1

Suppose that the proportion of the white crest alleles (r) is given by w and that of the Red crest allele (R) is given by p. We have that p+w=1. The probability that an individual has 2 r alleles is given by w*w since for each allele position the probability is w. Only these individuals have a White phenotype. Hence, we get that w^2=$\frac{1759}{1759+11088}$; the right hand side is the proportion of white birds in the total population. Doing the calculations, this yields that w=0.37. From this, we calculate that p=0.63. The possible ways we have heterozygous individuals are the combinations Rr and rR. The probability for each of those is p*w. Thus, the total probability is 2pw. This is equal to 0.466=0.47. This is the fraction of the future population that is going to be heterozygous assuming the conditions of the Handy-Weinberg equilibrium like random reproductive matching etc.