Question

Problem ***. Gray squirrels normally have a medium gray fur color. However, some squirrels have been observed with a very dark gray phenotype. Fur color is controlled at a single locus, with the allele for medium gray being completely dominate to the dark gray allele. Researchers studied a population of 1839 gray squirrels in Eastern Pennsylvania and observed that dark gray squirrels had a higher fecundity and fitness. Dark gray squirrels produced about 8 offspring on average with an expected survivorship probability of 89%. Medium gray squirrels produced 7.6 offspring on average with an expected survivorship rate of 83%.

1. Calculate the absolute fitness of medium gray and dark gray squirrels. Assume that heterozygotes have the medium gray phenotype and the same fitness as medium gray squirrels.
2. Calculate the relative fitness of each genotype using the most fit as your reference.
3. Calculate the genotypic frequencies and allele frequencies if the dark gray squirrels make up 22% of the population.
4. Calculate w-bar for the population.
5. Calculate the frequencies of each genotype in the population after one generation.

Answer 1

let the alleles for medium grey = GG and Gg

for darg grey = gg

absolute fitness is calculated by comparing both the genotype, since dark grey has greater absolute fitness 8 it becomes the reference

dark grey - 8/8 = 1.0

medium grey - 7.6/8 = 0.95 absolute fitness

If we assume that the population is in hardy Weinberg equilibrium then the frequency of dark grey phenotype that is freq (aa) = q2. Frequency (aa) = 22% = 0.22 and square root of this is 0.46, which is q , the frequency of dark grey squirrels . The frequency of medium grey allele is p , equals to 1-q , so p = 0.54

Genotype AA is p2 = 0.29

Genotype aa is q2 = 0.22

Heterozygote 2pq= 2(0.46)(0.54) = 0.49