The white “Spirit” black bear (or Kermode), Ursus americanus kermodei, differs from the ordinary black bear by a single amino acid change in the melanocortin 1 receptor gene (MC1R). In this population, the gene has two forms (or alleles): the “white” allele b and the “black” allele B.  

The trait is recessive: white bears have two copies of the white allele of this gene (bb), whereas a bear is black if it has one or two copies of the black allele (Bb or BB). Both color morphs and all three genotypes are found together in the bear population of the northwest coast of British Columbia. If possessing the white allele has no effect on growth, survival, reproductive success, or mating patterns of individual bears, then the frequency of individuals with 0, 1, or 2 copies of the white allele (b) in the population will follow a binomial distribution. To investigate, Hedrick and Ritland (2012) sampled and genotyped 87 bears from the northwest coast: 42 were BB, 24 were Bb, and 21 were bb. Assume that this is a random sample of bears.

a. Calculate the fraction of b alleles in the population (remember, each bear has two copies of the gene).

b. With your estimate of the fraction of b alleles, and assuming a binomial distribution, calculate the expected frequency of bears with 0, 1, and 2 copies.

c. Compare the observed and expected frequencies in a graph. Describe how they differ.