The inbreeding coefficient F for this population of desert bighorn sheep is approximately 0.415.
Here's how to calculate the inbreeding coefficient F for the population of desert bighorn sheep:
Calculate gene frequencies:
Let p be the frequency of the c allele and q be the frequency of the C allele.
Since the alleles are in Hardy-Weinberg equilibrium (no selection, migration, or mutation), and we know the number of homozygous recessive individuals (5 with curled coats), we can calculate p^2 = 5/50.
Therefore, p = √(5/50) = 0.1 and q = 1 - p = 0.9.
Calculate expected frequencies of genotypes:
Under Hardy-Weinberg equilibrium, the expected frequencies of genotypes are:
CC: q^2 = 0.9^2 = 0.81
Cc: 2pq = 2 * 0.1 * 0.9 = 0.18
cc: p^2 = 0.1^2 = 0.01
Compare expected and observed frequencies:
We are given that 16 sheep are heterozygous carriers (Cc), which matches the expected frequency (0.5 * 50 * 0.18 = 9).
This further supports the assumption of Hardy-Weinberg equilibrium.
Calculate inbreeding coefficient F:
F measures the probability that two alleles at a given locus are identical by descent (due to non-random mating).
For autosomal genes like in this case, F can be calculated as:
F = (1 - Observed heterozygosity) / (1 - Expected heterozygosity)
Plugging in the values, we get:
F = (1 - 16/50) / (1 - 0.18)
F = 0.34 / 0.82
F ≈ 0.415
Therefore, the inbreeding coefficient F for this population of desert bighorn sheep is approximately 0.415.
This value indicates a moderately high level of inbreeding within the population, which could have consequences for genetic diversity and individual fitness.