In an isolated population of 50 desert bighorn sheep, a mutant recessive allele c when homozygous causes curled coats in both males and females. The normal dominant allele C produces straight coats. A biologist studying these sheep counts four with curled coats. She also takes blood samples from the population for DNA analysis, which reveals that 17 of the sheep are heterozygous carriers of the c allele. What is the inbreeding coefficient F for this population?

Verified step by step guidance

1. Identify the given information: total population size (N = 50), number of individuals with the recessive phenotype (curled coats, which are homozygous recessive cc = 4), and number of heterozygous carriers (Cc = 17).
2. Calculate the observed frequency of the recessive homozygous genotype (cc) in the population: \(\hat{q^2} = \frac{\text{number of cc individuals}}{N} = \frac{4}{50}\).
3. Calculate the observed frequency of the heterozygous genotype (Cc) in the population: \(\hat{2pq} = \frac{17}{50}\).
4. Estimate the allele frequencies under Hardy-Weinberg equilibrium: the frequency of the recessive allele \(q\) can be estimated as \(q = \sqrt{\hat{q^2}}\), and the dominant allele frequency \(p = 1 - q\).
5. Use the formula for the inbreeding coefficient \(F\), which measures the reduction in heterozygosity compared to Hardy-Weinberg expectations: \(F = \frac{(2pq)_{expected} - (2pq)_{observed}}{(2pq)_{expected}}\), where \((2pq)_{expected} = 2pq\) calculated from allele frequencies assuming random mating, and \((2pq)_{observed}\) is the observed heterozygote frequency from the data.

Key Concepts

Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle provides a baseline to predict genotype frequencies in a large, randomly mating population without evolutionary forces. It relates allele frequencies (p and q) to genotype frequencies (p², 2pq, q²). Deviations from expected frequencies can indicate factors like inbreeding or selection.

Inbreeding Coefficient (F)

The inbreeding coefficient (F) measures the probability that two alleles at a locus are identical by descent. It quantifies the reduction in heterozygosity due to inbreeding compared to Hardy-Weinberg expectations. F ranges from 0 (no inbreeding) to 1 (complete inbreeding).

Genotype Frequencies and Phenotype Expression of Recessive Alleles

Recessive traits appear only in individuals homozygous for the recessive allele (cc). Heterozygous carriers (Cc) show the dominant phenotype but carry the recessive allele. Counting phenotypes and genotypes helps estimate allele frequencies and detect deviations caused by inbreeding.