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. span>Step 1: Understand the problem. We have a population of 50 desert bighorn sheep. The allele c is recessive and causes curled coats when homozygous (cc). The allele C is dominant and results in straight coats. We need to find the inbreeding coefficient F.</span
2. span>Step 2: Identify the given data. We know there are 4 sheep with curled coats (cc), and 17 sheep are heterozygous carriers (Cc). The total population is 50 sheep.</span
3. span>Step 3: Calculate the observed frequency of the homozygous recessive genotype (cc). This is the number of sheep with curled coats divided by the total population: \( f(cc) = \frac{4}{50} \).</span
4. span>Step 4: Calculate the observed frequency of the heterozygous genotype (Cc). This is the number of heterozygous carriers divided by the total population: \( f(Cc) = \frac{17}{50} \).</span
5. span>Step 5: Use the Hardy-Weinberg principle to estimate the expected frequencies of the genotypes under random mating, and then use these to calculate the inbreeding coefficient F, which measures the reduction in heterozygosity due to inbreeding.</span

Key Concepts

Inbreeding Coefficient (F)

The inbreeding coefficient (F) quantifies the probability that two alleles at a locus in an individual are identical by descent. It ranges from 0 (no inbreeding) to 1 (complete inbreeding). Inbreeding can lead to an increase in homozygosity and can affect the genetic health of a population, making it crucial for understanding genetic diversity and potential vulnerabilities.

Allele Frequencies

Allele frequency refers to how often a particular allele appears in a population's gene pool. It is calculated by dividing the number of copies of the allele by the total number of alleles for that gene in the population. Understanding allele frequencies is essential for calculating the inbreeding coefficient and assessing genetic variation within a population.

Heterozygosity

Heterozygosity is the presence of different alleles at a gene locus in an individual. It is an important measure of genetic diversity within a population. High levels of heterozygosity are generally associated with greater adaptability and resilience to environmental changes, while low heterozygosity can indicate inbreeding and reduced genetic health.