A botanist studying water lilies in an isolated pond observed three leaf shapes in the population: round, arrowhead, and scalloped. Marker analysis of DNA from 125 individuals showed the round-leaf plants to be homozygous for allele r1, while the plants with arrowhead leaves were homozygous for a different allele at the same locus, r2. Plants with scalloped leaves showed DNA profiles with both the r1 and r2 alleles. Frequency of the r1 allele was estimated at 0.81. If the botanist counted 20 plants with scalloped leaves in the pond, what is the inbreeding coefficient F for this population?

Verified step by step guidance

1. Identify the genotypes corresponding to each leaf shape: round leaves are homozygous r1r1, arrowhead leaves are homozygous r2r2, and scalloped leaves are heterozygous r1r2.
2. Use the allele frequency given: frequency of allele r1 (p) = 0.81. Calculate the frequency of allele r2 (q) as q = 1 - p.
3. Calculate the expected genotype frequencies under Hardy-Weinberg equilibrium: expected frequency of heterozygotes (r1r2) is 2pq = 2 \times p \times q.
4. Determine the observed frequency of heterozygotes from the data: observed heterozygote frequency = number of scalloped plants / total plants = 20 / 125.
5. Use the formula for the inbreeding coefficient F, which measures the reduction in heterozygosity: \(F = \frac{\text{expected heterozygosity} - \text{observed heterozygosity}}{\text{expected heterozygosity}} = \frac{2pq - \text{observed heterozygote frequency}}{2pq}\).

Key Concepts

Allele Frequency and Genotype Frequency

Allele frequency refers to how common an allele is in a population, expressed as a proportion. Genotype frequency is the proportion of individuals with a specific genotype. For a locus with two alleles, the sum of allele frequencies equals 1, and genotype frequencies can be predicted under Hardy-Weinberg equilibrium using p², 2pq, and q².

Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium describes a theoretical state where allele and genotype frequencies remain constant across generations in a large, randomly mating population without evolutionary forces. It provides expected genotype frequencies (p², 2pq, q²) based on allele frequencies, serving as a baseline to detect deviations caused by factors like inbreeding.

Inbreeding Coefficient (F)

The inbreeding coefficient (F) measures the probability that two alleles at a locus are identical by descent, indicating the level of inbreeding. It quantifies deviations from Hardy-Weinberg expectations, especially reductions in heterozygosity. F is calculated by comparing observed heterozygosity to expected heterozygosity under random mating.