In a population where only the total number of individuals with the dominant phenotype is known, how can you calculate the percentage of carriers and homozygous recessives?

Verified step by step guidance

1. Identify the given information: the total number of individuals with the dominant phenotype. This includes both homozygous dominant (AA) and heterozygous carriers (Aa).
2. Recall that the Hardy-Weinberg principle can be used to estimate genotype frequencies in a population. The key equation is \(p^2 + 2pq + q^2 = 1\), where \(p\) is the frequency of the dominant allele and \(q\) is the frequency of the recessive allele.
3. Understand that the dominant phenotype frequency corresponds to \(p^2 + 2pq\), and the recessive phenotype frequency corresponds to \(q^2\). Since you know the proportion of dominant phenotypes, you can express this as \(p^2 + 2pq = \text{given dominant phenotype frequency}\).
4. Calculate \(q^2\) (the frequency of homozygous recessive individuals) by subtracting the dominant phenotype frequency from 1: \(q^2 = 1 - (p^2 + 2pq)\). Then, find \(q\) by taking the square root of \(q^2\).
5. Use the relationship \(p + q = 1\) to find \(p\). Finally, calculate the percentage of carriers (heterozygous individuals) using \$2pq\(, and the percentage of homozygous recessives using \)q^2$.

Key Concepts

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework to relate allele and genotype frequencies in a population under ideal conditions. It assumes no mutation, migration, selection, or genetic drift, allowing calculation of genotype proportions from phenotype data using p² + 2pq + q² = 1, where p and q are allele frequencies.

Phenotype to Genotype Relationship

Phenotypes reflect observable traits, but multiple genotypes can produce the same phenotype, especially for dominant traits. Knowing only the dominant phenotype frequency means both homozygous dominant (AA) and heterozygous carriers (Aa) are included, requiring further calculations to separate these genotypes.

Calculating Carrier and Homozygous Recessive Frequencies

Using the frequency of the recessive phenotype (q²), one can find q (allele frequency of recessive allele) by taking the square root. Then, p = 1 - q. The carrier frequency (heterozygous, 2pq) and homozygous recessive frequency (q²) can be calculated, enabling estimation of genotype percentages from phenotype data.