If the initial allele frequencies are p = 0.5 and q = 0.5 and allele a is a lethal recessive, what will be the frequencies after 1, 5, 10, 25, 100, and 1000 generations?

Verified step by step guidance

1. Understand the problem context: allele 'a' is a lethal recessive, meaning individuals with genotype 'aa' do not survive to reproduce. The initial allele frequencies are given as \(p = 0.5\) for the dominant allele and \(q = 0.5\) for the recessive lethal allele.
2. Recall that in a population with a lethal recessive allele, the homozygous recessive genotype frequency (\(q^2\)) will be eliminated each generation because those individuals do not survive. This affects the allele frequencies in subsequent generations.
3. Use the Hardy-Weinberg principle adjusted for selection against the recessive homozygote. The genotype frequencies before selection are: \(p^2\) (AA), \$2pq\( (Aa), and \)q^2\( (aa). Since 'aa' individuals die, only \)p^2\( and \)2pq$ contribute to the next generation.
4. Calculate the new allele frequencies after selection using the formulas: \[ \text{New } p = \frac{p^2 + pq}{1 - q^2} \] \[ \text{New } q = \frac{pq}{1 - q^2} \] where the denominator \$1 - q^2$ is the proportion of surviving individuals.
5. Iterate this calculation for each generation (1, 5, 10, 25, 100, 1000) by using the updated allele frequencies from the previous generation as the starting values for the next, to observe how \(p\) and \(q\) change over time under selection against the lethal recessive allele.

Key Concepts

Allele Frequencies and Hardy-Weinberg Equilibrium

Allele frequencies represent the proportion of different alleles in a population's gene pool. The Hardy-Weinberg principle predicts stable allele frequencies in an ideal population without evolutionary forces. Understanding initial frequencies (p and q) is essential to track changes over generations, especially when selection acts on specific alleles.

Lethal Recessive Alleles and Natural Selection

A lethal recessive allele causes death when homozygous (aa), removing those individuals from the population. This selection pressure reduces the frequency of the recessive allele over time, as homozygous recessive individuals do not reproduce. Heterozygotes (Aa) typically survive, allowing the allele to persist at low frequencies.

Genetic Drift and Long-Term Allele Frequency Changes

Genetic drift refers to random fluctuations in allele frequencies, especially in small populations, which can affect allele persistence. Over many generations, selection against lethal recessives and drift influence allele frequencies, often leading to a decrease in the lethal allele but rarely complete elimination without mutation or migration.