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Chapter 16: Problem 390

Derive the Hardy-Weinberg probabilities in a population with random mating.

Short Answer

Expert verified
In a population at Hardy-Weinberg equilibrium with random mating and two alleles (A and a), the genotype frequencies can be derived using the allele frequencies (p and q). The frequencies are: homozygous dominant (AA): \(p^2\), heterozygous (Aa): \(2pq\), and homozygous recessive (aa): \(q^2\).

Step by step solution

01

Identify the genotype frequencies

To find the genotype frequencies, we'll use the allele frequencies (p and q) and the assumption of random mating.
02

Calculate the homozygous dominant (AA) frequency

The probability of an individual inheriting the dominant allele A from both parents is: AA frequency = \(p \cdot p = p^2\)
03

Calculate the heterozygous (Aa) frequency

The probability of an individual inheriting the dominant allele A from one parent and the recessive allele a from the other parent (or vice versa) is: Aa frequency = \(2 \cdot (p \cdot q)\) We multiply by 2 because there are two possible ways: either the A allele comes from the mother and the a allele comes from the father, or the A allele comes from the father and the a allele comes from the mother.
04

Calculate the homozygous recessive (aa) frequency

The probability of an individual inheriting the recessive allele a from both parents is: aa frequency = \(q \cdot q = q^2\)
05

Summarize the Hardy-Weinberg genotype frequencies

Finally, we combine the genotype frequencies derived in Steps 2-4: - AA frequency: \(p^2\) - Aa frequency: \(2pq\) - aa frequency: \(q^2\) These probabilities represent the expected genotype frequencies in a population at Hardy-Weinberg equilibrium with random mating.

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