Question

in a population of cattle, the following color distribution was noted: 36% red (rr), 48% roan (rr), and 16% white (rr). this population is in a hardy-weinberg equilibrium. what will be the distribution of genotypes in the next generation if the hardy-weinberg assumptions are met?

Answer 1

According to Hardy-Weinberg's theory, if a population is in equilibrium, its allelic and genotypic frequencies will remain the same through generations. The distribution of genotypes in the next generation will be 36% RR, 48% Rr, 16% rr.

What is the Hardy-Weingberg equilibrium?

The Hardy-Weinberg equilibrium is a theory that states that populations in equilibrium are not evolving.

In these population, alleleic and genotypic frequencies remain the same generation after generation.

Assuming a diallelic gene,

⇒ The allelic frequencies in a locus are represented as p and q.

• The frequency of the dominant allele p(X) is p

• The frequency of the recessive allele p(x) is q

⇒ The genotypic frequencies after one generation are

• p² (Homozygous dominant genotypic frequency),

• 2pq (Heterozygous genotypic frequency),

• q² (Hom0zygous recessive genotypic frequency).

The addition of the allelic frequencies equals 1

p + q = 1.

The sum of genotypic frequencies equals 1

p² + 2pq + q² = 1

In the exposed example,

• F(RR) = p² = 36% = 0.36
• F(Rr) = 2pq = 48% = 0.48
• F(rr) = q² = 16% = 0.16

These are the genotypic frequencies in the current generation. If this population is in Hardy-Weinberg equilibrium, its frequencies will remain the same in the following generation.

The distribution of genotypes in the next generation will be

• 36% RR
• 48% Rr
• 16% rr

You can learn more about the Hardy-Weinberg equilibrium at

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