# Breeding Sloths: Understanding Dominant and Recessive Alleles

## What are the phenotypes observed in the sloth population?

The phenotypes observed in the sloth population are black fur and beige fur. By breeding the sloths in captivity, it was determined that black fur is the dominant allele (A) and beige fur is the recessive allele (a).

## How many sloths in the wild population have black fur and how many have beige fur?

Out of the 500 animals observed in the wild sloth population, 455 of them have black fur and 45 of them have beige fur.

## Using the Hardy-Weinberg equation, determine the frequency of each genotype: AA, Aa, and aa.

Based on the Hardy-Weinberg equation (p² + 2pq + q² = 1), calculate the frequency of each genotype in the sloth population.

## Final answer:

The frequency of each genotype (AA, Aa, and aa) in the sloth population can be calculated using the Hardy-Weinberg equation. From the given data, the frequency of the dominant allele (A) is 0.91 and the frequency of the recessive allele (a) is 0.09. Using these values, the frequency of AA is 0.8281, the frequency of Aa is 0.1638, and the frequency of aa is 0.0081.

## Explanation:

To determine the frequency of each genotype (AA, Aa, and aa) in the sloth population, we can use the Hardy-Weinberg equation: p² + 2pq + q² = 1. In this equation, p represents the frequency of the dominant allele (A) and q represents the frequency of the recessive allele (a).

From the data given, the frequency of the dominant allele (p) is calculated by dividing the number of animals with black fur by the total number of animals. So, p = 455/500 = 0.91. The frequency of the recessive allele (q) can be calculated by subtracting the frequency of the dominant allele from 1.

So, q = 1 - 0.91 = 0.09. Now we can substitute these values into the Hardy-Weinberg equation to calculate the frequencies of each genotype.

The frequency of AA (p²) = (0.91)² = 0.8281, the frequency of aa (q²) = (0.09)² = 0.0081, and the frequency of Aa (2pq) = 2(0.91)(0.09) = 0.1638.