# Predicting Sloth Offspring Claw Lengths

## How can we predict the claw lengths of sloth offspring?

Given the population of sloths with variable forepaw claw lengths, how many offspring are expected to have long and short claws?

## Prediction of Sloth Offspring Claw Lengths:

In a population of sloths, 1.8 offspring are expected to have long claws, 8.4 offspring are expected to have short claws, and 7.8 offspring are expected to be heterozygous.

## Explanation:

In a population of sloths in Hardy Weinberg equilibrium, the long claw allele is dominant over the short claw allele. Given that there are 38 sloths with long claws and 82 sloths with short claws, we can calculate the frequency of each allele. The total number of sloths is 120 (38 + 82), so the frequency of the long claw allele is 38/120 = 0.3167 and the frequency of the short claw allele is 82/120 = 0.6833.

Since the population is in Hardy Weinberg equilibrium, we can use the allele frequencies to calculate the expected genotype frequencies. The frequencies of homozygous long claw (LL) individuals can be calculated by squaring the frequency of the long claw allele: (0.3167)^2 = 0.1. The frequencies of homozygous short claw (SS) individuals can be calculated by squaring the frequency of the short claw allele: (0.6833)^2 = 0.4678. The frequency of heterozygous (LS) individuals can be calculated by multiplying the frequencies of the long claw and short claw alleles: 2 * (0.3167) * (0.6833) = 0.4334.

To predict the number of offspring with long and short claws, we can use these genotype frequencies. If 18 baby sloths are born into the population, we can expect that approximately 0.1 * 18 = 1.8 individuals will have long claws, 0.4678 * 18 = 8.4 individuals will have short claws, and 0.4334 * 18 = 7.8 individuals will be heterozygous.