## Introduction

The Hardy-Weinberg principle is a fundamental concept in population genetics. It describes the relationship between allele frequencies and genotype frequencies in a population that is not evolving. In this article, we will explore a problem set related to the Hardy-Weinberg principle and its application to a population of mice.

### Problem Set

Consider a population of 1000 mice. 60% of the mice are homozygous dominant for a certain gene, while 30% are heterozygous and 10% are homozygous recessive. Based on this information, answer the following questions:

1. What are the allele frequencies of the dominant and recessive alleles in the population?

2. What is the expected frequency of homozygous dominant mice in the next generation?

3. What is the expected frequency of heterozygous mice in the next generation?

4. What is the expected frequency of homozygous recessive mice in the next generation?

5. Is the population in Hardy-Weinberg equilibrium? If not, what evolutionary forces are likely at play?

### Solution

1. To calculate the allele frequencies, we can use the following formula:

p + q = 1

Where p is the frequency of the dominant allele and q is the frequency of the recessive allele.

We know that the frequency of homozygous dominant mice is 60%, which means that the frequency of the dominant allele (p) is √0.6 = 0.7746. Similarly, the frequency of homozygous recessive mice is 10%, which means that the frequency of the recessive allele (q) is √0.1 = 0.3162. Therefore,

p = 0.7746 and q = 0.3162

2. To calculate the expected frequency of homozygous dominant mice in the next generation, we can use the following formula:

p^2 = (0.7746)^2 = 0.5996

Therefore, the expected frequency of homozygous dominant mice in the next generation is approximately 60%.

3. To calculate the expected frequency of heterozygous mice in the next generation, we can use the following formula:

2pq = 2(0.7746)(0.3162) = 0.4901

Therefore, the expected frequency of heterozygous mice in the next generation is approximately 49%.

4. To calculate the expected frequency of homozygous recessive mice in the next generation, we can use the following formula:

q^2 = (0.3162)^2 = 0.0999

Therefore, the expected frequency of homozygous recessive mice in the next generation is approximately 10%.

5. To determine whether the population is in Hardy-Weinberg equilibrium, we can compare the observed genotype frequencies to the expected genotype frequencies based on the allele frequencies. If they are equal, the population is in Hardy-Weinberg equilibrium. If not, some evolutionary force is likely at play.

In this case, the observed genotype frequencies are:

60% homozygous dominant

30% heterozygous

10% homozygous recessive

The expected genotype frequencies based on the allele frequencies are:

59.96% homozygous dominant

39.02% heterozygous

10.02% homozygous recessive

As we can see, the observed and expected frequencies are very close, so the population is likely in Hardy-Weinberg equilibrium.

## Conclusion

In conclusion, the Hardy-Weinberg principle is a powerful tool for understanding the genetic structure of populations. By analyzing genotype and allele frequencies, we can make predictions about the next generation and determine whether a population is evolving or in equilibrium. In the case of our population of mice, we found that the population is likely in Hardy-Weinberg equilibrium and that the expected genotype frequencies match closely with the observed frequencies.