A sample of 500 field mice contains 225 individuals that are D₁D₁, 175 that are D₁D₂, and 100 that are D₂D₂.
Is this population in H-W equilibrium? Use the chi-square test to justify your answer.

Verified step by step guidance

1. Step 1: Calculate the observed genotype frequencies. Divide the number of individuals for each genotype by the total population size (500). For example, the frequency of D₁D₁ is 225/500, D₁D₂ is 175/500, and D₂D₂ is 100/500.
2. Step 2: Determine the allele frequencies. Use the observed genotype counts to calculate the frequency of each allele (D₁ and D₂). For D₁, add twice the number of D₁D₁ individuals to the number of D₁D₂ individuals, then divide by twice the total population size. Similarly, calculate the frequency of D₂.
3. Step 3: Use the Hardy-Weinberg equilibrium formula to calculate the expected genotype frequencies. For D₁D₁, use p²; for D₁D₂, use 2pq; and for D₂D₂, use q², where p is the frequency of D₁ and q is the frequency of D₂. Multiply these frequencies by the total population size (500) to get the expected genotype counts.
4. Step 4: Perform the chi-square test. Use the formula χ² = Σ((O - E)² / E), where O represents the observed counts and E represents the expected counts for each genotype. Calculate the chi-square value by summing the contributions from D₁D₁, D₁D₂, and D₂D₂.
5. Step 5: Compare the calculated chi-square value to the critical value from a chi-square distribution table at the appropriate degrees of freedom (df = number of genotypes - 1 = 3 - 1 = 2) and significance level (commonly 0.05). If the chi-square value is less than the critical value, the population is in Hardy-Weinberg equilibrium; otherwise, it is not.

Key Concepts

Hardy-Weinberg Equilibrium

Hardy-Weinberg Equilibrium (HWE) is a principle that describes a population's genetic variation in the absence of evolutionary forces. For a population to be in HWE, it must meet five conditions: no mutations, random mating, no natural selection, extremely large population size, and no gene flow. If these conditions are met, allele and genotype frequencies will remain constant from generation to generation.

Chi-Square Test

The Chi-Square Test is a statistical method used to determine if there is a significant difference between observed and expected frequencies in categorical data. In the context of HWE, it helps assess whether the observed genotype frequencies deviate from those expected under HWE. A high chi-square value indicates a significant difference, suggesting that the population may not be in equilibrium.

Genotype Frequencies

Genotype frequencies refer to the proportion of different genotypes within a population. In this case, the frequencies of D₁D₁, D₁D₂, and D₂D₂ genotypes can be calculated from the sample size. These frequencies are compared to the expected frequencies derived from allele frequencies under HWE to evaluate if the population is in equilibrium.