Chi Square Hardy-Weinberg Equilibrium Calculator

This calculator utilizes the Chi-square test to assess whether observed genotype frequencies for an autosomal trait, involving up to 5 alleles, align with Hardy-Weinberg expectations. You can either input allele frequencies directly in the specified fields at the bottom or have them inferred from the observed genotype counts provided.

Hardy-Weinberg Equilibrium Calculator

Hardy-Weinberg Equilibrium Calculator

Related Tools

Hardy-Weinberg Allele Frequency Calculator
Punnett square Calculator
Eyes Color Calculator
Hair Color Calculator
Child Traits Calculator

Understanding the Chi-square Test and Hardy-Weinberg Equilibrium

The Chi-square test is a statistical method used to compare observed data (o) with expected data (e).

A population is considered to be in Hardy-Weinberg equilibrium for a particular gene if it meets five key conditions: random mating, no mutations, no migration, no natural selection, and a sufficiently large population size.

Under these conditions, the allele frequencies in a population should remain constant over time.

The Hardy-Weinberg equations help estimate genotype and allele frequencies in such populations.

If these conditions are not met, the equations might not accurately predict the frequencies. However, a population may still show expected Hardy-Weinberg data even in the presence of some evolutionary forces.

Hardy-Weinberg Equations

For traits exhibiting incomplete dominance, heterozygotes can be distinguished from homozygous dominant individuals, enabling direct calculation of genotype and allele frequencies without needing Hardy-Weinberg equations.

This direct calculation can then be compared to Hardy-Weinberg values to determine if the population is in equilibrium.

Example Calculation

Suppose we have a population of 60 individuals: 20 are green (GG), 15 are yellow (GY), and 25 are blue (YY). These observed values will be used for the Chi-square analysis.

Sample Data: – GG = 20 – GY = 15 – YY = 25

First, we need to calculate the allele frequencies.

In this population of 60 individuals, each individual has two alleles, resulting in 120 alleles in total.

Each green (GG) individual has two G alleles, and each yellow (GY) individual has one G allele. Therefore, there are 55 G alleles in the population.

The frequency of the G allele is 55/120 ≈ 0.46, and the frequency of the Y allele is 65/120 ≈ 0.54.

Allele Frequency Calculations: – G = 0.46 – Y = 0.54

Next, we calculate the expected frequencies for each genotype using the Hardy-Weinberg equations.

Expected Frequency Calculations:

  • GG = (0.46)^2 = 0.21
  • GY = 2 * (0.46) * (0.54) = 0.50
  • YY = (0.54)^2 = 0.29

To find the expected numbers for each genotype, multiply these frequencies by the total number of individuals (60).

Expected Value Calculations:

  • GG = 0.21 * 60 = 12.6
  • GY = 0.50 * 60 = 30
  • YY = 0.29 * 60 = 17.4

With both observed and expected values, we can use the Chi-square formula to calculate the Chi-square value.

Chi-square Calculation:

χ² = Σ ((o – e)² / e)
χ² = ((20 – 12.6)² / 12.6) + ((15 – 30)² / 30) + ((25 – 17.4)² / 17.4)
χ² = 4.34 + 7.50 + 3.32 = 15.15

The calculated Chi-square value is 15.15. For a p-value of 0.05 and 1 degrees of freedom (df = number of genotype categories – 1), the critical value is 3.84. Since the Chi-square value (15.15) exceeds the critical value (3.84), we reject the hypothesis that the observed and expected values are equivalent.

This suggests that the population is not in Hardy-Weinberg equilibrium.

Scroll to Top