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

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**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.

Dr. Sumeet is a seasoned geneticist turned wellness educator and successful financial blogger. GenesWellness.com, leverages his rich academic background and passion for sharing knowledge online to demystify the role of genetics in wellness. His work is globally published and he is quoted on top health platforms like Medical News Today, Healthline, MDLinx, Verywell Mind, NCOA, and more. Using his unique mix of genetics expertise and digital fluency, Dr. Sumeet inspires readers toward healthier, more informed lifestyles.