Calculating the Proportion of Homozygotes for Multiple Alleles in a Diploid Population

In population genetics, understanding the distribution of genotypes—especially homozygotes—is crucial for predicting genetic diversity and disease prevalence. When a gene locus has more than two alleles, the Hardy-Weinberg principle can be extended to calculate the expected proportion of homozygotes in a diploid population.

Hardy-Weinberg Principle for Multiple Alleles

For a locus with n alleles in a diploid population, the sum of all genotype frequencies is:

^{(p1+p2+…+pn)2=1(p1+p2+…+pn)2=1}

Where p1,p2,…,pnp1,p2,…,pn are the frequencies of each allele.

The proportion of all homozygotes is the sum of the squares of the allele frequencies:

^{Proportion of homozygotes=p12+p22+…+pn2Proportion of homozygotes=p12+p22+…+pn2}

(A) All Alleles Are Equally Abundant

If all alleles are equally abundant, each allele has a frequency of $1/n$:

^{Proportion of homozygotes=n×(1/n)2=n×(1/n2)=1/nProportion of homozygotes=n×(1/n)2=n×(1/n2)=1/n}

So, when all alleles are equally abundant, the proportion of homozygotes is $1/n$.

(B) All Alleles Are Not Equally Abundant

If alleles are not equally abundant, some allele frequencies will be higher and others lower. Since squaring a number less than 1 makes it even smaller, but higher frequencies contribute disproportionately more to the sum, the sum of the squares (proportion of homozygotes) becomes greater than $1/n$.

Thus, when alleles are not equally abundant, the proportion of homozygotes is greater than $1/n$.

Correct Option

The correct answer is (2) 1/n and >1/n.

Why This Matters

• Genetic Diversity: Lower homozygosity (closer to $1/n$) indicates higher genetic diversity.

• Population Health: Higher homozygosity (greater than $1/n$) can increase the risk of recessive genetic disorders.

• Conservation Biology: Helps in assessing the genetic health of endangered species populations.

Conclusion

In a diploid population with $n$ alleles at a locus, the proportion of homozygotes is $1/n$ when all alleles are equally abundant and greater than $1/n$ when alleles are not equally abundant.

Correct answer: (2) 1/n and >1/n