Hardy-Weinberg Theorem for Triploid Organisms: Understanding Genotype Frequencies

The Hardy-Weinberg principle is a cornerstone of population genetics, providing a mathematical model to predict genotype frequencies in populations under specific conditions. While it’s most commonly applied to diploid organisms (with two sets of chromosomes), it can be extended to polyploid organisms, such as triploids, which have three sets of chromosomes per cell. But how does the equation change for triploid organisms?

Hardy-Weinberg Principle for Diploids

For diploid organisms with two alleles (p and q), the Hardy-Weinberg equation is:

(p+q)2=p2+2pq+q2=1(p+q)2=p2+2pq+q2=1

This equation predicts the frequencies of the three possible genotypes (AA, Aa, aa) in a population at equilibrium.

Generalization for Polyploidy

The Hardy-Weinberg principle can be generalized for organisms with more than two sets of chromosomes (polyploids). For a polyploid organism with ploidy level $c$, the equation becomes:

(p+q)c=1(p+q)c=1

For triploid organisms ($c=3$), the equation is:

(p+q)3=1(p+q)3=1

This expansion predicts the genotype frequencies for all possible combinations of the two alleles across three chromosome sets. For example, the possible genotypes are AAA, AAa, Aaa, and aaa, with corresponding frequencies derived from the expansion.

Why Not Other Options?

• (p + q + r) = 1 and (p + q + r)^2 = 1: These forms are used for loci with three alleles, not for triploid ploidy.

• (p + q + r)^3 = 1: This would be used for a triploid organism with three alleles at a locus, but the question specifies only two alleles.

• (p + q)^3 = 1: This is the correct representation for a triploid organism with two alleles.

Example: Genotype Frequency Calculation for Triploids

Expanding (p+q)3(p+q)3 gives:

(p+q)3=p3+3p2q+3pq2+q3(p+q)3=p3+3p2q+3pq2+q3

• p3p3: Frequency of AAA genotype

• 3p2q3p2q: Frequency of AAa genotype

• 3pq23pq2: Frequency of Aaa genotype

• q3q3: Frequency of aaa genotype

Conclusion

For a triploid organism with two alleles, the Hardy-Weinberg theorem for genotype frequency is represented as:

(p+q)3=1(p+q)3=1

Correct answer: (1) (p + q)^3 = 1