Introduction

It's easy to extend the Hardy-Weinberg principle to multiple alleles at a single locus. In fact, we already did this when we were discussing the ABO blood group polymorphism. Just to get some notation out of the way, though, let's define $x_{ij}$ as the frequency of genotype $A_iA_j$ and $p_i$ as the frequency of allele $A_i$. Then

$$x_{ij} = \left\{ \begin{array}{ll} p_i^2 & \mbox{if $i = j$} \\ 2p_ip_j & \mbox{if $i \ne j$} \end{array} \right.$$

Unfortunately, the simple principles we've learned for understanding selection at one locus with two alleles don't generalize completely to selection at one locus with many alleles (or even three).

• For one locus with two alleles, heterozygote advantage guarantees maintenance of a polymorphism.

• For one locus with multiple alleles, there are many different heterozygote genotypes. As a result, there is not a unique pattern identifiable as ``heterozygote advantage,'' and selection may eliminate one or more alleles at equilibrium even if all heterozygotes have a higher fitness than all homozygotes.