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Genotypes A 1 A 1 A 1 A 2 A 2 A 2

Genotypic frequencies p^22 pq q^2

= 0.01 0.18 0.81

Note that the genotypic frequencies (proportions) also sum to 1.

That relationship between allelic frequencies and genotypic frequencies is the

Hardy–Weinberg equilibrium law. Formally it holds only when the population is large,

its individuals mate at random, and there is no migration, mutation, or selection.

In practice, however, it is highly robust to deviations from these assumptions and

can be accepted as a close approximation to the actual relationship between allelic

frequency and genotypic frequency for two alleles at a single locus. The Hardy–

Weinberg equilibrium holds equally for more than two alleles at a locus so long as

it is calculated in terms of one allele against all the others. Alleles of the two types

A 1 and not-A 1 (not-A 1 =A 2 +A 3 +A 4 , etc.) also take Hardy–Weinberg equilibrium

proportions.

The number and frequency of different alleles at a locus can be determined fairly

easily by electrophoresis or DNA sequencing. If pijis the frequency of allele iat locus

jin the population as a whole, the proportion of individuals heterozygous at that

locus may be estimated as:

providing that the number of individuals njexamined for locus jis greater than 30.

If fewer, hjis underestimated but can be corrected by multiplying by 2nj/(2nj−1).

Thus the more alleles at a locus the higher the value of hj, and the less diverse the

frequencies of the alleles the higher is hj.

Mean heterozygosity is estimated as:

where Lis the number of loci examined. Hvaries considerably between species for

reasons that are not understood. As estimated by one-dimensional electrophoresis of

loci controlling production of proteins, Hranges between 0.00 and 0.26 for mam-

mals with an average at about 0.04. Heterozygosity estimated in the same way yields

H=0.036 for both white-tailed and mule deer (Gavin and May 1988) and H=0.029

for leopards. Figure 17.1 shows the frequency distribution of Hfor 169 species of

mammals. Note first that the distribution is shaped like a reverse J: most species have

a low Hbut a few break out of that pattern to return a high H. Second, a substan-

tial proportion (10.6%) of mammalian species are homozygous at all loci examined

by electrophoresis.

Genetic variability can be reported also as the proportion of polymorphic loci in

the population (i.e. the proportion of loci for which there is more than one allele

within the population as a whole). This is not the same asHabove. If all but one

individual in the population were homozygous at locus Athat locus is nonetheless

scored as polymorphic. The proportion of polymorphic loci within the population

is therefore higher than the average heterozygosity (the proportion of heterozygous

loci in an average individual), usually about three times higher. Further, it is an

HLhj

j

(/ )= (^1) ∑
hpjij
i
=− (^1) ∑^2
292 Chapter 17