Large, random-mating populations will, under certain assumptions, reach a
genetic equilibrium in which genotypic proportions tend to remain constant.
Hardy-Weinberg law: In a large,
random-mating population of diploids with no unbalanced mutation, unbalanced
migration, or selection in any form, the genotypic proportions tend to remain
constant. This constancy is called a genetic equilibrium, with
equilibrium frequencies given by the equation
p2 AA + 2pq Aa + q2 aa = 1
or, more simply,
p2 + 2pq + q2 = 1
p stands for the frequency of A; q for the frequency of a;
p + q = 1
p2 is the frequency of AA homozygotes; gametes are all A
2pq represents the frequency of Aa heterozygotes. Half of their gametes
(pq)
are A, the other half are a.
q2 is the frequency of aa homozygotes; gametes are all a
To find the new frequency of allele A, add p2 + pq
= p (p + q) = p (1) = p,
so the frequency of allele A remains p.
To find the new frequency of allele a, add pq + q2
= q (p + q) = q (1) = q,
so the frequency of allele a remains q.
A Hardy-Weinberg equilibrium can be established in a single generation
of random mating.
Exceptions to the Hardy-Weinberg law:
- If the population is not large, genetic drift occurs:
gene frequencies can fluctuate randomly in either direction simply
by chance.
- Populations may not mate at random. Inbreeding (increased mating
among related individuals) results in more homozygotes. Assortative mating
is mating according to phenotype, with mating between phenotypically similar
individuals being either more frequent (positive assortment) or less
frequent (negative assortment).
- Mutation in only one direction can cause one allele slowly to replace
another. Mutation in both directions results in an equilibrium with frequencies
determined by the mutation rates.
- Migration between populations always causes the gene frequencies of the
receiving population to shift towards those of the immigrants.
- Selection occurs whenever different genotypes contribute genes unequally
to the next generation.
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