Large, random-mating populations will, under certain assumptions, reach a
genetic equilibrium in which genotypic proportions tend to remain constant.
Mendel's laws
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.
H-W equilibrium
Sample problem
Exceptions to the Hardy-Weinberg law (departures from equilibrium):
- Mutations:
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.
- Migrations:
Migration between populations always causes the gene frequencies of the
receiving population to shift towards those of the immigrants.
- Nonrandom mating:
- 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).
- Genetic drift:
If the population is not large, gene frequencies can fluctuate
randomly in either direction simply by chance.
- Selection occurs whenever different genotypes contribute genes unequally
to the next generation. This is the most important and most frequent departure
from equilibrium conditions.
REVIEW:
Study guide and vocabulary
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