p. 1 of 8
Population Genetics I
The material presented here considers a single diploid genetic locus, with two alleles
A
and
a
;
their relative frequencies in the population will be denoted as
p
and
q
(with q = 1
−
p).
Hardy-Weinberg equilibrium (review)
Requirements:
1.
no selection
2.
no mutation
3.
no stochastic (random) effects, i.e. infinitely large population
4.
no emigration or immigration
5.
random mating
If these conditions hold,
allele frequencies will not change
and genotype frequencies will be
AA = p
2
,
Aa = 2pq
,
aa = q
2
(1)
Effect of selection
In the following selection is assumed to be
constant
over time, and
density-
and
frequency-
independent
: each genotype has a constant fitness, regardless of the generation, the population
density, and the relative frequencies of the genotypes.
The main results will be:
1.
equilibria are:
a)
fixation of one allele (
i.e. p
= 1 or
p
= 0), or
b)
a mixture (polymorphism), if the heterozygote is either
• more
fit than either homozygote (in which case the polymorphism is stable), or
• less
fit than either homozygote (in which case the polymorphism is unstable).
2.
the rate of evolution (change in mean fitness) is (approximately) proportional to the genetic
variance times the strength of selection (Fisher’s “fundamental theorem of natural selec-
tion”)
3.
selection maximizes (approximately) the mean fitness of the population
4.
the rate of change in the relative frequency of a rare allele is slower for a recessive allele than
a dominant allele