Evolution__3rd_Edition

206 PART 2 / Evolutionary Genetics
. . . and non-random mating
Natural selection may work on each
locus independently ...
. . . producing multiplicative
fitnesses
linkage equilibrium, random sampling is equally likely to move it towards, as away
from, the equilibrium. Most natural populations are probably near linkage equilibrium
(see below, Figure 8.5), and then the balance between the random creation of linkage
disequilibrium and its destruction by recombination, in small enough populations, is
such that linkage disequilibrium will persist.
The third factor is non-random mating. If individuals with gene A 1 tend to mate
with B 1 types rather than B 2 types, A 1 B 1 haplotypes will have excess frequency over that
for random mating. (The exact effect depends on whether it is homozygous A 1 /A 1 individuals
that mate non-randomly, or the homozygotes and the A 1 /A 2 heterozygotes, and
on whether they mate preferentially only with B 1 /B 1 homozygotes, or with B 1 /B 2 heterozygotes
too. But the general effect of non-random mating on linkage disequilibrium is
not complicated.)
The three processes other than selection probably account for some cases of linkage
disequilibrium in nature. The process that has most interested evolutionary biologists,
however, is natural selection. Let us now consider how we can model the effect of
selection on haplotype frequencies.
8.8 Two-locus models of natural selection can be built
The effect of natural selection on haplotype frequencies in two-locus models, like its
effect on gene frequencies in single-locus models, depends on the fitnesses of the genotypes.
We have to write down the fitness of each genotype, and there are many possible
ways in which it can be done. In one of the simplest two-locus models, the fitness of a
two-locus genotype is the product of the fitnesses of its two single-locus genotypes. The
model is realistic if the fitness effect of one locus is independent of the genotype at
the other. Suppose, for example, that the A locus influences survival from age 1 to
6 months, such that:
Genotype A 1 /A 1 A 1 /A 2 A 2 /A 2
Chance of survival to age 6 months w 11 w 12 w 22
and the other locus influences survival from age 6 to 12 months:
Genotype B 1 /B 1 B 1 /B 2 B 2 /B 2
Chance of survival from 6 to 12 months x 11 x 12 x 22
The total chance of surviving from age 1 to 12 months would then be the product of
the two genotypes that an individual possessed because selection at age 1–6 months is
independent of selection at age 6–12 months:
A 1 /A 1 A 1 /A 2 A 2 /A 2
B 1 /B 1 w 11 x 11 w 12 x 11 w 22 x 11
B 1 /B 2 w 11 x 12 w 12 x 12 w 22 x 12
B 2 /B 2 w 11 x 22 w 12 x 22 w 22 x 22
..