Evolution__3rd_Edition

202 PART 2 / Evolutionary Genetics
Recombination breaks down
linkage disequilibrium
It is interesting to know if a
population is in linkage equilibrium
or disequilibrium
The equilibrial haplotype proportions have D = 0. At equilibrium:
Haplotype Equilibrial frequency
A1B1 A1B2 A2B1 A2B2 a = p1q1 b = p1q2 c = p2q1 d = p2q2 These are the haplotype frequencies we have met before and called linkage equilibrium.
We can now see why it is called an “equilibrium.” In the absence of selection, the action
of recombination will drive the haplotypes to these frequencies and then keep them
there.
Recombination randomizes genic associations over time. If an excess of one haplotype
such as A 1 B 1 exists, recombination will tend to break it down, and A 1 will end up
with B 1 and B 2 in their population proportions (q 1 and q 2 ) and B 1 with A 1 and A 2 in
their population proportions (p 1 and p 2 ). At linkage equilibrium, each of the two alleles
at the A locus, A 1 and A 2 , are then associated with B 1 in the same proportion.
Linkage equilibrium is, in a way, the analogy for a two-locus system of the Hardy–
Weinberg equilibrium for the one-locus system. It describes the equilibrium that is
reached in the absence of selection, and in an infinite, randomly mating population.
Linkage equilibrium, however, is a property of haplotypes, not genotypes. A diploid
individual has two haplotypes, and at equilibrium the genotypes at each locus will be in
Hardy–Weinberg proportions while the haplotypes are at linkage equilibrium. Notice
also that whereas the Hardy–Weinberg equilibrium for one locus is reached instantly in
one generation (Section 5.3, p. 98), it takes several generations for linkage equilibrium
to be reached. 2
Linkage equilibrium has a three-fold interest. The Hardy–Weinberg theorem for one
locus was the simplest model in single-locus population genetics and it illustrated how
to construct a model with recurrence relations for gene frequencies. The model of linkage
equilibrium is, likewise, the simplest model for two loci and shows us how to construct
a recurrence relation for haplotype frequencies. Its second interest, also like the
Hardy–Weinberg theorem, is that it provides a theoretical baseline telling us whether
anything interesting is going on in a population. Deviations from Hardy–Weinberg
proportions in a natural population suggest that selection, or non-random mating, or
sampling effects may be operating. Likewise, if two loci are in linkage disequilibrium,
we can also suspect that one or more of these variables are at work. If the first thing we
had discovered about Papilio memnon had been its high linkage disequilibrium, we
should have been led on to study how selection was operating on the loci, and perhaps
2 The terms “linkage equilibrium” and “linkage disequilibrium” are not very satisfactory. They were first
used by Lewontin and Kojima in 1960. “Linkage disequilibrium” can exist without linkage a among genes on
different chromosomes a and it can also exist at equilibrium, as we shall see. It is, however, like the Hardy–
Weinberg equilibrium, an equilibrium under certain specifiable conditions. The word linkage is avoided in
certain other terms, such as “gametic phase equilibrium,” which are also in use; but linkage disequilibrium is
the commonest term. Also, there are other ways of measuring non-random associations between genes besides
D, but all the points of principle can be made with D.
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