Evolution__3rd_Edition

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A haplotype is a haploid
combination of genes at more than
one locus
CHAPTER 8 / Two-locus and Multilocus Population Genetics 199
8.4 Two-locus genetics is concerned with haplotype
frequencies
The theory of population genetics for a single locus is concerned with gene frequencies.
The analogous variable in two-locus population genetics is haplotype frequency. (The
term haplotype has two meanings. Here it refers to a combination of alleles at more
than one locus. It is also used, in DNA sequencing, to refer to the base sequence of one
of an individual’s two sets of DNA.) For two loci with two alleles each (A 1 and A 2 , B 1
and B 2 ) there are four haplotypes, A 1 B 1 , A 1 B 2 , A 2 B 1 , A 2 B 2 . A diploid individual’s genotype
will be something like A 1 B 1 /A 1 B 2 . 1 It has two haplotypes, one inherited from each
parent, just as a one-locus genotype contains two genes from the two parents. If the
A- and B-loci are on the same chromosome, each haplotype is a gene combination on a
chromosome; but haplotypes can also be specified for loci on different chromosomes.
The frequency of a haplotype in a population can be counted as the number of gametes
bearing a particular combination of genes. A haplotype can be specified for any number
of loci. We shall mainly discuss two-locus haplotypes, but the haplotypes in the Papilio
memnon example had five loci, and the mimetic patterns of Heliconius are controlled by
12 or 15 gene loci. As this chapter will show, to understand the evolution of haplotype
frequencies, we need some concepts that do not exist for gene frequencies. Two-locus
population genetics is therefore not simply a doubled-up version of single-locus population
genetics.
8.5 Frequencies of haplotypes may or may not be in
linkage equilibrium
We can begin by asking a question like the one that led to the Hardy–Weinberg
theorem for one locus. In the absence of selection, and in an infinite population
with random mating, what will be the equilibrium frequencies of haplotypes? The
question for multiple loci will lead us to another important concept, called linkage
equilibrium.
The simplest case is for two loci with two alleles each. The crucial trick is to write the
observed haplotype frequencies in terms of the gene frequencies at each locus, plus or
minus a correction factor, called D. Let the gene frequency in the population of A 1 = p 1 ,
A 2 = p 2 , B 1 = q 1 , and B 2 = q 2 . Then:
1 In this chapter, oblique strokes indicate diploid genotypes. Thus A 1 /A 1 is a diploid genotype at one locus.
The convention is to prevent confusion with haplotypes, which are written here without an oblique stroke,
e.g., the A 1 B 1 haplotype. A haplotype refers to the alleles at two (or more) loci that an individual received from
one of its parents. A diploid individual has two haplotypes. Haplotypes have two different letters (for two loci),
one-locus genotypes have only one letter. Diploid two-locus genotypes are also here written with an oblique
stroke, e.g., A 1 B 1 /A 2 B 2 .