## Multi-locus population genetics - What is a haplotype?

Three reasons why linkage equilibrium is interesting:

1. The model of linkage equilibrium is the simplest model for two loci and shows us how to construct a recurrence relation for haplotype frequencies.

2. Like the Hardy-Weinberg theorem, linkage equilibrium 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, in some special form involving the two loci. We look at some of these special forms later in the tutorial.

3. Linkage equilibrium can tell us whether the more complex two-locus theory is needed in a real case. The theory of population genetics for a single locus is satisfactory for populations in linkage equilibrium. It is when genes become non-randomly associated that a two locus model is needed.

This example shows why:

At linkage equilibrium, A1 and A2 are equally associated with B1. To understand evolution at the A-locus we can then ignore the relative fitnesses of B1 and B2, because if B1 is fitter than B2, the association with B1 will benefit A1 and A2 equally. In this case a one locus model is sufficient.

But if A1 is more associated with B1 than is A2 (i.e. there is linkage disequilibrium), then any advantage of B1 over B2 will passively give rise to an advantage to A1. To understand frequency changes of A1 we then need to know the relative fitnesses of B1 and B2, and the degree of association A1 has with them: we need a two locus model.

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