The Coalescent

With the exception of a small proportion of studies that use historical specimens from museums or other sources, phylogeographic studies typically use genetic information from current samples to reconstruct historical events. Inferences of past events are possible because most mutations arise at a single point in time and space. Assuming neutrality, the subsequent spread of each new mutation (allele) will be influenced by dispersal patterns, population sizes, natural selection and other processes that may be deduced from the contemporary distributions of these mutations. We may be able to make these deductions if we can determine when different alleles shared their most recent common ancestor (MRCA).

An MRCA can be identified using the coalescent, which is based on a mathematical theory that was laid out by Kingman (1982) to describe the genealogy of selectively neutral genes by looking backwards in time. If we apply the coalescent to the sequences of multiple alleles that have been identified at a particular locus, we can retrace the evolutionary histories of these alleles by looking back to the point at which they coalesce (come together). Although the

Figure 5.5 The evolutionary relationships of six haplotypes within a single population. Shaded circles are used to show how the lineages of haplotypes 3, 4 and 5 can be traced back to two coalescent events, which are indicated by double circles. Working backwards through time, the first of these coalescent events identifies the most recent common ancestor (MRCA) of haplotypes 3 and 4, whereas the second coalescent event identifies the MRCA of all three haplotypes

Figure 5.5 The evolutionary relationships of six haplotypes within a single population. Shaded circles are used to show how the lineages of haplotypes 3, 4 and 5 can be traced back to two coalescent events, which are indicated by double circles. Working backwards through time, the first of these coalescent events identifies the most recent common ancestor (MRCA) of haplotypes 3 and 4, whereas the second coalescent event identifies the MRCA of all three haplotypes mathematical theory underlying the coalescent is too complicated for a detailed analysis in this book (see Hudson, 1990, for a review), the overall concept is relatively straightforward. This is illustrated by Figure 5.5, which shows us how we can work backwards through eight generations to reconstruct the history of six different genetic lineages within a particular population. Of the three lineages that have been highlighted in this example, haplotypes 3 and 4 coalesce relatively recently whereas the MRCA of all three lineages occurred in the more distant past.

If we go back far enough in time, all of the alleles within any population (discounting recent immigrants) should eventually coalesce to a single ancestral allele, but the time that this takes varies enormously and is influenced primarily by Ne. The importance of Ne can be realized if we discount the possibility of natural selection (because this would preclude randomness) and think of haplotypes as randomly picking their parents as we go back in time (Rosenberg and Nordborg, 2002). Whenever two different haplotypes pick the same parents, they coalesce. Since there are fewer potential parents to choose from when Ne is small, coalescence should occur relatively rapidly. If a population has a constant size of Ne and individuals within this population mate randomly during each generation, then the likelihood that two different haplotypes pick the same parent in the preceding generation and coalesce is 1/2Ne for a nuclear diploid locus and, in most cases, 1/Nef for mitochondrial DNA (Nef is the effective size of the female population). It must therefore follow that the probability of them picking different parents and remaining distinct is 1 — 1/2Ne or 1 — 1/Nef. The average time to coalescence of all gene copies in a population is 4Ne generations for diploid genes and Ne generations for mitochondrial genes.

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