Coalescents, Phylogenies, and Likelihoods.

When phylogenies get down below the species level, they turn into coalescents. Individual genetic loci then have genealogies that are, in the absence of recombination, trees. But as one moves along the genome, recombination moves branches and changes the trees, with the result that other loci more than a few kilobases away usually have very different trees. Between species their trees of ancestry are very similar; the difference in their behavior within and between species is an indication that there really is something different, and nonarbitrary, about the species level. When one looks at the problems of estimation involving these trees, one can get overly involved in estimating the tree itself. But the interest in doing so is limited, as there may be a million completely different coalescent trees for different parts of the genome. Furthermore, the number of varying sites available for estimating each is quite limited, so that each is poorly estimated. The solution to this quandary is to realize that the genealogies are generated by a random process of genetic drift, possibly with other evolutionary forces intervening. What we need to know is not the trees themselves, but the parameters of these evolutionary forces and of population structure, such as effective population size, migration rates, population growth rates. The coalescent process defined by J.F.C. Kingman (1, 2) was the foundation of this theory. Coalescent likelihood methods have been developed by two groups, ours and Griffiths and Tavare's. The two approaches use the same statistical methods and models, and differ mostly in the computational methods. The likelihood for a population sample is the sum over all possible genealogies, summing the probability of that genealogy given the parameters, multiplied by the probability of the sample of sequences