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Unformatted text preview: Population genetics: inference using the coalescent Peter Beerli November 6, 2005 1 Simple estimators The coalescent gives an excellent framework for population genetics, but does not really talk about inference, in many cases we would need to know the genealogy (topology and times) or some rela- tionship between number of variable sites and population size. Watterson constructed an estimator using the number of segregating sites assuming an infinite sites mutation model and his estimator is = S/ n- 1 X i =1 1 i where S is the number of segregating sites in the sample. Recognize that the population size here is = 4 N locus . The mutation rate is typically used on a per locus basis. Wattersons estimator is very simple and delivers good estimates, for more complicated scenarios there are no such simple estimators available. Simple estimators for more difficult scenarios often assumed that the true genealogy is known. Most often we have no clue about the true genealogy but we approximate this true genealogy using the data and generate the best genealogy using phylogenetic inference. This approach has a difficulty because it only works well when this one tree is much better than all the others. Several methods to estimate population growth are based on this method, for example the skyline plot approach by Pybus and friends. 2 Maximum likelihood Estimating parameters of a population genetic model is rather simple under the likelihood principle because we can calculate probabilities for the Kingman coalescent, we also know how to calculate 1 BSC5936-Fall 2005 Computational Evolutionary Biology trees from genetic data assuming a mutation model. But how to do this in praxis. We simple start with a rather basic observation that we want in principle to to find the values of the parameters...
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