%0 Journal Article %1 lessard2010recurrence %A Lessard, Sabin %D 2010 %J J. Appl. Probab. %K Moran_model ewens_sampling_formula recurrence_relations sampling_formula wright_fisher_model %N 3 %P 732--751 %R 10.1239/jap/1285335406 %T Recurrence equations for the probability distribution of sample configurations in exact population genetics models %U http://dx.doi.org/10.1239/jap/1285335406 %V 47 %X Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to 0. Computations of the total variation distance for the distribution of the number of types in the sample suggest that the exact Moran model provides a better approximation for the sampling formula under the exact Wright-Fisher model than the Ewens sampling formula in the limit of the Kingman coalescent with nonrecurrent mutation. On the other hand, this model seems to provide a good approximation for a Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.

@article{lessard2010recurrence, abstract = {Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to 0. Computations of the total variation distance for the distribution of the number of types in the sample suggest that the exact Moran model provides a better approximation for the sampling formula under the exact Wright-Fisher model than the Ewens sampling formula in the limit of the Kingman coalescent with nonrecurrent mutation. On the other hand, this model seems to provide a good approximation for a Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough. }, added-at = {2011-03-10T20:30:00.000+0100}, author = {Lessard, Sabin}, biburl = {https://www.bibsonomy.org/bibtex/239d6302e1334c5a5762603075c8ef8b6/peter.ralph}, coden = {JPRBAM}, doi = {10.1239/jap/1285335406}, fjournal = {Journal of Applied Probability}, interhash = {c175e85d86f6b95ac5d657a05b4a8b21}, intrahash = {39d6302e1334c5a5762603075c8ef8b6}, issn = {0021-9002}, journal = {J. Appl. Probab.}, keywords = {Moran_model ewens_sampling_formula recurrence_relations sampling_formula wright_fisher_model}, mrclass = {60C05 (92Dxx)}, mrnumber = {2731345}, number = 3, pages = {732--751}, timestamp = {2011-03-31T06:56:35.000+0200}, title = {Recurrence equations for the probability distribution of sample configurations in exact population genetics models}, url = {http://dx.doi.org/10.1239/jap/1285335406}, volume = 47, year = 2010 }