The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proved difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of genealogies can be used to analytically compute likelihoods of demographic models from configurations of mutations in short sequence blocks (Lohse et al. 2011). Although the GF has a simple, recursive form, the size of such likelihood calculations explodes quickly with the number of individuals and applications of this framework have so far been mainly limited to small samples (pairs and triplets) for which the GF can be written by hand. Here we investigate several strategies for exploiting the inherent symmetries of the coalescent. In particular, we show that the GF of genealogies can be decomposed into a set of equivalence classes that allows likelihood calculations from nontrivial samples. Using this strategy, we automated blockwise likelihood calculations for a general set of demographic scenarios in Mathematica. These histories may involve population size changes, continuous migration, discrete divergence, and admixture between multiple populations. To give a concrete example, we calculate the likelihood for a model of isolation with migration (IM), assuming two diploid samples without phase and outgroup information. We demonstrate the new inference scheme with an analysis of two individual butterfly genomes from the sister species Heliconius melpomene rosina and H. cydno.
We thank Lynsey Bunnefeld for discussions throughout the project and Joshua Schraiber and one anonymous reviewer for constructive comments on an earlier version of this manuscript. This work was supported by funding from the United Kingdom Natural Environment Research Council (to K.L.) (NE/I020288/1) and a grant from the European Research Council (250152) (to N.H.B.).
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Lohse K, Chmelik M, Martin S, Barton NH. Efficient strategies for calculating blockwise likelihoods under the coalescent. Genetics. 2016;202(2):775-786. doi:10.1534/genetics.115.183814
Lohse, K., Chmelik, M., Martin, S., & Barton, N. H. (2016). Efficient strategies for calculating blockwise likelihoods under the coalescent. Genetics, 202(2), 775–786. https://doi.org/10.1534/genetics.115.183814
Lohse, Konrad, Martin Chmelik, Simon Martin, and Nicholas H Barton. “Efficient Strategies for Calculating Blockwise Likelihoods under the Coalescent.” Genetics 202, no. 2 (2016): 775–86. https://doi.org/10.1534/genetics.115.183814.
K. Lohse, M. Chmelik, S. Martin, and N. H. Barton, “Efficient strategies for calculating blockwise likelihoods under the coalescent,” Genetics, vol. 202, no. 2, pp. 775–786, 2016.
Lohse K, Chmelik M, Martin S, Barton NH. 2016. Efficient strategies for calculating blockwise likelihoods under the coalescent. Genetics. 202(2), 775–786.
Lohse, Konrad, et al. “Efficient Strategies for Calculating Blockwise Likelihoods under the Coalescent.” Genetics, vol. 202, no. 2, Genetics Society of America, 2016, pp. 775–86, doi:10.1534/genetics.115.183814.
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