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Inference of gene flow in the process of speciation: Efficient maximum-likelihood implementation of a generalised isolation-with-migration model

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  • Costa, Rui J.
  • Wilkinson-Herbots, Hilde M.

Abstract

The ‘isolation with migration’ (IM) model has been extensively used in the literature to detect gene flow during the process of speciation. In this model, an ancestral population split into two or more descendant populations which subsequently exchanged migrants at a constant rate until the present. Of course, the assumption of constant gene flow until the present is often over-simplistic in the context of speciation. In this paper, we consider a ‘generalised IM’ (GIM) model: a two-population IM model in which migration rates and population sizes are allowed to change at some point in the past. By developing a maximum-likelihood implementation of this model, we enable inference on both historical and contemporary rates of gene flow between two closely related populations or species. The GIM model encompasses both the standard two-population IM model and the ‘isolation with initial migration’ (IIM) model as special cases, as well as a model of secondary contact. We examine for simulated data how our method can be used, by means of likelihood ratio tests or AIC scores, to distinguish between the following scenarios of population divergence: (a) divergence in complete isolation; (b) divergence with a period of gene flow followed by isolation; (c) divergence with a period of isolation followed by secondary contact; (d) divergence with ongoing gene flow. Our method is based on the coalescent and is suitable for data sets consisting of the number of nucleotide differences between one pair of DNA sequences at each of a large number of independent loci. As our method relies on an explicit expression for the likelihood, it is computationally very fast.

Suggested Citation

  • Costa, Rui J. & Wilkinson-Herbots, Hilde M., 2021. "Inference of gene flow in the process of speciation: Efficient maximum-likelihood implementation of a generalised isolation-with-migration model," Theoretical Population Biology, Elsevier, vol. 140(C), pages 1-15.
    • Handle: RePEc:eee:thpobi:v:140:y:2021:i:c:p:1-15
    DOI: 10.1016/j.tpb.2021.03.001
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    References listed on IDEAS

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    1. Richard E. Chandler & Steven Bate, 2007. "Inference for clustered data using the independence loglikelihood," Biometrika, Biometrika Trust, vol. 94(1), pages 167-183.
    2. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    3. Wilkinson-Herbots, Hilde M., 2012. "The distribution of the coalescence time and the number of pairwise nucleotide differences in a model of population divergence or speciation with an initial period of gene flow," Theoretical Population Biology, Elsevier, vol. 82(2), pages 92-108.
    4. Thomas Mailund & Anders E Halager & Michael Westergaard & Julien Y Dutheil & Kasper Munch & Lars N Andersen & Gerton Lunter & Kay Prüfer & Aylwyn Scally & Asger Hobolth & Mikkel H Schierup, 2012. "A New Isolation with Migration Model along Complete Genomes Infers Very Different Divergence Processes among Closely Related Great Ape Species," PLOS Genetics, Public Library of Science, vol. 8(12), pages 1-19, December.
    5. Jody Hey, 2005. "On the Number of New World Founders: A Population Genetic Portrait of the Peopling of the Americas," PLOS Biology, Public Library of Science, vol. 3(6), pages 1-1, May.
    6. Kumagai, Seiji & Uyenoyama, Marcy K., 2015. "Genealogical histories in structured populations," Theoretical Population Biology, Elsevier, vol. 102(C), pages 3-15.
    7. Wilkinson-Herbots, Hilde M., 2008. "The distribution of the coalescence time and the number of pairwise nucleotide differences in the “isolation with migration†model," Theoretical Population Biology, Elsevier, vol. 73(2), pages 277-288.
    8. Chen, Hua, 2012. "The joint allele frequency spectrum of multiple populations: A coalescent theory approach," Theoretical Population Biology, Elsevier, vol. 81(2), pages 179-195.
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    Cited by:

    1. Hobolth, Asger & Rivas-González, Iker & Bladt, Mogens & Futschik, Andreas, 2024. "Phase-type distributions in mathematical population genetics: An emerging framework," Theoretical Population Biology, Elsevier, vol. 157(C), pages 14-32.

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