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Local fluctuations of genetic processes defined on two time scales, with applications to effective size estimation

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  • Hössjer, Ola
  • Tyvand, Peder A.

Abstract

In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes Ne, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy–Weinberg equilibrium.

Suggested Citation

  • Hössjer, Ola & Tyvand, Peder A., 2020. "Local fluctuations of genetic processes defined on two time scales, with applications to effective size estimation," Theoretical Population Biology, Elsevier, vol. 131(C), pages 79-99.
    • Handle: RePEc:eee:thpobi:v:131:y:2020:i:c:p:79-99
    DOI: 10.1016/j.tpb.2019.11.006
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    References listed on IDEAS

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    1. Hössjer, O. & Laikre, Linda & Ryman, Nils, 2016. "Effective sizes and time to migration–drift equilibrium in geographically subdivided populations," Theoretical Population Biology, Elsevier, vol. 112(C), pages 139-156.
    2. Hössjer, Ola & Olsson, Fredrik & Laikre, Linda & Ryman, Nils, 2015. "Metapopulation inbreeding dynamics, effective size and subpopulation differentiation—A general analytical approach for diploid organisms," Theoretical Population Biology, Elsevier, vol. 102(C), pages 40-59.
    3. Hössjer, Ola & Jorde, Per Erik & Ryman, Nils, 2013. "Quasi equilibrium approximations of the fixation index under neutrality: The finite and infinite island models," Theoretical Population Biology, Elsevier, vol. 84(C), pages 9-24.
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    1. Hössjer, O. & Laikre, Linda & Ryman, Nils, 2016. "Effective sizes and time to migration–drift equilibrium in geographically subdivided populations," Theoretical Population Biology, Elsevier, vol. 112(C), pages 139-156.
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