The distribution of allele frequencies obtained from diffusion approximations to Wright–Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright–Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection. The genotypes composed of alleles differing from each other only at the neutral level have the same fitness and evolve under neutrality. We show that with an appropriate scaling of the mutation parameter with respect to the number of alleles at each level, the frequencies of alleles at the selected and the neutral level are conditionally independent of each other, conditional on knowing the number of alleles at all levels. This conditional independence allows us to simulate from the joint stationary distribution of the allele frequencies. We use these simulated frequencies to perform inference on parameters of the model with two levels of genetic variability using Approximate Bayesian Computation.
|Number of pages||10|
|Journal||Theoretical Population Biology|
|State||Published - Jul 2018|
Bibliographical noteFunding Information:
We thank an anonymous reviewer for their careful reading of an earlier draft of this manuscript and for catching mistakes in the proof. Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number P20GM104420 . The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
© 2018 Elsevier Inc.
- Approximate Bayesian Computation
- Balancing selection
- Diffusion approximation
- K-allele models
- Wright–Fisher model
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics