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2022 Asymptotic behaviour of sampling and transition probabilities in coalescent models under selection and parent dependent mutations
Martina Favero, Henrik Hult
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Electron. Commun. Probab. 27: 1-13 (2022). DOI: 10.1214/22-ECP472

Abstract

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral selection graph. Several relevant quantities related to these fundamental models are not explicitly known when mutations are parent dependent. Examples include the probability that a sample taken from a population has a certain type configuration, and the transition probabilities of their block counting jump chains. In this paper, asymptotic results are derived for these quantities, as the sample size goes to infinity. It is shown that the sampling probabilities decay polynomially in the sample size with multiplying constant depending on the stationary density of the Wright-Fisher diffusion and that the transition probabilities converge to the limit of frequencies of types in the sample.

Acknowledgments

The authors would like to thank the anonymous reviewer whose comments led to an improvement of the manuscript.

Citation

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Martina Favero. Henrik Hult. "Asymptotic behaviour of sampling and transition probabilities in coalescent models under selection and parent dependent mutations." Electron. Commun. Probab. 27 1 - 13, 2022. https://doi.org/10.1214/22-ECP472

Information

Received: 26 February 2021; Accepted: 5 June 2022; Published: 2022
First available in Project Euclid: 17 June 2022

arXiv: 2011.04385
Digital Object Identifier: 10.1214/22-ECP472

Subjects:
Primary: 60J90
Secondary: 60J70 , 92D15

Keywords: ancestral selection graph , Coalescent , parent dependent mutations , Population genetics , Wright-Fisher diffusion

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