Martina Favero: Stochastic processes in population genetics under strong selection

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Abstract

Wright–Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. We consider the asymptotic strong-selection regime where the selective advantage of one allele grows to infinity, while the other parameters remain fixed, under a finite-allele mutation model, with possibly parent-dependent mutation. In this regime, the Wright–Fisher diffusion can be approximated either by a Gaussian process or by a process whose components are independent continuous-state branching processes with immigration. While the first process becomes degenerate at stationarity, the latter does not and provides a simple, analytic approximation for the leading term of the sampling probability. Furthermore, using another approach based on a recursion formula, we characterise all remaining terms to provide a full asymptotic expansion for the sampling probability. Finally, we study the asymptotic behaviour of the conditional ancestral selection graph and establish an asymptotic duality relationship between this and the diffusion.

About Martina

Martina Favero is a postdoctoral researcher at Stockholm university. Prior to that, she was a postdoc at Stockholm University and obtained her PhD at the Royal Institute of Technology (KTH). Her research interests lie at the interface between probability theory, mathematical statistics and their applications to population genetics and infectious diseases.