Wright-Fisher model and its approximations in population genetics

Abstract

The Wright–Fisher model provides a central stochastic framework for the study of allele
frequency dynamics in population genetics. Despite its importance, exact inference under
the model is frequently computationally intractable in settings involving large population
sizes, long evolutionary timescales, and multiple loci. In this thesis, a range of methods is developed
to improve inference under the Wright–Fisher model, with particular focus on time series genomic
data and ancient DNA.
Two moment-based approximations for the two-locus Wright–Fisher model with selection are
developed, namely logistic normal and hierarchical beta approximations. These approaches avoid
the support limitations of Gaussian approximations and offer substantial computational savings
relative to diffusion-based methods. The hierarchical beta approximation is shown to provide the
strongest overall performance among the moment-based approaches studied.
Bayesian methods are further developed for the inference of natural selection, migration,
and temporally varying selection intensity from aDNA. Uncertainty due to postmortem damage,
fragmentation, low coverage, missing data, and genotype error is explicitly modelled through
genotype likelihood and genotype posterior frameworks, and the methodology is extended to allow
backward-in-time simulation, linkage, and epistasis. The methods are applied to ancient chicken
and horse datasets, demonstrating their usefulness for reconstructing evolutionary histories from
challenging genomic data.

Date of Award	9 Dec 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Feng Yu (Supervisor) & Zhangyi He (Supervisor)