Ancestral structures in population genetics and a generalisation to birth-death processes with catastrophes

Ancestral structures have become of paramount importance in the study of population genetics, the branch of biology that investigates the evolution of the genetic composition of populations. In the framework of the two-type Moran model with mutation and selection, we use the pruned-lookdown ancestral selection graph (pLD-ASG), which consists of a set of potential ancestors of the sampled individual at any given time, to investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past, far beyond the most recent common ancestor of the population (thus connecting population genetics to phylogeny), and analyse the mutation process along this line. Relative to the neutral case (that is, without selection), we obtain a general bias towards the beneficial type, an increase in the beneficial mutation rate, and a decrease in the deleterious mutation rate. This sheds new light on previous analytical results. We discuss our findings in the light of a well-known observation at the interface of phylogeny and population genetics, namely, the difference in the mutation rates (or, more precisely, mutation fluxes) estimated via phylogenetic methods relative to those observed in pedigree studies.<br /><br /> We then establish a connection between the pLD-ASG and the killed ancestral selection graph (k-ASG), a different genealogical structure used to determine the type distribution of an individual at present. This motivates us to prove more general connections between the absorption probabilities of a class of birth-death processes with killing and the stationary tail distributions of a related class of birth-death processes with catastrophes. Major components of the proofs include an excursion decomposition of sample paths, a generalised detailed-balance condition, and representations of our processes in terms of superpositions of simpler processes. An overarching role is played by Siegmund duality, which allows us to invert the relationship between the processes. We then apply our results to the k-ASG and the pLD-ASG in a finite population setting and its diffusion limit.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bielefeld

Year

2024

Author dc:creator

• Di Gaspero, Enrico

Repository record source_url

https://pub.uni-bielefeld.de/record/3000409

OAI identifier oai:identifier

oai:pub.uni-bielefeld.de:3000409