Stochastic Geometry, Data Structures and Applications of Ancestral Selection Graphs

Abstract

The genealogy of a random sample of a population of organisms can be represented as a rooted binary tree. Population dynamics determine a distribution over sample genealogies. For large populations of constant size and in the absence of selection effects, the coalescent process of Kingman determines a suitable distribution. Neuhauser and Krone gave a stochastic model generalising the Kingman coalescent in a natural way to include the effects of selection.

The model of Neuhauser and Krone determines a distribution over a class of graphs of randomly variable vertex number, known as ancestral selection graphs. Because vertices have associated scalar ages, realisations of the ancestral selection graph process have randomly variable dimensions.

A Markov chain Monte Carlo method is used to simulate the posterior distribution for population parameters of interest. The state of the Markov chain Monte Carlo is a random graph, with random dimension and equilibrium distribution equal to the posterior distribution.

The aim of the project is to determine if the data is informative of the selection parameter by fitting the model to synthetic data.