Mathematical aspects of population genetics

Population genetics deals with the evolution of genomes as a result of the drift of point mutations throughout a population over long timescales. Mathematically, mutations, genetic drift and natural selection are modelled as Markovian processes which lead to a type of partial differential equation known as the forward Kolmogorov equation. There are a number of interesting unanswered questions in this field related to the estimation of mutation rates from allele frequencies, modelling the effects of growing or shrinking populations, and the relationship of population genetics with phylogenetics. 

PUBLICATIONS

Genetic drift in populations governed by a Galton-Watson branching process
By: Burden, Conrad J.; Simon, Helmut
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 109   Pages: ‏ 63-74   Published: ‏ JUN 2016

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates
By: Burden, Conrad J.; Tang, Yurong
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 112   Pages: ‏ 22-32   Published: ‏ DEC 2016

Rate matrix estimation from site frequency data
By: Burden, Conrad J.; Tang, Yurong
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 113   Pages: ‏ 23-33   Published: ‏ FEB 2017

Mutation in populations governed by a Galton-Watson branching process
By: Burden, Conrad J.; Wei, Yi
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 120   Pages: ‏ 52-61   Published: ‏ MAR 2018

Stationary distribution of a 2-island 2-allele Wright-Fisher diffusion model with slow mutation and migration rates
By: Burden, Conrad J.; Griffiths, Robert C.
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 124   Pages: ‏ 70-80   Published: ‏ DEC 2018

The stationary distribution of a sample from the Wright-Fisher diffusion model with general small mutation rates
By: Burden, Conrad J.; Griffiths, Robert C.
JOURNAL OF MATHEMATICAL BIOLOGY   Volume: ‏ 78   Issue: ‏ 4   Pages: ‏ 1211-1224   Published: ‏ MAR 2019
    
The transition distribution of a sample from a Wright-Fisher diffusion with general small mutation rates
By: Burden, Conrad J.; Griffiths, Robert C.
JOURNAL OF MATHEMATICAL BIOLOGY   Volume: ‏ 79   Issue: ‏ 6-7   Pages: ‏ 2315-2342   Published: ‏ DEC 2019

Coalescence in the diffusion limit of a Bienayme-Galton-Watson branching process
By: Burden, Conrad J.; Soewongsono, Albert C.
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 130   Pages: ‏ 50-59   Published: ‏ DEC 2019

Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation-drift model
By: Vogl, Claus; Mikula, Lynette C.; Burden, Conrad J.
THEORETICAL POPULATION BIOLOGY   Volume: ‏ 134   Pages: ‏ 106-118   Published: ‏ AUG 2020