Population Genetics

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Abstract

Population genetics is concerned with genetic differences within and across populations, and the dynamics of how populations evolve as a result of the propagation of genetic mutations occurring within the germlines of individuals. This article provides a mathematical approach to the most commonly used population genetics models, including Wright-Fisher and related models, and also the less-commonly encountered Bienaymé-Galton-Watson branching model. Topics include fixation times, mutations and their relationship to substitution rates in neutral evolution, selection, multiple alleles, the diffusion limit via the forward Kolmogorov equation, multiple alleles, coalescent theory, and parameter estimation.

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Conrad Burden is an associate professor in the Mathematical Sciences Institute at the Australian National University lecturing in bioinformatics and biological modelling. His research interests include mathematical population genetics, alignment-free sequence comparison, the analysis of high-throughput sequencing data, and the physico-chemical modelling of microarrays. Before making the move into bioinformatics in 2003 he spent 20 years as a theoretical physicist followed by a short period working in the IT industry. He graduated from the University of Queensland with first class honours in Applied Mathematics in 1979 and The Australian National University with a PhD in Theoretical Physics in 1983. Between 1983 and 1988 he held postdoctoral fellowships in theoretical physics at the Weizmann Institute of Science, Glasgow University, The Australian National University and Flinders University. Between 1988 and 1999 he held a research position in the Department of Theoretical Physics, Australian National University, working mainly in quantum field theory and subatomic particle physics. Between 1999 and 2002 he was a programmer/developer in the IT industry. He is a Fellow of the Australian Institute of Physics.

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