We develop and study the high-density limit of various new models in mathematical pop- ulation genetics. These models extend the Λ-Fleming–Viot process when there are two genetic types at the locus of study. Given a finite sample from a population undergoing these dynamics, a key tool for understanding the corresponding genealogy is the method of duality. We introduce the reproduction-linked mutation mechanism and consider how this affects the process of relative allelic frequencies and the genealogy. The second generalization incorporates two forms of natural selection – differential killing and differential birth. We contrast the structure of their genealogies. Several properties of the block size spectra of the Kingman and Beta coalescents are also investigated, including their behaviour as they come down from infinity.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:664774 |
| Date | January 2015 |
| Creators | Miller, Luke Rex |
| Contributors | Etheridge, Alison M. |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:60a9fcc7-b939-4075-be31-ed69014ad898 |
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