Probability Models of Population Structure and Gene Flow
There is a substantial interest in the relationship between population structure and the patterns of genetic variation. In structured populations, these patterns heavily depend on gene flow, the movement of genetic material from one population to another. In spatially structured populations, gene fl...
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| Format: | Dissertation |
| Language: | English |
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ProQuest Dissertations & Theses
01-01-2021
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| Online Access: | Get full text |
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| Summary: | There is a substantial interest in the relationship between population structure and the patterns of genetic variation. In structured populations, these patterns heavily depend on gene flow, the movement of genetic material from one population to another. In spatially structured populations, gene flow can be quantified by the spatial motion of ancestral lineages - the description of where the ancestors of modern individuals lived at times in the past. Understanding the stochastic motion of these lineages is key to explaining patterns of genetic variability. In Chapter 1 we describe a new model for a population evolving on Zd in which the demographic parameters of subpopulations depend on the population density in a local neighbourhood. After suitable scaling, tracing numbers of adults in the population we arrive at a system of interacting SDEs. The motion of a lineage ancestral to an individual sampled from such a population follows a random walk in a random environment and we establish this motion in the scaling limit. In contrast to classical models in which ancestral lineages are drawn into regions of high population density, in our setting, a lineage is attracted to regions of high fecundity. In Chapter 2 we study the movement of ancestral lineages in a model in which local population sizes are determined by the presence of transient, patchy resources. Habitats are either bad or good and population sizes in good habitats are so large that, given the opportunity, lineages will always move from bad to good habitats. Lineages traced back through time can be explicitly described and we highlight the role of the spatial and temporal autocorrelation structure in determining the behaviour of lineage movement. The typical displacement between an individual and their ancestors may differ substantially from that predicted based on typical offspring dispersal. Population structure need not be spatial; eg in some species, mating is restricted to occurring between individuals from distinct self-incompatible classes, termed mating types. Gene flow between these classes occurs only at the times of rare bouts of sexual reproduction. The evolutionary mechanism that drove the establishment of self-incompatibility is still a debated topic. In a new approach, in Chapter 3 we address this by quantifying the population genetic diversity and the probability of 'effectual sex' as a function of the number of self-incompatible classes. Our results permit a novel understanding of the early origins of sex. |
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