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Title: | Eco-evolutionary dynamics of finite populations from first principles |
Authors: | Guttal, Vishwesha Balakrishnan, Rohini BHAT, ANANDA SHIKHARA Dept. of Biology 20181024 |
Keywords: | Ecology Evolution Stochastic processes Statistical physics Mathematical biology Theoretical ecology Mathematical evolution Population biology Population dynamics Biology Mathematical modelling Applied mathematics Evolutionary ecology Eco-evolutionary dynamics |
Issue Date: | May-2023 |
Citation: | 175 |
Abstract: | Several recent theoretical studies have shown that noise can have strong impacts on evolutionary dynamics in the limit of small population sizes. In this thesis, I analytically describe the evolutionary dynamics of finite fluctuating populations from first principles to capture the fundamental phenomena underlying such noise-induced effects. Starting from a density-dependent 'birth-death process' describing a population of individuals with discrete traits, I derive stochastic differential equations (SDEs) for how the relative population sizes and trait frequencies change over time. These SDEs generically reveal a directional evolutionary force, 'noise-induced selection', that is particular to finite, fluctuating populations and is present even when all types have the same fitness. The strength of noise-induced selection depends directly on the difference in turnover rates between types and inversely on the total population size. Noise-induced selection can reverse the direction of evolution predicted by infinite-population frameworks. This general derivation of evolutionary dynamics helps unify and organize several previous studies — typically performed for specific evolutionary and ecological contexts — under a single set of equations. My SDEs also recover well-known results such as the replicator-mutator equation, the Price equation, and Fisher's fundamental theorem in the infinite population limit, illustrating consistency with known formal descriptions of evolution. Finally, I extend the birth-death formalism to one-dimensional quantitative traits through a 'stochastic field theory' that yields equations such as Kimura's continuum-of-alleles and Lande's gradient dynamics in the infinite population limit and provides an alternative approach to modelling the evolution of quantitative traits that is more accessible than current measure-theoretic approaches. |
URI: | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7813 |
Appears in Collections: | MS THESES |
Files in This Item:
File | Description | Size | Format | |
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20181024_Shikhara_Bhat_MS_Thesis.pdf | MS Thesis | 5.63 MB | Adobe PDF | View/Open |
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