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Space matters : evolution and ecology in structured populations

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Title: Space matters : evolution and ecology in structured populations
Author: Zukewich, Joshua William Anthony
Degree Master of Science - MSc
Program Mathematics
Copyright Date: 2012
Publicly Available in cIRcle 2012-10-19
Abstract: The inclusion of spatial structure in biological models has revealed important phenomenon not observed in “well-mixed” populations. In particular, cooperation may evolve in a network-structured population whereas it cannot in a well-mixed population. However, the success of cooperators is very sensitive to small details of the model architecture. In Chapter 1 I investigate two popular biologically-motivated models of evolution in finite populations: Death-Birth (DB) and Birth-Death (BD) processes. Under DB cooperation may be favoured, while under BD it never is. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Whether structure can promote the evolution of cooperation should not hinge on a somewhat artificial ordering of birth and death. I propose a mixed rule where in each time step DB (BD) is used with probability δ (1 − δ). I then derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. The only qualitatively different outcome occurs when using just BD (δ = 0). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally I show that, for any mixed BD-DB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma. Chapter 2 addresses the Competitive Exclusion Principle: the maximum number of species that can coexist is the number of habitat types (Hardin, 1960). This idea was borne out in island models, where each island represents a different well-mixed niche, with migration between islands. A specialist dominates each niche. However, these models assumed equal migration between each pair of islands, and their results are not robust to changing that assumption. Débarre and Lenormand (2011) numerically studied a two-niche model with local migration. At the boundary between niches, generalists may stably persist. The number of coexisting species may be much greater than the number of habitat types. Here, I derive the conditions for invasion of a generalist using an asymptotic approach. The prediction performs well (compared with numerical results) even for not asymptotically small parameter values (i.e. epsilon ≈ 1).
URI: http://hdl.handle.net/2429/43512
Scholarly Level: Graduate

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