��������

The prevalence of cooperative behavior is a fundamental problem in evolutionary biology. Because cooperative behaviors impose a cost, cooperative individuals are vulnerable to exploitation by Defectors that do not contribute and instead benefit from the cooperation of others. The bacteriophage ϕ6 shows strategies of cooperation and defection during infection. While replicating inside a host cell, ϕ6 viruses produce essential proteins in the host cell cytoplasm. Because coinfection is possible, a virus does not have exclusive access to its own products. Cooperators viruses produce products while Defector viruses produce less and instead steal from Cooperators. Previous work found that ϕ6 is trapped in the prisoner’s dilemma, predicting that Defectors will replicate faster than Cooperators and out-compete them; cooperation is doomed. Still, cooperative ϕ6 exist, so there must be a mechanism that maintains cooperation. Defectors are advantaged when coinfection is common and there is ample opportunity to extort Cooperators. However, this advantage wanes when coinfection is less common, and Cooperators are advantaged when single infection is common. The rates of single infection and coinfection are modulated by the densities of hosts and viruses. We propose that environmental feedback, or the interplay between viral and host densities, might maintain cooperation in ϕ6 populations. We develop and analyze a mathematical model that incorporates environmental feedback and find that for many parameter combinations, environmental feedback leads to the co-existence of Cooperators and Defectors.

From the microscopic to the macroscopic level, biological life exhibits directed migration in response to environmental conditions. Chemotaxis enables microbes to sense and move towards nutrient-rich regions or to avoid toxic ones. Socio-economic factors drive human populations from rural to urban areas. However, migration affects the quantity and quality of desirable resources. The effect of collective movement is especially significant when in response to the generation of public goods. Microbial communities can, for instance, alter their environment through the secretion of extracellular substances. Some substances provide antibiotic-resistance, others provide access to nutrients or promote motility. However, in all cases the maintenance of such public goods requires costly cooperation and is consequently susceptible to exploitation. The threat of exploitation becomes even more acute with motile individuals as defectors can avoid the consequences of their cheating. Here, we propose a model to investigate the effects of targeted migration based on the production of ecological public goods and analyze the interplay between social conflicts and migration. In particular, individuals can locate attractive regions by moving towards higher cooperator densities or avoid unattractive regions by moving away from defectors. Both migration patterns not only shape an individual's immediate environment but also affects the population as a whole. For example, defectors hunting cooperators in search of the public good have a homogenizing effect on population densities. They limit the production of the public good and hence inhibit the growth of the population. In contrast, aggregating cooperators promote the spontaneous formation of heterogeneous density distributions. The positive feedback between cooperator aggregation and public goods production, however, poses analytical and numerical challenges due to its tendency to develop discontinuous distributions. Thus, different modes of directed migration bear the potential to enhance or inhibit the emergence of complex and sometimes dynamic spatial arrangements. Interestingly, whenever patterns emerge in the form of heterogeneous density distributions, cooperation is promoted, on average, population densities rise, and the risk of extinction is reduced.

Population structures can be crucial determinants of evolutionary processes. For the spatial Moran process certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (Diaz et al. 2013 Proc. R. Soc. A 469 20130193). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probability remains close to 1-1/ r⁴ H for population size N → ∞ and structural parameter H > 1. This correction resolves the differences between the two aforementioned papers. We also confirm that in the limit N,H → ∞ superstars remain capable of providing arbitrarily strong selective advantages to any beneficial mutation, eliminating random drift. In addition, we investigate the robustness of amplification in superstars,and find that it appears to be a fragile phenomenon with respect to changes in the selection or mutation processes.

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).