PhD Studentship - Stochastic Evolution of Populations in Fluctuating Environments

University of Leeds

Why does cooperation abound in Nature? Why are there so many coexisting species and not just a few dominant ones? These are issues of paramount importance in biology and ecology. In fact, while there are many examples of cooperative behaviour in Nature, these challenge Darwinian evolution since, in the absence of appropriate mechanisms, cooperation is not sustained by evolution [1].

The dynamics of the population composition is often coupled with the evolution of its size, resulting in a coupling between demographic fluctuations and environmental noise. This is particularly relevant to microbial communities, which can experience sudden environmental changes. As an example, we can consider population consisting of a two strains of bacteria, with a “free-rider” strain having a constant selective advantage over the other (cooperators) that produces a public good. While free riders always prevail in the absence of randomness, the probability that cooperators take over is greatly enhanced when the population size is driven by a carrying capacity that randomly switches from a state of abundance in which the population size is large to a state of scarcity in which the population shrinks [2] Evolutionary game theory (EGT) describes the dynamics of populations in which the success of one type depends on the actions of the others, and provides a suitable framework to model the evolution of cooperation.

While EGT models have been extensively studied, little is known about the joint effect of coupled environmental and demographic randomness on cooperation, and even less is known about their effects in spatial settings. Hence, objectives of this project are: - Generalization of the approach of Ref.[2] and analysis of how environmental randomness affects the evolution of EGT cooperation scenarios. We will consider paradigmatic EGT models and public goods games in finite well-mixed populations of fluctuating size, e.g. with a randomly switching carrying capacity. The probability that cooperation prevails and the mean time for this to happen will be studied, as well as the population size distribution. - Study of the spatially-extended counterparts of EGT cooperation scenarios, with the population is arranged on lattices of interconnected patches of fluctuating size between which individuals can migrate. The circumstances under which space favours/hinders the evolution of cooperation will be analysed. - Study of the influence of environmental noise on species diversity in the voter model with speciation when the population size fluctuates. This reference neutral model (selection is neglected) will be studied on lattices of patches of fluctuating size connected by migration. We will be particularly interested in the species-area relationship measuring how the number of observed species increases upon enlarging the sampled area.

The ultimate goal will be to gain a thorough understanding of the evolution of populations subject to randomness stemming from a coupling between environmental factors and demographic stochasticity. It is expected that the theoretical predictions could be tested experimentally, e.g. in microbial communities with engineered switching strains.

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Northern England