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Using game theory we provide mathematical proof that if a species of asexually reproducing microbes does not possess maximum variability in competitive abilities amongst its individual organisms, then that species is vulnerable to replacement by competitors. Furthermore, we prove that such maximally variable species are neutral towards each other in competition for limited resources; they coexist. Our proof is constructive: given one species which does not possess maximum variability, we construct a species with the same (or lower) mean competitive ability which can invade, in the sense that its expected value in competition is positive whereas the expected value of the non-maximally variable species is negative. Our results point towards the mechanistic underpinnings for the frequent observations that (1) microbes are characterized by large intra-specific variability and that (2) the number of extant microbe species is very large.
Movement is fundamental to life, shaping population dynamics, biodiversity patterns, and ecosystem structure. Recent advances in tracking technology have enabled fundamental questions about movement to be tackled, leading to the development of the mo
How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperato
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a beneficial mutatio
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player an
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, howeve