Effects of noise and uncertainty on decision making, evolutionary games and ecological communities

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Traditional models of evolutionary systems are frequently formulated in terms of deterministic differential equations, with fixed coefficients and in which the effects of interactions are instantaneous. This approach neglects the effects of uncertainty, intrinsic noise, and delay. At the same time, noise is known to have strong effects in many evolutionary systems, especially when the evolving population is small. Interaction coefficients in ecological communities are frequently not known, generating uncertainty. Delay in the effects of reactions arise for example in the context of gestational periods, or when rewards from actions in a game are only paid out at a later time.The aims of this thesis are: (i) to develop new mathematical approaches to systems with noise and uncertainty, (ii) to use and further develop tools from statistical physics to study the combined effects of delay and intrinsic noise in evolutionary games, (iii) to understand whether noisy sampling in iterated games can identify optimal strategies.