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

进化系统的传统模型通常是用确定性微分方程来表述的，这些方程具有固定的系数，并且相互作用的影响是瞬时的。这种方法忽略了不确定性、固有噪声和延迟的影响。与此同时，众所周知，噪音在许多进化系统中都有很强的影响，尤其是当进化种群很小的时候。生态群落的相互作用系数常常是未知的，产生了不确定性。反应效果的延迟出现在妊娠期的情境中，或者游戏中行动的奖励只能在较晚的时间内支付。本论文的目的是：(i)开发新的数学方法来研究具有噪声和不确定性的系统，（ii）使用并进一步开发统计物理工具来研究进化博弈中延迟和固有噪声的综合效应，（iii）了解迭代博弈中的噪声采样是否可以确定最佳策略。

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.