Dieckmann U, Law R
Theoretical Biology Section, University of Leiden, The Netherlands.
J Math Biol. 1996;34(5-6):579-612. doi: 10.1007/BF02409751.
In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space. A quantitative description of this stochastic process in terms of a master equation is derived. By determining the first jump moment of this process we abstract the dynamic of the mean evolutionary path. To first order the resulting equation coincides with a dynamic that has frequently been assumed in evolutionary game theory. Apart from recovering this canonical equation we systematically establish the underlying assumptions. We provide higher order corrections and show that these can give rise to new, unexpected evolutionary effects including shifting evolutionary isoclines and evolutionary slowing down of mean paths as they approach evolutionary equilibria. Extensions of the derivation to more general ecological settings are discussed. In particular we allow for multi-trait coevolution and analyze coevolution under nonequilibrium population dynamics.
在本文中，我们发展了一种生态群落中共进化的动力学理论。该推导明确考虑了进化变化的随机成分，并且基于个体层面的生态过程。我们表明，共进化动态可以被设想为群落性状空间中的有向随机游走。通过主方程对这一随机过程进行了定量描述。通过确定该过程的一阶跳跃矩，我们提取了平均进化路径的动态。一阶近似下，所得方程与进化博弈论中经常假设的动态相一致。除了恢复这个标准方程外，我们还系统地建立了其 underlying 假设。我们提供了高阶修正，并表明这些修正可能会产生新的、意想不到的进化效应，包括移动进化等斜线以及平均路径在接近进化平衡时的进化减速。讨论了将推导扩展到更一般生态环境的情况。特别是，我们考虑了多性状共进化，并分析了非平衡种群动态下的共进化。
