Fluc­tu­a­tion domains in adap­tive evo­lu­tion

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains–parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

我们推导了表型进化（phenotypic evolution）中平行轨迹间差异的表达式，推广了可预测适应性动力学（adaptive dynamics）或数量遗传学（quantitative genetics）中平均进化路径的经典结论。我们阐明了该表达式如何催生“波动域”这一概念：适应度景观（fitness landscape）可分为两类区域，一类进化速率极具可预测性（源于涨落耗散（fluctuation dissipation）），另一类进化速率则高度可变（源于涨落增强（fluctuation enhancement））。这些波动域由适应度景观的曲率所决定：曲率为正的区域（如适应谷（adaptive valleys）或分支点（branching points））会出现涨落增强现象；曲率为负的区域（如适应峰（adaptive peaks））则会出现涨落耗散现象。我们针对限制性资源的隐性与显性竞争生态场景，对上述动力学过程展开了探究。