基于变分原理的演化动力学
Evolutionary dynamics from a variational principle
摘要：
我们用一个思想实验证明，基于适应度的种群动力学进化方法不能对进化系统的长期行为做出定量的、可证伪的预测。进化系统的一个关键特征是持续不断地产生新种〈动〉<动>。这些新物种改变了现有物种的生存条件。即使是{ \em达尔文的恶魔}，一个假设的实体，在给定的时间内对所有物种的丰度及其适应度函数有确切的了解，也不能预先说明这些新奇事物对现有种群的影响。我们认为，适应性总是{ \it a postiori}知识-它测量但不能解释为什么一个物种有繁殖成功与否。为了克服这些概念上的限制，变分原理提出了一个自旋模型的进化系统的设置。我们推导出一个功能，这是最一般的进化制定的动力系统，即进化轨迹因果地出现作为一个功能的最小化。这个功能允许推导的渐近多样性的随机演化系统的平均场近似的解析解。我们测试这些近似相应的模型的数值模拟，并发现在多样性曲线的相变位置很好的协议。该模型还能够从几个人造和自然进化系统中再现时间序列的程式化事实。光将被扔在如何物种和他们的适应度景观动态共同进化。
英文摘要：
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic of evolutionary systems is the ongoing endogenous production of new species. These novel entities change the conditions for already existing species. Even {\em Darwin's Demon}, a hypothetical entity with exact knowledge of the abundance of all species and their fitness functions at a given time, could not pre-state the impact of these novelties on established populations. We argue that fitness is always {\it a posteriori} knowledge -- it measures but does not explain why a species has reproductive success or not. To overcome these conceptual limitations, a variational principle is proposed in a spin-model-like setup of evolutionary systems. We derive a functional which is minimized under the most general evolutionary formulation of a dynamical system, i.e. evolutionary trajectories causally emerge as a minimization of a functional. This functional allows the derivation of analytic solutions of the asymptotic diversity for stochastic evolutionary systems within a mean-field approximation. We test these approximations by numerical simulations of the corresponding model and find good agreement in the position of phase transitions in diversity curves. The model is further able to reproduce stylized facts of timeseries from several man-made and natural evolutionary systems. Light will be thrown on how species and their fitness landscapes dynamically co-evolve.
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