基于个体的自适应动力学模型和正则方程的有效模拟
Efficient Simulations of Individual Based Models for Adaptive Dynamics and the Canonical Equation
摘要：
我们提出了一个更快的算法，基于个人的模拟自适应动态的基础上，一个简单的修改标准Gillespie算法模拟随机出生-死亡过程。我们提供了一个分析解释，表明在确定性极限下，基于修改后的算法的模拟会产生与从标准吉莱斯皮算法获得的相同的自适应动力学方程以及相同的进化分支条件。基于此算法，我们提供了一个直观和简单的解释正则方程的自适应动力学。通过算例比较了该算法与标准Gillespie算法的性能，证明了该算法的有效性。我们还研究了一个例子，使用该算法研究演化动力学在多维表型空间和研究问题的可预测性的进化。
英文摘要：
We propose a faster algorithm for individual based simulations for adaptive dynamics based on a simple modification to the standard Gillespie Algorithm for simulating stochastic birth-death processes. We provide an analytical explanation that shows that simulations based on the modified algorithm, in the deterministic limit, lead to the same equations of adaptive dynamics as well as same conditions for evolutionary branching as those obtained from the standard Gillespie algorithm. Based on this algorithm, we provide an intuitive and simple interpretation of the canonical equation of adaptive dynamics. With the help of examples we compare the performance of this algorithm to the standard Gillespie algorithm and demonstrate its efficiency. We also study an example using this algorithm to study evolutionary dynamics in a multi-dimensional phenotypic space and study the question of predictability of evolution.
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