Methods for approximating stochastic evolutionary dynamics on graphs
Methods for approximating stochastic evolutionary dynamics on graphs
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DOI：
10.1016/j.jtbi.2019.02.009
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发表时间：
2019-05-07
影响因子：
2
通讯作者：
Sharkey, Kieran J.
中科院分区：
文献类型：
--
作者：
Overton, Christopher E.;Broom, Mark;Sharkey, Kieran J.
种群结构对进化有重要影响。对于一些具有足够对称性的系统，可以在进化图论的数学框架内导出与进化过程的结果相关的分析结果。然而，对于更复杂的异质结构，需要计算密集型的方法，如基于个体的随机模拟。通过调整统计物理的方法，包括矩封闭技术，我们首先展示了如何推导出现有的均匀对近似模型和精确的中性漂移模型。然后，我们开发节点级近似随机演化过程的任意复杂结构的人口表示的有限图，它可以捕捉不同的动态人口中的各个节点。使用这些近似，我们评估固定概率的入侵突变体在给定的初始条件下，动态遵循标准的进化过程，如入侵过程。随机模拟的输出比较显示我们的近似描述的随机过程和预测的概率固定的突变体在广泛的图形的有效性。这些模型的构建有利于系统的分析，是有价值的，更好地了解种群结构对进化过程的影响。(C)2019作者爱思唯尔有限公司出版
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes. (C) 2019 The Authors. Published by Elsevier Ltd.