Evolutionary Dynamics on Graphs - the Effect of Graph Structure and Initial Placement on Mutant Spread
Evolutionary Dynamics on Graphs - the Effect of Graph Structure and Initial Placement on Mutant Spread
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DOI：
10.1080/15598608.2011.10412035
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发表时间：
2011-01-01
影响因子：
0.6
通讯作者：
Stadler, B. T.
中科院分区：
文献类型：
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作者：
Broom, M.;Rychtar, J.;Stadler, B. T.
我们研究有限和结构化群体中的随机出生-死亡过程，并分析突变体的固定概率如何取决于其初始位置。特别是，我们研究了固定概率如何取决于引入突变体的顶点的度数，以及哪些顶点是其邻居。我们发现，在固定图中，突变体的固定概率与起始顶点的度数呈负相关。对于一般的突变适应度 r，我们根据邻居的固定概率给出相对固定概率的近似值，这对于考虑结构相对简单但有许多顶点的图（例如小世界网络类型）非常有用，并将我们的近似值与模拟结果进行比较。此外，我们还探讨了哪些类型的图有利于突变体固定，哪些类型不利于突变体固定。我们发现随机放置的突变体的固定概率与该图上顶点度数的变化之间存在高度正相关。
We study the stochastic birth-death process in a finite and structured population and analyze how the fixation probability of a mutant depends on its initial placement. In particular, we study how the fixation probability depends on the degree of the vertex where the mutant is introduced, and which vertices are its neighbours. We find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex. For a general mutant fitness r, we give approximations of relative fixation probabilities in terms of the fixation probabilities of neighbours which will be useful for considering graphs of relatively simple structure but many vertices, for instance of the small world network type, and compare our approximations to simulation results. Further, we explore which types of graphs are conducive to mutant fixation and which are not. We find a high positive correlation between a fixation probability of a randomly placed mutant and the variation of vertex degrees on that graph.