Evolutionary dynamics on small-order graphs
Evolutionary dynamics on small-order graphs
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DOI：
10.1080/09720502.2009.10700618
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发表时间：
2009-01-01
影响因子：
1.7
通讯作者：
Stadler, B.
中科院分区：
文献类型：
--
作者：
Broom, M.;Rychtar, J.;Stadler, B.
我们研究了Lieberman等人推广的结构有限种群的随机生灭模型。[E.Lieberman，C.Hauert和M.A.Nowak(2005)，图的进化动力学，自然，第433卷，第312-316页]。我们考虑从3到8的所有可能的连通无向图。对于每个图，使用蒙特卡罗马尔可夫链模拟，我们确定了在每个可能的顶点引入的突变的固定概率。我们证明了固定概率依赖于顶点和图。随机放置的突变体在星图中固定的几率最高，紧随其后的是星形图形，而规则和几乎规则的图形的固定概率最低。我们还发现，在一个固定的图中，突变体的固定概率与起始顶点的程度呈负相关。
We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [E. Lieberman, C. Hauert and M. A. Nowak (2005), Evolutionary dynamics on graphs, Nature, Vol. 433, pp. 312-316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability of a mutant introduced at every possible vertex. We show that the fixation probability depends on the vertex and on the graph. A randomly placed mutant has the highest chances of fixation in a star graph, closely followed by star-like graphs, and the fixation probability is lowest for regular and almost regular graphs. We also find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex.