An analysis of the fixation probability of a mutant on special classes of non-directed graphs
An analysis of the fixation probability of a mutant on special classes of non-directed graphs
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DOI：
10.1098/rspa.2008.0058
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发表时间：
2008-10-08
影响因子：
3.5
通讯作者：
Rychtar, J.
中科院分区：
文献类型：
--
作者：
Broom, M.;Rychtar, J.
人们对具有非同质结构的种群的进化动力学研究越来越感兴趣。在本文中，我们遵循 Lieberman 等人的模型。 （Lieberman et al. 2005 Nature 433, 312 316）图上的进化动力学。我们研究了非有向等权图的情况，并找到了两类简单图中单个突变体的固定概率的解决方案。我们进一步证明，在这些类之外的图上找到类似的解决方案要复杂得多。最后，我们以数字方式研究我们选择的类别并讨论图表的许多特征；例如，我们找到不同初始起始位置的固定概率，并观察到与非结构化群体相比，有利突变体的平均固定概率总是增加。
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312 316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations.