Askari Marziyeh, Samani Keivan Aghababaei
Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042707. doi: 10.1103/PhysRevE.92.042707. Epub 2015 Oct 13.
The ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics. Fixation probability and Average Fixation Time (AFT) are two important parameters to quantify this ability. In this paper we introduce an analytical approach for exact calculation of AFT. Using this method we obtain AFT for two types of evolutionary graphs: cycle graph, as a highly homogeneous graph and star graph, as a highly heterogeneous graph. We use symmetries of these graphs to calculate AFT. Analytical results are confirmed with simulation. We also examine the effect of adding some random edges to each of these structures.
突变个体取代整个种群的能力是进化动力学中的基本问题之一。固定概率和平均固定时间（AFT）是量化这种能力的两个重要参数。在本文中，我们引入了一种用于精确计算AFT的解析方法。使用这种方法，我们获得了两种类型进化图的AFT：作为高度均匀图的循环图和作为高度异质图的星型图。我们利用这些图的对称性来计算AFT。通过模拟证实了解析结果。我们还研究了给这些结构中的每一个添加一些随机边的效果。
