Ashcroft Peter, Traulsen Arne, Galla Tobias
Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042154. doi: 10.1103/PhysRevE.92.042154. Epub 2015 Oct 28.
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.
马尔可夫过程中固定动力学的研究主要集中在吸收的平均时间上。如果分布广泛且有偏斜，这可能并不充分。我们计算了具有两个吸收态的一步生灭过程中固定时间的分布。这些分布用过程的谱来表示，并且我们在特征空间中给出了不同的表示形式，即仅向前的过程。这些表示形式允许对固定时间分布进行高效采样。作为一个应用，我们研究了进化博弈动力学，其中入侵的突变体可能达到固定或灭绝。我们还强调了中位数固定时间，它可能类似于具有低突变率且无吸收态的系统中的混合时间，而平均固定时间则没有这样的解释。
