Liu Xuesong, Pan Qiuhui, Kang Yibin, He Mingfeng
School of Mathematical Science, Dalian University of Technology, Dalian 116024, China.
School of Mathematical Science, Dalian University of Technology, Dalian 116024, China; School of Innovation Experiment, Dalian University of Technology, Dalian 116024, China.
J Theor Biol. 2015 Dec 21;387:214-20. doi: 10.1016/j.jtbi.2015.09.016. Epub 2015 Sep 28.
We combined the standard Moran and Fermi process into a mixed process with two strategies C (co-operation) and D (defection). In a well-mixed population of size N+M, N individuals have the same update mechanism as that of Moran process, while the other M individuals have the same update mechanism as that of Fermi process. We obtain the balance equations of the conditional fixation time and unconditional fixation time. What these equations are doing is to make numerical sense for all the figures. We find that the expectation values of conditional fixation times of a single co-operator are smaller than the average values of the standard Moran and Fermi process. In addition, the conditional fixation time of a single co-operator with update rule of Moran is larger than that of Fermi when the intensity of selection is sufficiently small. The simulation results show that the unconditional fixation time of a co-operator who obtains more information is smaller. In addition, the larger the difference of individuals׳ payoff, the smaller the unconditional fixation time.
我们将标准的莫兰过程和费米过程结合成一个具有两种策略C（合作）和D（背叛）的混合过程。在一个大小为N + M的完全混合种群中，N个个体具有与莫兰过程相同的更新机制，而另外M个个体具有与费米过程相同的更新机制。我们得到了条件固定时间和无条件固定时间的平衡方程。这些方程的作用是使所有数据在数值上有意义。我们发现单个合作者的条件固定时间的期望值小于标准莫兰过程和费米过程的平均值。此外，当选择强度足够小时，具有莫兰更新规则的单个合作者的条件固定时间大于费米过程的条件固定时间。模拟结果表明，获得更多信息的合作者的无条件固定时间更短。此外，个体收益差异越大，无条件固定时间越短。
