Ohtsuki Hisashi, Bordalo Pedro, Nowak Martin A
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA.
J Theor Biol. 2007 Nov 21;249(2):289-95. doi: 10.1016/j.jtbi.2007.07.005. Epub 2007 Jul 18.
Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.
有限种群中的进化博弈动力学为研究频率依赖适应度性状的选择提供了一个新框架。最近，已经描述了进化动力学的“三分之一定律”，该定律指出，如果当策略A的频率为1/3时A的适应度大于B的适应度，那么具有选择优势的策略A会在B种群中固定下来。到目前为止，这种关系适用于所研究的所有进化过程，从莫兰过程到图上的博弈。然而，“数字”1/3的由来尚不清楚。在本文中，我们通过研究潜在的随机过程给出了一个直观的解释。我们发现，在一次入侵尝试中，一个个体与B参与者互动的平均频率是与A参与者互动频率的两倍，这就产生了三分之一定律。我们还表明，三分之一定律意味着A的平均马尔萨斯适应度是正的。
