The one-third law of evolutionary dynamics.
The one-third law of evolutionary dynamics.
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DOI：
10.1016/j.jtbi.2007.07.005
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发表时间：
2007-11
影响因子：
2
通讯作者：
H. Ohtsuki;P. Bordalo;M. Nowak
中科院分区：
文献类型：
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作者：
H. Ohtsuki;P. Bordalo;M. Nowak
有限种群中的进化博弈动力学为研究具有频率依赖适应度的性状选择提供了一个新的框架。最近，进化动力学的“三分之一定律”被描述，该定律指出，当A具有1/3的频率时，如果A的适应度大于B的适应度，则策略A固定在具有选择优势的B种群中。这一关系适用于迄今所考察的所有进化过程，从Moran过程到图上的博弈。然而，“数字”的起源1/3并不为人所知。在本文中，我们通过研究潜在的随机过程提供了一个直观的解释。我们发现，在一次入侵尝试中，个人与B-玩家的互动频率平均是与A-玩家的两倍，这产生了三分之一的定律。我们还证明了三分之一定律意味着A的平均马尔萨斯适合度是正的。
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 frequency 1/3. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the “number” 1/3 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.