CREED, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.
J Theor Biol. 2011 May 7;276(1):78-85. doi: 10.1016/j.jtbi.2011.01.044. Epub 2011 Feb 3.
The well-known replicator dynamics is usually applied to 2-player games and random matching. Here we allow for games with n players, and for population structures other than random matching. This more general application leads to a version of the replicator dynamics of which the standard 2-player, well-mixed version is a special case, and which allows us to explore the dynamic implications of population structure. The replicator dynamics also allows for a reformulation of the central theorem in Van Veelen (2009), which claims that inclusive fitness gives the correct prediction for games with generalized equal gains from switching (or, in other words, when fitness effects are additive). If we furthermore also assume that relatedness is constant during selection - which is a reasonable assumption in a setting with kin recognition - then inclusive fitness even becomes a parameter that determines the speed as well as the direction of selection. For games with unequal gains from switching, inclusive fitness can give the wrong prediction. With equal gains however, not only the sign, but also even the value of inclusive fitness becomes meaningful.
著名的复制者动态通常应用于 2 人游戏和随机匹配。在这里，我们允许有 n 名玩家的游戏，以及除随机匹配之外的其他种群结构。这种更一般的应用导致了复制者动态的一个版本，其中标准的 2 人、充分混合的版本是一个特例，并且允许我们探索种群结构的动态影响。复制者动态还允许重新表述范维伦（Van Veelen）（2009 年）的中心定理，该定理声称，广义等同收益转换的博弈中，适合度可以给出正确的预测（换句话说，当适合度效应是可加的）。如果我们进一步假设在选择过程中亲缘关系是恒定的 - 在亲缘识别的环境中这是一个合理的假设 - 那么适合度甚至成为一个确定选择速度和方向的参数。对于转换收益不等的博弈，适合度可能会给出错误的预测。然而，对于等同收益，不仅适合度的符号，甚至其值都变得有意义。
