Rand DA
Nonlinear Dynamics Laboratory, Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K.
J Theor Biol. 1998 Aug 21;193(4):631-648. doi: 10.1006/jtbi.1998.0730.
Group selection can overcome individual selection for selfishness and favour altruism if there is variation among the founders of the spatially distinct groups, and groups with many altruists become substantially larger (or exist longer) than groups with few. Whether altruism can evolve in populations that do not have an alternation of local population growth and global dispersal ("viscous populations") has been disputed for some time. Limited dispersal protects the altruists from the non-altruists, but also hinders the export of altruism. In this article, we used the Pair Approximation technique (tracking the dynamics of pairs of neighbours instead of single individuals) to derive explicit invasion conditions for rare mutants in populations with limited dispersal. In such viscous populations, invading mutants form clusters, and ultimately, invasion conditions depend on the properties of such clusters. Thus there is selection on a higher level than that of the individual; in fact, invasion conditions define the unit of selection in viscous populations. We treat the evolution of altruism as a specific example, but the method is of more general interest. In particular, an important advantage is that the spatial aspects can be incorporated into game theory in a straightforward fashion; we will specify the ESS for a more general model. The invasion condition can be interpreted in terms of inclusive fitness. In contrast with Hamilton's model, the coefficient of relatedness is not merely a given genetical constant but depends on local population dynamical processes (birth, dispersal and death of individuals). With a simple birth rate function, Hamilton's rule is recovered: the cost to the donor should be less than the benefit to the recipient weighted with the coefficient of relatedness. As the coefficient of relatedness is roughly proportional to an individual's number of neighbours, benefits to the recipient must be substantial to outweigh the costs, confirming earlier studies. We discuss the consequences for the evolution of dispersal and outline how the method may be extended to study evolution in interacting populations.Copyright 1998 Academic Press
如果在空间上相互分离的群体的创建者之间存在差异，并且利他主义者较多的群体比利他主义者较少的群体规模显著更大（或存在时间更长），那么群体选择就可以克服个体的自私选择，从而有利于利他主义。一段时间以来，利他主义是否能够在没有局部种群增长和全球扩散交替出现的种群（“黏性种群”）中进化一直存在争议。有限的扩散保护了利他主义者免受非利他主义者的影响，但也阻碍了利他主义的传播。在本文中，我们使用配对近似技术（追踪邻居对而不是单个个体的动态）来推导有限扩散种群中稀有突变体的明确入侵条件。在这种黏性种群中，入侵的突变体形成簇，最终，入侵条件取决于这些簇的特性。因此，存在比个体层面更高层次的选择；事实上，入侵条件定义了黏性种群中的选择单位。我们将利他主义的进化作为一个具体例子来处理，但该方法具有更广泛的意义。特别地，一个重要的优点是空间方面可以以一种直接的方式纳入博弈论；我们将为一个更一般的模型指定ESS。入侵条件可以用广义适合度来解释。与汉密尔顿模型不同，亲缘系数不仅仅是一个给定的遗传常数，而是取决于局部种群动态过程（个体的出生、扩散和死亡）。通过一个简单的出生率函数，可以恢复汉密尔顿法则：捐赠者的代价应该小于接受者的收益乘以亲缘系数。由于亲缘系数大致与个体的邻居数量成正比，接受者的收益必须足够大才能超过成本，这证实了早期的研究。我们讨论了对扩散进化的影响，并概述了该方法如何扩展以研究相互作用种群中的进化。版权所有1998年学术出版社
