Dept Math and Stats, Queen's University, Kingston, ON, K7L 3N6, Canada.
Evolution. 2011 Mar;65(3):849-59. doi: 10.1111/j.1558-5646.2010.01162.x. Epub 2010 Nov 5.
Recent work on the evolution of behaviour is set in a structured population, providing a systematic way to describe gene flow and behavioural interactions. To obtain analytical results one needs a structure with considerable regularity. Our results apply to such "homogeneous" structures (e.g., lattices, cycles, and island models). This regularity has been formally described by a "node-transitivity" condition but in mathematics, such internal symmetry is powerfully described by the theory of mathematical groups. Here, this theory provides elegant direct arguments for a more general version of a number of existing results. Our main result is that in large "group-structured" populations, primary fitness effects on others play no role in the evolution of the behaviour. The competitive effects of such a trait cancel the primary effects, and the inclusive fitness effect is given by the direct effect of the actor on its own fitness. This result is conditional on a number of assumptions such as (1) whether generations overlap, (2) whether offspring dispersal is symmetric, (3) whether the trait affects fecundity or survival, and (4) whether the underlying group is abelian. We formulate a number of results of this type in finite and infinite populations for both Moran and Wright-Fisher demographies.
最近关于行为进化的研究是在结构化群体中进行的，为描述基因流动和行为相互作用提供了一种系统的方法。为了获得分析结果，需要具有相当规则性的结构。我们的结果适用于这样的“同质”结构（例如，晶格、循环和岛屿模型）。这种规律性通过“节点传递性”条件来正式描述，但在数学中，这种内部对称性可以通过数学群理论来强有力地描述。在这里，该理论为许多现有结果的更一般版本提供了优雅的直接论证。我们的主要结果是，在大型“群体结构”群体中，对他人的主要适应度效应在行为进化中不起作用。这种特征的竞争效应抵消了主要效应，并且包含适合度的效应由行为者对其自身适合度的直接效应给出。该结果取决于许多假设，例如（1）代际是否重叠，（2）后代扩散是否对称，（3）特征是否影响繁殖力或存活率，以及（4）基础群体是否阿贝尔。我们为有限和无限群体中的 Moran 和 Wright-Fisher 人口统计学制定了许多具有这种类型的结果。
