Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138.
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104.
Proc Natl Acad Sci U S A. 2022 Jul 12;119(28):e2119656119. doi: 10.1073/pnas.2119656119. Epub 2022 Jul 5.
In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly heterogeneous spatial structures. As a result, one of the most difficult obstacles lies in making analytical deductions, either qualitative or quantitative, about the long-term outcomes of evolution. The "structure-coefficient" theorem is a well-known approach to this problem for mutation-selection processes under weak selection, but a general method of evaluating the terms it comprises is lacking. Here, we provide such a method for populations of fixed (but arbitrary) size and structure, using easily interpretable demographic measures. This method encompasses a large family of evolutionary update mechanisms and extends the theorem to allow for asymmetric contests to provide a better understanding of the mutation-selection balance under more realistic circumstances. We apply the method to study social goods produced and distributed among individuals in spatially heterogeneous populations, where asymmetric interactions emerge naturally and the outcome of selection varies dramatically, depending on the nature of the social good, the spatial topology, and the frequency with which mutations arise.
为了适应种群结构很少简单的经验事实，现代进化动力学研究允许复杂和高度异质的空间结构。因此，最困难的障碍之一在于对进化的长期结果进行定性或定量的分析推论。对于弱选择下的突变-选择过程，“结构系数”定理是解决这个问题的一种著名方法，但缺乏对其组成项进行评估的一般方法。在这里，我们使用易于解释的人口统计指标为固定（但任意）大小和结构的种群提供了这样一种方法。这种方法包含了一大类进化更新机制，并将定理扩展到允许不对称竞争，以在更现实的情况下更好地理解突变-选择平衡。我们将该方法应用于研究空间异质种群中个体之间产生和分配的社会商品，其中不对称相互作用自然出现，选择的结果因社会商品的性质、空间拓扑结构以及突变发生的频率而有很大差异。
