Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;
Department of Zoology, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
Proc Natl Acad Sci U S A. 2021 Oct 19;118(42). doi: 10.1073/pnas.2105252118.
Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.
在社会困境中进行合作投资可以自发地多样化，在充分混合的群体中稳定共存高贡献者和低贡献者。在这里，我们将分析扩展到新兴的（空间）结构化群体中的多样性。我们使用对合近似法，推导出了在结构化群体中稀有突变体入侵适应性的解析表达式，从而得出了一个空间适应动态框架。这使我们能够根据群体结构来预测出现的变化，包括奇异策略的存在和位置，以及与充分混合群体相比它们的收敛和进化稳定性。基于空间适应动态和广泛的个体模拟，我们发现，空间结构对连续社会困境中的进化多样化具有显著而多样的影响。更具体地说，空间适应动态表明，通过进化分支自发多样化受到抑制，但模拟表明，空间维度提供了新的多样化模式，这些模式是由有限大小突变和群体结构的相互作用驱动的。尽管空间适应动态无法捕捉到这些新模式，但它们仍然可以基于入侵分析来理解。特别是，群体结构改变了入侵适应性，并且可以在特征空间中开辟新的区域，突变体可以在这些区域中入侵，但这些区域可能无法通过小的突变步骤到达。相反，需要在特定方向上随机出现的较大突变或较小突变序列来跨越不利特征的区域。其净效应是，空间结构往往会促进多样化，尤其是在选择较强时。
