Data from: Multidimensional (co)evolutionary stability

The complexity of biotic and abiotic environmental conditions is such that the fitness of individuals is likely to depend on multiple traits. Using a synthetic framework of phenotypic evolution which draws from adaptive dynamics and quantitative genetics approaches, we explore how the number of traits under selection influences convergence stability and evolutionary stability in models for co-evolution in multi-dimensional phenotype spaces. Our results allow us to identify three different effects of trait dimensionality on stability: i) a "combinatorial effect": without epistasis and genetic correlations, a higher number of trait dimensions offers more opportunities for equilibria to be unstable; ii) epistasis interactions, ie, fitness interactions between traits, that tend to destabilize evolutionary equilibria; this effect increases with the dimension of phenotype space. These first two effects influence both convergence stability and evolutionary stability, while iii) genetic correlations (due eg to pleiotropy or linkage disequilibrium) can only affect convergence stability. We illustrate the general prediction that increased dimensionality destabilizes evolutionary equilibria using examples drawn from well-studied classical models of: frequency-dependent competition for resources, adaptation to a spatially heterogeneous environment, and antagonistic coevolution. In addition, our analyses show that increased dimensionality can favor diversification, e.g. in the form of local adaptation, as well as evolutionary escape.生物与非生物环境条件的复杂性使得个体适合度（fitness）大概率依赖于多个性状。本研究采用融合适应性动力学（adaptive dynamics）与数量遗传学（quantitative genetics）的表型进化综合框架，探讨了受选择作用的性状数量如何影响多维表型空间协同进化（co-evolution）模型中的收敛稳定性（convergence stability）与进化稳定性（evolutionary stability）。研究结果揭示了性状维度对稳定性的三类不同影响：其一为“组合效应”：在上位性（epistasis）与遗传相关（genetic correlations）不存在的情况下，性状维度越多，进化平衡点出现不稳定的概率越高；其二为上位性互作效应：即性状间的适合度互作，这类互作通常会破坏进化平衡点的稳定性，且该效应随表型空间维度的提升而增强。前两类效应同时影响收敛稳定性与进化稳定性，而其三为遗传相关效应：这类相关由多效性（pleiotropy）或连锁不平衡（linkage disequilibrium）引发，仅能影响收敛稳定性。本研究通过三类得到充分研究的经典模型实例，验证了“维度提升会破坏进化平衡点稳定性”这一通用预测，所涉及的模型包括：资源竞争中的频率依赖型竞争、空间异质环境下的适应性进化，以及拮抗协同进化（antagonistic coevolution）。此外，本研究的分析还表明，提升性状维度可促进物种分化，例如以局部适应（local adaptation）的形式，同时也能推动进化逃逸（evolutionary escape）。