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.