Persistence and near persistence via trait evolution: Pathways to coexistence

In community ecology, predictions on whether or not interacting species will coexist are often formed by considering invasion criteria: each species must be able to increase when rare in a resident community at ecological equilibrium. However, when considering trait evolution, for example of competing species, this concept must be refined to account for evolution potentially feeding back on population dynamics. We analyze a model of two competing species whose quantitative traits evolve under stabilizing selection, assuming fixed but potentially unequal intraspecific trait variances. Using persistence theory, we derive conditions under which both species persist for all initial trait values, and we introduce the concept of 'near persistence', in which coexistence holds for a specific, biologically relevant, subset of initial trait configurations. Our analysis reveals that equal trait variances between species, which is commonly assumed in previous work, yield highly specific outcomes and obscure a broader set of coexistence scenarios that emerge under asymmetric trait variation. We identify fifteen distinct qualitative dynamical regimes as a function of initial conditions and trait variances. Moreover, we show that invasion analysis must often be performed at multiple eco-evolutionary equilibria, as invader dynamics may converge to different trait values depending on the ecological and evolutionary context. We discuss the biological implications of these results and perspectives for future work.