Eco-evolutionary community dynamics: covariation between diversity and invasibility across temperature gradients

Understanding biodiversity gradients is a long-standing challenge, and progress requires theory unifying ecology and evolution. Here, we unify concepts related to the speed of evolution, the influence of species richness on diversification, and niche-based coexistence. We focus on the dynamics, through evolutionary time, of community invasibility and species richness across a broad thermal gradient. In our framework, the evolution of body size influences the ecological structure and dynamics of a trophic network, and organismal metabolism ties temperature to eco-evolutionary processes. The framework distinguishes ecological invasibility (governed by ecological interactions) from evolutionary invasibility (governed by local ecology and constraints imposed by small phenotypic effects of mutation). The model yields four primary predictions: (1) ecological invasibility declines through time and with increasing temperature; (2) average evolutionary invasibility across communities increases and then decreases through time as the richness-temperature gradient flattens; (3) in the early stages of diversification, richness and evolutionary invasibility both increase with increasing temperature; and (4) at equilibrium, richness does not vary with temperature, yet evolutionary invasibility decreases with increasing temperature. These predictions emerge from the "evolutionary-speed" hypothesis, which attempts to account for latitudinal species richness gradients by invoking faster biological rates in warmer, tropical regions. The model contrasts with predictions from other richness-gradient hypotheses, such as "niche conservatism" and "species energy." Empirically testing our model's predictions should help distinguish among these hypotheses.