The effects of trade-off shape and dimensionality on eco-evolutionary dynamics in resource competition

Organisms invariably experience trade-offs in their capacities for interacting with their environments. In resource competition, this often means that an organism's ability to acquire one resource can only come at the cost of less ability with others. If the traits governing resource acquisition are under selection and heritable, this will induce eco-evolutionary dynamics along the trade-off. For Lotka-Volterra models derived from MacArthur resource competition models and for explicit resource models with two resources, the shape and dimensionality of trade-offs has seen substantial study. However, how the joint effects of trade-off shapes and the number of resources under competition affect eco-evolutionary outcomes has seen relatively little. For example, is diversification through evolutionary branching more or less likely when the number of resources increases? Here, we will present techniques complementary to existing ones for recasting trade-offs in an implicit form. Combining adaptive dynamics and resource-competition theory, we derive expressions for directional and stabilizing/disruptive selection. We apply our techniques to two models of resource competition and investigate how the number of resources and trade-off shapes affect the stability characteristics of the generalist strategy, and how diverse a community of consumers can be assembled through successive evolutionary branching. We find that even for these simple and highly symmetric models, outcomes are surprisingly complex and idiosyncratic. Taken together, our results deepen our understanding of the eco-evolutionary dynamics of resource competition for multiple resources.