A mathematical framework of consumer-resource dynamics: How to incorporate interactions between interactions in evolutionary process

TL;DR

This paper introduces a new mathematical framework to model complex consumer-resource interactions, including intra-population dynamics and evolutionary processes, revealing conditions for long-term ecological stability.

Contribution

It develops a novel mathematical model that incorporates interactions between interactions and separates ecological and evolutionary timescales, advancing understanding of stability in consumer-resource systems.

Findings

Model produces stable consumer-resource coexistence states.

Intra-population interactions promote long-term ecological stability.

Evolutionary outcomes can lead to either consumer or resource dominance.

Abstract

A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of consumer--resource interactions. Both the consumer and resource are assumed to consist of several (sub)species, which interact between themselves in addition to incorporating the deleterious effects of the consumer on the resource. Separating the ecological and evolutionary time scales, we allow our mathematical model to evolve, with the evolutionary steps chosen according to the (divergent) objective functions of the consumer and the resource. Numerical simulations show that the model, along with the expected outcomes of either consumer or resource winning the evolutionary battle, is capable of producing also the (quasi)stationary state of consumer--resource coexistence with monotone growth of both the consumer and resource fitnesses. Such stable states highlight the importance of the intra-population interactions, which, despite the opposite evolutionary goals of the consumer and the resource, lead to long term ecological stability.