A new geometric framework for niche theory and consumer resource models

A fundamental problem in ecology is to understand when species can coexist in an ecosystem. One major paradigm for addressing this is Niche theory and Consumer Resource Models (CRMs). Niche theory and CRMs have played a foundational role in our ecological understanding by highlighting the central role of ecological competition in shaping ecosystem function and structure. Many of the central intuitions of niche theory (Tilman's R*, species coexistence cones) were developed using geometric arguments for analyzing CRMs. Here, we present a new, simple yet powerful, geometric framework for understanding species coexistence in CRMs based on convex polytopes in the space of consumer preferences. We show that this new geometric picture can be used to predict which species can co-exist, enumerate all possible ecologically stable steady-states, and all allowed transitions between these steady-states. Our geometric picture also naturally allows us to understand how changing species' attributes affects species co-existence and niche differentiation. Collectively, these results constitute a qualitatively new way of understanding the role of species' consumption preferences in ecosystems and niche theory.