Emergent competition shapes the ecological properties of multi-trophic ecosystems

Ecosystems are commonly organized into trophic levels --organisms that occupy the same level in a food chain (e.g., primary producers, herbivores, carnivores). A fundamental question in theoretical ecology is to understand how the interplay between trophic structure, diversity, and competition shapes the ecological properties of ecosystems. To address this problem, we analyze a generalized Consumer Resource Model with three trophic layers using the cavity method and numerical simulations. Unlike many previous works, our model explicitly includes many different types of species at each trophic level. We find that intra-trophic diversity gives rise to ``emergent competition" between species within a trophic level due to feedbacks mediated by other trophic levels. We show that this emergent competition mediates a crossover from a regime of top-down control (populations are limited by predators) to a regime of bottom-up control (populations are limited by primary producers) and that the crossover between these regimes can be characterized by a simple order parameter related to species packing and the number of surviving species. Collectively, these results highlight the importance of intra-trophic diversity for understanding multitrophic ecosystems and suggest a simple criterion for determining whether an ecosystem exhibits top-down or bottom-up control.