Emergent competition shapes top-down versus bottom-up control in multi-trophic ecosystems

Ecosystems are commonly organized into trophic levels-organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic structure, diversity, and competition shapes the properties of ecosystems. To address this problem, we analyze a generalized Consumer Resource Model with three trophic levels using the zero-temperature cavity method and numerical simulations. We derive the corresponding mean-field cavity equations and show that intra-trophic diversity gives rise to an effective "emergent competition" term between species within a trophic level due to feedbacks mediated by other trophic levels. This emergent competition gives rise to 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 is captured by a simple order parameter related to the ratio of surviving species in different trophic levels. We show that our theoretical results agree with empirical observations, suggesting that the theoretical approach outlined here can be used to understand complex ecosystems with multiple trophic levels. Ecosystems are commonly organized into trophic levels-organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). In this study, we use methods originating from spin glass physics to theoretically analyze the statistical properties of large and diverse ecosystems with multiple trophic levels. Our analysis successfully quantifies the strength of intra-level competitions and results in a simple criteria for determining whether an ecosystem exhibits top-down control (e.g. herbivores populations are limited by predators) or bottom-up control (e.g. herbivores populations are limited by the availability of plants). Somewhat surprisingly, we find that whether a system exhibits top-down or bottom-up control dependent solely on the ratio of surviving species at different trophic levels.