Food-web architecture governs when predator advantage supports collective persistence

A recurring question across biological systems is when gains accrued by one part of a system also benefit the whole, and when they instead impose a collective cost. In ecological communities, consumers can increase their energetic gains through trophic interactions, yet those same interactions also determine whether all species persist. Here we show that food-web architecture governs whether predator advantage supports collective persistence, and that omnivory is a key condition under which the two diverge. Using a Lotka- Volterra-type food-web model formulated in terms of energy fluxes, we compare predator output power with the probability of feasibility, which quantifies the range of growth conditions compatible with positive coexistence. In two-species systems, these objectives show no generic alignment. In trophic chains, by contrast, increasing encounter rates makes predator advantage and coexistence mutually reinforcing. Basal omnivory reverses this pattern by shifting the power optimum towards the boundary of coexistence, where the intermediate consumer is lost. This pattern persists in larger networks, under heterogeneous encounter rates, and with saturating functional responses. Our results identify food-web architecture as the determinant of whether local energetic advantage scales up as collective persistence or instead becomes a coexistence cost.