Geometric scaling of non-consumptive interactions generates sublinear density dependence and reshapes coexistence

Abstract

The shape of density-dependence governs species persistence, and ecosystem stability. Yet, whether per-capita growth declines sublinearily, or superlinearily with density remains hotly debated. Growth rates across the tree of life have been shown to decline sublinearly with density, whereas theory founded on resource competition predicts the opposite. Here, we resolve this discrepancy and show that sublinearity can readily emerge from geometric constraints on consumer interactions. By linking inter individual spacing, movement and interference rates, we derive two limiting-interference regimes, one of which the well-mixed limit recovers the form of classic Beddington DeAngelis interference response. We then developed an individual-based model from first principles which reproduces the derived sublinearity response, and further use empirical data from published consumer-resource experiments that also bears the signature of sublinear density-dependence. Further, embedding the interference mechanisms underlying the emergence of sublinear density-dependence in coexistence theory opens a new regime for species coexistence where classical theory fails to predict. Our framework indicates that non-consumptive interactions are not merely a correction to resource competition but might be a distinct axis along which diverse communities may potentially coexist.