A modelling technique unifying four paradigms of metacommunity theory

Metacommunity theory explains how species distributions arise from local population dynamics and dispersal between habitat patches. Four conceptual paradigms—patch dynamics, species sorting, mass effects, and demographic stochasticity—have emerged as frameworks for understanding metacommunity structure and dynamics, but their integration remains an open problem. Here we introduce a probabilistic-stochastic-deterministic (PSD) modelling framework that unifies these paradigms within a single mathematical description. PSD approximates individual-based models (IBM) with computational efficiency comparable to ordinary differential equations (ODE) while capturing demographic stochasticity and permitting analytical treatment. Through validation against IBM simulations in single-patch communities and spatially explicit metacommunities with rock-paper-scissors dynamics, we demonstrate that PSD accurately reproduces IBM behaviour where ODE models fail, specifically when demographic stochasticity dominates during immigration. For metacommunities with long-distance dispersal, we analytically derive the period of a slow collective oscillations, revealing body-mass and dispersal-rate dependencies invisible to ODE theory. Our analysis shows that the four paradigms represent valid descriptions in different regions of parameter space, controlled by individual body-mass, immigration rate, and regional species richness. The PSD framework thus provides both a practical simulation tool and an analytical machinery for predicting metacommunity dynamics across ecological regimes.