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.