Decomposing invasion growth rates reveals mechanisms of species persistence across spatial environmental variation

Environmental variations across space make evaluating species coexistence outcomes essential for predicting species distributions and biodiversity maintenance. Coexistence theory, particularly the framework of Modern Coexistence Theory (MCT), defines the invasion growth rate (IGR) as the key criterion for coexistence and provides expressions to decompose IGR into multiple components. However, MCT’s mathematical complexity limits empirical applications outside purposefully designed experiments. Here, we developed a process-based mechanistic framework that enables the evaluation of coexistence outcomes and their spatial variation in empirical systems by using time series abundance data. The proposed novel framework decomposes IGR into key mechanistic processes including environmental suitability, interspecific competition, niche differences, and fitness differences. It further links these processes hierarchically with multiple external drivers and translates the relationships into spatially explicit extinction risk assessments. As a case study, we applied the framework to an 18-year rocky intertidal dataset to quantify how IGRs of Chthamalus dalli and Gloiopeltis furcata , as well as their mechanistic processes, varied across space. The results showed that bare space availability and effective shore level were the most influential external drivers, while environmental suitability and fitness difference were identified as the key contributors to IGR variation. The framework proposed in this study enables quantification of coexistence mechanisms and extinction risk in any ecosystem using time-series abundance data and spatially replicated environments. The framework successfully quantified direct and indirect pathways of environmental drivers in a rocky intertidal system, enabled the mapping of coexistence outcomes across sites, and provided predictive capacity for extinction risk based on IGR thresholds. Overall, this framework represents a generalizable and empirically applicable approach to linking coexistence theory with environmental heterogeneity, offering new opportunities for predicting biodiversity responses under environmental change.