Abundance-mediated species interactions.

Species interactions shape biodiversity patterns, community assemblage, and the dynamics of wildlife populations. Ecological theory posits that the strength of interspecific interactions is fundamentally underpinned by the population sizes of the involved species. Nonetheless, prevalent approaches for modeling species interactions predominantly center around occupancy states. Here, we use simulations to illuminate the inadequacies of modeling species interactions solely as a function of occupancy, as is common practice in ecology. We demonstrate erroneous inference into species interactions due to error in parameter estimates when considering species occupancy alone. To address this critical issue, we propose, develop, and demonstrate an abundance-mediated interaction framework designed explicitly for modeling species interactions involving two or more species from detection/non-detection data. We present Markov chain Monte Carlo (MCMC) samplers tailored for diverse ecological scenarios, including intraguild predation, disease- or predator-mediated competition, and trophic cascades. Illustrating the practical implications of our approach, we compare inference from modeling the interactions in a three-species network involving coyotes (Canis latrans), fishers (Pekania pennanti), and American marten (Martes americana) in North America as a function of occupancy states and as a function of abundance. When modeling interactions as a function of abundance rather than occupancy, we uncover previously unidentified interactions. Our study emphasizes that accounting for abundance-mediated interactions rather than simple co-occurrence patterns can fundamentally alter our comprehension of system dynamics. Through an empirical case study and comprehensive simulations, we demonstrate the importance of accounting for abundance when modeling species interactions, and we present a statistical framework equipped with MCMC samplers to achieve this paradigm shift in ecological research.