Abstract:

Background: Understanding how environmental filtering, biotic interactions, and neutral processes jointly shape species distributions and community structure is a central question in modern community ecology. However, traditional diversity indices, ordination analyses, and single-species distribution models (SDMs) cannot simultaneously integrate species associations, environmental gradients, functional traits, and phylogenetic relationships, thereby limiting their ability to disentangle community assembly mechanisms. 

Framework: Joint species distribution models (JSDMs), particularly the hierarchical modelling of species communities (HMSC) framework, offer a unified and flexible Bayesian tool for community-level mechanistic inference. This study provides a systematic review of the statistical structure, mathematical foundations, and inferential mechanisms of HMSC, and establishes a complete analytical workflow encompassing data organization, model specification, Markov Chain Monte Carlo estimation, model evaluation, ecological interpretation, and predictive applications. A step-by-step tutorial, Joint Species Distribution Modelling with HMSC, accompanies the review and illustrates the practical implementation of HMSC through bryophyte community data and fully reproducible R code. 

Theory: In the theoretical component, we clarify how HMSC integrates environmental gradients, species traits, phylogenetic relationships, and spatial structure within a unified hierarchical Bayesian framework to distinguish statistical signals of environmental filtering, biotic filtering, and dispersal limitation. Methodologically, we dissect the mathematical structure of latent variable models, elucidate the boundaries of ecological interpretation for residual correlations, and provide a conceptual basis for differentiating species co-occurrence signals from environmental effects and unobserved factors. We further compare HMSC with other mainstream JSDMs implementations and traditional community analytical methods, highlighting their relative advantages and ecological applicability. 

Applications: On the applied side, we synthesize the rapidly expanding use of JSDMs across forest, wetland, grassland, marine, urban, and microbial ecosystems, demonstrating their value in conservation planning, invasive species risk assessment, co-occurrence network analysis, and scenario-based forecasting. With the advancement of GPU-accelerated computation, migration learning, and high-dimensional modelling frameworks, HMSC greatly improves ecological niche estimation and distribution prediction for rare species and enables community modelling for tens of thousands of taxa. Overall, JSDMs and HMSC in particular represent a methodological shift from single-species prediction toward integrative, multi-species and multi-dimensional ecological modelling. They provide an efficient, scalable, and uncertainty-aware platform that strengthens ecological theory testing, enhances understanding of community assembly mechanisms, and supports biodiversity conservation and management decisions.

Key words: community ecology, joint species distribution models, hierarchical modelling of species communities, environmental filtering, neutral processes, Bayesian models