Erola Fenollosa , Sean E. H. Pang, Natalie Briscoe, Antoine Guisan, Rob Salguero-Gomez

Risk assessments of invasive species are among the most challenging applications of species distribution models (SDMs). This challenge arises from the disequilibrium in invasive distributions, where recorded occurrences do not fully represent the species' potential range. The spatiotemporal dynamics of invasive populations are shaped by intraspecific variability, human-mediated introductions, novel biotic interactions, climate change, and ecological niche shifts, which are only indirectly incorporated into correlative SDMs. Predicting future potential distributions under these conditions requires moving beyond traditional frameworks reliant on historical climatic data to models that explicitly capture the mechanisms underlying species potential. Mechanistic niche models (MNMs) address these limitations as process-explicit models that integrate species' physiological performance across environmental gradients. By incorporating physiological constraints and vital rates, MNMs define species distribution limits, offering a mechanistic understanding of species-environment relationships and enabling more robust predictions under changing conditions. However, a unified MNM framework remains elusive. In this review we delve into the theoretical foundations of MNMs, emphasizing their advantages over correlative approaches, especially for invasive species. We provide insights into diverse modelling techniques across taxa and examine the benefits and limitations of MNMs for predicting species distributions under novel conditions. Our systematic review revealed that MNMs have been applied sparingly to invasive species, focusing primarily on insects and plants, likely due to high data requirements. While MNMs do not explicitly capture spatial processes, they remain the most suitable approach for defining species distribution limits under novel conditions, but their success depends on the relevance of input data and effective parameterization, including genotype selection, model type, experimental conditions, and physiological curve-fitting techniques. MNMs offer significant potential for advancing ecological research and providing robust tools for evidence-based management decisions. By addressing key challenges, they can enhance our understanding of invasive species and other populations in disequilibrium under changing environmental conditions.