Evolution of species' range and niche in changing environments

What determines the limits to adaptation and to a species' range is a fundamental question, especially relevant in the context of current rapid environmental change. Yet, to date, no predictive theory incorporates the feedback between ecology and evolution while accounting for the evolution of genetic variance under selection, mutation, dispersal, and genetic drift. This study outlines a comprehensive theory showing that under joint evolutionary and population dynamics, the limits of adaptation are fundamentally determined by the three measurable parameters: i) the effective environmental gradient, ii) the effective rate of temporal change, and iii) the neighbourhood size, which represents the local population size accessible via dispersal. Dispersal across heterogeneous environments supports higher local genetic variance, facilitating adaptation to a faster temporal change. However, local diversity is depleted by genetic drift, which is measured by the inverse of neighbourhood size. Extending earlier predictions in stable environments, I use scaling arguments to derive a generalized expansion threshold -- a tipping point where adaptation fails and the species' range can no longer expand. Beyond this threshold, species' ranges also tend to fragment, particularly when temporal change incurs a high fitness cost. The onset of fragmentation is rapid and associated with a loss of genetic variance. The theory not only identifies new phenomena but also establishes a fundamental relationship between these core measurable parameters. It provides a predictive framework for understanding species' range and niche limits while advancing the theoretical foundations for assessing population resilience of spatially structured populations under unprecedented environmental change.