Code from: Evolution of species' range and niche in changing environments

What causes species' niche and range margins to shift is not only a
fundamental theoretical question, but also directly affects how we assess
the resilience of natural populations in current and future environments.
Yet despite the urgent need for a theory that can predict evolutionary and
ecological responses in times of accelerated climate change, the
assumptions of current eco-evolutionary theory remain restrictive, with
predictions neglecting important interactions between ecological and
evolutionary forces. In this study, I provide quantitative, testable
predictions on limits to adaptation in changing environments, which arise
from the feedback between selection, genetic drift, and population
dynamics. This eco-evolutionary feedback creates a tipping point beyond
which adaptation fails as genetic drift overwhelms selection, and
species' ranges contract from the margins or fragment abruptly --
even under gradual environmental change. This "expansion
threshold'' is determined by three parameters: two quantifying
the effects of spatial and temporal variability on the fitness of the
population, and one capturing the impact of genetic drift: the reduction
of local genetic diversity across generations in finite populations.
Genetic drift is strong in populations with small "neighbourhood
size''. Increasing dispersal, such as via assisted migration,
enlarges neighbourhood size, counteracting the loss of genetic variation
due to genetic drift. This increases adaptive potential and can facilitate
evolutionary rescue in changing environments. Conversely, beyond the
expansion threshold, local genetic variance becomes depleted, increasing
extinction probability. The theory provides general predictions for
species' range and niche dynamics beyond standard ecological niche
models, highlighting the fundamental impact of eco-evolutionary
interactions.