Learning Ecological Cost Surfaces of Climate-Driven Range Shifts via Inverse Optimal Transport

Species are redistributing under climate change, yet climatic niche models frequently mispredict the pace of observed shifts. Conservation planning depends on resistance surfaces, maps of how strongly landscapes impede movement, which are commonly assumed from expert opinion or geographic distance rather than inferred from redistribution. This framing is inverted here, treating resistance as an unknown recovered from observed redistribution. Representing each species’ distribution as a discrete measure on a 50 km grid over the eastern United States, the observed shift is modeled as a Kullback–Leiblerrelaxed unbalanced optimal-transport coupling from the historical distribution toward a climate-feasible niche-model target, and a shared cost over geographic distance, climatic dissimilarity, and elevation contrast is learned by backpropagating through entropic Sinkhorn iterations. Across 101 Breeding Bird Survey species admitted purely on data sufficiency, the learned cost lowers predictive Wasserstein distance on 33 held-out species against geography-only transport (33/33, p < 10−9), climateonly projection (33/33), and climate velocity (30/33). The learned elevation term produces a 1,100 km high-resistance corridor coinciding with the Appalachian chain given no barrier prior. However, two limitations bound this. The climate-to-elevation ratio is unidentified across an eightfold range, and on the unbiased sample a no-change baseline outperforms the framework in 26 of 33 cases. This reverses the advantage seen on a literature-curated subset, and quantifies how strongly species selection can inflate apparent forecasting skill.