Improving transferability of species distribution models in a Poisson point-process framework

Reliable predictions of species distributions are central to conservation planning, invasive-species management, and climate-change assessment. We improve model transferability by addressing the extrapolation problem that arises when a model trained in one region is applied to another, assuming stationarity of ecological processes. In Poisson point process models commonly used for species distribution prediction, standard maximum likelihood estimation becomes unreliable when the intensity model is misspecified and the covariate distribution differs between the training and test regions, leading to systematic bias and inaccurate intensity estimates. To mitigate this problem, we adapt importance weighting to spatial point processes. Each training location is scaled by the ratio of its covariate density in the target region to that in the source region, and estimation proceeds by maximizing the resulting importance-weighted likelihood. This adjustment tailors inference to the covariate distribution that actually prevails in the test region, improving model transferability. We establish the theoretical properties of the resulting estimator. Under mild regularity conditions, it converges to the pseudo-true parameter that minimizes Kullback–Leibler divergence in the test region, is asymptotically normal, and has a closed-form sandwich covariance. We then assess the predictive performance of the weighted estimator through simulation studies and an empirical application to European bryophyte species, demonstrating its ability to improve transferability under covariate shift.