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Climate change poses a threat to biodiversity, and it is unclear whether species can adapt to or tolerate new conditions, or migrate to areas with suitable habitats. Reconstructions of range shifts that occurred in response to environmental changes since the last glacial maximum (LGM) from species distribution models (SDMs) can provide useful data to inform conservation efforts. However, different SDM algorithms and climate reconstructions often produce contrasting patterns, and validation methods typically focus on accuracy in recreating current distributions, limiting their relevance for assessing predictions to the past or future. We modeled historically suitable habitat for the threatened North American tree green ashFraxinus pennsylvanicausing 24 SDMs built using two climate models, three calibration regions, and four modeling algorithms. We evaluated the SDMs using contemporary data with spatial block cross‐validation and compared the relative support for alternative models using a novel integrative method based on coupled demographic‐genetic simulations. We simulated genomic datasets using habitat suitability of each of the 24 SDMs in a spatially‐explicit model. Approximate Bayesian computation (ABC) was then used to evaluate the support for alternative SDMs through comparisons to an empirical population genomic dataset. Models had very similar performance when assessed with contemporary occurrences using spatial cross‐validation, but ABC model selection analyses consistently supported SDMs based on the CCSM climate model, an intermediate calibration extent, and the generalized linear modeling algorithm. Finally, we projected the future range of green ash under four climate change scenarios. Future projections using the SDMs selected via ABC suggest only minor shifts in suitable habitat for this species, while some of those that were rejected predicted dramatic changes. Our results highlight the different inferences that may result from the application of alternative distribution modeling algorithms and provide a novel approach for selecting among a set of competing SDMs with independent data.