Successful implementation of evolutionary management programs to rescue climatically threatened species requires identification of adaptive genetic variation. Although current genotype-environment association methods have been successful in identifying adaptive variation, they can be improved in two important aspects. First, most existing methods do not account for genotype uncertainty in widely available low-coverage whole-genome sequencing data. Researchers often restrict analysis to loci for which genotypes can be inferred reliably or call the most probable genotype, allowing the use of traditional genotype-based methods, such as BayeScEnv and Bayenv. However, discarding data and false genotype calls increases the uncertainty in estimates of genetic variation and introduces systematic biases. Second, most methods use phenomenological approaches, such as logistic regression, to partition estimated genetic variation into adaptive and non-adaptive components. Consequently, current approaches may inadvertently fail to account for evolutionary processes, such as migration-selection balance. Structured migration between climatically disparate locations can produce deviations from a smooth S-shape response curve, which can be difficult to accommodate using generalized linear regression models. To overcome these challenges, we developed a method that accounts for genotype uncertainty in sequencing data and propagates this uncertainty to inform the parameters of a model of evolution. A key feature of this evolutionary model is that it mechanistically describes how genetic variation arises from joint interactions between local adaptation, structured migration, mutation, and drift. We apply our approach to analyze multiple synthetic datasets and a real dataset of North American rosy-finches (3.7 million SNPs), a high-alpine, climatically threatened clade of bird species. ### Competing Interest Statement The authors have declared no competing interest. U.S. National Science Foundation, 2222525, 1927177, 2222524, 2222526 U.S. National Science Foundation, 2138259, 2138286, 2138307, 2137603, 2138296