Abstract
Molecular evolution offers an insightful theory to interpret the genomic consequences of thermal adaptation to previous events of climate change beyond range shifts. However, disentangling often mixed footprints of selective and demographic processes from those due to lineage sorting, recombination rate variation, and genomic constrains is not trivial. Therefore, here we condense current and historical population genomic tools to study thermal adaptation and outline key developments (genomic prediction, machine learning) that might assist their utilization for improving forecasts of populations' responses to thermal variation. We start by summarizing how recent thermal-driven selective and demographic responses can be inferred by coalescent methods and in turn how quantitative genetic theory offers suitable multi-trait predictions over a few generations via the breeder's equation. We later assume that enough generations have passed as to display genomic signatures of divergent selection to thermal variation and describe how these footprints can be reconstructed using genome-wide association and selection scans or, alternatively, may be used for forward prediction over multiple generations under an infinitesimal genomic prediction model. Finally, we move deeper in time to comprehend the genomic consequences of thermal shifts at an evolutionary time scale by relying on phylogeographic approaches that allow for reticulate evolution and ecological parapatric speciation, and end by envisioning the potential of modern machine learning techniques to better inform long-term predictions. We conclude that foreseeing future thermal adaptive responses requires bridging the multiple spatial scales of historical and predictive environmental change research under modern cohesive approaches such as genomic prediction and machine learning frameworks.