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Understanding the genomic signatures, genes, and traits underlying local adaptation of organisms to heterogeneous environments is of central importance to the field evolutionary biology. To identify loci underlying local adaptation, models that combine allelic and environmental variation while controlling for the effects of population structure have emerged as the method of choice. Despite being evaluated in simulation studies, there has not been a thorough investigation of empirical evidence supporting local adaptation across these alleles. To evaluate these methods, we use 875 Arabidopsis thaliana Eurasian accessions and two mixed models (GEMMA and LFMM) to identify candidate SNPs underlying local adaptation to climate. Subsequently, to assess evidence of local adaptation and function among significant SNPs, we examine allele frequency differentiation and recent selection across Eurasian populations, in addition to their distribution along quantitative trait loci (QTL) explaining fitness variation between Italy and Sweden populations and cis‐regulatory/nonsynonymous sites showing significant selective constraint. Our results indicate that significant LFMM/GEMMA SNPs show low allele frequency differentiation and linkage disequilibrium across locally adapted Italy and Sweden populations, in addition to a poor association with fitness QTL peaks (highest logarithm of odds score). Furthermore, when examining derived allele frequencies across the Eurasian range, we find that these SNPs are enriched in low‐frequency variants that show very large climatic differentiation but low levels of linkage disequilibrium. These results suggest that their enrichment along putative functional sites most likely represents deleterious variation that is independent of local adaptation. Among all the genomic signatures examined, only SNPs showing high absolute allele frequency differentiation (AFD) and linkage disequilibrium (LD) between Italy and Sweden populations showed a strong association with fitness QTL peaks and were enriched along selectively constrained cis‐regulatory/nonsynonymous sites. Using these SNPs, we find strong evidence linking flowering time, freezing tolerance, and the abscisic‐acid pathway to local adaptation. [ABSTRACT FROM AUTHOR]