Little is known about how quickly natural populations adapt to changes in their environment and how temporal and spatial variation in selection pressures interact to shape patterns of genetic diversity. We here address these issues with a series of genome scans in four overfished populations of Atlantic cod (Gadus morhua) studied over an 80-year period. Screening of >1000 gene-associated single-nucleotide polymorphisms (SNPs) identified 77 loci that showed highly elevated levels of differentiation, likely as an effect of directional selection, in either time, space or both. Exploratory analysis suggested that temporal allele frequency shifts at certain loci may correlate with local temperature variation and with life history changes suggested to be fisheries induced. Interestingly, however, largely nonoverlapping sets of loci were temporal outliers in the different populations and outliers from the 1928 to 1960 period showed almost complete stability during later decades. The contrasting microevolutionary trajectories among populations resulted in sequential shifts in spatial outliers, with no locus maintaining elevated spatial differentiation throughout the study period. Simulations of migration coupled with observations of temporally stable spatial structure at neutral loci suggest that population replacement or gene flow alone could not explain all the observed allele frequency variation. Thus, the genetic changes are likely to at least partly be driven by highly dynamic temporally and spatially varying selection. These findings have important implications for our understanding of local adaptation and evolutionary potential in high gene flow organisms and underscore the need to carefully consider all dimensions of biocomplexity for evolutionarily sustainable management. SNP_identity.txtThis tab-separated file contains a complete list of the SNPs analyzed in the study. For each SNP we provide the linkage group and specific linkage map position (where available), the accession reference ID (dbSNP), the original publication for the SNP discovery (source), whether the locus was included in the quality-filtered 1047 and 160 SNP data sets, and any miscellaneous notesSNP_genotypes_1047This tab-separated file contains the genotype data for the initial analysis of the 4T 1928 and the 4T 2008 samples with the full 1047 SNP panel.Genepop_1047The data from file "SNP_genotypes_1047.txt" presented in Genepop format.SNP_genotypes_160This tab-separated file contains the genotype data for samples from 4T, 3Ps, 3NO and 4VsW analyzed with the 160 SNP panel.Genepop_160The data from file "SNP_genotypes_160.txt" presented in Genepop format.Env_and_demographic_dataThis tab-delimited file contains the environmental and demographic data used in the correlation analysis of temporal trends within the 4T management area. Description of the variables and the data sources can be found in Table S1. PMRNmean is fish length in cm, the mean individual weight at ages 5-7 is in kg, the biomass at ages 3+ is in tons, the mortality indices (M, F and Z) are estimated instantaneous rates, and the temperature variables are in degrees Celcius. Missing (not available) data are indicated by blanks.