Increasing evidence shows that structural variants represent an overlooked aspect of genetic variation with consequential evolutionary roles. Among those, copy number variants (CNVs), including duplicated genomic region and transposable elements (TEs) may contribute to local adaptation and/or reproductive isolation among divergent populations. Those mechanisms suppose that CNVs could be important drivers of population genetic structure, whose study is generally restricted to the use of SNPs. Taking advantage of recent developments allowing CNV analysis from RAD-seq data, we investigated how variation in fitness-related traits, local thermal conditions and demographic history are associated with CNVs, and how subsequent copy number variation drives population genetic structure in a marine fish, the capelin (Mallotus villosus). We collected 1536 DNA samples from 35 sampling sites in the north Atlantic Ocean and identified 6620 CNVs. We found associations between CNVs and the gonadosomatic index, suggesting that duplicated regions could affect female fitness by modulating oocyte production. We also detected 105 CNV candidates associated with water temperature, among which 20% corresponded to genomic regions located within the sequence of protein-coding genes, suggesting local adaptation to cold water by means of gene amplification. We also identified 175 CNVs associated with the divergence of three parapatric glacial lineages, of which 24% were located within protein-coding genes, which might contribute to genetic incompatibilities and ultimately, reproductive isolation. Lastly, our analyses unveiled a hierarchical, complex CNV population structure determined by temperature and local geography, that was very different from that inferred based on SNPs in a previous study. Our findings underscore the complementarity of those two types of markers in population genomics studies.