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 regions and transposable elements (TEs), may contribute to local adaptation and/or reproductive isolation among divergent populations. Those mechanisms suppose that CNVs could be used to infer neutral and/or adaptive population genetic structure, whose study has been restricted to microsatellites, mitochondrial DNA and Amplified fragment length polymorphism markers in the past and more recently the use of single nucleotide polymorphisms (SNPs). Taking advantage of recent developments allowing CNV analysis from RAD-seq data, we investigated how variation in fitness-related traits, local environmental 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 1538 DNA samples from 35 sampling sites in the north Atlantic Ocean and identified 6620 putative CNVs. We found associations between CNVs and the gonadosomatic index, suggesting that six 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 sequence amplification. We also identified 175 CNVs associated with the divergence of three previously defined parapatric glacial lineages, of which 24% were located within protein-coding genes, making those loci potential candidates for reproductive isolation. Lastly, our analyses unveiled a hierarchical, complex CNV population structure determined by temperature and local geography, which was in stark contrast to that inferred based on SNPs in a previous study. Our findings underline the complementarity of those two types of genomic variation in population genomics studies.