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Background The functional divergence of duplicate genes (ohnologues) retained from whole genome duplication (WGD) is thought to promote evolutionary diversification. However, species radiation and phenotypic diversification are often temporally separated from WGD. Salmonid fish, whose ancestor underwent WGD by autotetraploidization ~95 million years ago, fit such a ‘time-lag’ model of post-WGD radiation, which occurred alongside a major delay in the rediploidization process. Here we propose a model, ‘lineage-specific ohnologue resolution’ (LORe), to address the consequences of delayed rediploidization. Under LORe, speciation precedes rediploidization, allowing independent ohnologue divergence in sister lineages sharing an ancestral WGD event. Results Using cross-species sequence capture, phylogenomics and genome-wide analyses of ohnologue expression divergence, we demonstrate the major impact of LORe on salmonid evolution. One-quarter of each salmonid genome, harbouring at least 4550 ohnologues, has evolved under LORe, with rediploidization and functional divergence occurring on multiple independent occasions >50 million years post-WGD. We demonstrate the existence and regulatory divergence of many LORe ohnologues with functions in lineage-specific physiological adaptations that potentially facilitated salmonid species radiation. We show that LORe ohnologues are enriched for different functions than ‘older’ ohnologues that began diverging in the salmonid ancestor. Conclusions LORe has unappreciated significance as a nested component of post-WGD divergence that impacts the functional properties of genes, whilst providing ohnologues available solely for lineage-specific adaptation. Under LORe, which is predicted following many WGD events, the functional outcomes of WGD need not appear ‘explosively’, but can arise gradually over tens of millions of years, promoting lineage-specific diversification regimes under prevailing ecological pressures. Electronic supplementary material The online version of this article (doi:10.1186/s13059-017-1241-z) contains supplementary material, which is available to authorized users.