BACKGROUND: Gene and genome duplication events increase the amount of genetic material that might then contribute to an increase in the genomic and phenotypic complexity of organisms during evolution. Thus, it has been argued that there is a relationship between gene copy number and morphological complexity and/or species diversity. This hypothesis implies that duplicated genes have subdivided or evolved novel functions compared to their pre-duplication proto-orthologs. Such a functional divergence might be caused by an increase in evolutionary rates in one ortholog, by changes in expression, regulatory evolution, insertion of repetitive elements, or due to positive Darwinian selection in one copy. We studied a set of 2466 genes that were present in Danio rerio, Takifugu rubripes, Tetraodon nigroviridis and Oryzias latipes to test (i) for forces of positive Darwinian selection; (ii) how frequently duplicated genes are retained, and (iii) whether novel gene functions might have evolved. RESULTS: 25% (610) of all investigated genes show significantly smaller or higher genetic distances in the genomes of particular fish species compared to their human ortholog than their orthologs in other fish according to relative rate tests. We identified 49 new paralogous pairs of duplicated genes in fish, in which one of the paralogs is under positive Darwinian selection and shows a significantly higher rate of molecular evolution in one of the four fish species, whereas the other copy apparently did not undergo adaptive changes since it retained the original rate of evolution. Among the genes under positive Darwinian selection, we found a surprisingly high number of ATP binding proteins and transcription factors. CONCLUSION: The significant rate difference suggests that the function of these rate-changed genes might be essential for the respective fish species. We demonstrate that the measurement of positive selection is a powerful tool to identify divergence rates of duplicated genes and that this method has the capacity to identify potentially interesting candidates for adaptive gene evolution.