Fishes represent an extremely diverse group of vertebrates with a deeply rooted evolutionary history. An understanding of their biology is being enriched by advancements in phylogenetic analysis and genomics, which are providing the framework for deciphering their evolutionary relationships and the molecular details that govern their evolution. Recent discoveries about the structure and function of fish genomes suggest the occurrence of large-scale genome level duplications within the stem lineage of the Actinopterygii (ray-finned fishes). However, little is understood about the effects, if any, of this event in relation to organismal complexity or species diversity. In this manuscript, I propose a hypothesis to test whether there is a likely relationship linking vertebrate genomes, organisms and species diversity. In so doing, I discuss the problems inherent in defining the complexity of genomes and organisms and provide simplifying assumptions that enable a preliminary test of the hypothesis. Results of this test suggest the likelihood of linkage between large-scale genome changes and organismal complexity early in vertebrate evolution but not in the evolution of the ray-finned fishes. A particularly interesting implication of the results is that there may be a limit to the effects of genome level duplications on organismal complexity and species diversity.