One of the striking observations from recent whole-genome comparisons is that changes in the number of specialized genes in existing gene families, as opposed to novel taxon-specific gene families, are responsible for the majority of the difference in genome composition between major taxa. Previous models of duplicate gene evolution focused primarily on the role that neutral processes can play in evolutionary divergence after the duplicates are already fixed in the population. By instead including the entire cycle of duplication and divergence, we show that specialized functions are most likely to evolve through strong selection acting on segregating alleles at a single locus, even before the duplicate arises. We show that the fitness relationships that allow divergent alleles to evolve at a single locus largely overlap with the conditions that allow divergence of previously duplicated genes. Thus, a solution to the paradox of the origin of organismal complexity via the expansion of gene families exists in the form of the deterministic spread of novel duplicates via natural selection.