Unisexual vertebrates are model systems for understanding the evolution of sex. Many predominantly clonal lineages allow occasional genetic recombination, which may be sufficient to avoid the accumulation of deleterious mutations and parasites. Introgression of paternal DNA into an all-female lineage represents a one-way flow of genetic material. Over many generations, this could result in complete replacement of the unisexual genomes by those of the donor species. The process of genome replacement may be counteracted by contemporary dispersal or by positive selection on hybrid nuclear genomes in ecotones. I present a conceptual model that relates nuclear genome replacement, positive selection on hybrids and biogeography in unisexual systems. I execute an individual-based simulation of the fate of hybrid genotypes in contact with a single host species. I parameterize these models for unisexual salamanders in the Ambystoma genus, for which the frequency of genome replacement has been a source of ongoing debate. I find that, if genome replacement occurs at a rate greater than 1/10,000 in Ambystoma, then there must be compensating positive selection in order to maintain observed levels of hybrid nuclei. Future researchers studying unisexual systems may use this framework as a guide to evaluating the hybrid superiority hypothesis.