The prevalence of polyploidy among flowering plants is surprising given the hurdles impeding the establishment and persistence of novel polyploid lineages. In the absence of strong assortative mating, reproductive assurance, or large intrinsic fitness advantages, new polyploid lineages face almost certain extinction through minority cytotype exclusion. Consequently, much work has focused on a search for adaptive advantages associated with polyploidy such as increased competitive ability, enhanced ecological tolerances, and increased resistance to pathogens. Yet, no consistent adaptive advantages of polyploidy have been identified. Here, to investigate the potential for autopolyploid establishment and persistence in the absence of any intrinsic fitness advantages, we develop a simulation model of a diploid population that sporadically gives rise to novel autopolyploids. The autopolyploids have only very small levels of initial assortative mating or niche differentiation, generated entirely by dosage effects of genome duplication, and they have realistic levels of reproductive assurance. Our results show that by allowing assortative mating and competitive interactions to evolve, establishment of novel autopolyploid lineages becomes common. Additional scenarios where adaptive optima change over time reveal that rapid environmental change promotes the replacement of diploid lineages by their autopolyploid descendants. These results help to explain recent empirical findings that suggest that many contemporary polyploid lineages arose during the Cretaceous-Tertiary extinction, without invoking adaptive advantages of polyploidy.