Polyploidy contributes massively to the taxonomic and genomic diversity of angiosperms, but certain aspects of polyploid evolution are still enigmatic. The establishment of a new polyploid lineage following whole-genome duplication (WGD) is a critical step for all polyploid species, but this process is difficult to identify and observe in nature. Mathematical models offer an opportunity to study this process by varying parameters related to the populations, habitats, and organisms involved in the polyploid establishment process. While several models of polyploid establishment have been published previously, very few incorporate spatial factors, including spatial relationships between organisms, habitat shape, or population density. This study presents a stochastic, spatial model of polyploid establishment that shows how factors such as habitat shape and dispersal type can influence the fixation and persistence of nascent polyploids and modulate the effects of other factors. This model predicts that narrow, constrained habitats such as roadsides and coastlines may enhance polyploid establishment, particularly in combination with frequent clonal reproduction, limited dispersal, and high population density. The similarity between this scenario and the growth of many invasive or colonizing species along disturbed, narrow habitats such as roadsides may offer a partial explanation of the prevalence of polyploidy among invasive species.