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Hermaphroditic plants experience inbreeding through both self-fertilization and bi-parental inbreeding. Therefore, many plant species have evolved either heteromorphic (morphology-based) or homomorphic (molecular-based) self-incompatibility (SI) systems. These SI systems limit extreme inbreeding through self-fertilization and, in the case of homomorphic SI systems, have the potential to limit bi-parental inbreeding, which is common when dispersal is restricted to a local region. Homomorphic SI species are prevalent across the angiosperms, and it is often assumed that the potential to reduce bi-parental inbreeding may be a factor in their success. To test this assumption, we developed a spatially-explicit, individual-based simulation of plant populations with either heteromorphic SI or one of three different types of homomorphic SI. In our simulations, we varied dispersal distance and the presence of inbreeding depression. We found that autozygosity in the homomorphic SI populations was significantly lower than in the heteromorphic SI populations and that this reduction was due to bi-parental inbreeding avoidance. As expected, the differences between the homomorphic and heteromorphic SI populations were more pronounced when seed and pollen dispersal was limited. However, levels of homozygosity and inbreeding depression between these plant populations were not different. At low dispersal, homomorphic SI populations also suffered reduced female fecundity and had smaller census population sizes. Our results suggest that bi-parental inbreeding avoidance was unlikely to be a major driver in the evolution of homomorphic SI systems.