Sporophytic self-incompatibility (SSI) is a self-pollen recognition system that enforces outcrossing in plants. Recognition in SSI systems is typically controlled by a complex locus (5-locus) with separate genes that determine pollen and stigma specificity. Experimental studies show that S-alleles can be dominant, recessive, or codominant, and that the dominance level of a given S-allele can depend upon whether pollen or stigma specificity is examined. Here and in the companion paper by Llaurens and colleagues, the evolution of dominance in single-locus SSI is explored using numerical models and simulation. Particular attention is directed at factors that can cause S-allele dominance to differ in pollen versus stigma. The effect of recombination between the S-locus and modifier locus is also examined. The models predict that limitation in the number of compatible mates is required for the evolution of S-allele dominance in the stigma but not in the pollen. Tight linkage between the S-locus and modifier promotes the evolution of S-allele dominance hierarchies. Model results are interpreted with respect to published information on the molecular basis of dominance in SSI systems, and reported S-allele dominance relationships in a variety of species. These studies show that dominant S-alleles are more common in the pollen than in the stigma, a pattern that when interpreted in light of model predictions, suggests that mate limitation may be relatively infrequent in natural populations with SSI.