A Markov model of pollinator activity is used to study the effect of constancy on rare plant species. Roughly, constancy is the tendency of the pollinator to continue searching for a flower of the species last visited. The model involves and abundant plant speciesA and two uncommon plant species,B andC, where the pollinator does not distinguish betweenB andC. The effect on the frequency of pollinator visits to speciesB whenC has newly invaded the colony is determined. It is shown that, under the right conditions, constancy and competition for pollinator services can result in an explosion in the number of specimens ofB present in future generations. Conversely, ifC becomes extinct constancy and competition for pollinator services can result in the extinction of speciesB.