Do pollen carryover and pollinator constancy mitigate effects of competition for pollination?

Pollinator constancy and pollen carryover are both thought to mitigate competitive effects that result when shared pollinators cause loss of pollen to heterospecific flowers. I present analytical and simulation models to investigate how pollinator constancy and pollen carryover interact with each other and with the relationship between pollen receipt and seed set to determine pollination success in competitive environments. With inconstant pollinators, increased pollen carryover reduces variance in pollen receipt without affecting average pollen receipt. Consequently, for flowers requiring at least a threshold quantity of pollen for success, rare flowers with inconstant pollinators benefit from reduced carryover, especially for high pollen receipt thresholds, whereas common flowers benefit from increased carryover, especially for low receipt thresholds. Pollinator constancy is predicted to increase pollen receipt, especially if pollen carryover rates are low. As a result, increased pollinator constancy reduces the range of pollen receipt thresholds for which carryover is beneficial. Similarly, for flowers whose pollination success is a convex function of pollen receipt, carryover is expected to increase fecundity if pollinators are inconstant, but with even a low degree of pollinator constancy, carryover reduces fecundity. These results predict that rare plants with many ovules per flower benefit from dispersing aggregations of pollen, especially if their pollinators exhibit constancy, whereas plants with inconstant pollinators and low thresholds of pollen receipt benefit from pollen grains dispersing individually to increase the number of flowers reached by the pollen.