WHY POLLINATORS VISIT ONLY A FRACTION OF THE OPEN FLOWERS ON A PLANT - THE PLANTS POINT-OF-VIEW

We analyze the so-called 'exponential decay' model of pollen transfer for the case in which pollinators visit a fraction of the open flowers on a plant. The analysis is limited to the simplest case of a self-incompatible species, in which self pollen does not interfere with seed set. Plants can manipulate the number of flowers visited per pollinator approach by adjusting attractiveness of flowers so as to maximize pollen export (male fitness). In the model the length of the visitation sequence that is optimal for the plant (f) over cap always decreases with pollen deposition rate k(1), pollen uptake rate k(2), and the number of pollinator approaches to the plant X, but increases with the total number of flowers F. We assume that the average number of pollinator approaches X increases with the total number of flowers F, but slower than proportionality. It then follows that the optimal fraction of flowers a pollinator visits after arriving on the plant ((f) over cap/F) decreases with the total number of flowers F. Furthermore, the male fitness gain per flower generally decreases with number of flowers, except for the condition of 'inefficient' pollen transfer with very small values of k(1), k(2), and X, or when the plant has only a few flowers. The latter conditions should favour high nectar production and mass blooming. The known range of parameters suggests that male fitness increases with the total number of flowers slower than proportionality.