BIFURCATIONS IN A POLLINATION-MUTUALISM SYSTEM WITH NECTARLESS FLOWERS

摘要

This paper considers a pollination-mutualism system in which owering plants have strategies of secreting and cheating: secretors produce a substantial volume of nectar in owers but cheaters produce none. Accordingly, oral visitors have strategies of neglecting and selecting: neglectors enter any ower encountered but selectors only enter full owers since they can discriminate between secretors and cheaters. By combination of replicator equations and two-species dynamical systems, the games are described by a mathematical model in this paper. Dynamics of the model demonstrate mechanisms by which nectarless owers can invade the secretor-pollinator system and by which a cyclic game between nectarless owers and pollinators could occur. Criteria for the persistence of nectarless owers are derived in terms of the given parameters (factors), including the nectar-producing cost and cheaters' efficiency. Numerical simulations show that when parameters vary, cheaters would vary among extinction, persistence in periodic oscillations, and persistence without secretors (i.e., cheaters spread widely). We also consider the evolution of plants in a constant state of pollinator population, and the evolution of pollinators in a constant state of plant population. Dynamics of the models demonstrate conditions under which nectarless owers (resp. selectors) could persist.