Dynamics of a plant-nectar-pollinator model and its approximate equations

This paper studies effect of nectar on pollination-mutualisms. By rigorous analysis on a plant-nectar-pollinator model, we demonstrate mechanisms by which the decay rate of nectar, the nectar-consumption rate by pollinator and the nectar-production rate by plant could lead to persistence/extinction of pollination-mutualisms. For example, (i) when the decay rate is small, the pollinator survives in the system and pollination-mutualisms persist, in which the plant approaches an enhanced density. (ii) When the decay rate is intermediate, the pollinator can survive in the system only if the initial density of nectar is not below a threshold. (iii) When the decay rate is large, the pollinator goes to extinction even though the plant and nectar persist. Furthermore, we study the approximate equations of the model, in which nectar is assumed to rapidly approach a steady state. We exhibit complete analysis on the equations, which extends previous results. A new finding in comparing the two models is that the initial value of nectar plays a role in persistence of pollination-mutualisms. Our results coincide with experimental observations while numerical simulations confirm and extend the results.