POPULATION-DYNAMICS OF RESOURCE LIMITED PLANTS AND THEIR POLLINATORS

In this paper we build upon and generalize an earlier model of the int eractions between a plant and its pollinator (Ingvarsson and Lundberg, 1995). In this model we assume that the performance of the pollinator population is directly linked to the size of the plant population. To avoid the problem of both populations growing exponentially we have, without loss of generality, assumed the plant population to be resourc e limited. Analysis of the system shows that there exists either two o r no internal equilibrium points. The case with no equilibrium points corresponds to the trivial case where the system cannot persist, resul ting in the extinction of both the plant and-pollinator population. Wh en the two internal equilibrium points do exist, one of them will alwa ys be unstable. This unstable equilibrium can be viewed as an equivale nt of the threshold criteria derived in Ingvarsson and Lundberg (1995) in the sense that whenever the system is initiated above the unstable equilibrium point, persistence of the system is assured, while both s pecies will go extinct whenever the system is initiated below the unst able equilibrium point. The analytical results were verified by numeri cal simulations of the system. We conclude that the existence of a thr eshold criteria, below which the system cannot persist is a general fe ature of plant-pollinator systems. We discuss how the existence of the threshold criteria will affect the persistence of plant-pollinator sy stems in light of, for instance, habitat fragmentation or stochastic r eductions in the densities of either the plant or pollinator populatio n. We further highlight some recent empirical studies that indicate th e existence of a threshold in natural populations below which extincti on is inevitable. (C) 1998 Academic Press.