Global asymptotic stability of plant-seed bank models

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.