A MODEL FOR ANNUAL PLANT DYNAMICS WITH SEED BANK AND DENSITY-DEPENDENT EFFECTS
A model is proposed for the population dynamics of an annual plant with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). In this model, demographic parameters (dormancy and germination rate) of the seeds of the year are different from those of the seeds of the seed bank. First, a simple linear matrix model is deduced from the life cycle graph and a more complicated model is built by introducing density dependence effect. The obtained system, nonlinear with delay, can be simplified by a change of variables. A non-trivial fixed point of this system is obtained and the conditions of stability are studied. Under certain conditions (choice of exponential law for functional response of density dependence and absence of seed mortality before germination) we show that conditions of stability depend only on 3 parameters, the dormancy rate of the seeds of the year, dormancy rate of the seeds of the seed bank and the maximum potential fecundity of adults. Study of the behaviour of this model in the parameter space shows that the domain of demographic stability can be reduced if the dormancy rate of seeds of the year is low, even if the dormancy rate of seeds of the seed bank is high.