Modeling the population dynamics of annual plants with seed bank and density dependent effects

A model is proposed for the population dynamics of an annual plant (Sesbania vesicaria) with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). A simple linear matrix model is deduced from the life cycle graph. The dominant eigenvalue of the projection matrix is estimated from demographic parameters derived from field studies. The estimated values for population growth rate () indicates that the study population should be experiencing a rapid exponential increase, but this was not the case in our population.The addition of density dependent effects on seedling survivorship and adult fecundity, effects for which field studies provide evidence, considerably improves our model. Depending on the demographic parameters, the model leads to stable equilibrium, oscillations, or chaos. Study of the behaviour of this model in the parameter space shows that the existence of a seed bank allows higher among-year variation of adult fecundity, without leaving the region of demographic stability. Field data obtained over 3 years confirm this prediction.