Modeling and analysis of a density-dependent structured population model for American chestnut (Castanea dentata)

Background/Question/Methods

Density-dependent regulatory factors impact the dynamics of many populations.  Population modelers often times only consider one density-dependent factor when constructing structured population models, and these factors are often assumed to be either monotonically increasing or monotonically decreasing functions of some measure of population abundance.  However, in perennial plant populations it is possible that conspecifics from one life-history stage (e.g. seedlings) can elicit a different density-dependent feedback than conspecifics from another life-history stage (e.g. mature plants).  Therefore, it is important to include all of the important density-dependent feedbacks when modeling population dynamics.  

Results/Conclusions

We developed a density-dependent matrix model for the American chestnut (Castanea dentata), where seedling recruitment is subject to density-dependent feedback from adult conspecifics as well as other seedlings.  The former exhibits a decreasing relationship with population abundance while the latter an increasing relationship with population abundance.  Using methods from systems and control theory we show that, for much of parameter space, there is a unique, globally asymptotically stable equilibrium population vector that is independent of initial population vector.  We derive a formula for this equilibrium population and show how sensitive the equilibrium size of each life-history stage of the population is to changes in population data (for example, we show how the equilibrium population changes when the population goes from healthy to diseased).  We further show how our results can be extended to integral projection models (IPMs) and explore how the addition of stochasticity impacts model predictions.