Growth dynamics of tropical savanna grass species using projection matrices

Savannas are very important tropical ecosystems characterized by co-dominance of herbaceous vegetation and less abundant trees and shrubs. Models of the dynamics of the spatial distribution of aboveground components of grass plants can be a useful tool to understand the dynamics of savanna ecosystems. We developed a model of grass plant growth as a collection of the individual dynamic behavior of shoots inspired in data for plants of three species of common grasses in the Venezuelan savannas. The species are: Elyonurus adustus (Trin.) E. Ekman., Leptocoryphium lanatum (Kunth) Nees and Andropogon semiberbis (Nees) Kunth. These species represent various types of architecture and regeneration response to fire. The individual-shoot model is based on shoot emergence, mortality, and elongation given by Richards’ equation, plus a few simple geometric considerations. Model output is shoot density in each cell of a square grid at several vertical levels. Differences in patterns of shoot density among species are explained by changing a set of parameter values related to growth form and phenology. Vertical distribution of shoot density was calculated from the simulation results and the field data with the purpose of deriving a simpler lumped shoot-population model. This simpler demographic model is based on a projection matrix that predicts the essential dynamics of growth in the vertical dimension. The transient and final behavior of vertical distribution of shoot density are calculated with the matrix model and compared to field data yielding good fit as assessed by the root mean square (RMS) error of difference between the field data and the model results. This error is of the same magnitude as the RMS difference among the three field data replicates. Sensitivity analysis of the matrix model for the three species was used to identify those vertical levels for which the damping ratio is more sensitive to a perturbation. For early and precocius species ( E. adustus and L. lanatum), the top level is more sensitive whereas the late blooming species ( A. semiberbis) is more sensitive at lower levels. Although developed for these three species, the matrix model is generic and therefore can be applied to plants with the basic growth form of perennial grasses of seasonal savanna ecosystems. Applications include scaling-up the individual-shoot model to larger areas and analysis of savanna dynamics subject to fire.