Humid savanna-forest dynamics: A matrix model with vegetation-fire interactions and seasonality

Rainfall seasonality and vegetation-fire feedbacks characterize humid savannas and tropical forests dynamics. In these ecosystems fire occurrence is influenced by the amount of grass, and trees respond to fire differently according to their height. Here we present a spatially implicit matrix model of humid savanna-forest dynamics. The state variables are the fraction of space occupied by trees and the grass biomass density. Rainfall seasonality is included using a discrete seasonal time step, distinguishing between wet and dry seasons. The demography of trees is taken into account considering different size classes and describing their dynamics with transition matrices, which depend on the season and presence/absence of fire. The occurrence of fire is represented by a Bernoulli variable, whose probability of occurrence is function of grass density. We explore different fire probabilities at the savanna-forest boundary and show different behaviors of the ecosystems. We investigate also the model's behavior with matrices of three Acacia species taken from literature.