“Forest–grass” global vegetation model with forest age structure

Abstract

In the paper [Ecol. Modell. 124 (1999) 131], a set of “simplest” models of the global vegetation pattern (GVP) was suggested. All these models are based on the simple probabilistic “urn” schemes and their dynamics were sufficiently complex to present nonlinear phenomena such as multiple equilibriums and hysteresis. Although these schemes are simple, sufficiently complex behaviour is implied. Expressed in terms of equations with biologically motivated parameters, only three equilibriums corresponding to “grass ”, transition “grass–forest” and “forest” zones exist. Stability domains of these equilibriums do not intersect in the parameter space. Since at each geographical point, the GVP dynamics is described by the same dynamical system with different parameters; then this difference is defined by the change in annual temperature and precipitation. We also assume that at any point there are both tree and grass “seeds”. In order to reduce the number of independent parameters, we formulate two additional hypotheses. Let τ m and τ l , i.e. the age of maturity and the life span for trees. Then, (1) the ratio k τ = τ m / τ l must be constant for coniferous and deciduous trees and (2) τ m = τ ml ( T). Both these hypotheses have been tested. As a result only one parameter, which governs the intensity of competition within a mature tree cohort, remained free and it could be used for the tuning purposes. Since the final GVP substantially depends on the border shape between forest, grass and mixed biomes in the climatic space {temperature, precipitation}; then in order to obtain better coincidence between the real and modelled GVP, we should modify the classic Lieth diagram. After calibrating parameters using climatic and vegetation data we developed a model, which predicts vegetation distribution in satisfactory agreement with observation for the present day. It is also shown that a “relaxation” time (time to reach equilibrium) for a transition zone is more than one order greater than the time for “pure” grass and forests equilibriums. This means that a real transformation of the GVP under climate change is a very slow process.