Lotka-Volterra models and the global vegetation pattern

How can such a classic object of mathematical ecology as the Lotka-Volterra competition model for a community of n competing species be used for descr iption of the global vegetation dynamics under the climate change? We assum e that the present spatial distribution of global vegetation is a stable eq uilibrium solution of corresponding Lotka-Volterra equations. The problem i s how to construct some discrete structure on a continuous set of parameter s, in this context remaining in a framework of a continuous model descripti on? The problem can be solved if a dynamical system with multiple equilibri a is considered. In this case, a continuous quasi-stationary change of para meters induces a jump from one to another equilibrium, since they have diff erent stability domain in the parametric space. On this conceptual base a s pecial class of Lotka-Volterra equations is developed and a biologically in terpreted procedure for estimating their coefficients is suggested. For thi s we must have maps of the annual production and biomass, a life span of ea ch vegetation type, and a map of the current geographical distribution of d ifferent vegetation, i.e. the current global vegetation pattern (GVP). The latter is needed for the construction of the 'elementary map', which is an important part of the model. Another important part is the formula, which d escribes an annual production dependence on the temperature and precipitati on (for instance, Lieth's formula can be used). Considering a one-dimension al particular case for n = 2 we have the analytical formulas describing a s hift of borders between two vegetation zones under the climate change. It w as shown that two different types of the transition zones, namely, 'soft' a nd 'hard', exist in this case. If the soft zone is characterised by the con tinuous and smooth replacement of one type of vegetation by another, then t he hard zone is a typical 'fractal' structure with a mosaic of different ve getation. A special calibration procedure for the Lotka-Volterra model desc ribing the dynamics of one-dimensional GVP with n types of vegetation is su ggested. It is based on the stability theorem for a system with multiple eq uilibria and a special averaging method applying to real geographical distr ibutions of the annual production and the biomasses. The results are used f or estimating the shift of one transition zone between taiga and steppe in the Central Siberia under the climate change (CO2-doubling scenario). (C) 2 000 Elsevier Science B.V. All rights reserved.