Simplest dynamic models of the global vegetation pattern

The changes in the global vegetation pattern (GVP) under climatic and anthr opogenic stress is one of the most important problems in global modelling. The idea of considering only two types of global vegetation (forest and gra ssland communities) instead of several dozen types las is usually done in d ifferent 'biome' models) was already suggested in our work (Svirezhev, Y.M. , Tarko, A.M., 1981. SCOPE 16, 355-364), when the global carbon cycle was m odelled, and recently it has been reanimated in a more general form by Brov kin et al. (Brovkin, V., Ganopolsky, A., Svirezhev, Y., 1997. Ecol. Model. 101, 251-261) Introducing into consideration the two spatial scales (the ma cro- and microscales, respectively) we use the macroscale for calculation o f the function p(x, y, t) defined as a part of a macrounit occupied by fore st communities. A macrounit is a macroscale area comprising a 'forest-grass ' mosaic of elementary areas, each of them covered by either forest or gras s. Each territorial microscale unit (microunit) is covered by only one type of vegetation. It is defined as one particle ('forest' or 'grass'). One ma crounit is considered to represent an 'urn' and special 'urn' schemes are u sed for its dynamic description. If only a 'point' evolution of GVP is stud ied, only local interactions (inside one macrounit) among microunits or par ticles are considered. The urn scheme corresponding to a simple 'forest-gra ss' model without age structure gives us equations which display a stable e quilibrium only under unrealistic assumptions. But even the simplest accoun t of age structure stabilises the system. The further generalisation of an age structure model for forest particles gives us a set of stable equilibri a for very realistic conditions. The corresponding 'urn' scheme is a type o f generalisation of the well-known 'gap models'. Both discrete and continuo us forms of dynamical systems generated by the 'urn' scheme" are considered . In particular, a full study for the case of a two-age forest containing y oung and mature trees is carried out. (C) 1999 Elsevier Science B.V. All ri ghts reserved.