Simplest dynamic models of the global vegetation pattern

Abstract

The changes in the global vegetation pattern (GVP) under climatic and anthropogenic stress is one of the most important problems in global modelling. The idea of considering only two types of global vegetation (forest and grassland communities) instead of several dozen types (as is usually done in different ‘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 modelled, and recently it has been reanimated in a more general form by Brovkin et al. (Brovkin, V., Ganopolsky, A., Svirezhev, Y., 1997. Ecol. Model. 101, 251–261). Introducing into consideration the two spatial scales (the macro- and microscales, respectively) we use the macroscale for calculation of the function p( x, y, t) defined as a part of a macrounit occupied by forest communities. A macrounit is a macroscale area comprising a ‘forest–grass’ mosaic of elementary areas, each of them covered by either forest or grass. Each territorial microscale unit (microunit) is covered by only one type of vegetation. It is defined as one particle (‘forest’ or ‘grass’). One macrounit is considered to represent an ‘urn’ and special ‘urn’ schemes are used for its dynamic description. If only a ‘point’ evolution of GVP is studied, only local interactions (inside one macrounit) among microunits or particles are considered. The urn scheme corresponding to a simple ‘forest–grass’ model without age structure gives us equations which display a stable equilibrium only under unrealistic assumptions. But even the simplest account of age structure stabilises the system. The further generalisation of an age structure model for forest particles gives us a set of stable equilibria for very realistic conditions. The corresponding ‘urn’ scheme is a type of generalisation of the well-known ‘gap models’. Both discrete and continuous 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 young and mature trees is carried out.