Virtual Biospheres: Complexity versus Simplicity

A different view of these questions would be to ask how the complexity of the biosphere connects with these problems. This complexity may connect with a sufficiently complex arrangement of the biosphera machina including a lot of different positive and negative feedback systems, a tangled network of different causal loops, and so forth. But the complexity may also be defined by different multiple equilibria when either one equilibrium or others can be attained as a result of multiple bifurcations when the evolutionary tree has a very complex topology. In order to answer these questions, we consider the system “biosphere + climate” as a nonlinear system with multiple equilibria. Note that in considering this problem we shall remain within a framework of simple, zero-dimensional models. It is necessary to say a few words about the history of this problem. It seems to us that it was first formulated in 1926 (at a qualitative level, of course) by V. Vernadsky2 in the form of an idea about the interdependence between vegetation and climate. Then Kostitzin3 realized this idea in the form of the first mathematical model for co-evolution of the atmosphere (climate) and biota. It is interesting that he obtained the époques glaciers as self-oscillations of this system. Recently, Watson and Lovelock4 further developed Vernadsky’s idea. They considered the causal loop between surface temperature and two types of vegetation (by means of albedo). The