Modeling of complex ecosystems, extension of deserts and violation of the short water cycle

Abstract

The large ecosystems (region, country, and planet) have many properties common with complex systems. The main such characteristics include dynamic instability (e.g. weather dependence), weak causality (many possible causes per event) and event driven behavior (especially in arid and semi-arid areas). This paper focuses attention on modeling ecosystems by approaches used for complex systems.When modeling complex ecosystems, we usually encounter the following difficulties: partiality, large amounts of data and uncertainties of conclusions. It can be said that none of the known approaches solves these difficulties perfectly. The most common is the physical approach, sometimes reinforced by statistical procedures. The physical approach to modeling leads to a complicated description of phenomena associated with relatively simple geometry. A complicated description usually requires a large amount of data (measured or simulated) and thus more complicated calculations. If we assume emergences in the ecosystem, a physical approach is not appropriate at all. In the presented article we apply the approach of so-called structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complex geometry (in our case pre geometry). It does not require as much data and calculations are simple. The price paid is a qualitative interpretation of the results, which carries a special type of uncertainty. The structural invariant used in the article is the invariant Matroid and Bases of Matroid (M, BM) in combination with Ramsey graph theory. In addition, the article introduces a calculus that describes the emergent phenomenon using two quantities - the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. The developed method is used for a novel application of modeling the process of desertification of Earth. In this approach, we understand desertification as an emergent evolutionary operation of the Earth's development. In the sequence of two large previous emergences (warming of the Earth about 11,700 years ago and drying of the earth beginning about6000 years ago), the time of possible further emergences related to the “desert expansion” operation is calculated. The second application of the method is the analysis of the operation “violation of Short Water Cycle” in the landscape and its possible contribution to the desertification.