Integration of Case Studies on Global Change by Means of Qualitative Differential Equations

We present a novel methodology to integrate qualitative knowledge from different case studies on Global Change related issues into a single framework. The method is based on the concept of qualitative differential equations (QDEs) which represents a mathematically well-defined approach to investigate classes of ordinary differential equations (ODEs) used in conventional modeling exercises. These classes are defined by common qualitative features, e.g., monotonicity, signs, etc. Using the QSIM-algorithm it is possible to derive the set of possible solutions of all ODEs in the class. By this one can formulate a common, qualitatively specified cause–effect scheme valid for all case studies. The scheme is validated by testing it against the actually observed histories in the study regions with respect to their reconstruction by the corresponding QDE. The method is outlined theoretically and exemplary applied to the problem of land-use changes due to smallholder agriculture in developing countries. It is shown that the seven case-studies used can be described by a single cause–effect scheme which thus constitutes a pattern of Global Change. As a generally valid prerequisite for sustainability of this kind of land-use the presence of wage labor is shown to represent a decisive factor.