Complexity in Soil Systems: What Does It Mean and How Should We Proceed?

Abstract:

The complex soil systems approach is needed fundamentally for the development of integrated, interdisciplinary methods to measure and quantify the physical, chemical and biological processes taking place in soil, and to determine the role of fine-scale heterogeneities. This presentation is aimed at a review of the concepts and observations concerning complexity and complex systems theory, including terminology, emergent complexity and simplicity, self-organization and a general approach to the study of complex systems using the Weaver (1948) concept of “organized complexity.” These concepts are used to provide understanding of complex soil systems, and to develop experimental and mathematical approaches to soil microbiological processes. The results of numerical simulations, observations and experiments are presented that indicate the presence of deterministic chaotic dynamics in soil microbial systems. So what are the implications for the scientists who wish to develop mathematical models in the area of organized complexity or to perform experiments to help clarify an aspect of an organized complex system? The modelers have to deal with coupled systems having at least three dependent variables, and they have to forgo making linear approximations to nonlinear phenomena. The analogous rule for experimentalists is that they need to perform experiments that involve measurement of at least three interacting entities (variables depending on time, space, and each other). These entities could be microbes in soil penetrated by roots. If a process being studied in a soil affects the soil properties, like biofilm formation, then this effect has to be measured and included. The mathematical implications of this viewpoint are examined, and results of numerical solutions to a system of equations demonstrating deterministic chaotic behavior are also discussed using time series and the 3D strange attractors.