The 1st part of the presentation will include a general description of the experimental results by Becks et al. (2005), who studied microbial food web dynamics in a chemostat, which was composed of a nutrient, two microbes (rods and cocci) that consumed nutrient, and a predator that consumed both microbes. For a fixed set of chemostat feeding rates, the three microbe concentrations were measured at approximately daily time intervals. Time series of concentrations produced both classical and apparently chaotic dynamics.
The results of the Becks et al. experiments motivated the development of a new mathematical model consisting of four coupled nonlinear differential equations, with the microbial populations as functions of time. Based on the results of experiments and modeling, a modified version of the Monod kinetics equation has been developed. The modified Monod equation is used to simulate that predators can change their preference for rods vs. cocci from 1:1 at low rod/cocci populations to 4:1 at high rod/cocci populations. Numerical solutions of the new system of equations show high sensitivity to initial conditions, and transition from steady state to periodic and deterministic chaotic oscillations of microbial populations. Examples of the deterministic chaotic 3-D attractors for certain parameter sets will be presented.
The 2nd part of the presentation will be devoted to attempts to introduce Shannon Information Theory and its extension to analyze the developed model. Calculations are based on the idea that a strange attractor can produce probability distributions for each of the underlying value sets of dependent variables, and probability distributions can be used to assess Shannon measures in an ecological context. Emphasis is on conceptual accuracy.
Additional lines of study are suggested, including: 1) extending the model to include a spatial dimension, thereby removing the assumption of instantaneous mixing, and 2)performing additional laboratory experiments to involve multiple microbial prey-predator populations.
About the Speaker: Fred Molz (Professor, Clemson University)
Dr. Molz’s teaching and research interests relate to hydraulics and contamiant transport in the groundwater-soil-plant-atmosphere system. Disciplines relevant to these interests include hydrology, soil physics, geochemistry, environmental biology, numerical modeling and nonlinear dynamics.
Recent research projects have involved computer modeling of transport processes in laboratory constructed wetlands, simulation of reactive plutonium transport in variably saturated soils exposed to climate and experimental/theoretical studies of turbulent sedimentation in flocculant-aided, storm-water retention ponds. Courses taught by Dr. Molz during the past decade included: Geohydrology, Groundwater and Contaminant Transport, Subsurface and Wetland Hydraulics, Surface and Subsurface Transport and Numerical Methods in Process Simulation (flow and transport). Consulting activities have made him aware of the acute environmental problems faced by government and industry.
Professor Fred Molz is a Collaborator on the Department of Energy, Experimental Program to Stimulate Competitive Research Implementation Project “Radionuclide Waste Disposal: Development of Multi-scale Experimental and Modeling Capabilities” (2014-Present).