1 DTU Data Analysis, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
The variability of parameter estimates in microbiological degradation models has not received much attention in the literature. This in spite of the fact that the parameters are used in models for predicting and controlling microbiological processes of commercial interest. Furthermore, the accuracy of the parameter estimates are depending of the choice of estimation method, this fact has not either received much attention, all though an unsuitable estimation method can lead to estimates which are quite different from the ``true'' values. The present thesis describes various nonlinear estimation techniques and describes analysis techniques for testing the reproducibility of a given experiment. The parameter estimation method employed for the experiments in this study is based on an iterative maximum likelihood method and the test statistic is an approximated likelihood ratio test. The estimations were carried out by the nonlinear estimation program Dekimo (developed at IMM by Bilbo and Sommer), available on request. The program successfully fitted all experiments. A few estimations were also carried out by the Lineweaver-Burk linearization, but the estimated parameters fitted the data poorly due to the inappropriate estimation method. The examination of reproducibility/variability were carried out for two kinds of experiments: A single substrate experiment with toluene and a dual substrate experiment with toluene and benzene. A pure culture, isolated from soil, grew with benzene and/or toluene as the only carbon and energy source. The substrates were degraded in batches under aerobic conditions. The Monod model was employed to describe the biological processes in the single substrate system, and 'Bailey & Ollis' model was employed to describe the processes in the dual substrate system. In the single substrate system 9 identical experiments were performed on three different days, and in the dual substrate system 12 identical experiments were performed on four different days. The data are available on the address: http://www.imm.dtu.dk/documents/ftp/phdliste/phd31.abstract.html Experimental observations indicate that these microbiological degradation experiments have a limited reproducibility, i.e. that a common set of parameter estimates could not be employed to describe all experiments. However, experiments carried out on the same days (within runs) were more uniform than experiment carried out on different days (between runs). In the single substrate system a common sets of parameter estimates for experiments within runs fitted the data very well, whereas common sets of parameter estimates for experiments between runs fitted the data poorly and were moreover strongly rejected to be identical by the likelihood ratio test. In the dual substrate system a common set of parameter estimates could not be accepted nor within the runs neither between the runs. Never the less, experiments within the runs were more uniform compared to experiments carried out on different days (between the runs). The lag phases within runs were thus exactly the same, but were quite different from experiments from different runs. The limited reproducibility is probably caused by variability in the precultures, more precisely, variations in the activity level of the precultures just before used as inoculum. Facing the fact that these microbiological degradation experiments have a limited reproducibility one must in general expect large variability on the parameter estimates.