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Mineralization of terbuthylazine
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<p><strong>This example is part of the <a class="external-link" href="https://groups.nceas.ucsb.edu/non-linear-modeling/projects">NCEAS non-linear modelling project</a></strong></p>
<p><strong>By Anders Nielsen</strong></p>
<p>Terbuthylazine is a herbicide used in agriculture. It is a so-called s-triazin like atrazine, which has been banned in Denmark after suspicion of causing cancer.<br />Terbuthylazine can be bound to the soil, but free terbuthylazine can be washed into the drinking water. Some bacteria can mineralize it. This data is part of a larger experiment to determine the ability of certain bacteria to mineralize terbuthylazine, and to estimate the mineralization rate.</p>
<p>This is a fairly straightforward nonlinear least-squares problem, with normally distributed residuals and no random effects or latent variables. The deterministic part of the model is the solution to a set of coupled ordinary differential equations (ODEs) for the concentrations in different compartments. Because the ODEs are linear, the deterministic solution can be found directly in terms of a matrix exponential, for which functions exist in all three of ADMB, BUGS, and R. From there it is simply a matter of defining a normal likelihood, or equivalently a least-squares expression, and minimizing it. The main differences appear in the speed and robustness of the matrix exponential formulations in different software tools.</p>
<p><a class="external-link" href="https://groups.nceas.ucsb.edu/non-linear-modeling/projects/min/WRITEUP/min.pdf">Documentation</a></p>
<p><a class="external-link" href="https://groups.nceas.ucsb.edu/non-linear-modeling/projects/min">Source code</a></p>
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