A class of compartmental models for long-distance tracer transport in plants

•Systematic comparison of models regarding quality of fit to tracer transport data.•Model class allows construction of numerous models with adjustable complexity.•A designated model filter removes irrelevant and redundant models.•Different optimal models were found for exemplary data sets.

Studies of long-distance tracer transport in plants result in spatio-temporal data sets. Compartmental tracer transport models can be used to quantitatively characterize or compare such data sets derived from different experiments. Depending on the specific experimental situation it might be necessary to apply different models. Here, we present a general class of compartmental tracer transport models which allows a systematic comparison of different models regarding the quality of fitting to the experimental data. This model class is defined by a system of partial differential equations (PDEs) for an arbitrary number of parallel compartments with individual transport velocities and numerous lateral exchange connections. A large number of model instances with adjustable complexity can be derived from this model class by permitting only certain model parameters such as flux velocities or exchange rates between compartments to be non-zero. Since some of these models are either inconsistent or redundant we designed a model filter using combinatory rules in order to keep only valid and unique models. A numerical solver for the PDEs was implemented using finite volumes and a weighted essentially non-oscillatory (WENO) scheme. Several candidate models were fitted to experimental data using a Monte Carlo multi-start strategy to approximate the global optimum within a certain parameter space. Analysis of exemplary tracer transport experiments on sugar beet, radish and maize root resulted in different best models depending on the respective data and the required fit quality.