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Nonparametric estimation of rate equations for nutrient uptake

Abstract Knowledge of the rate of a biological process is important for characterizing the system and is necessary for gaining a deeper understanding of the process. Consider measurements, Y, made over time on a system following the model Y = f(t) + e, where f is a smooth, unknown function and e is measurement error. Although most statistical methodology has focused on estimating f(t) or f′(t), in some applications what is of real biological interest is the relationship between f and f′. One example is the study of nitrogen absorption by plant roots through a solution depletion experiment. In this case f(t) is the nitrate concentration of the solution surrounding the roots at time t and – f′(t) is the absorption rate of nitrate by plant roots at time t. One is interested in the rate of nitrate absorption as a function of concentration; that is, one is interested in Φ, where Φ(f) = – f′. Knowledge of Φ is important in quantifying the ability of a particular plant species to absorb nitrogen and in comparing...