Maximum likelihood estimation of primary productivity coefficients

Computing parameters of primary productivity models from empirical data encounters the difficulty that Liebig's law of minimum is involved. For many of the data points used to fit the model it may not be evident which factor is the respective limiting one; it may even be different from the independent variables used. The introduction of a suitable statistical data model, however, allows a Maximum Likelihood procedure to be applied which simultaneously optimizes the parameters and classifies the data. Moreover, the proposed procedure is quite insensitive to data points whose limiting factor is not contained in the actual set of independent variables. Applicability of the method is demonstrated using a set of productivity measurements compiled by H. Lieth in 1975; numerical results, of course, may be subject to change as more data become available.