Maximum likelihood prediction of lake acidity based on sedimented diatoms

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Abstract
As an example of ecological gradient analysis, Gaussian response functions, with Poisson or quasi‐Poisson error distribution, were fitted for diatom taxa on a pH gradient. It is possible to predict or infer the pH of lake water from the fitted curves using the method of maximum likelihood, which is easily implemented in standard non‐linear regressionprograms. Due to overdis‐persion with respect to the Poisson distribution, moment estimates forthe negative binomial distribution were also applied, both in estimating the species response curves and in prediction. Simulations indicated that the theoretical maximum precision (measuredby standard deviation of prediction errors) in our data set was 0.17 pH units. The observed errors were much greater (SD 0.35 to 0.43). It seems that roughly equal proportions of the excess error were caused (1) by systematic differences between the training (estimation) data and the validation (prediction) data, and (2) from a misspecified model. It is suggested that the error due to model misspecification consists of inadequacy of the presumed error distribution and of inadequacy of the simple Gaussian response function.