Statistical analysis of functional response experiments

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Abstract
The aim of this paper is to highlight the benefits of a full data analysis of a functional response data set, compared to the usual one‐pass regression analysis. In a biological control setting where the choice of organism is often based on comparative studies of the functional responses, it is imperative to have both reliable estimates and a feeling of the degree of confidence one is willing to put on the figures. We analyzed a data set involving the freshwater predator Notonecta glauca (Hemiptera) preying on Asellus aquaticus during 24 h. The specific aim of the analysis was to test whether the functional response is of type II or type III. The different stages of a complete analysis are (1) a preliminary inspection of the data, (2) model building, (3) a model check and (4) a combination of the results with independent information. We argue that the analysis is best done with the predation rate as response and define a test for the location of its maximum. The existence of a maximum is typical for type III functional response. We explain why the binomial distribution is a natural error distribution, and how to implement the regression analysis within the family of generalized linear models using two competing link functions, the logit and the reciprocal. There is marked overdispersion which increases with increasing prey numbers. We use prior weights to take account of it. Using all available data, a type III functional response is warranted with the reciprocal link, but not with the logit link Model checks using Pearson residuals and regression diagnostics based on point deletions show that three points have a particularly strong influence on the parameter estimates. If these are deleted, the functional response type III is then warranted for both link functions. The complete analysis enables us to determine the various degrees of uncertainty and to draw biological conclusions with corresponding confidence. We are convinced that the data set shows a type III functional response, but we are less sure about which link function to choose. Furthermore, the marked overdispersion at high density, the regression diagnostics, as well as independent information on a change in the behaviour of the prey at high density, indicate that the experimental conditions may have changed as a function of the prey density.