FITTING NONLINEAR ENVIRONMENTAL GRADIENTS TO COMMUNITY DATA: A GENERAL DISTANCE-BASED APPROACH

A distance-based method is provided for the analysis and modeling of multivariate community data in response to a nonlinear gradient. Any reasonable dissimilarity measure can be used, and the method provides a natural extension from canonical analysis of principal coordinates (CAP) to nonlinear canonical analysis through the use of a link function, much like the extension of linear models to generalized linear models. The form of the nonlinear link function needs to be specified and will depend on the particular ecological system and the nature of the gradient. For example, an exponential decay curve could be used to model community structure after an environmental impact as a nonlinear function of time. This curve is used in our first example, where community structure is modeled as a nonlinear function of habitat size. Our second example uses a logistic curve to model change in community structure through a region of habitat transition from grassland to woodland. Computationally, this methodology uses a standard nonlinear optimization procedure to find the values of the parameters that maximize the correlation of the principal coordinates (obtained from an appropriately chosen distance measure) with the chosen form of nonlinear gradient. A simple randomization procedure is used to test the significance of the fitted nonlinear gradient over and above the fit of the linear gradient, and bootstrap confidence intervals for parameters are readily obtained. Any reasonable form of nonlinear gradient can be used, and it can be modeled as a nonlinear function of multiple environmental variables, making this a very flexible and versatile procedure for modeling multivariate ecological systems.

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