To fix or not to fix the species limits,that is the ecological question: Response to Jari Oksanen

Abstract. We respond to Oksanen's recent comments in “Why the beta-function cannot be used to estimate skewness of species responses”. We agree with Oksanen's criticisms concerning correlated parameters when fitting beta-functions. We argue that response functions can be reasonably estimated using beta-functions only for those species whose range limits obviously fall within the observed length of an environmental gradient and our original description included explicit recognition of this need. The simulated data used by Oksanen contains only one species that would meet our criteria for defining the limits and the shape of this species is recovered by fitting a beta-function. Beta-functions are shown to recover reasonable approximations of the true shapes when fitted to simulated data, generated without error, and representing species with either skewed or symmetrical response shapes if using realistic estimates of the species limits. When arbitrary limits are imposed then distorted shapes result. Using similar data from 500 simulated data sets generated under the assumption of a Poisson error structure, beta-functions gave conservative estimates of the degree of skewness for those data sets representing skewed species and no evidence of skewness for those data sets representing symmetrical species. We conclude that despite Oksanen's concerns the conclusions drawn by the current authors and colleagues with respect to the degree of skewness shown by species response functions along a common gradient are robust to the fitting procedures used. While we agree that the fitting of beta-functions is not the best approach to modelling skewed responses we argue that it will not mislead the user as to the presence or extent of skewness if used with reasonable and data driven estimates of the species limits.