Density dependence and the response surface methodology

Applying response surface methodology to ecological problems endeavours to disentangle the roles of endogenous and exogenous factors in population flu ctuations. We explored the reliability of response surface methodology in r evealing two fundamental properties of a given population series. whether t he density dependence is direct or delayed. and whether it is linear or non linear. This was done using simulated time series with known properties as well as a large set of real population time series. We show the importance of seeking the simplest form of the response surface among several alternat ives, by fitting a set of response surfaces from simple first order to more complex second order nonlinear models to each time series. Performance of the models was judged by three methods: cross-validation, adjusted coeffici ent of determination, and checking residual behaviour. The results show tha t with proper model validation. the response surface methodology is not onl y capable of finding the numerical relationship between population growth r ate and its size or density, bur can also be used to reliably reveal the de lay in density dependence when it is of significant importance. However, ju dging nonlinearity on the basis of the response surface is generally not as evident. We reanalysed the data sets of urchin and Taylor and show that va lidated analysis leads to a somewhat smaller set of dynamical alternatives being accepted. Finally, we applied the method to a long-term data set on t hree grouse species. The results show strong evidence for delayed density d ependency. Response surface methodology and data fitting to Royama's form o f feedback function show very convergent results.