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Applying response surface methodology to ecological problems endeavours to disentangle the roles of endogenous and exogenous factors in population fluctuations. We explored the reliability of response surface methodology in revealing two fundamental properties of a given population series: whether the density dependence is direct or delayed, and whether it is linear or nonlinear. 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 alternatives, 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 coefficient of determination, and checking residual behaviour. The results showthat with proper model validation, the response surface methodology is not only capable of finding the numerical relationship between population growth rate and its size or density, but can also be used to reliably reveal the delay in density dependence when it is of significant importance. However, judging nonlinearity on the basis of the response surface is generally not as evident. We reanalysed the data sets of Turchin and Taylor and show that validated analysis leads to a somewhat smaller set of dynamical alternatives being accepted. Finally, we applied the method to a long-term data set on three grouse species. The results show strong evidence for delayed density dependence.Response surface methodology and data fitting to Royamais form of feedback function show very convergent results. [ABSTRACT FROM AUTHOR]

We studied the spatial covariation of breeding success of black grouse and capercaillie and densities of mammalian generalist predators in Finland. Our study was based on six years' data from the Finnish wildlife triangle censuses (1989--1994). At the nation-wide level (100 x 100 km grids), the proportion of hens with a brood in August covaried regionally in the two species and decreased towards southern Finland, whereas the brood sizes were not related to latitude. The relative densities of red fox and pine marten correlated negatively with theproportion of grouse hens with a brood and were two- to three-fold higher in southernmost Finland than elsewhere in the country. The relative density of stoat, however, increased with latitude. The results support the hypothesis that higher generalist predator densities are responsible for lower breeding success of forest dwelling grouse moving southwards in Fennoscandia. The results also suggest that the stoat is of minor importance as nest and brood predator compared to red fox and pine marten. In northern Finland, on a smaller spatial scale (about 25 km2), the increasing red fox density decreased the probability of an observed grouse hen being with a brood in low vole years, whereas in years of high vole densities no effect was detected in logistic regression analysis. In contrast to northern results, the red fox density in southern Finland, although generally higher, did not predict the spatial variation in breeding success of grouse either in high or in low vole years. The brood size of grouse was not related to red fox density. Our results agree with the alternative prey hypothesis in northern, but not in southern Finland. In addition tohigher amplitude of vole cycles in northern than in southern Finland, this inconsistency can probably be related to regional differences in both prey and predator communities. [ABSTRACT FROM AUTHOR]