Structural risk minimization: a robust method for density-dependence detection and model selection

Statistically distinguishing density-dependent from density-independent populations and selecting the best demographic model for a given population are problems of primary importance. Traditional approaches are PBLR (parametric bootstrapping of likelihood ratios) and Information criteria (IC), such as the Schwarz information criterion (SIC), the Akaike information criterion (AIC) or the Final prediction error (FPE). While PBLR is suitable for choosing from a couple of models, ICs select the best model from among a set of candidates. In this paper, we use the Structural risk minimization (SRM) approach. SRM is the model selection criterion developed within the Statistical learning theory (SLT), a theory of great generality for modelling and learning with finite samples. SRM is almost unknown in the ecological literature and has never been used to analyze time series. First, we compare SRM with PBLR in terms of their ability to discriminate between the Malthusian and the density-dependent Ricker model. We rigorously repeat the experiments described in a previous study and find out that SRM is equally powerful in detecting density-independence and much more powerful in detecting density-dependence. Then, we compare SRM against ICs in terms of their ability to select one of several candidate models; we generate, via stochastic simulation, a huge amount of artificial time series both density-independent an