VC-dimension and structural risk minimization for the analysis of nonlinear ecological models

The problem of distinguishing density-independent (DI) from density-dependent (DD) demographic time series is important for understanding the mechanisms that regulate populations of animals and plants. We address this problem in a novel way by means of Statistical Learning Theory. First, we estimate the VC-dimensions of the best known nonlinear ecological models through the methodology proposed by Vapnik et al. (1994). Then, we generate noisy artificial time series, both DI and DD, and use Structural Risk Minimization (SRM) to recognize the model underlying the data from among a suite of alternative candidates. The method shows an encouraging ability in distinguishing between DI and DD time series.