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. [V. Vapnik, E. Levin, Y. Cun, Measuring the VC-dimension of a learning machine, Neural Comput. 6 (1994) 851-876]. 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.