Model selection in demographic time series using VC-bounds

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 (SLT); SLT is built around the idea of VC-dimension, a complexity index for classes of parameterized functions. Though VC-dimensions of nonlinear models are generally unknown, in the linear case VC-dimension actually corresponds to the number of free parameters; this allows one to straightforwardly apply the model selection framework developed within SLT, and called Structural Risk Minimization (SRM). We generate noisy artificial time series, both DI and DD, and use SRM to recognize the model underlying the data, choosing among a suite of both density-dependent and independent demographies. We show that SRM significantly outperforms traditional model selection approaches, such as the Schwartz Information Criterion and Final Prediction Error in recognizing both density-dependence and independence.