Table 2

Parametric bootstrap test for the significance of additional predictor variables. Comparisons are made only across the best models previously selected with the GVC criterion. The models with previous disease levels and seasonality as the predictor variables are labeled as “dynamic seasonal,” and the model that in addition incorporates the ENSO index is labeled as “seasonal ENSO” (τf = 11). The mean, SD, and maximum (Max.) value of Δi r 2 are computed from the bootstrap data with n = 1000. We assess first the significance of adding the ENSO index as a predictor variable by considering the dynamic seasonal models as the null hypothesis. In all cases, the addition of ENSO as a predictor variable is highly significant (α = 0.001). We then assess the significance of considering previous disease levels as a predictor variable. We compare the seasonal ENSO model, which does incorporate previous disease levels, to the corresponding model built only from the seasonal clock and the ENSO index, which we label “environmental” (τf = 11, k = 3) . The environmental model performs poorly, withr 2 = 44% (even for an equal number of neurons k). The addition of previous disease levels as a predictor variable is highly significant (α = 0.001). For all comparisons, we also recorded the number of times that the cross-validation criterion failed to select the correct model (the null model). This frequency is given as the probability of Δi V c being negative in the last column. Results show that this frequency is extremely small for all comparisons.

Null modelAlternative modelObserved Δ0r2Mean Δir2SD Δir2Max. Δir2Prob. ΔiVc< 0
Dynamic seasonal (d = 1)Seasonal ENSO12.034.901.1210.300.03
Dynamic seasonal (d = 2)Seasonal ENSO9.932.001.777.610.024
EnvironmentalSeasonal ENSO23.371.471.186.460.069