Systematic error is of minor importance to feedback structure estimates derived from time series of nonlinear population indices

Abstract

Most modern population dynamics analyses of time series use simple population indices for ecological inference. These indices, collected for many years for various agricultural pests or game animals, are generally believed not to distort systematically feedback estimates because the assumption of linearity to population size roughly holds. To assess the relative importance of this assumption, we examined the effect of nonlinearity in a burrow index for voles on feedback estimates obtained through autoregressive modeling. We show that the issue of linearity is of less importance to ecological inference because the feedback estimates are routinely obtained on a logarithmic scale. Transforming data to logs has a strong linearization effect, removing most of the nonlinearity observed on the original scale. We conclude that the statistical tools for ecological inference, such as autoregressive log-linear models, are sufficiently robust to the systematic error imposed by index nonlinearity and that indices are valuable sources of ecological information even in situations when the assumed linear functional forms to population size were not exactly validated. We suggest that for time series modelers, the issue of a large sampling variation in small “noisy” populations is by far a more burning one than the systematic error due to index nonlinearity.