Moran effect on nonlinear population processes

I investigate the efficacy of the Moran effect as applied to natural population processes. The Moran effect, the correlated density-independent disturbances that bring independently oscillating local populations into synchrony, was originally conceived as an attribute of a linear model system. However, it applies only approximately to natural populations. as they are inherently nonlinear in their density-dependent structure, given that no animal has an unlimited reproductive capacity. The degree of approximation, as measured by the degree of correlation among populations involved, is shown to depend, given the density-dependent structure, on the variances of the random disturbances. In particular, if the unperturbed density-dependent process converges to an equilibrium density, approximation is good when the variances are equal among the populations involved and comparatively small, but it worsens as the variances and their differences increase. For those processes that do not converge, when unperturbed, but exhibit bounded oscillations, the degree of approximation tends to deteriorate considerably, or may practically collapse, even if the disturbances are not large in variance. A sample correlation coefficient is often spurious if the observed population processes to be correlated are highly autocorrelated and limited in length. To detect spuriousness, the density-independent disturbances must somehow be estimated from the data. Three methods (moving-average, linear regression, and nonlinear regression) are considered, and their merits and demerits are discussed. Results of the present investigation are summarized with respect to the interpretations (or diagnoses) of sample cross-correlation functions.