Moran Effect on Nonlinear Population Processes

Abstract

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.

Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models

“…In contrast, studies of cyclic red grouse populations in five different regions in northern England showed that climatic conditions in May and January can force the populations within each region to oscillate in synchrony (Cattadori et al 2005). This study does not report any travelling wave phenomena and instead suggests that, in these red grouse populations, cycles are synchronized by a Moran effect (Koenig 2002;Royama 2005). The differences in the findings of these two studies may be due in part to differences in the scale and the type of analysis.…”

Enhanced Moran effect by spatial variation in environmental autocorrelation

“…However, the cross-correlation of population density was consistently smaller than that of the environmental driving, r p or. This finding confirms results from field and theoretical studies 12,19,20,23 .…”

“…Given that environmental fluctuations can be spatially correlated over large distances, the Moran effect was considered as a major mechanism for generating population synchrony under natural [9][10][11][12][13][14] and laboratory conditions [15][16][17] . It was generalized to include nonlinear density dependence, populations in nonidentical habitats, the influence of dispersal, cyclic populations, species interactions and various combinations of these factors 9,12,[18][19][20][21][22][23] . All these studies found that the correlation of independent populations, not coupled by dispersal, remains bounded by the environmental correlation, r p rr, which should limit the Moran effect as a driver of population synchrony.…”

“…While spatial variability is commonly thought to reduce population synchrony 12,19,20,23 , here we perform a series of laboratory experiments to show that it may either suppress or enhance the intensity of noise-induced spatial synchronization: (i) in the absence of spatial variations (identical habitats and noise colours) we reproduce the Moran theorem, r p ¼ r; (ii) spatial variations in habitat properties suppress the Moran effect, r p or; and (iii) we provide evidence from experiments, theoretical analyses and numerical simulations that the Moran effect can be significantly enhanced, r p 4r, by spatial variations in environmental autocorrelation. Thus, our major finding is the counterintuitive result that the correlation between otherwise independent populations can be larger than that of their respective environments (enhanced Moran effect) if the populations experience environmental fluctuations with different noise colour.…”

Synchrony in tritrophic food chain metacommunities

“…Synchrony is the consequence of two independent factors: the dispersal of populations among patches and the existence of common meteorological driving forces (Moran effect). The theory is well established; see [10,29,42] for dispersal, [54] for the Moran effect, and [16] for the mixed case.…”