reply: Nonlinearity and the Moran effect

Grenfell et al. reply — The Moran effect refers to systems of population dynamics that are linear: under these circumstances, the long-term correlation between population densities will be the same as the correlation between the random environmental perturbations. The Soay sheep exhibit significant nonlinearity in their density dependence (Fig. 2a of ref. 1). At low populations, numbers tend to increase exponentially, with mean growth rate r=0.24, whereas at high densities (above a threshold of 1,172 animals), the population tends to decline, with mean r=−0.29. Thus, when populations on two adjacent islands are both above their thresholds, both will tend to decline, and when both are below their thresholds, both will tend to increase.