Synchrony affects Taylor's law in theory and data.

Abstract

Taylor's law (TL) is a widely observed empirical pattern that relates the variances to the means of groups of nonnegative measurements via an approximate power law: variance _<i>g</i> ≈ <i>a</i> [Formula: see text] mean _<i>g</i>^<i>b</i> , where <i>g</i> indexes the group of measurements. When each group of measurements is distributed in space, the exponent <i>b</i> of this power law is conjectured to reflect aggregation in the spatial distribution. TL has had practical application in many areas since its initial demonstrations for the population density of spatially distributed species in population ecology. Another widely observed aspect of populations is spatial synchrony, which is the tendency for time series of population densities measured in different locations to be correlated through time. Recent studies showed that patterns of population synchrony are changing, possibly as a consequence of climate change. We use mathematical, numerical, and empirical approaches to show that synchrony affects the validity and parameters of TL. Greater synchrony typically decreases the exponent <i>b</i> of TL. Synchrony influenced TL in essentially all of our analytic, numerical, randomization-based, and empirical examples. Given the near ubiquity of synchrony in nature, it seems likely that synchrony influences the exponent of TL widely in ecologically and economically important systems.