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Taylor’s law (TL) is a widely observed empirical pattern that relates the variances to the means of groups of nonnegative measure- ments via an approximate power law: variance_g ≈ a × mean_g^b, where g indexes the group of measurements. When each group of measurements is distributed in space, the exponent b of this power law is conjectured to reflect aggregation in the spatial dis- tribution. TL has had practical application in many areas since its initial demonstrations for the population density of spatially dis- tributed 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 loca- tions to be correlated through time. Recent studies showed that patterns of population synchrony are changing, possibly as a con- sequence 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 b 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. 

Abstract Taylor's law (TL), a commonly observed and applied pattern in ecology, describes variances of population densities as related to mean densities via log(variance) = log(a) + b*log(mean). Variations among datasets in the slope,b, have been associated with multiple factors of central importance in ecology, including strength of competitive interactions and demographic rates. But these associations are not transparent, and the relative importance of these and other factors for TL slope variation is poorly studied. TL is thus a ubiquitously used indicator in ecology, the understanding of which is still opaque.The goal of this study was to provide tools to help fill this gap in understanding by providingproximate determinants of TL slopes, statistical quantities that are correlated to TL slopes but are simpler than the slope itself and are more readily linked to ecological factors.Using numeric simulations and 82 multi‐decadal population datasets, we here propose, test and apply two proximate statistical determinants of TL slopes which we argue can become key tools for understanding the nature and ecological causes of TL slope variation.We find that measures based on population skewness, coefficient of variation and synchrony are effective proximate determinants. We demonstrate their potential for application by using them to help explain covariation in slopes of spatial and temporal TL (two common types of TL).This study provides tools for understanding TL, and demonstrates their usefulness. 

Abstract During the 1980s, the North Sea plankton community underwent a well‐documented ecosystem regime shift, including both spatial changes (northward species range shifts) and temporal changes (increases in the total abundances of warmer water species). This regime shift has been attributed to climate change. Plankton provide a link between climate and higher trophic‐level organisms, which can forage on large spatial and temporal scales. It is therefore important to understand not only whether climate change affects purely spatial or temporal aspects of plankton dynamics, but also whether it affects spatiotemporal aspects such as metapopulation synchrony. If plankton synchrony is altered, higher trophic‐level feeding patterns may be modified. A second motivation for investigating changes in synchrony is that the possibility of such alterations has been examined for few organisms, in spite of the fact that synchrony is ubiquitous and of major importance in ecology. This study uses correlation coefficients and spectral analysis to investigate whether synchrony changed between the periods 1959–1980 and 1989–2010. Twenty‐three plankton taxa, sea surface temperature (SST), and wind speed were examined. Results revealed that synchrony inSSTand plankton was altered. Changes were idiosyncratic, and were not explained by changes in abundance. Changes in the synchrony ofCalanus helgolandicusandPara‐pseudocalanusspp appeared to be driven by changes inSSTsynchrony. This study is one of few to document alterations of synchrony and climate‐change impacts on synchrony. We discuss why climate‐change impacts on synchrony may well be more common and consequential than previously recognized.