Unfinished synchrony

Natural ecosystems, from rainforests to intestinal microbiomes, seem impossibly complicated. When consistent, large-scale statistical patterns are observed it is natural to ask whether they reflect the unseen actions of simpler universal processes—but what happens when these universal processes interact? Reuman et al. (1) use mathematical models to study the effect of combining two widely documented ecological phenomena: Taylor’s law (TL) and population synchrony. In doing so, they broaden the range of situations in which TL may be applied, as well as quantifying the effect that synchrony has on its predictions. This is particularly topical because synchrony is thought to be increasing as a result of climate change (2, 3).

Taylor (4) hypothesized that the mean of a sample of population counts and its variance are related via a power-law relationship: mean = a × (variance)^b. Taylor originally envisaged this as a quantitative measure of spatial aggregation. If the population is spatially aggregated, meaning that the individuals in the population tend to be located in clusters, the exponent b (also referred to as the slope) of TL will be >1. If the population is overdispersed, meaning that population members tend to be evenly spread, the exponent will be <1. If the population is distributed completely at random, then TL captures the “mean = variance” property of the Poisson distribution and so b = 1. TL therefore provides a way to infer spatial structure from population counts alone, without the need to observe the locations of individual population members.

The simplicity of TL has allowed its scope to be expanded considerably beyond its original use as a measure of spatial aggregation (5). Taylor’s original formulation deals with the mean and variance of population counts at different spatial locations, now referred to as spatial TL. This has since been extended to deal with the mean and variance calculated over different census times, referred to as temporal TL (6). When combined with the self-thinning law, which relates population density with body mass, TL leads to a prediction for the scaling of population variance with body mass (7, 8). Because TL deals with departures from the mean it has given insights into the ubiquitous effects of stochasticity in biology (9). It is estimated that TL has been established for at least 400 species (6, 10).

Cohen and Xu (11) showed that observations of TL ought not to be a surprise. They imagined an idealized world where each sampled population is independent of all others, and where all populations are statistically identical. In such a world, each sample at each census time is simply a random pick from a probability distribution. Their mathematical analysis showed that, provided this distribution is positively skewed (so that its mean is larger than its mode), TL always emerges. Cohen and Xu (11) do not claim that theirs is the only mechanism through which TL can arise, and other mechanisms have been proposed (6, 12). Nonetheless, the value of their simple model and transparent mathematical argument is that it allows scope for refinement, in this case to allow for the effect of synchrony.

Synchrony is the tendency for populations at geographically separate locations to be correlated. This often occurs as a result of a so-called Moran effect (13), for example due to similar prevailing weather conditions at nearby sites (Fig. 1A). We know that these environmental correlations can be at least as important as internal population dynamics (14), but the theory of Cohen and Xu (11) explicitly ignores any such correlations. The key advance made by Reuman et al. (1) is to generalize this theory to investigate the effects of synchrony on TL.

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Fig. 1.

(A) Moran effects occur when populations in distinct spatial locations experience similar environmental factors, for example prevailing weather conditions. (B) This can lead to some level of synchrony among populations being sampled at different sites. Each point in C shows the mean and variance across the six sampling sites at one of the 11 census times shown by vertical dotted lines in B. Spatial Taylor’s law says that a plot of log(mean) against log(variance) of population density is approximately linear. Reuman et al. (1) show that synchrony typically preserves the approximately linear relation but reduces the slope of TL.

Reuman et al. (1) ask two main questions. Is TL still valid when there is some synchrony among populations? If so, how does synchrony affect the slope of TL? They tackle these questions using mathematics and synthetically generated data and test their predictions using empirical data for aphid and plankton populations in the United Kingdom and for chlorophyll-a density off the coast of southern California. An empirical test of TL requires population samples over two axes of variation. In the case of spatial TL, these axes are spatial location and time, meaning that population samples are needed at different sites and at multiple census times (Fig. 1B). These two axes of variation give a single point estimate for the slope of TL. An empirical test of the theoretical prediction for the effect of synchrony on TL is more challenging because it requires a third axis of variation to provide a synchrony gradient. For Reuman et al. (1), this third axis is provided by the 20 species of aphid, 22 plankton groups, and 10 depths at which chlorophyll-a density was recorded.

The synthetic and empirical data show that, in most cases, TL is still valid when populations are synchronized but that synchrony tends to reduce the slope of TL (Fig. 1C). Some of the empirical datasets appear, at first glance, to contradict the theoretical predictions by exhibiting an increase in TL slope with synchrony. However, Reuman et al. (1) also test the effect of randomizing the time series at each site, which effectively destroys any synchrony that may have existed. By doing this, they tease the effects of synchrony apart from other factors and show that synchrony does reduce the slope of TL, as their theory predicts.

The type of synchrony considered by Reuman et al. (1) operates at the same spatial scale as that of the population sampling, so their study is effectively limited to linking large-scale synchrony and spatial TL. Intriguingly, if synchrony operates at finer spatial scales, meaning that different sampling sites become less correlated, this influences the slope of temporal TL (5, 15). This interplay between spatial and temporal scales of processes and measurements, and between the statistical phenomena of TL and synchrony, is not fully understood and offers a focus for future research. Frameworks linking theory to data, such as that provided by Reuman et al. (1), will be essential to this process.

The biological and socioeconomic value of maintaining diverse and functional ecosystems is generally acknowledged. The increasing environmental challenges of the Anthropocene all involve change, whether on global (e.g., climate) or microevolutionary (e.g., antimicrobial resistance) scales. Any empirically supported quantification of variability and its relation to spatiotemporal correlations is of fundamental value.