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Spatial synchrony may be tail‐dependent, that is, stronger when populations are abundant than scarce, or vice‐versa. Here, ‘tail‐dependent’ follows from distributions having a lower tail consisting of relatively low values and an upper tail of relatively high values. We present a general theory of how the distribution and correlation structure of an environmental driver translates into tail‐dependent spatial synchrony through a non‐linear response, and examine empirical evidence for theoretical predictions in giant kelp along the California coastline. In sheltered areas, kelp declines synchronously (lower‐tail dependence) when waves are relatively intense, because waves below a certain height do little damage to kelp. Conversely, in exposed areas, kelp is synchronised primarily by periods of calmness that cause shared recovery (upper‐tail dependence). We find evidence for geographies of tail dependence in synchrony, which helps structure regional population resilience: areas where population declines are asynchronous may be more resilient to disturbance because remnant populations facilitate reestablishment.

Extreme climatic events (ECEs) are becoming more frequent and more intense due to climate change. Furthermore, there is reason to believe ECEs may modify tail associations between distinct population vital rates, or between values of an environmental variable measured in different locations. Tail associations between two variables are associations that occur between values in the left or right tails of the distributions of the variables. Two positively associated variables can be principally left‐tail associated (i.e., more correlated when they take low values than when they take high values) or right‐tail associated (more correlated when they take high than low values), even with the same overall correlation coefficient in both cases. We tested, in the context of non‐spatial stage‐structured matrix models, whether tail associations between stage‐specific vital rates may influence extinction risk. We also tested whether the nature of spatial tail associations of environmental variables can influence metapopulation extinction risk. For instance, if low values of an environmental variable reduce the growth rates of local populations, one may expect that left‐tail associations increase metapopulation extinction risks because then environmental catastrophes are spatially synchronized, presumably reducing the potential for rescue effects. For the non‐spatial, stage‐structured models we considered, left‐tail associations betweenmore »vital rates did accentuate extinction risk compared to right‐tail associations, but the effect was small. In contrast, we showed that density dependence interacts with tail associations to influence metapopulation extinction risk substantially: For population models showing undercompensatory density dependence, left‐tail associations in environmental variables often strongly accentuated and right‐tail associations mitigated extinction risk, whereas the reverse was usually true for models showing overcompensatory density dependence. Tail associations and their asymmetries are taken into account in assessing risks in finance and other fields, but to our knowledge, our study is one of the first to consider how tail associations influence population extinction risk. Our modeling results provide an initial demonstration of a new mechanism influencing extinction risks and, in our view, should help motivate more comprehensive study of the mechanism and its importance for real populations in future work.

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Periodical cicadas exhibit an extraordinary capacity for self‐organizing spatially synchronous breeding behavior. The regular emergence of periodical cicada broods across the United States is a phenomenon of longstanding public and scientific interest, as the cicadas of each brood emerge in huge numbers and briefly dominate their ecosystem. During the emergence, the 17‐year periodical cicada speciesMagicicada cassiniis found to form synchronized choruses, and we investigated their chorusing behavior from the standpoint of spatial synchrony.

Cicada choruses were observed to form in trees, calling regularly every five seconds. In order to determine the limits of this self‐organizing behavior, we set out to quantify the spatial synchronization between cicada call choruses in different trees, and how and why this varies in space and time.

We performed 20 simultaneous recordings in Clinton State Park, Kansas, in June 2015 (Brood IV), with a team of citizen‐science volunteers using consumer equipment (smartphones). We use a wavelet approach to show in detail how spatially synchronous, self‐organized chorusing varies across the forest.

We show how conditions that increase the strength of audio interactions between cicadas also increase the spatial synchrony of their chorusing. Higher forest canopy light levels increase cicada activity, corresponding to faster and higher‐amplitude chorus cycling and tomore »greater synchrony of cycles across space. We implemented a relaxation‐oscillator‐ensemble model of interacting cicadas, finding that a tendency to call more often, driven by light levels, results in all these effects.

Results demonstrate how the capacity to self‐organize in ecology depends sensitively on environmental conditions. Spatially correlated modulation of cycling rate by an external driver can also promote self‐organization of phase synchrony.

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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 economicallymore »important systems.« less