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Synchrony among population fluctuations of multiple coexisting species has a major impact on community stability, i.e. on the relative temporal constancy of aggregate properties such as total community biomass. However, synchrony and its impacts are usually measured using covariance methods, which do not account for whether species abundances may be more correlated when species are relatively common than when they are scarce, or vice versa. Recent work showed that species commonly exhibit such ‘asymmetric tail associations’. We here consider the influence of asymmetric tail associations on community stability. We develop a ‘skewness ratio’ which quantifies how much species relationships and tail associations modify stability. The skewness ratio complements the classic variance ratio and related metrics. Using multi-decadal grassland datasets, we show that accounting for tail associations gives new viewpoints on synchrony and stability; e.g. species associations can alter community stability differentially for community crashes or explosions to high values, a fact not previously detectable. Species associations can mitigate explosions of community abundance to high values, increasing one aspect of stability, while simultaneously exacerbating crashes to low values, decreasing another aspect of stability; or vice versa. Our work initiates a new, more flexible paradigm for exploring species relationships and community stability. This article is part of the theme issue ‘Synchrony and rhythm interaction: from the brain to behavioural ecology’. 

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 between 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.