Abstract
Standard methods for studying the association between two ecologically important variables provide only a small slice of the information content of the association, but statistical approaches are available that provide comprehensive information. In particular, available approaches can reveal tail associations, that is, accentuated or reduced associations between the more extreme values of variables. We here study the nature and causes of tail associations between phenological or population‐density variables of co‐located species, and their ecological importance. We employ a simple method of measuring tail associations which we call the partial Spearman correlation. Using multidecadal, multi‐species spatiotemporal datasets on aphid first flights and marine phytoplankton population densities, we assess the potential for tail association to illuminate two major topics of study in community ecology: the stability or instability of aggregate community measures such as total community biomass and its relationship with the synchronous or compensatory dynamics of the community's constituent species; and the potential for fluctuations and trends in species phenology to result in trophic mismatches. We find that positively associated fluctuations in the population densities of co‐located species commonly show asymmetric tail associations; that is, it is common for two species’ densities to be more correlated when large than when small, or vice versa. Ordinary measures of association such as correlation do not take this asymmetry into account. Likewise, positively associated fluctuations in the phenology of co‐located species also commonly show asymmetric tail associations. We provide evidence that tail associations between two or more species’ population‐density or phenology time series can be inherited from mutual tail associations of these quantities with an environmental driver. We argue that our understanding of community dynamics and stability, and of phenologies of interacting species, can be meaningfully improved in future work by taking into account tail associations.
Highlights
All ecologists study relationships between biological and environmental variables and among biological variables
The partial Spearman correlation associated with the bounds lb and ub will be the portion of the Spearman correlation attributable to the points that fall between these boundary lines
Our results show that synchronous population-density or phenological time series of co-located species can very commonly show asymmetric tail association
Summary
All ecologists study relationships between biological and environmental variables and among biological variables. Earlier work showed that average sea surface temperature is an important correlate of phytoplankton abundance in our data (e.g., Defriez, Sheppard, Reid, & Reuman, 2016; Sheppard, Defriez, Reid, & Reuman, 2019a; Sheppard, Reid, & Reuman, 2017): cold water is associated with more phytoplankton, likely because upwelling and mixing of the surface and deeper ocean layers bring both nutrients and cold water to the photic zone If it is the case for a given location that very cold water is associated with no more Ceratium, on average, than is moderately cold water, that corresponds to a positive relationship and a left-tail association between the “coldness” of the surface water (measured, for instance, by how many degrees colder the water is than average) and Ceratium abundance. This paper focuses on whether and why population-density or phenological time series of co-located species may show asymmetric patterns in their tail associations, with a focus on positively associated variables because positive associations are what occurred in the available data. Our results and the conceptual considerations introduced above are good evidence, in our view, of the potential for tail association to make a crucial difference in how ecologists understand these important topics
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