Codes: A new approach to interspecific synchrony in population ecology using tail association

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, i.e., 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, i.e., 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.