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.

Methods
Plankton data preprocessing steps were the same as used by Ghosh et al. (Advances in Ecological Research 62:409–468., 2020).  First, to reduce the

effects of sampling variation on statistical results, we chose the subset of locations for which more than 35 years of data were available for all species. Second, for a given location, we excluded Ceratium species that were undetected for more than 10% of sampled years at that location. Finally, we considered only those locations for which at least two Ceratium species remained. Sea surface temperature data preprocessing was the same as used by Sheppard et al. (EPJ Nonlinear Biomedical Physics 5:1, 2017). Aphid's phenology data were a subset of a larger dataset covering 11 locations, analyzed previously by Sheppard et al. (Nature Climate Change 6:610, 2016) and Ghosh et al. (Advances in Ecological Research 62:409-468., 2020). Data preprocessing was the same as that of Sheppard et al. (2016). Locations were screened, leading to the removal of one of the original 11 sampling locations, by requiring at least 30 years of data be available for all species, again to reduce sampling variation of statistics. We also had time series of winter average temperature for each location and year. The winter temperature for year t was the average of December of year t -1 to March of year t.