All branches of ecology study relationships among environmental and biological variables. However, standard approaches to studying such relationships, based on correlation and regression, provide only a small slice of the complex information contained in such relationships. In Reuman Lab (USA), I explored the concepts that underpinned copulas and examined the potential for those concepts to improve our understanding of ecology for the first time (Ghosh, Sheppard, Holder, et al. 2020). Copulas provide a description of the dependence between two or more variables that can be mathematically proven to be complete (Joe 2014). Ranking each variable individually so that their respective marginals become uniform, copulas can isolate the underlying dependence structure, to be specific - the association between extreme values of corresponding variables (known as “tail-dependence”). Though the copula approach is used widely in finance or other quantitative science, in ecology it was rarely used and mainly was limited to hydrology. I introduced how this concept of “tail-dependence” could be impactful in various ecological fields to explore the occurrence, causes, and potential consequences.

Besides fitting data in a model-based parametric framework (max log-likelihood), I also came up with three computationally faster non-parametric measures (e.g., “partial Spearman correlation” approach) to measure such dependence. As often found in ecological data, dependence structures are distinct from that of a multivariate Gaussian/normal distribution - for analyzing non-Normal dependence, the copula is, indeed, a game changer.