Quantification of ecological complexity and resilience from multivariate biological metrics datasets using singular value decomposition entropy

Abstract

The concept of resilience has become popular in many disciplines far beyond its original use in the field of ecology. Despite of its wide use, it has received different definitions not always coincident. Such ambiguity is still more evident in its quantitative characterization. Most of the available methods are heavily context dependent and often difficult to apply in the practice. Here, we propose to define and calculate resilience starting from the data matrices resulting from multivariate measurements of different biological metrics.

• The resilience between two field scenarios (each one characterized by their corresponding datasets) can be conveniently captured as the difference between its respective data complexities.

• Complexity is quantified by means of the entropy associated to the spectral distribution of the singular values of each data matrix.

• The method proposed has been illustrated with a case study in which the resilience of a river (Ebro River, NE Spain) is calculated comparing six biological metrics associated to the phytoplankton, upstream and downstream to a series of large reservoirs that alter the natural river flow regime.