A Fractal Analysis of Biodiversity: The Living Planet Index

Abstract

The Living Planet Index (LPI) is a global index which measures the state of the world\textquotesingle s biodiversity. Analyzing the LPI solely by statistical trends provides, however, limited insight. Fractal Regression Analysis is a recently developed tool that has been successfully applied in multidisciplinary scientific contexts for time series analysis. This method is based on the construction of a fractal function tailored to the dataset from which directional coefficients, representing trends, and fractal coefficients, representing oscillations, may be computed. These coefficients allow us to classify the world\textquotesingle s regions according to the progression of the LPI, helping us to identify and mathematically characterize the region of Latin America and Caribbean and the category of freshwater as worst-case scenarios with respect to the evolution of biodiversity.

Keywords: Living Planet Index, fractal regression, functional equations, biodiversity, fractal coefficient