Quantification of non-power-law diversity scaling with local multifractal analysis

• Published in: Ecological informatics Vol. 48; pp. 48 - 59
• Main Authors: Yakimov, Basil N., Gelashvili, David B., Zhang, Yuxin, Markelov, Ivan N., Zhang, Shuang, Ma, Keming
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2018
• Subjects: Dominance; Effective diversity; Multifractal spectrum; Rarity; Renyi generalized dimensions; Spatial structure; Dominance; Renyi generalized dimensions; Rarity; Multifractal spectrum; Effective diversity; Spatial structure
• ISSN: 1574-9541
• DOI: 10.1016/j.ecoinf.2018.08.001

Description of spatial structure is in the focus of community ecology. Multifractal analysis is a prospective method because it connects fractal geometry tools with the conventional methodology of diversity analysis. The current version is based on a power-law scaling in the form of species-area relation. It is well suited for the description of self-similar communities. However, it is well known that many natural communities and theoretical models deviate from power-law diversity scaling. We propose to relax the requirement of self-similarity and introduce local multifractal analysis. This new method is based on a local approximation of the relation of effective diversity to scale. It is a fractal analysis in the sense of dealing with power-law approximations and estimation of scaling exponents within the framework of multifractal analysis. However, the multifractal spectra that resulted from this analysis do not characterize global scale-invariant properties but reflect details of diversity scaling specific for a given scale. In that sense, the analysis proposed is local. We present the results of analysis in theoretical and empirical contexts. Classical Fisher model of species abundance distribution deviate from power-law scaling and may be described with local multifractal spectra. We illustrate an empirical application in a case study of spatial structure of two temperate deciduous forests in different landscapes. Our approach provides new perspectives in the investigation of community spatial structure because it widens the scope of fractal analysis beyond self-similar communities. It may be adapted for other versions of multifractal analysis applied in community ecology. •The current version of multifractal analysis is restricted to self-similar communities.•We propose to relax the requirement of self-similarity and introduce local multifractal analysis.•We analyze the classic Fisher log-series SAD model.•We perform a case study of a spatial structure of two temperate forests.•Our approach provides new perspectives in the investigation of community spatial structure.