Higher-order dissimilarity in biodiversity: Identifying dissimilarities of spatial or temporal dissimilarity structures

Abstract

Elucidating biodiversity patterns and their background processes is critical in biodiversity science. Dissimilarity, which is calculated based on multivariate biological quantities, is a major component of biodiversity. As spatial and temporal biodiversity information availability increases, the scope of dissimilarity studies has been expanded to cover various levels and types of spatiotemporal biodiversity facets (e.g. gene, community and ecosystem function), and diverse pairwise dissimilarity indices have been developed. However, further development of the dissimilarity concept is required in comparative studies on spatiotemporal structures of biodiversity compositional patterns, such as those exploring commonalities of biogeographical boundaries among taxa, compared to the conventional ones to consider higher dimensions of dissimilarity: dissimilarity of dissimilarity structures. This study proposes a novel and general concept, higher-order dissimilarity (HOD), for quantitatively evaluating the dissimilarities of spatial or temporal dissimilarity structures among different datasets, proposes specific implementations of HOD as operational indices, and illustrates the potential resolution of scientific and practical questions through HOD. We further demonstrate the advantages of the HOD concept by applying it to actual patterns, such as long-term and/or large-spatial hypothetical monitoring datasets. Our conceptual framework on HOD extends the existing framework of biodiversity science and is versatile, with many potential applications in acquiring more valuable information from ever-increasing biodiversity data.