A spatial matrix factorization method to characterize ecological assemblages as a mixture of unobserved sources: An application to fish eDNA surveys

Abstract

Understanding how ecological assemblages vary in space and time is essential for advancing our knowledge of biodiversity dynamics and ecosystem functioning. Metabarcoding of environmental DNA (eDNA) is an efficient method for documenting biodiversity changes in both marine and terrestrial ecosystems. However, current methods fail to detect and display the biodiversity structure within and between eDNA samples limiting ecological and biogeographical interpretations. We present a spatial matrix factorization method that identifies optimal eDNA sample assemblages—called pools—assuming that taxonomic unit composition is based on a fixed number of unknown sources. These sources, in turn, represent taxonomic units sharing similar habitat properties or characteristics. The method aims to reduce the multi‐taxa composition structure into a low number of dimensions defined by these sources. This method is inspired by admixture analysis in population genetics. Using a marine fish eDNA survey on 263 sampling stations detecting 2888 molecular operational taxonomic units (MOTUs), we apply this method to analyse the biogeography and mixing patterns of fish assemblages at regional and large scales. At large scale, our analysis reveals six primary pools of fish samples characterized by distinct biogeographic patterns, with some mixtures between these pools. We identify pools composed of unique sources, corresponding to distinct and more isolated regions such as the Mediterranean and Scotia Seas. We also identify pools composed of a greater mix of sources, corresponding to geographically connected areas, such as tropical regions. Additionally, we identify the taxa underpinning the formation of each pool. In the regional analysis of Mediterranean eDNA samples, our method successfully identifies different pools, allowing the detection of not only geographic gradients but also human‐induced gradients corresponding to protection levels. Spatial matrix factorization adds a new method in community ecology, where each sample is considered as a mixture of K unobserved sources, to assess the dissimilarity of ecological assemblages revealing environmental and human‐induced gradients. Beyond the study of fish eDNA samples, this method has the potential to shed new light on any biodiversity survey and provide new bioindicators of global change.