Marine provinces rarely include fine-resolution biological data, and are often defined spatially across only latitude and longitude. Therefore, we aimed to determine how phytoplankton distributions define marine provinces across 3-dimensions (i.e., latitude, longitude, and depth). To do this, we developed a new algorithm called \texttt{bioprovince} which can be applied to compositional biological data. The algorithm first clusters compositional samples to identify spatially coherent groups of samples, then makes flexible province predictions in the broader 3d spatial grid based on environmental similarity. We applied \texttt{bioprovince} to phytoplankton Amplicon Sequencing Variants (ASVs) from five, depth-resolved ocean transects spanning north-south in the Pacific Ocean. In the surface layer of the ocean, our method agreed well with traditional Longhurst provinces. In some cases, the method revealed that with more granular taxonomic resolution afforded by ASVs, traditional Longhurst provinces were divided into smaller zones. Also, one of the major advances of this method is its ability to incorporate a third dimension, depth. Indeed, our analysis found significant depth-wise partitions throughout the Pacific with remarkable agreement in the equatorial region with the base of the euphotic zone. Our algorithm's ability to delineate 3-dimensional bioprovinces will enable scientists to discover new ecological interpretations of marine phytoplankton ecology and biogeography. Furthermore, as compositional biological data inherently exists in three spatial dimensions in nature, bioprovince is broadly applicable beyond marine plankton, offering a more holistic perspective on biological provinces across diverse environments.

翻译：传统海洋生物地理区系划分通常缺乏高分辨率的生物数据支撑，且多局限于经纬度二维空间框架。为此，本研究旨在探究如何依据浮游植物分布特征构建包含纬度、经度和深度信息的三维海洋生物地理区系。我们开发了一种适用于群落组成数据的全新算法——\texttt{bioprovince}。该算法首先对群落组成样本进行聚类以识别空间连贯的样本群组，继而基于环境相似性在三维空间网格中生成灵活的区系预测。我们将\texttt{bioprovince}算法应用于太平洋南北向五个深度解析航线的浮游植物扩增子序列变异体（ASVs）数据。在海洋表层，本方法与传统Longhurst区系划分结果高度吻合。在某些案例中，得益于ASVs提供的更高分类学分辨率，传统Longhurst区系被进一步细化为更精细的生态单元。本方法的重要突破在于能够整合第三维度——深度。分析结果显示太平洋水域存在显著的垂直分层现象，其中赤道区域的分区边界与真光层底部呈现高度一致性。该算法刻画三维生物区系的能力，将助力科学家重新阐释海洋浮游植物生态学与生物地理学规律。此外，鉴于自然界生物群落数据本质存在于三维空间，\texttt{bioprovince}算法在海洋浮游生物研究之外具有广泛适用性，可为不同环境下的生物地理区系研究提供更全面的分析视角。