1. Comparative biological studies often investigate the morphological, physiological or ecological divergence (or overlap) between entities such as species or populations. Here we discuss the weaknesses of using existing methods to analyse patterns of phenotypic overlap and present a novel method to analyse co‐occurrence in multidimensional space.
2. We propose a ‘hyperoverlap’ framework to detect qualitative overlap (or divergence) between point datasets and present the hyperoverlap r package which implements this framework, including functions for visualization. hyperoverlap uses support vector machines (SVMs) to train a classifier based on point data (such as morphological or ecological data) for two entities. This classifier finds the optimal boundary between the two sets of data and compares the predictions to the original labels. Misclassification is an evidence of overlap between the two entities. We demonstrate the theoretical and practical advantages of this method compared to existing approaches (e.g. single‐entity hypervolume models) using the bioclimatic data extracted from global occurrence records of conifers.
3. We find that there are instances where single‐entity hypervolume models predict overlap, but there are no observations of either entity in the shared hypervolume. In these instances, hyperoverlap reports nonoverlap. We show that our method is stable and less likely to be affected by sampling biases than current approaches. We also find that hyperoverlap is particularly effective for situations involving entities with a small number of data points (e.g. narrowly endemic species) for which single‐entity models cannot be reliably constructed.
4. We argue that overlap can be reliably detected using hyperoverlap, particularly for descriptive studies. The method proposed here is a valuable tool for studying patterns of overlap in a multidimensional space.

中文翻译：

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超重叠：检测n维空间中的生物重叠

1. 比较生物学研究经常调查实体（例如物种或种群）之间的形态，生理或生态差异（或重叠）。在这里，我们讨论使用现有方法分析表型重叠模式的缺点，并提出一种分析多维空间中共现的新方法。
2. 我们提出了一个“ hyperoverlap”框架来检测点数据集之间的定性重叠（或发散），并提出了实现该框架的hyperoverlap r包，包括可视化功能。hyperoverlap使用支持向量机（SVM）来基于两个实体的点数据（例如形态或生态数据）训练分类器。该分类器找到两组数据之间的最佳边界，并将预测结果与原始标签进行比较。分类错误是两个实体重叠的证据。通过使用从针叶树全球发生记录中提取的生物气候数据，我们证明了该方法与现有方法（例如单实体超体积模型）相比的理论和实践优势。
3. 我们发现，在某些情况下，单实体超容量模型会预测重叠，但是在共享超容量中没有观察到任何实体。在这些情况下，超重叠报告为非重叠。我们表明，与当前方法相比，我们的方法稳定且受采样偏差的影响较小。我们还发现，对于涉及数据点数量少的实体（例如狭义地方物种）的实体无法可靠构建单实体模型的情况，超重叠特别有效。
4. 我们认为，使用超重叠可以可靠地检测到重叠，特别是对于描述性研究而言。此处提出的方法是研究多维空间中重叠模式的宝贵工具。