Multispecies spatial data arise in many applications where interactions between different entities are central to system behaviour, including biomedical imaging, geospatial analysis, and species ecology. Despite their importance, relatively few quantitative tools exist to capture such interactions. In this work, we propose magnitude-based features for the analysis of multispecies spatial data. Magnitude is a real-valued invariant of finite metric spaces that can be interpreted as an effective number of points, incorporating both spatial configuration and scale. We develop global and local magnitude feature vectors and demonstrate their utility on synthetic tumour microenvironment data, and in tissue microarray data from human colorectal cancer samples. Locally, the method identifies distinct neighbourhood types and reveals spatial heterogeneity; in the model, this includes radial patterns associated with different qualitative outcomes of the simulations, while in the real-world data it reflects the importance of tertiary lymphoid structure-like interactions between B and T cell populations. Globally, the approach recovers known classifications of long-term simulation outcomes across parameter regimes in synthetic data, and suggests important roles for CD4+ T cells and CD163+ macrophages in distinguishing patients with favourable Crohn's like reactions from unfavourable diffuse immune infiltration. Together, these results suggest that magnitude-based features provide a powerful and flexible tool for the analysis of multispecies spatial data.

翻译：多物种空间数据出现在许多应用中，其中不同实体之间的相互作用是系统行为的关键，包括生物医学成像、地理空间分析和物种生态学。尽管其重要性，但捕获此类相互作用的定量工具相对较少。在这项工作中，我们提出基于量值的特征用于分析多物种空间数据。量值是有限度量空间的一个实值不变量，可解释为有效点数，同时整合了空间构型和尺度。我们开发了全局和局部量值特征向量，并在合成肿瘤微环境数据以及人类结直肠癌样本的组织微阵列数据中展示了其实用性。在局部，该方法识别出不同的邻域类型并揭示空间异质性；在模型中，这包括与模拟不同定性结果相关的径向模式，而在现实世界数据中，它反映了B细胞和T细胞群体之间三级淋巴结构样相互作用的重要性。在全局，该方法在合成数据中跨参数区间恢复了长期模拟结果的已知分类，并提示CD4+ T细胞和CD163+巨噬细胞在区分具有有利克罗恩样反应与不利弥漫性免疫浸润的患者中起重要作用。总之，这些结果表明基于量值的特征为多物种空间数据分析提供了强大且灵活的工具。