Species distribution models (SDMs) are widely used to assess the effects of environmental factors on species distributions. However, classical SDMs ignore inter-species dependencies. Multivariate SDMs (MSDMs), especially those based on latent Gaussian fields such as the multivariate Poisson log-normal (MPLN), address this limitation but face challenges related to computation, dimensionality, and interpretability. Pólya-splitting (PS) distributions offer an alternative, combining a model for total abundance with a multivariate allocation structure, and have natural interpretations from ecological process models. Yet, they lack flexibility in modeling correlation structures. Tree Pólya-splitting (TPS) distributions overcome this by introducing hierarchical structure such as a phylogenetic tree. In this paper, we extend TPS to account for zero-inflation, leading to the zero-inflated tree Pólya-splitting (Z-TPS) family. We detail its statistical properties, show how standard software enables efficient inference, and illustrate its ecological relevance using tree abundance data from over 180 genera across the Congo Basin tropical rainforest.

翻译：物种分布模型（SDMs）被广泛用于评估环境因素对物种分布的影响。然而，经典SDMs忽略了物种间的相互依赖性。多元SDMs（MSDMs），特别是那些基于潜高斯场（如多元泊松对数正态（MPLN））的模型，虽然解决了这一局限，但在计算、维度和可解释性方面面临挑战。波利亚分裂（PS）分布提供了一种替代方案，它结合了总丰度模型与多元分配结构，并从生态过程模型中获得了自然的解释。然而，它们在建模相关结构方面缺乏灵活性。树波利亚分裂（TPS）分布通过引入层次结构（如系统发育树）克服了这一不足。在本文中，我们扩展了TPS以处理零膨胀问题，从而提出了零膨胀树波利亚分裂（Z-TPS）分布族。我们详细阐述了其统计特性，展示了如何使用标准软件实现高效推断，并利用来自刚果盆地热带雨林180多个属的树木丰度数据说明了其生态相关性。