Zero-inflated binary Tree P\'olya splitting regression for multivariate count data

2026-01-21

AI Summary

This study addresses the limitations of traditional species distribution models, which often neglect interspecific dependencies and struggle with high-dimensional, zero-inflated multispecies abundance data due to computational inefficiency, poor interpretability, and inadequate representation of complex correlation structures. To overcome these challenges, we propose the Zero-inflated Tree-structured Pólya Split (Z-TPS) model, which uniquely integrates a zero-inflation mechanism into a tree-structured Pólya partition framework. By leveraging phylogenetic tree information, Z-TPS decouples total abundance from multivariate allocation processes, substantially enhancing its ability to capture excess zeros and interspecific correlations. The method maintains strong ecological interpretability while enabling efficient Bayesian inference. Empirical validation on data from over 180 tree genera in the Congo Basin demonstrates its superior fit and ecological explanatory power.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsConstraint Satisfaction and Optimization: Distributed CSP/OptimizationMachine Learning: Calibration & Uncertainty Quantification

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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. P\'olya-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 P\'olya-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 P\'olya-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.

Problem

• species distribution models
• multivariate count data
• zero-inflation
• inter-species dependencies
• computational scalability

Innovation

• zero-inflated
• Tree Pólya splitting
• multivariate count data
• species distribution modeling
• phylogenetic hierarchy