Modeling Animal Communication Using Multivariate Hawkes Processes with Additive Excitation and Multiplicative Inhibition

2026-03-06

AI Summary

This study addresses the challenge of modeling temporal dependencies in animal acoustic communication, where vocal events often influence subsequent calls through both excitatory and inhibitory mechanisms—a dual dynamic that existing models struggle to capture simultaneously. To this end, the authors propose a novel multivariate Hawkes process that innovatively integrates additive excitation with multiplicative inhibition. This formulation preserves the interpretability of branching processes while effectively disentangling baseline rates, excitation, and inhibition effects, thereby enhancing model identifiability. Parameters are estimated via Bayesian inference using Markov chain Monte Carlo (MCMC), and model validity is assessed through the random time change theorem. Experiments on acoustic data from meerkats and baleen whales reveal significant within- and cross-type excitation and inhibition among meerkat call types, whereas whale vocalizations predominantly exhibit intra-species excitation.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Multimodal Learning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Animal acoustic communication often exhibits temporal dependence, with calls triggering or suppressing subsequent calls within and across call types, individuals, or species. While Hawkes processes provide a natural framework for modeling excitation, incorporating inhibition in multivariate settings can raise identifiability issues and complicate parameter interpretation. We propose a flexible class of multivariate Hawkes processes that combines additive excitation with multiplicative inhibition. This formulation preserves the branching process interpretation of excitation while reducing confounding between excitation and inhibition, and allows direct quantification of background and excitation contributions to the event rate. Bayesian inference is conducted via Markov chain Monte Carlo, and model adequacy is assessed using the random time change theorem. The proposed methodology is evaluated through simulation and applied to two acoustic communication datasets: group-living meerkats, for which we analyze three selected call types with distinct behavioral roles, and a two-species baleen whale dataset involving humpback and North Atlantic right whales. The meerkat analysis reveals significant within- and cross-type excitation with cross-type inhibition, whereas the whale data show evidence primarily of within-species excitation.

Problem

• animal communication
• temporal dependence
• excitation and inhibition
• multivariate Hawkes processes
• identifiability

Innovation

• Multivariate Hawkes processes
• Additive excitation
• Multiplicative inhibition
• Bayesian inference
• Animal communication