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

TL;DR

This paper introduces a flexible multivariate Hawkes process model combining additive excitation and multiplicative inhibition to analyze animal communication, enabling clearer interpretation of excitation and inhibition effects.

Contribution

It proposes a novel Hawkes process formulation that incorporates inhibition without losing interpretability, and demonstrates its effectiveness on real animal communication data.

Findings

Meerkat calls show significant excitation and inhibition effects.

Whale data primarily exhibit within-species excitation.

Model provides a clear quantification of background and excitation contributions.

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.