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

Bokgyeong Kang, Erin M. Schliep, Alan E. Gelfand, Ariana Strandburg-Peshkin, Robert S. Schick

TL;DR

A flexible class of multivariate Hawkes processes that combines additive excitation with multiplicative inhibition is proposed, which 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.

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.

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

TL;DR

A flexible class of multivariate Hawkes processes that combines additive excitation with multiplicative inhibition is proposed, which 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.

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.
Paper Structure (22 sections, 16 equations, 6 figures, 6 tables)

This paper contains 22 sections, 16 equations, 6 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background on Hawkes Processes
  3. Univariate Hawkes Process
  4. Multivariate Hawkes Process
  5. Hawkes Process with Inhibition
  6. Multivariate Hawkes Processes with Additive Excitation and Multiplicative Inhibition
  7. Model Specification
  8. Motivation for the Additive–Multiplicative Parameterization
  9. Improved Interpretability
  10. Separation of Background and Excitation under Inhibition
  11. Enhanced Computational Efficiency
  12. Bayesian Inference
  13. Likelihood
  14. Prior Specification
  15. Model Assessment
  16. ...and 7 more sections

Figures (6)

  • Figure 1: Q-Q plots for $\hat{d}^{\ast}_{(i)}$ against an Exp(1) distribution. Gray shades represent 95% credible bands. Top and bottom labels denote generating and fitting models, respectively.
  • Figure 2: Observed call times by call type (y-axis) over time (x-axis) for three recorded days (facet panels) in 2017 for the meerkat dataset.
  • Figure 3: Q-Q plots for $\hat{d}^{\ast}_{(i)}$ against an Exp(1) distribution. Gray shades represent 95% credible bands. Facet labels denote models fitted to the meerkat dataset.
  • Figure 4: Excitatory (solid arrows) and inhibitory (dashed arrows) interactions among alarm, short note, and close calls in the meerkat dataset.
  • Figure 5: Observed call times by species (y-axis) over the two-day period from March 30 to March 31, 2009. Each vertical line represents the occurrence time of an individual call, with time shown on the x-axis.
  • ...and 1 more figures