Modelling Animal Interactive Rhythms in Communication

Abstract

Time is one crucial dimension conveying information in animal communication. Evolution has shaped animals' nervous systems to produce signals with temporal properties fitting their socio-ecological niches. Many quantitative models of mechanisms underlying rhythmic behaviour exist, spanning insects, crustaceans, birds, amphibians, and mammals. However, these computational and mathematical models are often presented in isolation. Here, we provide an overview of the main mathematical models employed in the study of animal rhythmic communication among conspecifics. After presenting basic definitions and mathematical formalisms, we discuss each individual model. These computational models are then compared using simulated data to uncover similarities and key differences in the underlying mechanisms found across species. Our review of the empirical literature is admittedly limited. We stress the need of using comparative computer simulations - both before and after animal experiments - to better understand animal timing in interaction. We hope this article will serve as a potential first step towards a common computational framework to describe temporal interactions in animals, including humans.

Keywords: agent-based modelling; bioacoustics; chorusing; evolutionary biology; evolutionary neuroscience; rhythm; turn-taking; zoology.

Figure 1.

Arousal model plotted using simulated data, showing lag-period plots for a simulated isochronous neighbour (left) and a constant-drift neighbour (right). In these graphs, the focal lag/delay (vertical) is plotted against the partner previous period (horizontal).

Figure 2.

Rose plots of the arousal model showing frequency distributions of relative phases, relative to a simulated isochronous neighbour (left) and a constant-drift neighbour (right).

Figure 3.

Phase-delay model plotted using simulated data, showing lag-period plots for a simulated isochronous neighbour (left) and a constant-drift neighbour (right). In these graphs, the focal lag/delay (vertical) is plotted against the partner previous period (horizontal).

Figure 4.

Rose plots of the phase-delay model showing frequency distributions of relative phases, relative to a simulated isochronous neighbour (left) and a constant-drift neighbour (right).

Figure 5.

Antisynchrony model plotted using simulated data, showing lag-period plots for a simulated isochronous neighbour (left) and a constant-drift neighbour (right). In these graphs, the focal lag/delay (vertical) is plotted against the partner previous period (horizontal).

Figure 6.

Rose plots of the antisynchrony model showing frequency distributions of relative phases, relative to a simulated isochronous neighbour (left) and a constant-drift neighbour (right).

Figure 7.

Period-adjust model plotted using simulated data, showing lag-period plots for a simulated isochronous neighbour (left) and a constant-drift neighbour (right). In these graphs, the focal lag/delay (vertical) is plotted against the partner previous period (horizontal).

Figure 8.

Rose plots of the period-adjust model showing frequency distributions of relative phases, relative to a simulated isochronous neighbour (left) and a constant-drift neighbour (right).

Figure 9.

Turn-taking model plotted using simulated data, showing lag-period plots for a simulated isochronous neighbour (left) and a constant-drift neighbour (right). In these graphs, the focal lag/delay (vertical) is plotted against the partner previous period (horizontal).

Figure 10.

Rose plots of the turn-taking model showing frequency distributions of relative phases, relative to a simulated isochronous neighbour (left) and a constant-drift neighbour (right).