An evolutionary model of rhythmic accelerando in animal vocal signalling

Yannick Jadoul; Taylor A. Hersh; Elias Fernández Domingos; Marco Gamba; Livio Favaro; Andrea Ravignani

doi:10.1371/journal.pcbi.1013011

An evolutionary model of rhythmic accelerando in animal vocal signalling

Yannick Jadoul^*, Taylor A. Hersh, Elias Fernández Domingos, Marco Gamba, Livio Favaro, Andrea Ravignani^*

^*Corresponding author for this work

Department of Clinical Medicine - Center for Music In the Brain

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, synchronization and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual’s incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.

Original language	English
Article number	e1013011
Journal	PLOS Computational Biology
Volume	21
Issue	4
ISSN	1553-734X
DOIs	https://doi.org/10.1371/journal.pcbi.1013011
Publication status	Published - Apr 2025

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title = "An evolutionary model of rhythmic accelerando in animal vocal signalling",

abstract = "Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, synchronization and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual{\textquoteright}s incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.",

author = "Yannick Jadoul and Hersh, {Taylor A.} and Domingos, {Elias Fern{\'a}ndez} and Marco Gamba and Livio Favaro and Andrea Ravignani",

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AU - Hersh, Taylor A.

AU - Domingos, Elias Fernández

AU - Gamba, Marco

AU - Favaro, Livio

AU - Ravignani, Andrea

N1 - Publisher Copyright: © 2025 Jadoul et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Y1 - 2025/4

N2 - Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, synchronization and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual’s incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.

AB - Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, synchronization and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual’s incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.

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An evolutionary model of rhythmic accelerando in animal vocal signalling

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