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Using neuronal models to capture burst-and-glide motion and leadership in fish
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-8745-4480
Univ Oslo, RITMO Ctr Interdisciplinary Studies Rhythm Time &, Oslo, Norway..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.ORCID iD: 0000-0002-1436-9103
2023 (English)In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 20, no 204Article in journal (Refereed) Published
Abstract [en]

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

Place, publisher, year, edition, pages
The Royal Society , 2023. Vol. 20, no 204
Keywords [en]
collective behaviour, swimming dynamics, neuronal dynamics, dynamical systems, fish behaviour
National Category
Bioinformatics (Computational Biology)
Identifiers
URN: urn:nbn:se:uu:diva-508872DOI: 10.1098/rsif.2023.0212ISI: 001030842300005PubMedID: 37464800OAI: oai:DiVA.org:uu-508872DiVA, id: diva2:1787107
Funder
Knut and Alice Wallenberg Foundation, 102 2013.0072EU, Horizon 2020, 101030688The Research Council of Norway, 262762Available from: 2023-08-11 Created: 2023-08-11 Last updated: 2024-02-21Bibliographically approved
In thesis
1. The Art of Modelling Oscillations and Feedback across Biological Scales
Open this publication in new window or tab >>The Art of Modelling Oscillations and Feedback across Biological Scales
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers in the field of mathematical biology. All papers aim to advance our understanding of biological systems through the development and application of innovative mathematical models. These models cover a diverse range of biological scales, from the nuclei of unicellular organisms to the collective behaviours of animal populations, showcasing the broad applicability and potential of mathematical approaches in biology. While the first three papers study mathematical models of very different applications and at various scales, all models contribute to the understanding of how oscillations and/or feedback mechanisms on the individual level give rise to complex emergent patterns on the collective level. In Paper I, we propose a mathematical model of basal cognition, inspired by the true slime mould, Physarum polycephalum. The model demonstrates how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. In Paper II, we propose a model of social burst-and-glide motion in pairs of swimming fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. In Paper III, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. Paper IV takes a reflective turn, advocating from a philosophical perspective the importance of developing new mathematical models in the face of current scientific challenges.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2024. p. 48
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 135
Keywords
mathematical biology, mathematical modelling, oscillations, feedback mechanisms, dynamical systems, individual-based models, complex systems
National Category
Mathematics
Research subject
Applied Mathematics and Statistics
Identifiers
urn:nbn:se:uu:diva-523639 (URN)978-91-506-3039-8 (ISBN)
Public defence
2024-04-12, Sonja Lyttkens (101121), Ångströmlaboratoriet, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2024-03-19 Created: 2024-02-21 Last updated: 2024-03-19

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Gyllingberg, LinnéaSumpter, David J. T.

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