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The lost art of mathematical modelling
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-8745-4480
Mozilla Fdn, 2 Harrison St,Suite 175, San Francisco, CA 94105 USA..
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: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 362, article id 109033Article in journal (Refereed) Published
Abstract [en]

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

Place, publisher, year, edition, pages
Elsevier BV , 2023. Vol. 362, article id 109033
Keywords [en]
Mathematical biology, Hybrid models, Critical complexity, Machine learning, Equation-free approaches
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-509274DOI: 10.1016/j.mbs.2023.109033ISI: 001038884800001PubMedID: 37257641OAI: oai:DiVA.org:uu-509274DiVA, id: diva2:1790555
Available from: 2023-08-23 Created: 2023-08-23 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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