Speaker
Description
Modelling biological systems imposes the challenge to balance realism and complexity. Precise mechanistic models are often difficult to analyse and thus yield little insight, whereas simpler conceptual models tend to lack justification, as they rely on implicit descriptions of the underlying mechanisms. Model reduction via timescale separation can mitigate this trade-off by allowing to derive models of the latter type from the former while essential properties remain unchanged.
Tikhonov-Fenichel reduction theory developed by Goeke and Walcher \cite{goeke2014} allows us to find all timescale separations of rates (i.e.\ slow-fast separations of processes) for polynomial ODE systems algorithmically and to compute the corresponding reductions \cite{goeke2015}. Therefore this is a systematic, coordinate-free approach to geometric singular perturbation theory, which can be readily applied using the \texttt{Julia} package \texttt{TikhonovFenichelReductions.jl} \cite{apelt2026a}.
Following \cite{apelt2025}, the starting point of this talk is a detailed ``super model'' describing the population dynamics of mutualistic partners. From this we consider embedded conceptual models derived via Tikhonov-Fenichel reduction theory. The focus lies on the relationship between the mathematical formalism and the underlying biology resulting in good interpretability of the reductions. This for instance enables us to answer the question under which circumstances mutualism may break down.
Bibliography
@article{apelt2025,
title = {Tikhonov-{{Fenichel}} Reductions and Their Application to a Novel Modelling Approach for Mutualism},
author = {Apelt, Johannes and Liebscher, Volkmar},
date = {2025-09},
journaltitle = {Theoretical Population Biology},
shortjournal = {Theoretical Population Biology},
pages = {16--35},
issn = {00405809},
doi = {10.1016/j.tpb.2025.08.004},
langid = {english}
}
@software{apelt2026a,
title = {{{TikhonovFenichelReductions}}.jl},
author = {Johannes Apelt},
date = {2026-01-23},
doi = {10.5281/ZENODO.18352148},
url = {https://zenodo.org/doi/10.5281/zenodo.18352148},
urldate = {2026-03-04},
organization = {Zenodo},
version = {v0.3.4}
}
@article{goeke2014,
title = {A Constructive Approach to Quasi-Steady State Reductions},
author = {Goeke, Alexandra and Walcher, Sebastian},
date = {2014-11},
journaltitle = {Journal of Mathematical Chemistry},
shortjournal = {J Math Chem},
volume = {52},
number = {10},
pages = {2596--2626},
issn = {0259-9791, 1572-8897},
doi = {10.1007/s10910-014-0402-5},
langid = {english}
}
@article{goeke2015,
title = {Determining “Small Parameters” for Quasi-Steady State},
author = {Goeke, Alexandra and Walcher, Sebastian and Zerz, Eva},
date = {2015-08},
journaltitle = {Journal of Differential Equations},
shortjournal = {Journal of Differential Equations},
volume = {259},
number = {3},
pages = {1149--1180},
issn = {00220396},
doi = {10.1016/j.jde.2015.02.038},
langid = {english},
}
