Universität zu Köln

Laroche, Lukas (2026). Population dynamics of cooperation and cheating in bacteria: A game-theoretical approach in discrete time. Masters thesis, Universität zu Köln.

PDF Masterthesis_Laroche_überarbeite_V2_mit Deckblatt.pdf - Updated Version Bereitstellung unter der CC-Lizenz: Creative Commons Attribution. Download (8MB)

Abstract

Antibiotic resistance in bacterial populations is highly cooperative. One example is the degradation of β-lactams by β-lactamase, which functions as a public good. Since laboratory experiments and clinical treatments are often based on periodic daily dosing rather than continuous exposure, this work investigates the population dynamics of resistant and susceptible bacteria using a discrete-time game-theoretic approach. Based on the time-continuous model by Yurtsev et al., the dynamics are mapped into discrete difference equations. The results show a transition from stable coexistence—analogous to a classical snowdrift game—to unpredictable, chaotic regimes driven by period-doubling bifurcations, which was verified using Lyapunov exponents. While classical evolutionary game theory excludes such dynamics for two interacting phenotypes, this work shows that strongly nonlinear, time-delayed feedbacks from the environment lift these theoretical constraints. Ultimately, the emergence of chaos suggests that rigid, periodic antibiotic treatments can lead to fundamentally unpredictable population states, underscoring the need for adaptive therapeutic strategies.

Item Type:	Thesis (Masters thesis)
Translated title:	Title Language Populationsdynamik von Kooperation und Betrug bei Bakterien: Ein spieltheoretischer Ansatz in diskreter Zeit German
Creators:	Creators Email ORCID ORCID Put Code Laroche, Lukas lukaslaroche@outlook.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-804317
Date:	2026
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institut für Biologische Physik
Subjects:	Generalities, Science Physics Life sciences
Uncontrolled Keywords:	Keywords Language Game Theory English Evolutionary Game Theory English Chaos English Chaos Theory English beta-lactam English beta-lactamase English antibiotic resistance English population dynamics English cooperation and cheating in bacteria English E. coli UNSPECIFIED Escherichia coli UNSPECIFIED discrete time English population dynamics in discrete time English discrete time dynamics English game theory in discrete time English evolutionary game theory in discrete time English
Date of oral exam:	2026
Referee:	Name Academic Title Krug, Joachim Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/80431