{"type": "FeatureCollection", "features": [{"id": "10.1080/0020739X.2023.2254314", "type": "Feature", "geometry": null, "properties": {"updated": "2026-09-22T16:17:24Z", "type": "Journal Article", "created": "2023-09-15", "title": "An optimal control problem for resource utilisation by microorganisms", "description": "Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that microorganisms regulate the uptake rate of a substrate to maximise their growth over the period of decomposition. The result is an optimal control problem consisting of two differential equations and auxiliary conditions that determine the optimal value of the control variable (the uptake rate), the remaining substrate at any given time, and the optimal completion time. This problem serves as a case study to illustrate the solution of differential equations and optimal control problems for students in undergraduate courses. The mathematical analysis of the problem requires rewriting the differential equations in reverse time along with the solution of a nonhomogeneous linear first order differential equation. We then return to modelling with some biologically motivated questions about how the parameters of the model representing environmental conditions and microbial functional traits affect the outcome. Finally, we discuss alternative ways to use the material with students.", "keywords": ["0301 basic medicine", "03 medical and health sciences", "Annan matematik", "05 social sciences", "resource utilisation", "Didactics", "microbial decomposition", "Didaktik", "Other Mathematics", "0503 education", "6. 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Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that microorganisms regulate the uptake rate of a substrate to maximise their growth over the period of decomposition. The result is an optimal control problem consisting of two differential equations and auxiliary conditions that determine the optimal value of the control variable (the uptake rate), the remaining substrate at any given time, and the optimal completion time. This problem serves as a case study to illustrate the solution of differential equations and optimal control problems for students in undergraduate courses. The mathematical analysis of the problem requires rewriting the differential equations in reverse time along with the solution of a nonhomogeneous linear first order differential equation. 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Clean water", "Optimal control"]}, "links": [{"href": "https://www.tandfonline.com/doi/pdf/10.1080/0020739X.2023.2254314"}, {"href": "https://doi.org/10.1080/0020739x.2023.2254314"}, {"rel": "related", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main/items/International%20Journal%20of%20Mathematical%20Education%20in%20Science%20and%20Technology", "name": "related record", "description": "related record", "type": "application/json"}, {"rel": "self", "type": "application/geo+json", "title": "10.1080/0020739x.2023.2254314", "name": "item", "description": "10.1080/0020739x.2023.2254314", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main/items/10.1080/0020739x.2023.2254314"}, {"rel": "collection", "type": "application/json", "title": "Collection", "name": "collection", "description": "Collection", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main"}], "time": {"date": "2023-09-15T00:00:00Z"}}, {"id": "10.1111/nph.19572", "type": "Feature", "geometry": null, "properties": {"updated": "2026-09-22T16:18:05Z", "type": "Journal Article", "created": "2024-02-12", "title": "Modelling optimal ligninolytic activity during plant litter decomposition", "description": "Summary

A large fraction of plant litter comprises recalcitrant aromatic compounds (lignin and other phenolics). Quantifying the fate of aromatic compounds is difficult, because oxidative degradation of aromatic carbon (C) is a costly but necessary endeavor for microorganisms, and we do not know when gains from the decomposition of aromatic C outweigh energetic costs.

To evaluate these tradeoffs, we developed a litter decomposition model in which the aromatic C decomposition rate is optimized dynamically to maximize microbial growth for the given costs of maintaining ligninolytic activity. We tested model performance against >\uffe2\uff80\uff89200 litter decomposition datasets collected from published literature and assessed the effects of climate and litter chemistry on litter decomposition.

The model predicted a time\uffe2\uff80\uff90varying ligninolytic oxidation rate, which was used to calculate the lag time before the decomposition of aromatic C is initiated. Warmer conditions increased decomposition rates, shortened the lag time of aromatic C oxidation, and improved microbial C\uffe2\uff80\uff90use efficiency by decreasing the costs of oxidation. Moreover, a higher initial content of aromatic C promoted an earlier start of aromatic C decomposition under any climate.

With this contribution, we highlight the application of eco\uffe2\uff80\uff90evolutionary approaches based on optimized microbial life strategies as an alternative parametrization scheme for litter decomposition models.

A large fraction of plant litter comprises recalcitrant aromatic compounds (lignin and other phenolics). Quantifying the fate of aromatic compounds is difficult, because oxidative degradation of aromatic carbon (C) is a costly but necessary endeavor for microorganisms, and we do not know when gains from the decomposition of aromatic C outweigh energetic costs.

To evaluate these tradeoffs, we developed a litter decomposition model in which the aromatic C decomposition rate is optimized dynamically to maximize microbial growth for the given costs of maintaining ligninolytic activity. We tested model performance against >\uffe2\uff80\uff89200 litter decomposition datasets collected from published literature and assessed the effects of climate and litter chemistry on litter decomposition.

The model predicted a time\uffe2\uff80\uff90varying ligninolytic oxidation rate, which was used to calculate the lag time before the decomposition of aromatic C is initiated. Warmer conditions increased decomposition rates, shortened the lag time of aromatic C oxidation, and improved microbial C\uffe2\uff80\uff90use efficiency by decreasing the costs of oxidation. Moreover, a higher initial content of aromatic C promoted an earlier start of aromatic C decomposition under any climate.

With this contribution, we highlight the application of eco\uffe2\uff80\uff90evolutionary approaches based on optimized microbial life strategies as an alternative parametrization scheme for litter decomposition models.