title: A model of a syntrophic relationship between two microbial species in a chemostat including maintenance.
abstract: Many microbial ecosystems can be seen as microbial 'food chains' where the different reaction steps can be seen as such: the waste products of the organisms at a given reaction step are consumed by organisms at the next reaction step. In the present paper we study a model of a two-step biological reaction with feedback inhibition, which was recently presented as a reduced and simplified version of the anaerobic digestion model ADM1 of the International Water Association (IWA). It is known that in the absence of maintenance (or decay) the microbial 'food chain' is stable. In a previous study, using a purely numerical approach and ADM1 consensus parameter values, it was shown that the model remains stable when decay terms are added. However, the authors could not prove in full generality that it remains true for other parameter values. In this paper we prove that introducing decay in the model preserves stability whatever its parameters values are and for a wide range of kinetics.
authors.affiliation: Irstea, UMR ITAP, 361 rue Jean-François Breton, 34196 Montpellier, France; Université de Haute Alsace, LMIA, 4 rue des Frères Lumière, 68093 Mulhourse, France. Electronic address: tewfik.sari@irstea.fr.
authors.forename: Tewfik
authors.initials: T
authors.lastname: Sari
authors.affiliation: INRA, UR050, Laboratoire de Biotechnologie de l'Environnement, 102 Avenue des Etangs, Narbonne F-11100, France. Electronic address: Jerome.Harmand@supagro.inra.fr.
authors.forename: Jérôme
authors.initials: J
authors.lastname: Harmand
mesh_terms: D000693:Anaerobiosis; D019149:Bioreactors / Q000382:microbiology; D003198:Computer Simulation; D017753:Ecosystem; D025461:Feedback, Physiological; D020387:Food Chain; D007700:Kinetics; D055641:Mathematical Concepts; D056265:Microbial Interactions / Q000502:physiology*; D008954:Models, Biological; D013559:Symbiosis / Q000502:physiology
keywords: Food chains; Maintenance; Microbial ecosystems; Stability; Syntrophic relationship