title: Cross-feeding dynamics described by a series expansion of the replicator equation.
abstract: Understanding how ecosystems evolve and how they respond to external perturbations is critical if we are to predict the effects of human intervention. A particular class of ecosystems whose dynamics are poorly understood are those in which the species are related via cross-feeding. In these ecosystems the metabolic output of one species is being used as a nutrient or energy source by another species. In this paper we derive a mathematical description of cross-feeding dynamics based on the replicator equation. We show that under certain assumptions about the system (e.g., high flow of nutrients and time scale separation), the governing equations reduce to a second-order series expansion of the replicator equation. By analysing the case of two and three species we derive conditions for co-existence and show under which parameter conditions one can expect an increase in mean fitness. Finally, we discuss how the model can be parameterised from experimental data.
authors.affiliation: Mathematical Sciences, University of Gothenburg and Chalmers University of Technology, 412 96 Göteborg, Sweden.
authors.forename: Torbjörn
authors.initials: T
authors.lastname: Lundh
authors.forename: Philip
authors.initials: P
authors.lastname: Gerlee
mesh_terms: D001419:Bacteria / Q000378:metabolism; D005075:Biological Evolution; D017753:Ecosystem; D006801:Humans; D055641:Mathematical Concepts; D053858:Metabolic Networks and Pathways; D008954:Models, Biological