Many functions carried out by microbes, such as degradation of man-made toxic compounds, require the joint metabolic effort of many bacterial species. In such bacterial communities the success of each species depends on the presence or absence of other species and chemical compounds, effectively joining the components of the community into a microbial ecosystem. A common mode of interaction in such ecosystems is cross-feeding or syntrophy, whereby the metabolic output of one species is being used as a nutrient or energy source by another species.
I have together with my colleague Torbjörn Lundh formulated and analysed a mathematical model of cross-feeding dynamics. 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.
The paper was recently published in Bulletin of Mathematical Biology: