On the coexistence of competing microbial species in a chemostat under cycling

It is known that two microbial species competing for a single rate-limiting nutrient cannot grow together in a chemostat under steady-state operation, but eventually the species with the lower specific growth rate at the particular operating conditions will become extinct. Coexistence of the two populations has been shown obtainable in chemostats under periodic operation. This is possible in cases where the specific growth rate functions of the two species are such that for certain values of the nutrient concentration the first species grows faster than the second, and for other values of the nutrient concentration the second species is the one growing faster. In a previous article it was demonstrated that, even in cases where the specific growth rate functions of the two species are such that one of the species grows faster than the other for all values of the nutrient concentration, extinction of either species is possible provided that time delay in the response of the species to changes in their fermentation environment is accounted for, and that the faster growing species is also faster in its response. Here, we show that coexistence of the two species is also possible in a significant range of the operating parameters. We develop a numerical algorithm with which we trace the boundary of the coexistence region in the entire operating parameter space and construct the operating diagram of the system.