Competition in a continuously fed vessel

Two microbial species grow on the same limiting nutrient. Their specific growth rates per hour are μP = 0.8S/(1+S) and μQ = 0.5S/(0.25+S), where S is nutrient concentration in mmol/L. A vessel is well mixed and diluted at rate D per hour, removing the same fraction of each population. A population grows when μ > D. Nutrient input is sufficient; no other limitation or interaction occurs. At a stable single-species state, μ = D. If one resident maintains nutrient below the level required by the other, the other cannot invade.