Nutrient recycling and allelopathy in a gradostat

Presented is a two-vessel gradostat model in which one microbial species excretes a toxin that increases the mortality of another as both species compete for a limiting nutrient resource. The model is intended to explore the role of allelopathy in blooms of harmful algae, such as red tide (Karenia brevis) and golden algae (Prymnesium parvum). This study introduces the model and its biological basis, and proceeds to the analysis of its asymptotic states to delineate the ecological outcomes of competitive exclusion and coexistence. Theoretical results are supported by a set of numerical simulations. A discussion of biological conclusions and similarities to other mathematical models is also presented.