{'fraction_non_alphanumeric': 0.021071115013169446, 'fraction_numerical': 0.0, 'mean_word_length': 5.551724137931035, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Geometric analysis of a model for cross‐feeding in the chemostat

A model for competition between bacterial strains in a chemostat is studied using a model reduction argument and phase portrait analysis for the specific case of trophic chain. The first strain feeds on glucose but secretes a metabolic intermediate (acetate), which the second strain consumes. However, the metabolic intermediate imposes a cost to growth to both strains. The geometric and asymptotic analysis of the reduced model allows a rigourous treatment of the role of this assumption in the emergence of coexistence (cross‐feeding) equilibria. Conditions for non‐existence of cross‐feeding equilibria are given for certain parameter ranges. In the case of trophic chains, existence of cross‐feeding equilibria does not rely only on the presence of the acetate specialist scavenging for the intermediate metabolite inside the resource‐limited chemostat environment. The glucose specialist must, in addition, possess a certain degree of tolerance to the metabolic intermediate. Relaxing the assumption of the cost of growth helps establish a cross‐feeding equilibrium.