Cooperation, privatization and cheating in microbial exoenzyme synthesis: theoretical analysis in view of biotechnological applications

Abstract

This study presents a mathematical framework for investigating the dynamics of coexistence and competition among heterotrophic microbes across different time scales. Focusing on metabolic interactions, we examine how three strategies: public metabolizing, private metabolizing, and cheating, shape population behaviour. The framework integrates generalized Lotka-Volterra dynamics with evolutionary game theory to capture the effects of resource exchange, particularly glucose made available by public metabolizers and sucrose as a shared substrate driving population growth. Game-theoretic payoffs encode ecological costs and benefits, enabling analysis of frequency-dependent interactions among strategies. To capture evolutionary realism, we implement laboratory-inspired simulations in which strategies can switch between generations, mimicking mutation or phenotypic plasticity in microbial populations. These eco-evolutionary dynamics reveal conditions under which all three strategies coexist at interior equilibria and show how variation in growth advantages and, illustratively, phenotype-switching perturbations produce evolutionary shifts. Numerical analysis identifies ecological thresholds and fitness asymmetries that determine system robustness, long-term coexistence, and the persistence of a synthetic, cross-kingdom system linked by nutrient exchange. Together, these insights provide general principles for microbial coexistence and offer design guidelines for ecosystem engineering, biotechnological applications, and the construction of stable synthetic communities under ecological and evolutionary constraints.