No abstract

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature, and have shown profound effects on the resulting eco-evolutionary dynamics. Incorporating linear environmental feedback law into replicator dynamics of two-player games, recent theoretical studies shed light on understanding the oscillating dynamics of social dilemma. However, detailed effects of more general nonlinear feedback loops in multi-player games, which is more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centered on cooperators not only accelerates the convergence of stable manifolds, but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population states. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments. POPULAR SUMMARYChanges in environment where individuals interact and compete can drastically impact evolutionary course and outcome in a wide variety of population systems, ranging from microbial cooperation to antibiotic resistance evolution. Such environmental changes are often unprecedented in the nature or simply the result of manual interventions using control devices like chemostat. There has been growing interest in incorporating environmental feedbacks into eco-evolutionary dynamics, yet it remains largely unknown if it is possible (and how) to steer ecoevolutionary dynamics with external switching feedback control laws that adjust selection gradient in the population systems. To fill this theoretical gap, we study eco-evolutionary dynamics of group cooperation with environmental feedbacks that modulate multi-person public goods game interactions. We find the existence of stable equilibrium manifold where the population can settle on and derive potential external control inputs that can steer the population to any desired states.In this work, we extend the mathematical framework of eco-evolutionary game dynamics to incorporate realistic asymmetrical environmental feedbacks, for game interactions organized by focal cooperators may have a different efficiency than the ones by defectors. Because of such complex interactions, multiple segments of stable and unstable manifolds can emerge from the population dynamical systems. Our work is in line with previous experimental work demonstrating the existence of (unstable) manifold ('separatrix') in population systems. Ou...

When a government agency considers tightening a standard on a pollutant, the agency often takes into account the proportion of firms that are able to meet the new standard (what we refer to as the industry’s “voluntary adoption level”) because a higher proportion indicates a more feasible standard. We develop a novel model of regulation in which the probability of a stricter standard being enacted increases with an industry’s voluntary adoption level. In addition, in our model, the benefit of a new green technology is both uncertain and correlated across firms, and firms’ decisions exhibit both strategic substitutability (because the marketing benefit of a new green technology decreases as more firms adopt it) and complementarity (because the stricter standard is more likely to be enforced as more firms adopt it). To analyze such strategic interaction among firms’ decisions under correlated and uncertain payoffs, we use the global game framework recently developed in economics. Our analysis shows that regulation that considers an industry’s voluntary adoption level, compared with regulation that ignores it, can more effectively motivate development of a new green technology. Interestingly, uncertainty in the payoff can, in some situations, help promote development of a new green technology. Finally, we find that more aggressive regulation (a higher probability of enforcing a stricter standard for a given voluntary adoption level) encourages more firms to adopt a green technology once the technology becomes available but may discourage a firm from developing it in the first place when facing intense competition. Therefore, for an industry with intense competition, a government agency should exercise caution about being too aggressive with regulation, which could potentially stifle innovation. This paper was accepted by Vishal Gaur, operations management.