Rule-Sensitive Eco-Evolution: A Phase Diagram of BD/DB/Imitation under Structure and Feedback

Construct a phase diagram over structural variables (average degree, degree variance), environmental coupling strength (edge-level), and update rule (BD/DB/imitation). Identify regions where macroscopic outcomes (fixation probabilities, cooperation levels, boundary equilibria) coincide across rules versus regions where they diverge. This extends Wu et al.’s equivalence results from well-mixed populations to structured, feedback-coupled systems, integrating structural levers and edge-level feedback. Controlled simulations and perturbative analysis will find rule-invariant manifolds and rule-specific bifurcations. This clarifies conflicting results caused by arbitrary micro-dynamic choices leading to different macro outcomes and guides experimental implementations targeting desired macroscopic behavior. The impact is a practical atlas for choosing or engineering update rules in microbial evolution experiments and ecological management where environmental feedback is significant.

References:

1. When do microscopic assumptions determine the outcome in evolutionary game dynamics. Bin Wu, Benedikt Bauer, T. Galla, A. Traulsen (2014).