Replication Data and Analysis Scripts for \Marker Gene Method: Identifying Stable Solutions in a Dynamic Environment\

Competitive Co-evolutionary Algorithms (CCEAs) are often hampered by complex dynamics such as intransitivity and the Red Queen effect, which can lead to unstable convergence. To address these challenges, this paper introduces the Marker Gene Method (MGM), a framework that designed to enhance stability  by using a \u2018marker gene\u2019 as a dynamic benchmark and an adaptive weighting mechanism to balance exploration and exploitation. We provide rigorous mathematical analysis,demonstrating that MGM creates strong attractors near Nash Equilibria within the Strictly Competitive Game (SCG) framework. Empirically, MGM demonstrates its efficacy across a spectrum of challenges: it stabilizes the canonical Rock-Paper-Scissors game, significantly improves the performance of C-RMOEA\\textbackslash{}D on ZDT benchmarks, and, when augmented with a Memory Pool (MP) extension, it successfully demonstrates robust convergence on the notoriously pathological Shapley Biased Game. This work presents a heoretically-grounded and empirically validated framework that substantially enhances the stability and robustness of CCEAs in complex competitive environments.