Steering the Evolutionary Game

Abstract

failure in cancer often arises from Darwinian selection for drug resistance. We introduce a hierarchical ecological control framework that reshapes the evolutionary fitness landscape on a slow timescale (microbiome modulation) to render the fast tumor--immune--drug dynamics curative. We prove existence and uniqueness of a Markov-perfect Nash equilibrium for the LQ fast game and formalize a conservative robust immune-influx threshold \(s_{crit,\max}^{rob}\le\tfrac{d}{n}a\). All nonlinear results are stated relative to \(s_{crit,\max}^{rob}\). Maintaining \(s(\mathbf{M})\ge s_{crit,\max}^{rob}+\delta\) renders the tumor-free state globally exponentially stable with rate \(\lambda=\min\{\tfrac{n\delta}{2d}, \tfrac{d-g_{\max}}{2}\}\) and explicit gain bounds. Robustness is established via: (i) spatial sufficiency using domain eigenvalues precluding sanctuaries, (ii) global asymptotic stability in probability under stochastic perturbations when \(L_z<\sqrt{\lambda/K}\) (and almost-sure convergence under additional recurrence conditions), (iii) quantitative tolerance to clonal heterogeneity when \(\Delta_a+\Delta_\kappa u_{d,\max}<\tfrac{n}{d} \delta\), (iv) delay and observer robustness under precise small-gain and observability conditions, and (v) an \(\epsilon\)-accurate Fenichel decomposition of the two-timescale game.

Using TCGA-derived priors, AI-synthesized policies enforce the stability margin along trajectories and achieve high efficacy with lower cytotoxic exposure. In Skin Cutaneous Melanoma (SKCM) the controller achieves 89% eradication (95% CI \(\pm6\)), maintains time-above-threshold at 92% ( \(\pm5\)), and reduces peak tumor burden by 57%; first response occurs in 28--35 days with a lower dose index. In colorectal cancer (CRC) the controller achieves 76% eradication ( \(\pm7\)) with 88% time-above-threshold ( \(\pm6\)). Across structured perturbations (5-clone heterogeneity, 14-day delay, stochastic noise, partial observability), individual eradication rates exceed 80% and remain 73% under combined stressors, aligning with the theory. These results establish ecological landscape engineering as a principled, general strategy for mitigating resistance in oncology.