Bayesian Decision-Making Shapes Phenotypic Landscapes from Differentiation to Cancer

Cells adapt their phenotypes in noisy microenvironments while maintaining robust decision-making. We develop a coarse-grained theoretical framework in which cellular phenotypic adaptation is described as Bayesian decision-making coupled to replication and diffusion. This leads to an effective Fokker--Planck equation with an emergent fitness landscape governing phenotypic dynamics. We identify distinct phenotypic regimes—homeostatic fixation, bistable decision-making, critical switching, and runaway explosion—and propose a biological interpretation in which homeostatic and bistable landscapes correspond to healthy differentiated cell states, whereas explosive landscapes capture stem-like or cancer-like behaviour. In the Gaussian setting, the correlation $\rho$ between intrinsic and extrinsic states directly encodes mutual information and acts as a bifurcation parameter: high correlation produces shallow or explosive landscapes associated with phenotypic plasticity, while reduced correlation stabilises differentiated fates by deepening potential wells. We further show that proliferation reshapes these landscapes in a nontrivial manner. Proliferation conditionally may stabilises local homeostasis without altering global confinement, or cooperate with biased environmental sensing to eliminate homeostasis/bistability and drive cancer-like phenotypic explosion even at high phenotypic fidelity. Finally, we show that negative intrinsic–extrinsic correlations suppress explosive dynamics but also reduce bistable plasticity, suggesting a robustness-plasticity trade-off. Together, our results suggest that development, tissue homeostasis, and carcinogenesis can be understood as information-driven deformations of a Bayesian phenotypic fitness landscape.