Repair-Dependent Competition Between Direct Driver Founding and Stochastic Tunneling Before Clonal Establishment

Abstract DNA repair may change not only whether damaged cells survive but also which mutational route produces successful progression. We compare direct two-driver founding in a single division with sequential stochastic tunneling through a transient one-driver lineage. Founders arise from an endogenous homeostatic mutation–repair equilibrium and initiate branching processes stopped by extinction, an irreversible commitment event, or a finite clone-size bound- ary; only commitment before the other outcomes counts as success. At each fixed size boundary, both routes contribute at order V^2 in a rare independent- driver mutation expansion, with V held unchanged across repair comparisons. Exact finite-state coefficients establish a repair-induced reversal of the dominant route after averaging over the homeostatic founder mixture. An opportunity–turnover–establishment identity shows why improved cellular demography need not increase divisions eligible for a second hit. With lesion-dependent post-hit outcomes, a sharp criterion describes overshoot in the unbounded subcritical model, while certified finite-clone examples demonstrate re-entrant dominance. The resulting biological observable is a repair-dependent mixture of successful routes, distinct from clinical cancer incidence. MSC Classification: 92D15 , 60J80 , 60J35