Mutation-Driven First-Passage Extinction in Spatial Digital Evolution: Inverse Mutation Scaling of Lineage Lifetime and Spatial Decoupling of the Error Threshold

Mutation rate is a fundamental parameter controlling evolutionary dynamics. Here we investigate lineage extinction in a spatial digital evolution model using large-scale simulations of 6,907 independent lineages (5,000 timesteps). We find a robust inverse scaling relationship between mutation rate and lineage lifetime, <T> proportional to mu^(-alpha), with alpha approximately 0.75-1.0, a relationship confirmed by Spearman correlation (rho = -0.792, p approximately 0), multiple regression (regression coefficient beta = -1.045 +/- 0.033, 95% CI: [-1.078, -1.011], R^2 = 0.580), and symbolic regression (PySR: log(L+1) approximately 0.777 - log(mu), implying L proportional to mu^(-1)). Lifetime distributions are well described by a log-normal distribution (sigma = 1.01), and variance-mean scaling follows Taylor's Law with exponent approximately 1.6, indicating intermediate stochasticity consistent with multiplicative fitness dynamics. These observations are consistent with a drift-dominated first-passage process in log-fitness space arising from mutation-dependent fitness costs. Surprisingly, the critical mutation threshold does not scale with genome length as predicted by classical quasispecies theory - spatial population structure decouples the error threshold from genome size. These results suggest that spatial constraints fundamentally alter mutation-driven extinction dynamics, revealing a simple scaling regime for lineage survival in spatial evolutionary systems.