Fisher Information Limits on Genetic Stability, Diversity, and Regulation.

Life and evolution require precise yet imperfect transmission of genetic information across generations. Accurate transmission maintains the genetic blueprint for phenotypes that succeed in current conditions, while some transmission error is necessary to generate heritable diversity that can further increase fitness and hedge against future environmental change. This background noise, however, risks excessive mutation accumulation that degrades fitness ("Muller's ratchet") or even destroys genetic information beyond recovery ("error catastrophe"). Across the history of life these competing pressures resolve into two regimes: during environmental fluctuation, a higher mutation rate aids survival; during prolonged stability, populations converge toward an evolutionarily stable state (ESS) in which mutations can only reduce fitness. We model this tension with a Fisher Information framework in which genetic inheritance is a noisy two-state channel. The nontrivial eigenvalue of the channel's symmetric circulant transition operator governs the decay of allelic contrast across generations; selection modifies this eigenvalue by suppressing the channel's switching (mutation) probability, acting as an anti-depolarizing force. We show this compensation is bounded: an instability boundary at