<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$p(1-p)=1/9$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>9</mn> </mrow> </math></EquationSource> </InlineEquation> marks the point beyond which selection can no longer maintain informational stability — a boundary that coincides with the loss of quantum coherence in the formally equivalent depolarizing channel and with thermodynamic fine-graining failure, suggesting that genetic stability, regulatory fidelity, and structural order share a common information-geometric limit. We apply this framework to cancer, framing carcinogenesis as an informational transition: a shift from host-regulated, high-fidelity transmission that maintains tissue homeostasis to a regime in which cells retain only the genetic and epigenetic changes that maximize their own proliferation — including loss of functions that serve the host and gain of functions that improve competition for space and nutrients and evasion of the predator-like immune response. Because cancer cells operate farther from this information-geometric limit than the normal cells around them, we propose that they may pursue an informational “niche construction” strategy: producing a mutagenic, acidic, hypoxic microenvironment that pushes neighboring host cells past the same collapse boundary, driving loss of function (e.g., “T cell exhaustion”) in infiltrating immune cells. We present empirical support for this framework together with specific, experimentally testable predictions.</p>

Fisher Information Limits on Genetic Stability, Diversity, and Regulation

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2026年8月5日

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J. S. Glasenapp,
R. A. Gatenby

摘要

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 $p(1-p)=1/9$ $p (1 - p) = 1 / 9$ marks the point beyond which selection can no longer maintain informational stability — a boundary that coincides with the loss of quantum coherence in the formally equivalent depolarizing channel and with thermodynamic fine-graining failure, suggesting that genetic stability, regulatory fidelity, and structural order share a common information-geometric limit. We apply this framework to cancer, framing carcinogenesis as an informational transition: a shift from host-regulated, high-fidelity transmission that maintains tissue homeostasis to a regime in which cells retain only the genetic and epigenetic changes that maximize their own proliferation — including loss of functions that serve the host and gain of functions that improve competition for space and nutrients and evasion of the predator-like immune response. Because cancer cells operate farther from this information-geometric limit than the normal cells around them, we propose that they may pursue an informational “niche construction” strategy: producing a mutagenic, acidic, hypoxic microenvironment that pushes neighboring host cells past the same collapse boundary, driving loss of function (e.g., “T cell exhaustion”) in infiltrating immune cells. We present empirical support for this framework together with specific, experimentally testable predictions.