An abstract evolutionary model points to a trade-off between how reliably a genotype produces a phenotype and how easily mutation can open a route to a different high-fitness outcome. In the model, higher penetrance — the probability that a genotype expresses a particular full phenotype — was associated with greater mutational robustness, but with lower adaptability to environmental change.
The result comes from a mathematical genotype–phenotype map built with globally interacting Ising spins, rather than from observations of organisms, cells or human populations. The analysis describes patterns within that model.
A centre of reliable expression
The researchers first examined a small system exhaustively, using six spins, three focal spins and a phenotypic-noise parameter of 0.03125. They calculated how often each genotype produced a given phenotype, the basis for measuring penetrance.
They then viewed the genotypes producing a chosen target phenotype as a network. The target-specific high-fitness network included genotypes with fitness greater than 0.5 at that noise level; its “core” was defined as the top 10% by betweenness centrality, a measure of how often a point lies on connecting routes through a network.
Higher-centrality genotypes had higher penetrance of the dominant phenotype. Under high noise, centrality was also correlated with fitness: core genotypes had high fitness, while peripheral genotypes had fitness of approximately 0.5. In plain terms, the model placed the most connected genotypes near the dependable centre of a high-fitness region.
Robustness is not the same as reach
The model measured mutational robustness by asking how far a genotype had to move through successive mutations before its average fitness fell to half its starting level. It also introduced a quantity called D, based on the minimum Hamming distance — the number of differing spin positions — to an alternative high-fitness region.
D was used as a geometric proxy for mutational accessibility, not as a complete measure of adaptation rate. Across the global model analysis, higher penetrance was associated with greater robustness but lower access to alternative adaptive regions. The pattern describes a structural trade-off in the modeled map; it does not establish that lower penetrance causes faster adaptation in nature.
The balance shifted when the target changed
The researchers next ran mutation–selection simulations in which mutation acceptance depended on the resulting change in genotypic fitness. With periodically switching target patterns, the simulations associated infrequent environmental changes with penetrance and frequent changes with adaptability along the same trade-off.
Summaries of the switching experiments averaged 1,000 evolutionary trajectories for each switching interval, including current-environment fitness and the share of trajectories ending at core genotypes. The reported pattern was therefore an average across those trajectories, not a single outcome.
A larger system preserved the broad pattern
To test whether the small-system trends persisted, the study used a larger simulation system with 20 spins and four focal spins. Unlike the small analysis, the larger-system validation relied on evolutionary simulations and sampled genotypes rather than exhaustive enumeration.
In those larger-system simulations, evolution under high noise produced more funnel-like phenotypic landscapes and more plateau-like local fitness landscapes than evolution under low noise. Genotypes evolved under high noise also tended to adapt more slowly to a new environment than genotypes evolved under low noise.
A theoretical result, not a biological verdict
The findings are limited to an abstract interacting-spin model. The reported relationships are directional: the analysis gives no formal uncertainty estimates or numerical effect sizes for the main comparisons.
Another limit is the measure D itself. It captures geometric proximity to another high-fitness region, but it is not a complete measure of adaptation rate. The study therefore describes a relationship in the chosen map, not a universal rule for evolution.
The document is an arXiv version 1 preprint dated 25 August 2026. The work was supported by the RIKEN Junior Research Associate Program, the ANRI Fellowship, JSPS KAKENHI grants 26K00057 and 26K00061, and the Novo Nordisk Foundation; the authors declared no competing interest.
Paper data and sources
Original title: Global geometry of the genotype-phenotype map illuminates a trade-off between penetrance and mutational adaptability
Authors: Yutaro Ikeda, Kunihiko Kaneko, Tetsuhiro S. Hatakeyama
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
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