Mount Fuji’s stubby peak: the genotypic density of additive landscapes near maximal fitness

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ID: 317518
2026
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Abstract
Additive fitness landscapes-also called Mount Fuji landscapes-are the simplest and most widely used models of sequence-function relationships. As such, they play essential roles across multiple areas of biology, including evolutionary theory, quantitative genetics, gene regulation, and protein science. One of the most basic properties of any fitness landscape is its genotypic density-the number of sequences near a given fitness value. Understanding this density is especially important near fitness peaks, as it quantifies the supply of high-fitness genotypes. Here I study the genotypic density of additive landscapes near fitness peaks. Although this density is well known to be approximately Gaussian near the middle of the fitness range, its behavior near maximal fitness has not been reported. I begin by deriving a saddle-point approximation that accurately describes the genotypic density of additive landscapes over virtually the entire fitness range. I then show that the log of this density follows a power law near maximal fitness, with the exponent determined by how much the best allele at each position outperforms its nearest competitor. This power-law behavior holds over a substantial fraction of fitness values, besting the Gaussian approximation on both simulated and empirical landscapes across roughly a quarter to a third of the fitness range. Under certain conditions this behavior also extends to globally epistatic landscapes (defined as nonlinear functions of one or more additive traits), though with a reduced range of validity. These findings advance our understanding of one of the most fundamental models of sequence-function relationships. In particular, they reveal that the uppermost reaches of Mount Fuji landscapes, rather than being sharply peaked, are actually quite stubby.
Reference Key
openalex_W7164889793 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Justin B. Kinney
Journal current genetics
Year 2026
DOI
10.1093/genetics/iyag133
URL
https://doi.org/10.1093/genetics/iyag133
Keywords Keywords not found

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