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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Kimura's Fixation Calculator: Providing Neutral Theory With Predictive Capacity

Authors: Day, Vox; Athos, Claude;

Kimura's Fixation Calculator: Providing Neutral Theory With Predictive Capacity

Abstract

Neutral theory has stood for fifty-seven years on a simple result: the substitution rate k equals the per-site mutation rate μ. This identity, derived by Kimura in three lines, rests on canceling two quantities that share a letter but not a meaning: the census number of breeding adults N (which supplies mutations) and the variance effective population size Nₑ (which governs drift and fixation). The cancellation in the derivation is valid in the special case of asexual bacteria where N ≈ Nₑ. It does not hold in sexually reproducing species, where Nₑ/N is typically ~0.1 (Frankham 1995). Rejecting the incorrect application of the derivation and treating the realized substitution rate as the minimum of three serial constraints—input flux, polymorphism throughput, and selection cost—yields Kimura’s Fixation Calculator. The selection-cost term is a simple expression in four independently measurable parameters (maximum reproductive differential s_max ≈ 1, Selective Turnover Coefficient d, genome length L, and effective population size Nₑ). The full calculator recovers k ≈ μ for bacteria while predicting the observed compression of rates across sexual eukaryotes, where the selection term sets a ceiling two to five orders of magnitude below textbook expectations based on the standard derivation. Validated on fourteen sexual species pairs plus the E. coli LTEE (all calibrations independent of molecular clocks), the calculator provides forward prediction of k from organismal parameters, inverse inference of divergence time or Nₑ from observed substitutions, and joint constraint surfaces. Where the textbook supplies a single number, the calculator returns a mechanistically grounded range consistent with observable biological reality.

Keywords

Kimura, Neutral Theory, substitution rate

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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