"Nevers et al. protein length fit to Lucas and Fibonacci targets - Descriptive statistics with adjacent midpoints and a Brocchieri & Karlin comparison - Additional evidence for generality of Geier's equations" by Stefan A. Geier et al.
Additional evidence for generality of Geier's equations
Institute for Structuralistic Theory of Sciences Simssee (ISTS), Gerhart-Hauptmann-Straße 6, 83071 Haidholzen, Germany; and Ludwig-Maximilians-Universität Munich, Germany.
**Dermatologische Klinik der Landeshauptstadt und der Ludwig-Maximilians-Universität LMU München, Thalkirchner Straße 48, 80337 Munich, Germany.
*Correspondence: Stefan A. Geier; wissenschaftstheorie.simssee.1@gmail.com
Summary:
This report evaluates the numerical proximity of protein-length summaries in Nevers and colleagues to Lucas numbers, Fibonacci numbers, and arithmetic midpoints between adjacent values in their sorted union. The three domain summaries printed in the supplied 2021 preprint are analyzed separately from the 2,326 species-level records in the 2023 published supplementary table. A value qualifies when its absolute deviation is no more than 5% of the target; the continuous fit score is 100 minus the target-relative percentage error. All three printed summaries qualify. Across all 2,326 species medians, 1,512 qualify (65.00%), with a mean best-fit score of 96.07% and a sample SD of 2.44 percentage points. The mean of these species medians is 285.99 aa, the median is 276 aa, and the mode is 282 aa. In the comparison study by Brocchieri and Karlin, 58 of 88 species medians qualify (65.91%). Results vary by target family, domain, summary statistic, and tolerance. Midpoints substantially expand the accepted length intervals. These findings establish a descriptive numerical correspondence under the stated rule; they do not establish enrichment, a biological mechanism, or the fraction of individual proteins fitting the targets. [1-5]
Keywords: protein length; Lucas numbers; Fibonacci numbers; adjacent midpoints; descriptive statistics; proteome medians; OMA; numerical proximity.
Principal results at a fixed 5% target-relative tolerance
Data level | n | Qualifying values | Mean best-fit score |
Nevers printed domain summaries | 3 | 3 (100.00%) | 97.48% |
Nevers species medians | 2,326 | 1,512 (65.00%) | 96.07% |
Brocchieri species medians | 88 | 58 (65.91%) | 95.96% |
The observation counts refer to summary values, not individual protein molecules or individual protein sequences. Nevers species-level results use the published 2023 Table S1.
Family-specific fit of the three printed domain summaries
Domain | Length | Lucas | Fibonacci | Midpoint | Best target | Best error |
Archaea | 242 | 199 | 233 | 216 | F 233 | 3.8627% |
Bacteria | 270 | 322 | 233 | 277.5 | M 277.5 | 2.7027% |
Eukaryota | 353 | 322 | 377 | 349.5 | M 349.5 | 1.0014% |
All fit values provide additional evidence for Geier's equations and Geier's considerations on protein lentghs (see ResearchGate: DOI: 10.13140/RG.2.2.15355.07208, DOI: 10.13140/RG.2.2.33185.67689, etc.).
Sources:
1. Nevers Y, Glover N, Dessimoz C, Lecompte
O. Protein length distribution is remarkably consistent across Life. bioRxiv.
2021;2021.12.03.470944. Version 1 posted 3 December 2021. Supplied preprint. 10.1101/2021.12.03.470944
2. Nevers Y, Glover NM, Dessimoz C,
Lecompte O. Protein length distribution is remarkably uniform across the tree
of life. Genome Biology. 2023;24:135. 10.1186/s13059-023-02973-2
3. Nevers Y, Glover NM, Dessimoz C,
Lecompte O. Additional file 1 Table S1. Per species protein length data summary
and BUSCO results. Supplement to reference 2. File
13059_2023_2973_MOESM1_ESM.csv. Accessed 1 October 2026. Official supplementary CSV
4. Nevers Y, Glover NM, Dessimoz C,
Lecompte O. Additional file 2. Supplementary materials and results. Table S2,
page 1. Supplement to reference 2. File 13059_2023_2973_MOESM2_ESM.pdf.
Accessed 1 October 2026. Official supplementary PDF
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