q-bio.PEApr 13, 2026

A molecular clock for writing systems reveals the quantitative impact of imperial power on cultural evolution

Authors: Hiroki Fukui

Organizations: Research Institute of Criminal Psychiatry / Sex Offender Medical Center · Dept. Neuropsychiatry, Kyoto University

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Abstract

Writing systems are cultural replicators whose evolution has never been studied quantitatively at global scale. We compile the Global Script Database (GSD): 300 writing and notation systems, 50 binary structural characters, and 259 phylogenetic edges spanning 5,400 years. Applying four methods -- phenetics, cladistics, Bayesian inference, and neural network clustering -- we find that scripts exhibit a detectable molecular clock. The best-fitting model (Mk+Gamma strict clock) yields a substitution rate of q = 0.226 substitutions/character/millennium (95% CI: 0.034-1.22; Delta BIC = -4.1 versus relaxed clock; Delta BIC = -1,364.7 versus Mk without rate variation). Political interventions break this clock: deviation from expected divergence times correlates with intervention intensity (Spearman rho = 0.556, p < 10^{-4}), and per-character rate analysis reveals that intervention selectively rewrites deep structural features rather than merely accelerating change (rate profile correlation rho = 0.320). We identify 30 major script replacement events and rank their destructive impact. A ceiling effect suppresses independent invention wherever writing already exists (Fisher's exact OR = 0.054, p < 10^{-6}), and colonial contact predicts script extinction (Cox HR = 5.25, p = 0.0006). The Spanish Empire extinguished the most scripts (6 of 12 contacted, 50%), followed by the Empire of Japan (3 of 9, 33.3%). Feature coding was validated by inter-rater reliability testing with two independent human coders (Cohen's kappa = 0.877; human-LLM kappa = 0.929; Fleiss' kappa = 0.911).

Figures & tables

Figure 1: Figure 1. Geographic distribution of 300 writing systems in the Global Script Database. Stars indicate independently invented scripts (n=4). Blue: living; gray: extinct.
Figure 2: Figure 2. Selected phylogenetic lineages of writing systems. Line color indicates transmission mechanism: blue = natural, orange = stimulus diffusion, salmon = religious mission, red = colonial imposition. Stars indicate independent inventions (n=4). Time axis in thousands of years.
Figure 3: Figure 3. Molecular clock of writing systems. (a) All 246 parent-child pairs ( R2=0.919R^{2}=0.919 , MAE = 979 yr). (b) Natural transmission only (n = 128, R2=0.876R^{2}=0.876 , MAE = 879 yr). (c) Political intervention only (n = 113, R2=0.957R^{2}=0.957 , MAE = 1,110 yr). Dashed line: y = x.
Figure 4: Figure 4. Per-character substitution rates for 50 structural features, ranked from most conservative to most variable. Color indicates feature domain. Left bars: natural transmission; right bars: political intervention. Features tied to physical substrate (directionality, medium, stroke construction) change at rates below 0.05/millennium; social and structural features exceed 1.0/millennium.
Figure 5: Figure 5. Top 20 script replacement events ranked by integrated destruction score. Color indicates mechanism. Sensitivity analysis confirms rank-order stability (Spearman ρ=0.989\rho=0.989 across 1,000 weight configurations).
EmpireScripts eliminatedScripts contactedExtinction rateNotable victims
Spanish Empire61250.0%Maya, Baybayin, Isthmian, Mixtec-Puebla, Aztec pictographs, Testerian
Empire of Japan3933.3%Kaidā glyphs, Sūchūma, Barazan
French Empire21513.3%Chũ Nôm, Mi’kmaw hieroglyphs
Chinese Empires (Jin/Ming/Qing)32611.5%Jurchen, Khitan Large, Khitan Small
Table 1: Imperial Script Destruction Rankings
Figure 6: Figure 6. Number of living writing systems through time ( −- 5000 BCE to 2000 CE). Shaded red: colonial era (1500–1900 CE). Colonial extinction rate = 8.75 scripts/century (4.2 ×\times background rate). Peak: 146 scripts (2000 CE).
Figure 7: Figure S1. Sensitivity analysis of destruction score rankings. Box plots show rank distribution across 1,000 random weight configurations (Dirichlet-sampled). Whiskers: 95% rank CI.
Figure 8: Figure S2. MCMC trace plots for Bayesian clock analysis. Top: strict clock (log q and log scale). Bottom: relaxed clock (log q, log scale, log rate_var). All 16 walkers shown. Gelman-Rubin R^<1.01\hat{R}<1.01 for all parameters.
Figure 9: Figure S3. Posterior distribution of the Gamma shape parameter α\alpha from the Mk+ Γ\Gamma strict clock model. Median α=0.51\alpha=0.51 (95% CI: 0.46–0.58). Values below 1 indicate strong rate heterogeneity among characters.
Figure 10: Figure S4. BIC comparison across four models: Mk strict, Mk relaxed, Mk+ Γ\Gamma strict, Mk+ Γ\Gamma relaxed. Mk+ Γ\Gamma strict is the best-fitting model (lowest BIC).
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