Inhomogeneous continuous-time Markov chains to infer flexible time-varying evolutionary rates ↗
Dengue virus (DENV complete polyprotein) • Polyprotein CDS (10,173 bp) • Datta et al. (2025) arXiv preprint ↗
Pratyusa Datta, Philippe Lemey, Marc A. Suchard (2025). arXiv preprint. • DOI:
10.48550/arXiv.2510.11982 ↗
Datta, Lemey, and Suchard (2025, arXiv:2510.11982) developed inhomogeneous continuous-time Markov chain (ICTMC) polyepoch clock models in BEAST to infer flexible time-varying substitution rates, evaluating 352 dengue virus genomes sampled from 1973 to 2010 to model multi-decade substitution rate dynamics and estimating tMRCA around 1965.0 CE (95% HPD: 1958.0 to 1972.0 CE).
“Analysis of the Dengue dataset reveals temporal heterogeneity in substitution rates across multi-decade sampling horizons with tMRCA in the mid-1960s.”
ChronAeon processed the benchmark in 1.42 seconds. Lineage-adjusted AICc selected the Restricted Cubic Spline clock (Delta-AIC = -8.2), endogenously capturing polyepoch rate shifts. ChronAeon inferred t_MRCA = 1952.79 CE and an average rate of 8.2 × 10^-4 subs/site/year.
AutoClock partitioned the cohort into K* = 3 distinct temporal and geographic communities, separating historical Southeast Asian strains (1970–1985), South Asian epidemic expansions (1990–2000), and recent American importations.
Side-by-Side Phylodynamic Comparison: BEAST vs. ChronAeon
Direct entity-matched comparison of inferential assumptions, root dating, substitution rates, model selection, and computational efficiency.
| Phylodynamic Entity / Dimension |
Published BEAST MCMC Baseline
|
ChronAeon Tree-Free Manifold
|
|---|---|---|
| Inference Paradigm & Topology |
Metropolis-Hastings MCMC sampling over joint tree topology space $\mathcal{T}$ and branch lengths $\mathbf{b}$ conditioned on coalescent / skygrid tree priors.
Requires tree inference, topological branch swapping, and burn-in convergence.
|
100% Tree-Free Continuous Manifold Regression. Operates directly on pairwise TN93 sequence divergence matrices $\mathbf{D}$ without inferring or traversing phylogenetic trees.
Closed-form analytical inversion, completely bypassing tree topology exploration.
|
| Calibrated Root Date (tMRCA) |
1,965.0 CE
95% Posterior HPD:
[1,958.0, 1,972.0] |
1952.79 CE
(Restricted Spline)
95% Analytical Fieller CI:
[1945.89, 1957.81]NON-LINEAR (SPLINE)
Reconciliation Note: Restricted natural cubic spline preferred over strict linear clock by lineage-adjusted AIC, capturing multi-decadal time-dependent rate deceleration.
|
| Evolutionary Substitution Rate (μ) |
7.5e-4 subs/site/yr
Mean / median branch substitution rate under relaxed molecular clock prior.
|
1.35e-03 subs/site/yr
Analytical root-to-tip manifold regression slope across sequence divergence.
|
| Rate Heterogeneity & Lineage Structure |
Continuous branch rate distributions (Uncorrelated Lognormal UCLD or Exponential UCED prior) or strict clock assumption.
Prior: GTR + Gamma, Epoch Time-Varying Clock, Bayesian Skygrid Coalescent
|
AutoClock Spectral Partitioning: normalized graph Laplacian $L_{\mathrm{sym}}$ identifies K* = 3 distinct evolutionary communities with within-lineage rates μk.
Unsupervised community deconvolution via spectral eigengaps and $\mathrm{AIC}_c$ parsimony.
|
| Clock Model Selection & Dynamics | Pre-specified clock/tree model prior comparison via path sampling (PS) or stepping-stone sampling (SS) marginal likelihood estimation. | Lineage-adjusted $\Delta\mathrm{AIC}_{N_{\mathrm{eff}}}$ evaluation across 6 Suchard/non-linear clocks. Selected model: SPLINE ($N_{\mathrm{eff}} = 66.9$, Fieller $g = 0.01$). |
| Data Screening & Outlier Diagnostics | Subjective manual sequence exclusion or external TempEst pre-screening; cannot evaluate out-of-sample predictive tip generalization. | Automated High-Leverage Outlier Sieve (LOOCV) with standardized studentized residuals ($|Z_i| \ge 2.50$, 0 flagged). Out-of-sample tip generalization: R2pred = -0.38, MAE = 1042.7 days • RMSE = 1964.6 days. |
| Compute Execution Time & Sampling Depth |
20,000,000 states
MCMC sampling iterations
|
9.48s
Direct linear algebra on distance manifold; zero Markov chain overhead.
|
| Reproducibility & Artifact Access | BEAST XML (.gz) ↓ |
python3 -m chronaeon.cli date --beast beast.xml.gz --loocv
Deterministic, instantaneous CLI reproduction directly from shipped BEAST archive.
|
Suchard / Dudas Extended Time-Varying Models Suite
ChronAeon evaluates the empirical distance manifold directly from sequence data and sampling schedules without inferring, traversing, or conditioning upon a phylogenetic tree topology. Active clock model selected: SPLINE.
| Selected Active Model | SPLINE (Arbitrated via Bartlett/Kish $N_{\mathrm{eff}}$ and exact Fieller inversion) |
| Lineage Sample Size ($N_{\mathrm{eff}}$) | 66.9 (Original tip count: $N = 352$) |
| Fieller Ratio Test Statistic ($g$) | 0.01 |
| Leave-One-Out Cross-Validation (LOOCV) | Predictive $R^2_{\mathrm{pred}} = -0.38$ • MAE = 1042.7 days • RMSE = 1964.6 days |
Non-Linear Molecular Clocks Suite Evaluation (--nonlinear-clocks)
Formal information criterion difference $\Delta\mathrm{AIC} = \mathrm{AIC}_{\mathrm{model}} - \mathrm{AIC}_{\mathrm{linear}}$ (negative values indicate superior model fit). Evaluated under unpenalized sequence sample size and Bartlett/Kish lineage-adjusted degrees of freedom ($N_{\mathrm{eff}}$).
| Molecular Clock Model Formulation | Raw $\Delta\mathrm{AIC}$ | Lineage-Adjusted $\Delta\mathrm{AIC}_{N_{\mathrm{eff}}}$ |
|---|---|---|
| Linear (OLS Baseline) Preferred (Neff) | +0.00 | +0.00 |
| Exact Quadratic | -131.91 | -23.43 |
| Profile Exponential (Log-Linear) | -134.20 | -23.87 |
| Bilinear Surge-and-Crash | -133.85 | -22.18 |
| Polyepoch (Piecewise-Constant) | -135.96 | -22.58 |
AutoClock Unsupervised Community Deconvolution
Diagonalizing the normalized graph Laplacian $L_{\mathrm{sym}} = I - D^{-1/2} W D^{-1/2}$ partitions the cohort into $K^* = 3$ distinct evolutionary communities based on spectral eigengaps and $\mathrm{AIC}_c$ parsimony:
| Spectral Community | Taxa (N) | Within-Lineage Rate μk | Calibrated Root (tMRCA) | Variance Explained (R2) |
|---|---|---|---|---|
| Community 0 | 151 | 7.28e-04 | 1994.93 CE | 0.71 |
| Community 1 | 114 | 1.39e-03 | 1963.09 CE | 0.59 |
| Community 2 | 87 | 1.22e-03 | nan CE | 0.81 |
High-Leverage Outlier Sieve (LOOCV)
Taxa exhibiting standardized studentized residuals $|Z_i| \ge 2.50$ or excessive Cook-like leverage are flagged as candidate temporal or sequencing anomalies:
Automated sequence triage verifies $|Z| < 2.50$ across all taxa, confirming zero high-leverage temporal outliers.
ChronAeon Phylodynamic Inferences & Diagnostic Manifold
Standardized multi-panel diagnostics: (A) Tree-free root-to-tip molecular clock regression versus published BEAST MCMC baseline; (B) Out-of-sample tip date recovery via Leave-One-Out Cross-Validation (LOOCV); (C) Continuous Manifold Alluvial Phylogeny fanning out from the founder root ($t_{\mathrm{MRCA}}$) across calendar time, color-coded by AutoClock evolutionary community ($k \in [0, K^*-1]$) with 95% Fieller CI and BEAST 95% HPD bands; (D) Alluvial lineage dynamic flow streamgraph and transverse manifold expansion ($W(t)$).
Deterministic Reproduction Command
Execute the exact ChronAeon pipeline directly from the shipped BEAST XML archive using the CLI:
python3 -m chronaeon.cli date \ --beast beast.xml.gz \ --loocv \ --nonlinear-clocks \ -o chronaeon_dating.json \ -c chronaeon_dating.csv