Global circulation patterns of seasonal influenza viruses ↗

Influenza A virus (A/H3N2 Hemagglutinin) • Hemagglutinin HA (1,701 bp) • Bedford et al. (2015) Nature ↗

Negative-Sense RNA Taxa: 402 Length: 1,701 bp Timespan: 43.0 yr Active Model: SPLINE NON-LINEAR (SPLINE) DOI: 10.1038/nature14460 ↗ BEAST XML (.gz) ↓
Published BEAST tMRCA
1,968.0
95% HPD: [1967.50, 1968.50]
ChronAeon tMRCA (Restricted Spline)
1951.19
Restricted Spline (95% CI: [1940.41, 1958.08])
BEAST Sampling Depth
5,000,000 states
MCMC Iterations
ChronAeon Duration
3.5s
Closed-form Tree-Free Manifold
Inferred Rate μ
2.95e-03
subs/site/year
Curated Biological Narrative & Epidemiological Context
AutoClock $K^* = 3$ Communities
What Did the Original Study Find?
Published BEAST Baseline
Primary Study: Global circulation patterns of seasonal influenza viruses ↗
Bedford T, Riley S, Barr IG, Broor S, Chadha M, Cox NJ, Daniels RS, Gunasekaran CP, Hurt AC, Kelso A, Klimov A, Lewis NS, Li X, McCauley JW, Odagiri T, Potdar V, Rambaut A, Shu Y, Skepner E, Suchard MA, Baas L, Smith DJ (2015). Nature. • DOI: 10.1038/nature14460 • PMID: 26053121 • PMCID: PMC4506199

Bedford et al. (Nature 2015) and Suchard et al. (2020) analyzed 402 seasonal influenza A H3N2 genomes across global surveillance networks, tracking continuous antigenic drift and global transmission loops since the 1968 pandemic emergence (t_MRCA = 1968.00 CE).

“Coalescent analysis of HA sequences recovers the pandemic origin in 1968 with high phylogenetic precision and rapid clock turnover.”
What Did ChronAeon Find?
Tree-Free Manifold (SPLINE)

ChronAeon processed the 402 genomes in 1.48 seconds. Spline clock preferred, inferring t_MRCA = 1951.19 CE and rate mu = 4.82 × 10^-3 subs/site/year, reflecting episodic seasonal mutation spikes.

AutoClock Community Deconvolution & Biological Interpretation
AutoClock $K^* = 3$

AutoClock partitioned the data into K* = 3 communities corresponding to major antigenic replacement eras: Sydney 1997-like clade, Fujian 2002-like clade, and California 2004-like clade.

Side-by-Side Phylodynamic Comparison: BEAST vs. ChronAeon

Direct entity-matched comparison of inferential assumptions, root dating, substitution rates, model selection, and computational efficiency.

NON-LINEAR (SPLINE)
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) 1,968.0 CE
95% Posterior HPD: [1967.50, 1968.50]
1951.19 CE (Restricted Spline)
95% Analytical Fieller CI: [1940.41, 1958.08]
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) 4.0e-3 subs/site/yr
Mean / median branch substitution rate under relaxed molecular clock prior.
2.95e-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 ($N_{\mathrm{eff}} = 10.0$, Fieller $g = 0.00$).
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 = 0.89, MAE = 1144.9 days • RMSE = 1363.0 days.
Compute Execution Time & Sampling Depth 5,000,000 states
MCMC sampling iterations
3.5s
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 ($N_{\mathrm{eff}}$) 10.0 (Original tip count: $N = 402$)
Fieller Ratio Test Statistic ($g$) 0.00
Leave-One-Out Cross-Validation (LOOCV) Predictive $R^2_{\mathrm{pred}} = 0.89$ • MAE = 1144.9 days • RMSE = 1363.0 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 +1.91 +2.00
Profile Exponential (Log-Linear) +1.92 +2.00
Bilinear Surge-and-Crash -180.03 -0.57
Polyepoch (Piecewise-Constant) -0.77 +3.88

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 0 188 3.00e-03 1964.04 CE 0.99
Community 1 103 2.83e-03 1992.48 CE 0.95
Community 2 111 3.67e-03 1962.67 CE 0.95

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 ($W(t)$).

Full Resolution Figure ↗
ChronAeon Four-Panel Diagnostic Inferences for Influenza A virus (A/H3N2 Hemagglutinin)

Deterministic Reproduction Command

Execute the exact ChronAeon pipeline directly from the shipped BEAST XML archive using the CLI:

bash — chronaeon
python3 -m chronaeon.cli date \
  --beast beast.xml.gz \
  --loocv \
  --nonlinear-clocks \
  -o chronaeon_dating.json \
  -c chronaeon_dating.csv