[Paper Review] Shrinkage-based random local clocks with scalable inference

Alexander A. Fisher, Xiang Ji+3 more|arXiv (Cornell University)|May 15, 2021

Genomics and Phylogenetic Studies4 citations

TL;DR

This paper introduces a scalable, Bayesian shrinkage-clock model that uses a heavy-tailed Bayesian bridge prior on incremental changes in log branch-specific clock rates to enable efficient inference of local clocks without prior knowledge of clock locations. By leveraging Hamiltonian Monte Carlo with closed-form gradients and linear-time recursive algorithms, the method achieves over 3-fold speedup over random local clocks and accurately recovers known clocks in rodent and influenza phylogenies, including in large-scale analyses of influenza surface glycoproteins.

ABSTRACT

Local clock models propose that the rate of molecular evolution is constant within phylogenetic sub-trees. Current local clock inference procedures scale poorly to large taxa problems, impose model misspecification, or require a priori knowledge of the existence and location of clocks. To overcome these challenges, we present an autocorrelated, Bayesian model of heritable clock rate evolution that leverages heavy-tailed priors with mean zero to shrink increments of change between branch-specific clocks. We further develop an efficient Hamiltonian Monte Carlo sampler that exploits closed form gradient computations to scale our model to large trees. Inference under our shrinkage-clock exhibits an over 3-fold speed increase compared to the popular random local clock when estimating branch-specific clock rates on a simulated dataset. We further show our shrinkage-clock recovers known local clocks within a rodent and mammalian phylogeny. Finally, in a problem that once appeared computationally impractical, we investigate the heritable clock structure of various surface glycoproteins of influenza A virus in the absence of prior knowledge about clock placement.

Motivation & Objective

• To address the computational intractability of random local clock models on large trees by developing a scalable inference framework.
• To overcome the over-shrinkage of autocorrelated clock models by allowing large, punctuated rate changes through heavy-tailed priors.
• To eliminate the need for a priori specification of clock locations or numbers in molecular clock analysis.
• To enable efficient, high-precision inference of heritable clock rate variation in large phylogenies using advanced MCMC sampling.
• To apply the model to real-world data, including influenza A virus glycoproteins, to uncover host-specific clock patterns.

Proposed method

• Proposes a Bayesian shrinkage-clock model where increments in log clock rates between parent and child nodes follow a Bayesian bridge prior with mean zero and heavy tails.
• Uses a collapsed spike-and-slab representation of the Bayesian bridge to encourage sparsity in rate changes while allowing large shifts when warranted.
• Employs Hamiltonian Monte Carlo (HMC) sampling in the increment space, exploiting differentiability of the Gaussian scale-mixture form of the bridge prior.
• Develops recursive post-order algorithms to compute the joint gradient of the log posterior in O(N) time, enabling linear scalability with tree size.
• Preconditions the HMC mass matrix using the Hessian of the log-prior to improve mixing and convergence speed.
• Implements the method in BEAST, integrating it with existing phylogenetic inference pipelines for time-measured trees.

Experimental results

Research questions

• RQ1 Can a Bayesian shrinkage model with heavy-tailed priors efficiently infer local clocks in large phylogenies without prior knowledge of clock locations?
• RQ2 Does the proposed HMC-based inference framework scale effectively to large trees while maintaining high sampling efficiency?
• RQ3 How does the shrinkage-clock model compare in accuracy and speed to the random local clock (RLC) model on simulated and real datasets?
• RQ4 What is the heritable clock structure of influenza A virus surface glycoproteins across avian and equine hosts, and are host-specific rate shifts detectable?
• RQ5 How sensitive are the inferred clock locations to the choice of bridge exponent α, and what trade-offs exist between coverage and computational cost?

Key findings

• The shrinkage-clock model achieves over 3-fold speedup in effective sample size per second compared to the random local clock on 20 simulated datasets with 40 taxa.
• The method recovers four known local clocks in the rodent and mammalian adaptive radiation, consistent with RLC estimates and prior studies.
• Influenza A N7 and H7 glycoprotein trees revealed 1 and 7 local clocks, respectively, with the N7 tree showing significant rate variation between eastern and western hemisphere avian lineages.
• Posterior mean root height estimates were 1798 (95% HPD: 1733–1855) for NA N7 and 1853 (1808–1897) for HA H7, within five years of previous estimates despite different tree priors.
• The model detected a slowdown in equine lineage rates, confirming prior findings, and identified a likely clock in the Eastern avian clade of NA N7.
• Users can adjust the bridge exponent α to tune clock detection sensitivity, with smaller α values improving clock resolution at the cost of increased computational time.