Additive Uncorrelated Relaxed Clock Models for the Dating of Genomic Epidemiology Phylogenies

Abstract

Phylogenetic dating is one of the most powerful and commonly used methods of drawing epidemiological interpretations from pathogen genomic data. Building such trees requires considering a molecular clock model which represents the rate at which substitutions accumulate on genomes. When the molecular clock rate is constant throughout the tree then the clock is said to be strict, but this is often not an acceptable assumption. Alternatively, relaxed clock models consider variations in the clock rate, often based on a distribution of rates for each branch. However, we show here that the distributions of rates across branches in commonly used relaxed clock models are incompatible with the biological expectation that the sum of the numbers of substitutions on two neighbouring branches should be distributed as the substitution number on a single branch of equivalent length. We call this expectation the additivity property. We further show how assumptions of commonly used relaxed clock models can lead to estimates of evolutionary rates and dates with low precision and biased confidence intervals. We therefore propose a new additive relaxed clock model where the additivity property is satisfied. We illustrate the use of our new additive relaxed clock model on a range of simulated and real datasets, and we show that using this new model leads to more accurate estimates of mean evolutionary rates and ancestral dates.

Salmonella enterica from a soldier from the 1652 siege of Barcelona (Spain) supports historical transatlantic epidemic contacts

“…We estimated a mutation rate for this clade over the clonal frame to 1.02 × 10 −4 mutations per site per year. This mutation rate corresponds well with the rates reported for other S. enterica serovars ( Okoro et al., 2012 ; Hawkey et al., 2013 ; Octavia et al., 2015 ) and is similar to recent estimates following equivalent approximations ( Didelot et al., 2021 ).

Figure 4 Temporal signal in the Paratyphi C clade (A) Regression of the root-to-tip distance and collection date of the samples present in the tree, with 1 × 10 7 permutations.

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Accounting for the Biological Complexity of Pathogenic Fungi in Phylogenetic Dating

“…Depending on the data, variations of the relaxed clock model, such as the fixed local clock, whereby the underlying tree has a constant rate, but the rate of each clade is able to differ from this global rate [ 99 ]; the uncorrelated relaxed clock, whereby each branch of the tree is allowed its own mutation rate independent of the rate on neighbouring branches [ 98 ]; or the random local clock, which forms an interim between the strict and relaxed clocks, where each branch can take a different rate or remain the same as one another [ 100 ]. More recently, additive clock models have been proposed that satisfy the additive property often unsatisfied by conventional relaxed clock models [ 101 ] and may in most cases be more appropriate than the conventional relaxed clock. In the fungal studies identified, both C. auris papers (Chow and Rhodes) utilised strict clock models, seemingly without comparison with alternative options.…”

Genomic epidemiology of SARS-CoV-2 transmission lineages in Ecuador

“…The systematically subsampled data set was analysed with BEAST v1.10.5 (https://github.com/beast-dev/beast-mcmc/releases/tag/v1.10.5pre_thorney) using a newly implemented method that estimates the tree likelihood at each point of the MCMC chain. This approach takes a data tree (the aforementioned re-rooted ML tree) instead of an alignment and significantly reduces analysis time by using a simple model to rescale the ML phylogeny into a time-calibrated tree (see 38). Under this approach, the likelihood of each branch length is defined as a function of a Poisson distribution with a mean directly proportional to the clock rate (38,39); we therefore used a rate of 6.28x10 -4 substitutions/site/year, based on the median clock rate estimate obtained from our exploratory analysis.…”

“…This approach takes a data tree (the aforementioned re-rooted ML tree) instead of an alignment and significantly reduces analysis time by using a simple model to rescale the ML phylogeny into a time-calibrated tree (see 38). Under this approach, the likelihood of each branch length is defined as a function of a Poisson distribution with a mean directly proportional to the clock rate (38,39); we therefore used a rate of 6.28x10 -4 substitutions/site/year, based on the median clock rate estimate obtained from our exploratory analysis. We also defined a coalescent Skygrid prior, similar to the one described for the exploratory analysis.…”