# Estimation of time scaled phylogenies

The principal functionality of TreeTime is estimating time trees from an initial tree topology, a set of date constraints (e.g. tip dates), and an alignment (optional). This tutorial uses data provided in the github repository github.com/neherlab/treetime_examples.

```
treetime --tree data/h3n2_na/h3n2_na_20.nwk --dates data/h3n2_na/h3n2_na_20.metadata.csv --aln data/h3n2_na/h3n2_na_20.fasta --outdir h3n2_timetree
```

The tree can be in newick or nexus format, the alignment in fasta or phylip, and the dates should be given as a tsv or csv file. TreeTime will attempt to parse dates, preferred formats are “%Y-%m-%d” or numerical as in YYYY.F (where ‘F’ is the fraction of the year that has passed, in days. For example 2016.04918 means that 18/366 days of 2016 have passed). This command will estimate an GTR model, a molecular clock model, and a time-stamped phylogeny. The results are saved to several files in the directory specified as outdir and printed to standard out:

```
Inferred GTR model:
Substitution rate (mu): 1.0
Equilibrium frequencies (pi_i):
A: 0.2983
C: 0.1986
G: 0.2353
T: 0.2579
-: 0.01
Symmetrized rates from j->i (W_ij):
A C G T -
A 0 0.8273 2.8038 0.4525 1.031
C 0.8273 0 0.5688 2.8435 1.0561
G 2.8038 0.5688 0 0.6088 1.0462
T 0.4525 2.8435 0.6088 0 1.0418
- 1.031 1.0561 1.0462 1.0418 0
Actual rates from j->i (Q_ij):
A C G T -
A 0 0.2468 0.8363 0.135 0.3075
C 0.1643 0 0.1129 0.5646 0.2097
G 0.6597 0.1338 0 0.1432 0.2462
T 0.1167 0.7332 0.157 0 0.2686
- 0.0103 0.0106 0.0105 0.0104 0
Root-Tip-Regression:
--rate: 2.613e-03
--chi^2: 22.16
--r^2: 0.98
--- saved tree as
h3n2_timetree/timetree.pdf
--- alignment including ancestral nodes saved as
h3n2_timetree/ancestral_sequences.fasta
--- saved divergence times in
h3n2_timetree/dates.tsv
--- tree saved in nexus format as
h3n2_timetree/timetree.nexus
--- root-to-tip plot saved to
h3n2_timetree/root_to_tip_regression.pdf
```

Other output files include an alignment with reconstructed ancestral sequences, an annotated tree in nexus format in which branch length correspond to years and mutations and node dates (in the numeric format detailed above) are added as comments to each node. In addition, the root-to-tip vs time regression and the tree are drawn and saved to file.

## Accounting for phylogenetic covariance

The root-to-tip distances of samples are expected to increase with sampling date and TreeTime uses this behavior to estimate clock rates. However, these root-to-tip distances are correlated due to shared ancestry. This can be efficiently accounted if the sequence data set is consistent with a simple strict molecular clock model, but can give misleading results when the molecular clock model is violated. This feature is hence off by default and can be switched on using the flag

```
--covariation
```

## Fixed evolutionary rate

If the temporal signal in the data is weak and the clock rate can’t be estimated confidently from the data, it is advisable to specify the rate explicitly. This can be done using the argument

```
--clock-rate <rate>
```

## Divergence times inference methods

TimeTree estimates optimal time trees by chosing node positions/ divergence times that optimize the joint or marginal likelihood.

The **joint maximum-likelihood** assignment corresponds to the global configuration with the highest likelihood, however it gives no information about the confidence of divergence time estimates.
The **marginal maximum-likelihood** assignment assigns nodes to their most likely divergence time after integrating over all possible configurations of the other nodes, it enables the computation of divergence time confidence intervals.

Which ‘method’ of divergence time estimation is used can be specified with the flag:

```
--time-marginal <method>
```

It is possible to run iterations of TreeTime using different methods.
If `‘false’`

or `‘never’`

, TreeTime uses the jointly most likely values for the divergence times. If `‘true’`

or `‘always’`

TreeTime uses the marginal inference mode at every
round of optimization, `‘only-final’`

(or `‘assign’`

for compatibility with previous versions) only uses the marginal distribution in the final round.

In versions 0.9 and higher the marginal-likelihood assignment was sped up by using the Fast Fourier Transform to calculate convolution integrals. Now the time complexity of marginal and joint likelihood calculations is comparable, whereas in versions prior to 0.9 the joint likelihood assignment was 2-3 times faster. To maintain compatibility with previous versions the joint maximum-likelihood assignment is still preformed as a default, however the marginal-likelihood assignment is now recommended.

## Confidence intervals

In its default setting, TreeTime does not estimate confidence intervals of divergence times.
Such estimates require calculation of the marginal probability distributions of the dates of the internal nodes.
To switch on confidence estimation, pass the flag `--confidence`

.
If the `--time-marginal`

method is in `['false', 'never']`

TreeTime will run another round of marginal timetree reconstruction to calculate the marginal probability distribution of the nodes. Otherwise, TreeTime will use the marginal
probability distribution calculated in the last round of time tree reconstruction and determine the region that contains 90% of the marginal probability distribution of the node dates.
These intervals are drawn into the tree graph and written to the dates file.

## Specify or estimate coalescent models

TreeTime can be run either without a tree prior or with a Kingman coalescent tree prior. The later is parameterized by a time scale ‘Tc’ which can vary in time. This time scale is often called ‘effective population size’ Ne, but the appropriate Tc has very little to do with census population sizes. To activate the Kingman Coalescent model in TreeTime, you need to add the flag

```
--coalescent <arg>
```

where the argument is either a floating point number giving the time scale of coalescence in units of divergence, ‘const’ to have TreeTime estimate a constant merger rate, or ‘skyline’.
In the latter case, TreeTime will estimate a piece-wise linear merger rate trajectory and save this in files ending on `skyline.tsv`

and `skyline.pdf`

The following command will run TreeTime on the ebola example data set and estimate a time tree along with a skyline (this will take a few minutes).

```
treetime --tree data/ebola/ebola.nwk --dates data/ebola/ebola.metadata.csv --aln data/ebola/ebola.fasta --outdir ebola --coalescent skyline
```

The number of grid points in the skyline model can be additionally specified using the flag

```
--n-skyline <n_skyline_grid_points>
```

The coalescent model requires the number of lineages in the tree at any given time for estimating the probability of a coalecent event. In the default setting the current estimates of divergence times are used for calculating the number of lineages, if the certainty of these estimates should be accounted for the posterior probability distributions of divergence times can be used by adding the flag

```
--n-branches-posterior
```

this should smooth the coalescence likelihood distributions.

## VCF files as input

In addition to standard fasta files, TreeTime can ingest sequence data in form of vcf files which is common for bacterial data sets where short reads are mapped against a reference and only variable sites are reported. The following example with a set of MtB sequences uses a fixed evolutionary rate of 1e-7 per site and year.

```
treetime --aln data/tb/lee_2015.vcf.gz --vcf-reference data/tb/tb_ref.fasta --tree data/tb/lee_2015.nwk --clock-rate 1e-7 --dates data/tb/lee_2015.metadata.tsv
```

For many bacterial data sets where the temporal signal in the data is weak, it is advisable to fix the rate of the molecular clock explicitly. Divergence times, however, will depend on this choice.