Estimating phylogenetic trees with phangorn

In phangorn: Phylogenetic Reconstruction and Analysis

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Introduction

These notes should enable the user to estimate phylogenetic trees from alignment data with different methods using the phangorn package [@Schliep2011] . Several functions of this package are also described in more detail in [@Paradis2012]. For more theoretical background on all the methods see e.g. [@Felsenstein2004; @Yang2006]. This document illustrates some of the package's features to estimate phylogenetic trees using different reconstruction methods.

Getting started

The first thing we have to do is to read in an alignment. Unfortunately there exist many different file formats that alignments can be stored in. In most cases, the function read.phyDat is used to read in an alignment. In the ape package [@Paradis2018] and phangorn, there are several functions to read in alignments, depending on the format of the data set ("nexus", "phylip", "fasta") and the kind of data (amino acid, nucleotides, morphological data). The function read.phyDat calls these other functions and transforms them into a phyDat object. For the specific parameter settings available look in the help files of the function read.dna (for phylip, fasta, clustal format), read.nexus.data for nexus files. For amino acid data additional read.aa is called. Morphological data will be shown later in the vignette Phylogenetic trees from morphological data.

We start our analysis loading the phangorn package and then reading in an alignment.

library(ape)
library(phangorn)
fdir <- system.file("extdata/trees", package = "phangorn")
primates <- read.phyDat(file.path(fdir, "primates.dna"),
                        format = "interleaved")

Distance based methods

After reading in the nucleotide alignment we can build a first tree with distance based methods. The function dist.dna from the ape package computes distances for many DNA substitution models, but to use the function dist.dna, we have to transform the data to class DNAbin. The function dist.ml from phangorn offers the substitution models "JC69" and "F81" for DNA, and also common substitution models for amino acids (e.g. "WAG", "JTT", "LG", "Dayhoff", "cpREV", "mtmam", "mtArt", "MtZoa" or "mtREV24").

After constructing a distance matrix, we reconstruct a rooted tree with UPGMA and alternatively an unrooted tree using Neighbor Joining [@Saitou1987; @Studier1988]. More distance methods like fastme are available in the ape package.

dm  <- dist.ml(primates)
treeUPGMA  <- upgma(dm)
treeNJ  <- NJ(dm)

We can plot the trees treeUPGMA and treeNJ with the commands:

plot(treeUPGMA, main="UPGMA")

plot(treeNJ, "unrooted", main="NJ")

Bootstrap

To run the bootstrap we first need to write a function which computes a tree from an alignment. So we first need to compute a distance matrix and afterwards compute the tree. We can then give this function to the bootstrap.phyDat function.

fun <- function(x) upgma(dist.ml(x))
bs_upgma <- bootstrap.phyDat(primates,  fun)

With the new syntax of R 4.1 this can be written a bit shorter:

bs_upgma <- bootstrap.phyDat(primates,  \(x){dist.ml(x) |> upgma})

Finally, we can plot the tree with bootstrap values added:

plotBS(treeUPGMA, bs_upgma, main="UPGMA")

Distance based methods are very fast and we will use the UPGMA and NJ tree as starting trees for the maximum parsimony and maximum likelihood analyses.

Parsimony

The function parsimony returns the parsimony score, that is the minimum number of changes necessary to describe the data for a given tree. We can compare the parsimony score for the two trees we computed so far:

parsimony(treeUPGMA, primates)
parsimony(treeNJ, primates)

The function most users want to use to infer phylogenies with MP (maximum parsimony) is pratchet, an implementation of the parsimony ratchet [@Nixon1999]. This allows to escape local optima and find better trees than only performing NNI / SPR rearrangements.

The current implementation is

1. Create a bootstrap data set $D_b$ from the original data set.
2. Take the current best tree and perform tree rearrangements on $D_b$ and save bootstrap tree as $T_b$.
3. Use $T_b$ and perform tree rearrangements on the original data set. If this tree has a lower parsimony score than the currently best tree, replace it.
4. Iterate 1:3 until either a given number of iteration is reached (minit) or no improvements have been recorded for a number of iterations (k).

treeRatchet  <- pratchet(primates, trace = 0, minit=100)
parsimony(treeRatchet, primates)

Here we set the minimum iteration of the parsimony ratchet (minit) to 100 iterations, the default number for k is 10. As the ratchet implicitly performs bootstrap resampling, we already computed some branch support, in our case with at least 100 bootstrap iterations. The parameter trace=0 tells the function not write the current status to the console. The function may return several best trees, but these trees have no branch length assigned to them yet. Now let's do this:

treeRatchet  <- acctran(treeRatchet, primates)

After assigning edge weights, we prune away internal edges of length tol (default = 1e-08), so our trees may contain multifurcations.

treeRatchet  <- di2multi(treeRatchet)

Some trees might have differed only between edges of length 0.

if(inherits(treeRatchet, "multiPhylo")){
  treeRatchet <- unique(treeRatchet)
}

As mentioned above, the parsimony ratchet implicitly performs a bootstrap analysis (step 1). We make use of this and store the trees which where visited. This allows us to add bootstrap support values to the tree.

plotBS(midpoint(treeRatchet), type="phylogram")
add.scale.bar()

If treeRatchet is a list of trees, i.e. an object of class multiPhylo, we can subset the i-th trees with treeRatchet[[i]].

While in most cases pratchet will be enough to use, phangorn exports some function which might be useful. random.addition computes random addition and can be used to generate starting trees. The function optim.parsimony performs tree rearrangements to find trees with a lower parsimony score. The tree rearrangements implemented are nearest-neighbor interchanges (NNI) and subtree pruning and regrafting (SPR). The latter so far only works with the fitch algorithm.

treeRA <- random.addition(primates)
treeSPR  <- optim.parsimony(treeRA, primates)
parsimony(c(treeRA, treeSPR), primates)

Branch and bound

For data sets with few species it is also possible to find all most parsimonious trees using a branch and bound algorithm [@Hendy1982]. For data sets with more than 10 taxa this can take a long time and depends strongly on how "tree-like" the data is. And for more than 20-30 taxa this will take almost forever.

(trees <- bab(primates[1:10,]))

Maximum likelihood

The last method we will describe in this vignette is Maximum Likelihood (ML) as introduced by Felsenstein [@Felsenstein1981].

Model selection

Usually, as a first step, we will try to find the best fitting model. For this we use the function modelTest to compare different nucleotide or protein models with the AIC, AICc or BIC, similar to popular programs ModelTest and ProtTest [@Posada1998; @Posada2008; @Abascal2005]. By default available nucleotide or amino acid models are compared.

The Vignette Markov models and transition rate matrices gives further background on those models, how they are estimated and how you can work with them.

mt <- modelTest(primates)

It's also possible to only select some common models:

load("Trees.RData")

mt <- modelTest(primates, model=c("JC", "F81", "K80", "HKY", "SYM", "GTR"), 
                control = pml.control(trace = 0))

The results of modelTest is illustrated in following table:

library(knitr)
kable(mt, digits=2)

To speed computations up the thresholds for the optimizations in modelTest are not as strict as for optim.pml (shown in the coming vignettes) and no tree rearrangements are performed, which is the most time consuming part of the optimizing process. As modelTest computes and optimizes a lot of models it would be a waste of computer time not to save these results. The results are saved as call together with the optimized trees in an environment and the function as.pml evaluates this call to get a pml object back to use for further optimization or analysis. This can either be done for a specific model, or for a specific criterion.

fit <- as.pml(mt, "HKY+G(4)+I")
fit <- as.pml(mt, "BIC")

Conducting a ML tree

To simplify the workflow, we can give the result of modelTest to the function pml_bb and optimize the parameters taking the best model according to BIC. Ultrafast bootstrapping [@minh2013] is conducted automatically if the default rearrangements="stochastic" is used. If rearrangements="NNI" is used, no bootstrapping is conducted.

fit_mt <- pml_bb(mt, control = pml.control(trace = 0))
fit_mt

We can also use pml_bb with a defined model to infer a phylogenetic tree.

fitGTR <- pml_bb(primates, model="GTR+G(4)+I")

Bootstrap

If we instead want to conduct standard bootstrapping [@Felsenstein1985; @Penny1985], we can do so with the function bootstrap.pml:

bs <- bootstrap.pml(fit_mt, bs=100, optNni=TRUE,
    control = pml.control(trace = 0))

Now we can plot the tree with the bootstrap support values on the edges and compare the standard bootstrap values to the ultrafast bootstrap values. With the function plotBS it is not only possible to plot these two, but also the transfer bootstraps [@Lemoine2018] which are especially useful for large data sets.

plotBS(midpoint(fit_mt$tree), p = .5, type="p", digits=2, main="Ultrafast bootstrap")

plotBS(midpoint(fit_mt$tree), bs, p = 50, type="p", main="Standard bootstrap")

plotBS(midpoint(fit_mt$tree), bs, p = 50, type="p", digits=0, method = "TBE", main="Transfer bootstrap")

If we want to assign the standard or transfer bootstrap values to the node labels in our tree instead of plotting it (e.g. to export the tree somewhere else), plotBS gives that option with type = "n": ``` {r assign_bs_values, eval=FALSE}

assigning standard bootstrap values to our tree; this is the default method

tree_stdbs <- plotBS(fit_mt$tree, bs, type = "n")

assigning transfer bootstrap values to our tree

tree_tfbs <- plotBS(fit_mt$tree, bs, type = "n", method = "TBE")

It is also possible to look at `consensusNet` to identify potential conflict.
```r
cnet <- consensusNet(bs, p=0.2)
plot(cnet, show.edge.label=TRUE)

Several analyses, e.g.bootstrap and modelTest, can be computationally demanding, but as nowadays most computers have several cores, one can distribute the computations using the parallel package. However, it is only possible to use this approach if R is running from command line ("X11"), but not using a GUI (for example "Aqua" on Macs) and unfortunately the parallel package does not work at all under Windows.

Exporting a tree

Now that we have our tree with bootstrap values, we can easily write it to a file in Newick-format: ``` {r write_tree, eval=FALSE}

tree with ultrafast bootstrap values

write.tree(fit_mt$tree, "primates.tree")

tree with standard bootstrap values

write.tree(tree_stdbs, "primates.tree")

tree with transfer bootstrap values

write.tree(tree_tfbs, "primates.tree")

## Molecular dating with a strict clock for ultrametric and tipdated phylogenies

When we assume a "molecular clock" phylogenies can be used to infer divergence times [@Zuckerkandl1965]. We implemented a strict clock as described in [@Felsenstein2004], p. 266, allowing to infer ultrametric and tip-dated phylogenies. We need a starting tree that fulfills the assumptions, so either the tree has to be ultrametric, or the constraints given by the tip dates.  
For an ultrametric starting tree we can use an UPGMA or WPGMA tree. 
```r
fit_strict <- pml_bb(primates, model="HKY+G(4)", method="ultrametric",
                     rearrangement="NNI", control = pml.control(trace = 0))

plot(fit_strict)

With phangorn we also can estimate tipdated phylogenies. Here we use a H3N2 virus data set from treetime [@treetime] as an example. Additionally to the alignment we also need to read in data containing the dates of the tips.

fdir <- system.file("extdata/trees", package = "phangorn")
tmp <- read.csv(file.path(fdir,"H3N2_NA_20.csv"))
H3N2 <- read.phyDat(file.path(fdir,"H3N2_NA_20.fasta"), format="fasta")

We first process the sampling dates and create a named vector. The lubridate package [@lubridate] comes in very handy dates in case one has to recode dates, e.g. days and months.

dates <- setNames(tmp$numdate_given, tmp$name)
head(dates)

Again we use the pml_bb function, which optimizes the tree given the constraints of the tip.dates vector.

fit_td <- pml_bb(H3N2, model="GTR+G(4)", method="tipdated", tip.dates=dates, 
               rearrangement="NNI", control = pml.control(trace = 0))

And at last we plot the tree with a timescale.

tree_td <- fit_td$tree
root_time <- max(dates) - max(node.depth.edgelength(tree_td))
plot(tree_td, show.tip.label = FALSE)
axisPhylo(root.time = root_time, backward = FALSE)

While the loglikelihood is lower than for an unrooted tree, we have to keep in mind that rooted trees use less parameters. In unrooted trees we estimate one edge length parameter for each tree, for ultrametric trees we only estimate a parameter for each internal node and for tipdated trees we have one additional parameter for the rate.

\newpage

Session info {.unnumbered}

sessionInfo()

References

phangorn documentation built on Jan. 23, 2023, 5:37 p.m.