# treestructure applied to structured coalescent simulation

#### Erik Volz

#### 2025-09-27

# Structured coalescent simulation

This example shows the function `trestruct` applied to a simulated structured coalescent tree that includes samples from a large constant size population and samples from three small ‘outbreaks’ which are growing exponentially. These simulations were generated with the phydynR package.

    library(ape)
    library(treestructure)
    library(ggtree)

Load the tree:

    ( tree <- ape::read.tree( system.file('sim.nwk', package = 'treestructure') ) )
    #>
    #> Phylogenetic tree with 275 tips and 274 internal nodes.
    #>
    #> Tip labels:
    #>   1, 1, 1, 1, 1, 1, ...
    #>
    #> Rooted; includes branch length(s).

Note that the tip labels corresponds to the deme of each sample. ‘1’ is the constant size reservoir, and ‘0’ is the exponentially growing deme.

This will run the `treestructure` algorithm under default setting:

    s <- trestruct( tree )
    #> Tree has NA or duplicated tip labels. Adding a unique id.
    #> Finding splits under nodes: 276
    #> Finding splits under nodes: 276 526
    #> Finding splits under nodes: 276 421
    #> Finding splits under nodes: 276 473

You can print the results:

    print(s)
    #> Call:
    #> .trestruct(tre = tre, minCladeSize = minCladeSize, minOverlap = minOverlap,
    #>     nodeSupportValues = nodeSupportValues, nodeSupportThreshold = nodeSupportThreshold,
    #>     nsim = nsim, level = level[1], ncpu = ncpu, verbosity = verbosity,
    #>     debugLevel = debugLevel, useNodeSupport = useNodeSupport,
    #>     tredat = tredat)
    #>
    #> Significance level: 0.01
    #> Number of clusters: 4
    #> Number of partitions: 2
    #> Number of taxa in each cluster:
    #>
    #>   1   2   3   4
    #>  25  25 200  25
    #> Number of taxa in each partition:
    #>
    #>   1   2
    #>  75 200
    #> ...
    #> For complete data, use `as.data.frame(...)`

## Plotting results

The default plotting behavior uses the `ggtree` package if available.

    plot(s)  + ggtree::geom_tiplab()

If not, or if desired, `ape` plots are available

    plot( s, use_ggtree = FALSE )

For subsequent analysis, you may want to turn the `treestructure` result into a dataframe:

    structureData <- as.data.frame( s )
    head( structureData )
    #>   taxon cluster partition
    #> 1   1_1       3         2
    #> 2   2_1       3         2
    #> 3   3_1       3         2
    #> 4   4_1       3         2
    #> 5   5_1       3         2
    #> 6   6_1       3         2

Each cluster and partition assignment is stored as a factor. You could use `split` to get a data frame for each partition. Suppose we want a tree corresponding to partition 1:

    with ( structureData,
           ape::keep.tip(s$tree, taxon[ partition==1 ] )
           ) -> partition1
    partition1
    #>
    #> Phylogenetic tree with 75 tips and 74 internal nodes.
    #>
    #> Tip labels:
    #>   143_0, 144_0, 145_0, 146_0, 147_0, 148_0, ...
    #>
    #> Rooted; includes branch length(s).
    plot(partition1)

## Parameter choice and number of clusters

Two parameters will have large influence on results:

1. `level` is the significance level for subdividing a clade into a new cluster. To detect more clusters, increase `p`, but note that this will also increase the false positive rate.
2. `minCladeSize` controls the smallest allowed cluster size in terms of the number of tips. With a smaller value, smaller clusters may be detected, but computation time will increase.

Example:

    trestruct( tree, level = .05, minCladeSize = 5 )
    #> Tree has NA or duplicated tip labels. Adding a unique id.
    #> Finding splits under nodes: 276
    #> Finding splits under nodes: 276 526
    #> Finding splits under nodes: 276 421
    #> Finding splits under nodes: 276 473
    #> Finding splits under nodes: 276 359
    #> Finding splits under nodes: 276 277
    #> Call:
    #> .trestruct(tre = tre, minCladeSize = minCladeSize, minOverlap = minOverlap,
    #>     nodeSupportValues = nodeSupportValues, nodeSupportThreshold = nodeSupportThreshold,
    #>     nsim = nsim, level = level[1], ncpu = ncpu, verbosity = verbosity,
    #>     debugLevel = debugLevel, useNodeSupport = useNodeSupport,
    #>     tredat = tredat)
    #>
    #> Significance level: 0.05
    #> Number of clusters: 6
    #> Number of partitions: 2
    #> Number of taxa in each cluster:
    #>
    #>   1   2   3   4   5   6
    #>  25  25  25   6  29 165
    #> Number of taxa in each partition:
    #>
    #>   1   2
    #>  75 200
    #> ...
    #> For complete data, use `as.data.frame(...)`

In practice, clustering thresholds are always subjective and the best value of the `level` parameter will depend on your application. One way to choose an appropriate `level` would be to use additional data associated with each sample. You can select the `level` which gives a set of clusters that explains the most variance in the data of interest (e.g. use the cluster as a factor in an ANOVA).

### CH index

Alternatively, in the absence of any additional data, the `treestructure` package supports using the CH index to compare different `level`s. This statistic is based on the ratio of the between-cluster and within-cluster variance of the time of each node (distance from the root) and returns the `level` such that this ratio is maximized. If you wish to use the CH index, pass `level = NULL` to `trestruct`, and read documentation for the `levellb`, `levelub`, and `res` parameters.