# TreeSearch: Morphological Phylogenetic Analysis in R

TreeSearch is an R package for phylogenetic analysis, optimized for discrete character data. Tree search may be conducted using equal or implied step weights with an explicit (albeit inexact) allowance for inapplicable character entries, avoiding some of the pitfalls inherent in standard parsimony methods. Profile parsimony and user-specified optimality criteria are supported. A graphical interface, which requires no familiarity with R, is designed to help a user to improve the quality of datasets through critical review of underpinning character codings; and to obtain additional information from results by identifying and summarizing clusters of similar trees, mapping the distribution of trees, and removing ‘rogue’ taxa that obscure underlying relationships. Taken together, the package aims to support methodological rigour at each step of data collection, analysis, and the exploration of phylogenetic results.

Martin R. Smith https://smithlabdurham.github.io/ (University of Durham)
2023-02-10

# 1 Introduction

Even in the phylogenomic era, morphological data make an important contribution to phylogenetic questions. Discrete phenotypic data improve the accuracy and resolution of phylogenetic reconstruction even when outnumbered by molecular characters, and are the only way to incorporate the unique perspective on historical events that fossil taxa provide .

One challenge with morphological analysis is the treatment of inapplicable character states: for example, ‘tail colour’ cannot logically be ascribed either of the states ‘red’ or ‘blue’ in a taxon that lacks a tail . This situation can profoundly mislead phylogenetic analysis, and is not handled appropriately by any standard Markov model or parsimony method.

Solutions to this issue have recently been proposed . Where a single ‘principal’ character (e.g. ‘tail’) exhibits $$n$$ ‘contingent’ characters (e.g. ‘tail colour’, ‘tail covering’), ‘exact’ solutions require the construction of multi-state hierarchies containing $$O(2^n)$$ entries, meaning that analysis is only computationally tractable for simple hierarchies with few contingent characters. Moreover, these approaches cannot accommodate characters that are contingent on more than one principal character: for example, characters describing appendages on a differentiated head may be contingent on the presence of the two characters ‘appendages’ and ‘differentiated head’.

Such situations can be approached using the flexible parsimony approximation proposed by Brazeau et al. (2019). TreeSearch scores trees using the “Morphy” C implementation of this algorithm . Morphy implements tree search under equal step weights. TreeSearch additionally implements implied step weighting , a method which consistently finds more accurate and precise trees than equal weights parsimony .

There has been lively discussion as to whether, with the rise of probabilistic approaches, parsimony remains a useful tool for morphological phylogenetics . Notwithstanding scenarios that go beyond the limits of parsimony, such as the simultaneous incorporation of stratigraphic data and other prior knowledge (e.g. Guenser et al. 2021), neither parsimony nor probabilistic methods consistently recover ‘better’ trees when gains in accuracy are balanced against losses in precision . Even if probabilistic methods may eventually be improved through the creation of more sophisticated models that better reflect the nature of morphological data , parsimony analysis remains a useful tool – not only because treatments of inapplicable character states are presently available, but also because it facilitates a deeper understanding of the underpinning data by emphasizing the reciprocal relationship between a tree and the synapomorphies that it implies.

Whatever method is used to find phylogenetic trees, a single consensus tree may fail to convey all the signal in a set of phylogenetic results . A set of optimal trees can be better interpreted by examining consensus trees generated from clusters of similar trees ; by exploring tree space and by automatically identifying, annotating and removing ‘wildcard’ taxa whose ‘rogue’ behaviour may reflect underlying character conflict or ambiguity . These methods are not always easy to integrate into phylogenetic workflows, so are not routinely included in empirical studies.

TreeSearch provides functions that allow researchers to engage with the three main aspects of morphological phylogenetic analysis: dataset construction and validation; phylogenetic search (including with inapplicable data); and the interrogation of optimal tree sets (Fig. 1). These functions can be accessed via the R command-line, as documented within the package and at ms609.github.io/TreeSearch, or through a graphical user interface (GUI). The GUI includes options to export a log of executed commands as a fully reproducible R script, and to save outputs in graphical, Nexus or Newick formats.

# 2 Implementation

## Tree scoring

TreeSearch can score trees using equal weights, implied weighting , or profile parsimony . The function TreeLength() calculates tree score using the “Morphy” phylogenetic library , which implements the Fitch (1971) and Brazeau et al. (2019) algorithms. Morphy returns the equal weights parsimony score of a tree against a given dataset. Implied weights and profile parsimony scores are computed by first making a separate call to Morphy for each character in turn, passed as a single-character dataset; then passing this value to the appropriate weighting formula and summing the total score over all characters.

Implied weighting is an approximate method that treats each additional step (i.e. transition between tokens) in a character as less surprising – and thus requiring less penalty – than the previous step. Each additional step demonstrates that a character is less reliable for phylogenetic inference, and thus more likely to contain additional homoplasy. The score of a tree under implied weighting is $$\sum{\frac{e_i}{e_i+k}}$$, where $$e_i$$ denotes the number of extra steps observed in character $$i$$, and is derived by subtracting the minimum score that the character can obtain on any tree from the score observed on the tree in question . The minimum length of a tree is one less than the number of unique tokens (excluding the inapplicable token ‘-’) that must be present.

Profile parsimony represents an alternative formulation of how surprising each additional step in a character is : the penalty associated with each additional step in a character is a function of the probability that a character will fit at least as well as is observed on a uniformly selected tree. On this view, an additional step is less surprising if observed in a character where there are more opportunities to observe homoplasy, whether because a character contains fewer ambiguous codings (a motivation for the ‘extended’ implied weighting of Goloboff (2014)) or because states are distributed more evenly in a character, whose higher phylogenetic information content corresponds to a lower proportion of trees in which no additional steps are observed.

TreeSearch calculates the profile parsimony score by computing the logarithm of the number of trees onto which a character can be mapped using $$m$$ steps, using theorem 1 of Carter et al. (1990). As computation for higher numbers of states is more computationally complex, the present implementation is restricted to characters that contain two informative applicable states, and uses the Fitch (1971) algorithm.

The TreeSearch GUI uses the routine MaximizeParsimony() to search for optimal trees using tree bisection and reconnection (TBR) searches and the parsimony ratchet . This goes beyond the heuristic tree search implementation in the R package phangorn by using compiled C++ code to rearrange trees, dramatically accelerating computation, and thus increasing the scale of dataset that can be analysed in reasonable time; and in supporting TBR rearrangements, which explore larger neighbourhoods of tree space: TBR evaluates more trees than nearest-neighbour interchanges or subtree pruning and regrafting, leading to additional computational expense that is offset by a decreased likelihood that search will become trapped in a local optimum .

By default, search begins from a greedy addition tree generated by function AdditionTree(), which queues taxa in a random order, then attaches each taxon in turn to the growing tree at the most parsimonious location. Search may also be started from neighbour-joining trees, or the results of a previous search.

Search commences by conducting TBR rearrangements – a hill-climbing approach that locates a locally optimal tree from which no tree accessible by a single TBR rearrangement has a better score. A TBR iteration breaks a randomly selected edge in the focal tree, and reconnects each possible pair of edges in the resultant sub-trees to produce a list of candidate trees. Entries that are inconsistent with user-specified topological constraints are removed; remaining trees are inserted into a queue and scored in a random sequence. If the score of a candidate tree is at least as good as the best yet encountered (within the bounds of an optional tolerance parameter $$\epsilon$$, which allows the retention of almost-optimal trees in order to improve accuracy – see e.g. Smith (2019a)), this tree is used as the starting point for a new TBR iteration. Otherwise, the next tree in the list is considered. TBR search continues until the best score is found a specified number of times; a specified number of TBR break points have been evaluated without any improvement to tree score; or a set amount of time has passed.

When TBR search is complete, iterations of the parsimony ratchet are conducted in order to search areas of tree space that are separated from the best tree yet found by ‘valleys’ that cannot be traversed by TBR rearrangements without passing through trees whose optimality score is below the threshold for acceptance. Each ratchet iteration begins by resampling the original matrix. A round of TBR search is conducted using this resampled matrix, and the tree thus produced is used as a starting point for a new round of TBR search using the original data. After a specified number of ratchet iterations, an optional final round of TBR search allows a denser sampling of optimal trees from the final region of tree space.

A simple example search can be conducted using a morphological dataset included in the package, taken from Vinther et al. (2008):

library("TreeSearch")
vinther <- inapplicable.phyData[["Vinther2008"]]
trees <- MaximizeParsimony(vinther, concavity = 10, tolerance = 0.05)

The MaximizeParsimony() command performs tree search under implied weights with a concavity value of 10 (concavity = Inf would select equal weights), retaining any tree whose score is within 0.05 of the best score.

The resulting trees can be summarised according to their scores (optionally, against a different dataset or under a different weighting strategy, as specified by concavity) and the iteration in which they were first hit:

TreeLength(trees, dataset = vinther, concavity = 10) |>
signif() |>         # truncate non-significant digits
table()             # tabulate by score

1.52814 1.54329  1.5641
3      45       4 
attr(trees, "firstHit")
  seed  start ratch1 ratch2 ratch3 ratch4 ratch5 ratch6 ratch7  final
0     29      4      0     10      7      2      0      0      0 

More flexible, if less computationally efficient, tree searches can be conducted at the command line using the TreeSearch(), Ratchet() and Bootstrap() commands, which support custom tree optimality criteria .

## Visualization

The distribution of optimal trees, however obtained, can be visualized through interactive mappings of tree space . The TreeSearch GUI supports the use of information theoretic distances ; the quartet distance ; or the Robinson–Foulds distance to construct tree spaces, which are mapped into 2–12 dimensions using principal coordinates analysis . The degree to which a mapping faithfully depicts original tree-to-tree distances is measured using the product of the trustworthiness and continuity metrics , a composite score denoting the degree to which points that are nearby when mapped are truly close neighbours (trustworthiness), and the degree to which nearby points remain nearby when mapped (continuity). Plotting the minimum spanning tree – the shortest path that connects all trees – can highlight stress in a mapping (grey lines in Fig. 2): the spatial relationships of trees are distorted in regions where the minimum spanning tree takes a circuitous route to connect trees that are mapped close to one another (see fig. 1a–b in Smith 2022a).

To relate the geometry of tree space to the underlying trees, each point in tree space may be annotated according to the optimality score of its corresponding tree under a selected step weighting scheme; by the relationships between chosen taxa that are inferred by that tree; and by the search iteration in which the tree was first found by tree search (Fig. 2).

Annotating trees by the iteration in which they were first found allows a user to evaluate whether a continuation of tree search is likely to yield more optimal trees. For example, if the retained trees were only recently found, the search may not yet have located a global optimum. Alternatively, if certain regions of tree space are visited only by a single ratchet iteration, it is possible that further isolated ‘islands’ remain to be found; continuing tree search until subsequent ratchet iterations no longer locate new clusters of trees will reduce the chance that optimal regions of tree space remain unvisited.

As the identification of clusters from mappings of tree space can be misleading , TreeSearch identifies clusters of trees from tree-to-tree distances using K-means++ clustering, partitioning around medoids and hierarchical clustering with minimax linkage . Clusterings are evaluated using the silhouette coefficient, a measure of the extent of overlap between clusters . The clustering with the highest silhouette coefficient is depicted if the silhouette coefficient exceeds a user-specified threshold; the interpretation of the chosen threshold according to Kaufman and Rousseeuw (1990) is displayed to the user. Plotting a separate consensus tree for each cluster often reveals phylogenetic information that is concealed by polytomies in the single ‘plenary’ consensus of all optimal trees .

Plenary consensus trees can also lack resolution because of wildcard or ‘rogue’ taxa, in which conflict or ambiguity in their character codings leads to an unsettled phylogenetic position . TreeSearch detects rogue taxa using a heuristic approach that seeks to maximize the phylogenetic information content (sensu Thorley et al. 1998) of a consensus tree created after removing rogue taxa from input trees. The position of an excluded taxon is portrayed by shading each edge or node of the consensus according to the number of times the specified taxon occurs at that position on an underlying tree [Fig. 3; after Klopfstein and Spasojevic (2019)], equivalent to the ‘branch attachment frequency’ of Phyutility .

Identifying taxa with an unstable position, and splits with low support, can help an investigator to critically re-examine character codings; to this end, each edge of the resulting consensus can be annotated with the frequency of the split amongst the tree set, or with a concordance factor denoting the strength of support from the underlying dataset.

## Dataset review

Ultimately, the quality of a dataset plays a central role in determining the reliability of phylogenetic results, with changes to a relatively small number of character codings potentially exhibiting an outsized impact on reconstructed topologies . Nevertheless, dataset quality does not always receive commensurate attention . One step towards improving the rigour of morphological datasets is to annotate each cell in a dataset with an explicit justification for each taxon’s coding , which can be accomplished in Nexus-formatted data files using software such as MorphoBank .

TreeSearch presents such annotations alongside a reconstruction of each character’s states on a specified tree, with inapplicable states mapped according to the algorithm of Brazeau et al. (2019). Neomorphic (presence/absence) and transformational characters are distinguished by reserving the token 0 to solely denote the absence of a neomorphic character, with tokens 1n used to denote the $$n$$ states of a transformational character . In order to identify character codings that contribute to taxon instability, each leaf is coloured according to its mean contribution to tree length for the visualized character .

This visualization of reconstructed character transitions can help to identify cases where the formulation of characters has unintended consequences ; where inapplicable states have been inconsistently applied ; where taphonomic absence is wrongly coded as biological absence ; where previous datasets are uncritically recycled ; or where taxa are coded with more confidence than a critical evaluation of available evidence can truly support. Insofar as the optimal tree and the underlying characters are reciprocally illuminating , successive cycles of phylogenetic analysis and character re-formulation can improve the integrity of morphological datasets, and thus increase their capacity to yield meaningful phylogenetic results .

# 3 Availability

TreeSearch can be installed through the Comprehensive R Archive Network (CRAN) using install.packages("TreeSearch"); the graphical user interface is launched with the command TreeSearch::EasyTrees(). The package has been tested on Windows 10, Mac OS X 10 and Ubuntu 20, and requires only packages available from the CRAN repository. Source code is available at https://github.com/ms609/TreeSearch/, and is permanently archived at Zenodo (https://dx.doi.org/10.5281/zenodo.1042590). Online documentation is available at https://ms609.github.io/TreeSearch/.

# 4 Acknowledgements

I thank Alavya Dhungana and Joe Moysiuk for feedback on preliminary versions of the software, and Martin Brazeau and anonymous referees for comments on the manuscript. Functionality in TreeSearch employs the underlying R packages ape , phangorn , Quartet , Rogue , shiny , shinyjs , TreeDist , and TreeTools . Icons from R used under GPL-3; Font Awesome, CC-BY-4.0.

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### Citation

Smith, "The R Journal: TreeSearch: Morphological Phylogenetic Analysis in R", The R Journal, 2023

BibTeX citation

@article{RJ-2023-019,
author = {Smith, Martin R.},
title = {The R Journal: TreeSearch: Morphological Phylogenetic Analysis in R},
journal = {The R Journal},
year = {2023},
note = {https://doi.org/10.32614/RJ-2023-019},
doi = {10.32614/RJ-2023-019},
volume = {14},
issue = {4},
issn = {2073-4859},
pages = {305-315}
}