Abstract
How best can we summarize sets of phylogenetic trees? Systematists have relied heavily on consensus methods, but if tree distributions can be partitioned into distinct subsets, it may be helpful to provide separate summaries of these rather than relying entirely upon a single consensus tree. How sets of trees can most helpfully be partitioned and represented leads to many open questions, but one natural partitioning is provided by the islands of trees found during tree searches. Islands that are of dissimilar size have been shown to yield majority-rule consensus trees dominated by the largest sets We illustrate this large island bias and approaches that mitigate its impact by revisiting a recent analysis of phylogenetic relationships of living and fossil amphibians. We introduce a revised definition of tree islands based on any tree-to-tree pairwise distance metric that usefully extends the notion to any set or multiset of trees, as might be produced by, for example, Bayesian or bootstrap methods, and that facilitates finding tree islands a posteriori. We extract islands from a tree distribution obtained in a Bayesian analysis of the amphibian data to investigate their impact in that context, and we compare the partitioning produced by tree islands with those resulting from some alternative approaches. Distinct subsets of trees, such as tree islands, should be of interest because of what they may reveal about evolution and/or our attempts to understand it, and are an important, sometimes overlooked, consideration when building and interpreting consensus trees. [Amphibia; Bayesian inference; consensus; parsimony; partitions; phylogeny; Chinlestegophis.]
Highlights
Phylogenetic analyses may recover multiple trees, either by design (e.g., Bayesian inference and resampling techniques) or because the data support multiple sufficiently optimal solutions
Strict consensus trees display just those splits that are present in all input trees, a subset of those displayed by majority-rule trees, and are mainly used to summarize sets of most parsimonious trees (MPTs)
The majority-rule consensus of these trees is highly congruent with their Bayesian analysis, it is noteworthy that none of the approximately 25 internal branches separating the Gymnophiona from their more traditional placement with Batrachia occur in every MPT and that, in a bootstrap analysis, none garnered support of more than 50%
Summary
Presence of each area of local instability is denoted by a plus sign (+), and the islands are identified by their size. To further ensure results were not unduly affected by stochastic errors introduced by the random draw of input trees, we repeated the random selection and consensus computations 1000 times (see Appendix A.1 for implementation, for single and multiple replicates) Both the strict and standard majority-rule consensus trees of these 1000 rarefied majority-rule consensus have the same topology as the weighted-by-island-size majority-rule consensus (Fig. 4), emphasizing that the two approaches are both attempting to remove large island bias by giving islands equal weight. Tahiri et al (2018) found that their k-medoids algorithm performs best with the nonsquared RF distance and the Silhouette validity index, and that it cannot deal with single cluster data sets We ran their k-medoids implementation under the recommended setting, which yielded two clusters for the MPT distribution, corresponding to the extended and restricted Lissamphibia groups of trees, so one cluster includes the three smallest islands, while the other is made up of the two largest islands. While unsurprising that the various methods considered sometimes yield somewhat different partitionings, it is noteworthy that several produce partitionings that are either identical to or otherwise similar to islands
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