On defining and finding islands of trees and mitigating large island bias

How best can we summarise 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 bootst...