title: The most parsimonious tree for random data.
abstract: Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree 'shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each possible binary phylogenetic tree has exactly the same distribution for its parsimony score. Despite this pleasing and slightly surprising symmetry, some binary phylogenetic trees are more likely than others to be a most parsimonious (MP) tree for a sequence of k such characters, as we show. For k=2, and unrooted binary trees on six taxa, any tree with a caterpillar shape has a higher chance of being an MP tree than any tree with a symmetric shape. On the other hand, if we take any two binary trees, on any number of taxa, we prove that this bias between the two trees vanishes as the number of characters k grows. However, again there is a twist: MP trees on six taxa for k=2 random binary characters are more likely to have certain shapes than a uniform distribution on binary phylogenetic trees predicts. Moreover, this shape bias appears, from simulations, to be more pronounced for larger values of k.
authors: Department for Mathematics and Computer Science, Ernst-Moritz-Arndt University, Greifswald, Germany.
authors: Mareike
authors: M
authors: Fischer
authors: Department for Mathematics and Computer Science, Ernst-Moritz-Arndt University, Greifswald, Germany.
authors: Michelle
authors: M
authors: Galla
authors: Department for Mathematics and Computer Science, Ernst-Moritz-Arndt University, Greifswald, Germany.
authors: Lina
authors: L
authors: Herbst
authors: Allan Wilson Centre, University of Canterbury, Christchurch, New Zealand. Electronic address: mike.steel@canterbury.ac.nz.
authors: Mike
authors: M
authors: Steel
mesh_terms: D015982:Bias; D008957:Models, Genetic; D010802:Phylogeny; D017422:Sequence Analysis, DNA
keywords: Central limit theorem; Maximum parsimony; Random data; Tree