The most parsimonious tree for random data

TL;DR

This paper investigates the bias of maximum parsimony in reconstructing phylogenetic trees from random data, revealing shape preferences and their persistence even as data size increases.

Contribution

It demonstrates that certain tree shapes are more likely to be MP trees from random data and analyzes how these biases behave with increasing data.

Findings

Caterpillar-shaped trees are more likely to be MP trees for small data sets.

Biases in tree shape preferences diminish as the number of characters increases.

Certain shape biases persist even with large data sets, contrary to initial expectations.

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 grows. However, again there is a twist: MP trees on six taxa are more likely to have certain shapes than a uniform distribution on binary phylogenetic trees predicts, and this difference does not appear to dissipate as $k$ grows.