Phylogenetic Applications of the Minimum Contradiction Approach on Continuous Characters

TL;DR

This paper explores how continuous variables can be represented as phylogenetic trees or split networks using the Minimum Contradiction method, with applications to biological craniofacial data and galaxy properties.

Contribution

It introduces conditions for representing continuous data as phylogenetic structures and demonstrates the method on biological and astronomical datasets.

Findings

Conditions for continuous variables to form X-trees or split networks.

Application of the method to craniofacial landmarks in Hominids.

Discretization of galaxy data without losing phylogenetic structure.

Abstract

We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa, the variables values can be embedded into a function with at most a local maxima and a local minima, and crossing any horizontal line at most twice. In real applications, the order of the taxa best satisfying the above conditions can be obtained using the Minimum Contradiction method. This approach is applied to 2 sets of continuous characters. The first set corresponds to craniofacial landmarks in Hominids. The contradiction matrix is used to identify possible tree structures and some alternatives when they exist. We explain how to discover the main structuring characters in a tree. The second set consists of a sample of 100 galaxies. In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.