Phylogenetic Applications of the Minimum Contradiction Approach on Continuous Characters

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 maximum and a local minimum, 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.

A six-parameter space to describe galaxy diversification

“…In the present case, the three strongly correlated parameters are not obviously redundant since they are not related by a direct causal relation (see Fraix-Burnet 2011). However, keeping all of them for the MCA analysis does not bring any more discriminating information than keeping only one (Thuillard & Fraix-Burnet 2009). As a consequence, since log σ is listed as one of the discriminant parameters, K abs and log(diam) can be disregarded in the analysis.…”

“…A.2) uses all parameters and explores them to determine the best order (partitioning) that can be obtained. It is possible to derive the discriminant capacity of the parameters according to their respective behaviour as formalised in Thuillard & Fraix-Burnet (2009). We find that:…”

“…It is a powerful tool for ascertaining whether the parameters can lead to a tree-like arrangement of the objects (Thuillard & Fraix-Burnet 2009). Using the parameters that fulfil this property, the method then performs an optimisation of the order and provides groupings with an assessment of their robustness.…”

“…Thuillard & Fraix-Burnet (2009) showed that the perfect order is linked to the convexity of the variables in the parameter space, and is obtained for specific properties of the variables along the order. It is then possible to detect the discriminant potentiality of the variables.…”

Phylogenetic Tools in Astrophysics

“…These distances are computed from the characters and the algorithms are generally extremely fast and efficient. It has always been somewhat surprising that character-and distance-based approaches yield similar results since the mathematical connection is still not obvious [9,10] . This might be due at least partly to the fact that the characters have an evolutionary information (the phylogenetic signal) that is not entirely lost when computing distances.…”