A reconsideration of inapplicable characters, and an approximation with step-matrix recoding.

Area of Science:

• Phylogenetics
• Computational Biology
• Evolutionary Biology

Background:

• Phylogenetic analysis relies on minimizing homoplasy (unexplained similarities) to select the best evolutionary tree.
• Hierarchical characters, where a secondary character depends on a primary one (e.g., tail color depends on tail presence), pose challenges for standard parsimony methods.
• Previous methods for evaluating homology in hierarchical characters used unintuitive 'subcharacters'.

Purpose of the Study:

• To propose a new, more intuitive method for evaluating homoplasy in hierarchical characters using x-transformations.
• To demonstrate how x-transformations maintain the link between minimizing homoplasy and maximizing explanatory power in phylogenetic inference.
• To extend this new formulation to address issues with various character types and enable natural integration with implied weighting.

Main Methods:

• Developed a formulation based on counting state changes rather than 'subcharacters' to quantify homoplasy.
• Introduced x-transformations to directly count homoplasy as the number of changes beyond the first into any given state.
• Proposed a recoding strategy for hierarchical characters into step-matrix form with derived transformation costs, compatible with software like TNT.

Main Results:

• X-transformations provide a direct and intuitive measure of homoplasy for hierarchical characters.
• This method clearly links homoplasy to the number of 'extra steps' (independent origins), reinforcing the principle of parsimony.
• The approach facilitates the derivation of transformation costs for recoding, allowing for accurate homology measurement of complex character structures.

Conclusions:

• X-transformations offer a superior, more intuitive framework for handling inapplicable hierarchical characters in phylogenetic analysis.
• This method enhances the evaluation of homology and improves the reconstruction of evolutionary relationships.
• The proposed recoding and cost derivation methods provide practical tools for phylogenetic software and analysis.