Document: How the phylogenetic method, Profile Parsimony, works
A figure illustrating properties of the phylogenetic inference method, Profile Parsimony.
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Profile Parsimony uses a measure of fit (of character data to a phylogenetic tree) that is linked to the number of steps (amount of "homoplasy") of each character on the tree.
In comparing phylogenetic trees, Profile Parsimony gives less credit to a one-step improvement that occurs in a character that already has high homoplasy. Critically, “high homoplasy” here is relative to the maximum number of steps for the given character. Profile Parsimony differs from so-called "concave" weighting functions, where low weight is given to high homoplasy for any given character (ignoring variation in the maximum number of steps among characters).
For background, see Faith and Trueman (2001) Towards an Inclusive Philosophy for Phylogenetic Inference. Syst. Biol. 50(3):331–350.