Self‐Weighted Optimization: Tree Searches and Character State Reconstructions under Implied Transformation Costs

Abstract

A method to assess the cost of character state transformations based on their congruence is proposed. Measuring the distortion of different transformations with a convex increasing function of the number of transformations, and choosing those reconstructions which minimize the distortion for all transformations, may provide a better optimality criterion than the linear functions implemented in currently used methods for optimization. If trees are optimized using such a measure, transformation costs are dynamically determined during reconstructions; this leads to selecting trees implying that the possible state transformations are as reliable as possible. The present method is not iterative (thus avoiding the concern of different final results for different starting points), and it has an explicit optimality criterion. It has a high computational cost; algorithms to lessen the computations required for optimizations and searches are described.