Some recent progress with methods for evolutionary trees

Sequences of macromolecules have "signals" or patterns that arise from a number of sources, particularly from shared common history or phylogeny. We discuss methods for inferring evolutionary trees from these patterns or signals under five properties desired for an ideal method. These five desiderata are that the methods be efficient (fast), consistent, powerful, robust, and falsifiable. Our conclusion is that corrections for multiple changes in sequences are the most important factor for any method to be consistent. Most optimality criteria, including compatibility and parsimony, become consistent when the sequences have appropriate corrections for multiple changes. Conversely, virtually no methods are consistent without adjustments for multiple changes. Hadamard conjugations are used to illustrate relationships between different methods and then illustrated by combining it with the closest tree optimality criterion. The data used to illustrate these recent developments include DNA sequences used to study