Progress with methods for constructing evolutionary trees

Evolutionists dream of a tree-reconstruction method that is efficient (fast), powerful, consistent, robust and falsifiable. These criteria are at present conflicting in that the fastest methods are weak (in their use of information in the sequences) and inconsistent (even with very long sequences they may lead to an incorrect tree). But there has been exciting progress in new approaches to tree inference, in understanding general properties of methods, and in developing ideas for estimating the reliability of trees. New phylogenetic invariant methods allow selected parameters of the underlying model to be estimated directly from sequences. There is still a need for more theoretical understanding and assistance in applying what is already known.