A chain is no stronger than its weakest link: double decay analysis of phylogenetic hypotheses.

In decay analyses the support for a particular split in most-parsimonious trees is its decay index, that is, the extra steps required of the shortest trees that do not include the split. By focusing solely on the support for splits, traditional decay analysis may provide an incomplete and potentially misleading summary of the support for phylogenetic relationships common to the most-parsimonious tree or trees. Here, we introduce double decay analysis, a new approach to assessing support for phylogenetic relationships. Double decay analysis is the determination of the decay indices of all n-taxon statements/partitions common to the most-parsimonious tree. The results of double decay analyses are presented in a partition table, but various approaches to graphical representation of the results, including the use of reduced consensus support trees, are also discussed. Double decay analysis provides a more comprehensive summary and facilitates a better understanding of the strengths and weaknesses of complex phylogenetic hypotheses than does traditional decay analysis. The limitations of traditional decay analyses and the utility of double decay analyses are illustrated with both contrived data and real data for sauropod dinosaurs.