Sphenodontid phylogeny and the problems of multiple trees

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Abstract
Application of optimality criteria, such as parsimony, for choosing among phylogenetic hypotheses sometimes yields multiple optimal solutions, necessitating the application of additional methodology. Phylogeneticists may adopt a conservative strategy of presenting only a summary of the multiple trees and/or they may attempt to further discriminate among them. Parsimony analysis of data for Sphenodon and its fossil relatives yields multiple trees and is used to illustrate and compare a variety of approaches for summarizing agreement and selecting among trees. Multiple trees may result from a lack of evidence or character incongruence. Only with the latter can techniques to discriminate among optimal trees be effective. Adoption of secondary optimality criteria depends on the same rationale as differential character weighting and is a poor substitute for weighting. Neither approach will necessarily solve the problem of multiple trees or remove the need for methods that summarize agreement among them. Many consensus methods produce summaries of optimal trees that are far from ideal. Reduced consensus methods and disqualifier faithful subtrees may have advantages over the alternatives. Safe taxonomic reduction may also reduce problems of multiple trees due to lack of evidence, and the experimental pruning of taxa provides a powerful technique for investigating agreement among multiple trees. Some consensus and weighting methods are sensitive to the treatment of arbitrary resolutions which presents some unsolved difficulties in their use and interpretation. Multiple analyses using modern techniques provide a more resolved hypothesis of sphenodontid interrelationships and a better understanding of remaining problems than previous studies.