Properties of Supertree Methods in the Consensus Setting

“Supertrees are in essence not more than generalised consensus trees. Perhaps it would be judicious to reach a satisfactory consensus on the use of consensus trees before tackling their generalisation.” (Bryant 2003:164). Supertree methods (SMs) are techniques for inferring (super)trees from sets of (input) trees. Classical consensus methods are SMs that were designed for the special case where input trees have identical leaf sets. The need for methods that can also combine information from input trees with nonidentical leaf sets has led to many alternative SMs. Some of these SMs are generalizations from conservative consensus methods (strict and semistrict) that do not resolve input tree conflicts (e.g., Gordon, 1986; Goloboff and Pol, 2002). Our focus here is on more liberal SMs, those capable of resolving conflicts among input trees. Liberal SMs comprise the majority of described methods and have been the most used in practice by biologists seeking well-resolved phylogenies. However, today's practitioners are confronted with choosing among a potentially bewildering array of liberal SM(s).