Extending the limits of supertree methods
Recently, two exact polynomial-time supertree methods have been developed in which the traditional input of rooted leaf-labelled trees has been extended in two separate ways. The first method, called RankedTree, allows for the inclusion of relative divergence dates and the second method, called AncestralBuild, allows for the inclusion of rooted trees in which some of the interior vertices as well as the leaves are labelled. The latter is particularly useful for when one has information that includes nested taxa. In this paper, we present two supertree methods that unite and generalise RankedTree and AncestralBuild. The first method is polynomial time and combines the allowable inputs of RankedTree and AncestralBuild. It determines if the original input is compatible, in which case it outputs an appropriate ‘ranked semi-labelled tree’. The second method lists all ‘ranked semi-labelled trees’ that are consistent with the original input. While there may be an exponential number of such trees, the second method outputs the next such tree in the list in polynomial time.