On consensus, collapsibility, and clade concordance

Consensus in cladistics is reviewed. Consensus trees, which summarize the agreement in grouping among a set of cladograms, are distinguished from compromise trees, which may contain groups that do not appear in all the cladograms being compared. Only a strict or Nelson tree is an actual consensus. This distinction has implications for the concept of support for cladograms: only those branches supported under all possible optimizations are unambiguously supported. We refer to such cladograms as strictly supported, in contrast to the semistrictly (ambiguously) supported cladograms output by various current microcomputer programs for cladistic analysis. Such semistrictly supported cladograms may be collapsed, however, by a variety of options in various programs. Consideration of collapsibility and optimization on multifurcations leads to some conclusions on the use of consensus. Consensus tree length provides information about character conflict that occurs between, not within, cladograms. We propose the dade concordance index, which employs the consensus tree length to measure inter-cladogram character conflict for all characters among a set of cladograms. (C) 1996 The Willi Hennig Society.