Explosions and hot spots in supertree methods

In phylogenetic systematics a problem of great practical and theoretical interest is to construct one or more large phylogenies (evolutionary trees), i.e., supertrees, from a given set of small phylogenies with overlapping sets of leaf labels. Although the methods being used to solve this problem are usually given plausible biological or theoretical justifications, occasionally it is possible to see that the result of a supertree method (SM) is explosive, and therefore logically meaningless, in the sense that it has been inferred from logical propositions that are contradictory. This paper presents the basic ideas and issues of how explosions affect the inference of rooted trees by SMs. We define the relevant concepts, give examples, and show how sometimes it is possible to identify hot spots in the input from which an SM may make explosive inferences that cannot be logically justified.