A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of edges incident to to a same vertex. A rooted trivalent diagram is a trivalent diagram with a distinguished edge, its root. We shall describe and analyze an a...

Most supertree algorithms combine collections of rooted phylogenetic trees with overlapping leaf sets into a single rooted phylogenetic tree. It is implicit in all these algorithms that the leaves of the rooted phylogenetic trees in the input collection, as a whole, represent non-nested taxa. Thus, for example, the “domestic dog” and “mammal” cannot be represented by two distinct leaves in such...

Given a set R of rooted phylogenetic trees on overlapping taxa, it takes polynomial time to decide whether or not there exists a rooted phylogenetic tree that is compatible with R. Since not all evolutionary histories for a set of species can be explained by a single tree, it is natural to ask for the minimum number of rooted phylogenetic trees needed such that each tree in R is compatible with...

Differences in water-acquisition strategies of tree root systems can determine the capacity to survive under severe drought. We evaluate the effects of field water shortage on early survival, growth and root morphological variables of two South American Mediterranean tree species with different rooting strategies during two growing seasons. One year-old Quillaja saponaria (deep-rooted) and Cryp...