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This paper introduces constNJ, the first algorithm for phylogeneticreconstruction of sets of trees with constrained pairwise rooted subtree-pruneregraft (rSPR) distance. We are motivated by the problem of constructing setsof trees which must fit into a recombination, hybridization, or similarnetwork. Rather than first finding a set of trees which are optimal accordingto a phylogenetic criterion (e.g. likelihood or parsimony) and then attemptingto fit them into a network, constNJ estimates the trees while enforcingspecified rSPR distance constraints. The primary input for constNJ is acollection of distance matrices derived from sequence blocks which are assumedto have evolved in a tree-like manner, such as blocks of an alignment which donot contain any recombination breakpoints. The other input is a set of rSPRconstraints for any set of pairs of trees. ConstNJ is consistent and a strictgeneralization of the neighbor-joining algorithm; it uses the new notion of"maximum agreement partitions" to assure that the resulting trees satisfy thegiven rSPR distance constraints.

constNJ: an algorithm to reconstruct sets of phylogenetic trees satisfying pairwise topological constraints