Title : Parsimony by consensus

Introduction This paper presents a new description of the maximum parsimony criterion. In particular, this paper demonstrates a new mathematical equivalence between Fitch parsimony as well as selection of certain types of consensus trees. The link between parsimony and consensus is intended to contribute to the discussion on parsimony as well as consensus and total evidence. A link between parsimony and consensus trees has already been established by the MRP (matrix representation with parsimony) method of Baum and Ragan (Baum, 1992; Ragan, 1992). Here, however, a link arises in the other direction: whereas Baum and Ragan use parsimony to solve a problem in consensus trees, in this paper parsimony itself is shown to be a consensus method. Unless otherwise indicated, the term parsimony denotes Fitch parsimony. In mathematics, as well as classification, a median of a set of objects is an object that has minimum summed distance to all the other objects. For this paper, we will thus use the notion that a median is an objective criteria or property (Thorley and Wilkinson, 2003). The idea was previously introduced into the field of consensus trees over two decades ago (Barthelemy and McMorris, 1986). In relation to phylogenetic trees, the notion of a median tree can be stated as follows. First, suppose we have a collection of phylogenetic trees {T 1 , ...T n } and some measure d(T i , T j) of 'distance' or 'dissimilarity' between any two trees. Then a median consensus tree can be defined as any tree T (since T is not necessarily 2 unique) that minimizes the following: n i=1 d(T, T i) = d(T, T 1) + d(T, T 2) + ... + d(T, T n). Of course, an actual median tree chosen may differ according to the exact distance measure chosen. Moreover, there may be more than one median consensus tree. There is however, one type of median consensus tree which is very familiar to all system-atists. If d is chosen to be the symmetric distance between trees (also known as the partition metric or Robinson-Foulds distance (Robinson and Foulds, 1981)) then the majority rule tree (Margush and McMorris, 1981) is a median consensus tree (Barthelemy and McMorris, 1986). u v w u v w Figure 1: A subtree prune and regraft. A subtree labeled u is removed from the vertex v and re-attached to the vertex w. But there are many other …