Criteria for optimising phylogenetic trees and the problem of determining the root of a tree.

The process of determining the optimal phylogenetic tree from amino acid sequences or comparable data is divided into six stages. Particular attention is given both to the criteria that are used when testing for the optimal tree and the problem of determining the position of the original ancestor. Four types of criteria for evaluating the optimal tree are considered: 1. parsimony (fewest total changes), 2. path lengths from an ancestor to existing species, 3. subtracting the difference between each pair of species as measured on the tree and as compared directly with the data ("excess differences"), 4. Moore Residual Coefficient. These criteria are examined on a set of test data and some of the reasons for the differences among them are discussed. For example, the "average percent standard deviation" weights excess differences unequally in inverse proportion to the square of the observed differences. The Moore Residual Coefficient and the "excess differences" will not necessarily give a value of zero when there are no duplicated changes unless there can only be two states for each character (i.e. binary data). The path length and difference criteria (as well as the Moore Residual Coefficient) give unequal weighting to the individual branches of the tree by counting some branches more times than others. Particularly because of this some criteria will reject trees that are equally parsimonious and the criteria are said to be invalid. However the criterion of parsimony is insensitive in that it can give the same value for several basic networks and it does not specify the position of the original ancestor, the root of the tree. The importance is emphasised of stating a model and examining its predictions before a criterion is chosen to select the best network. The number of rooted trees that can be derived from a basic network (or unrooted tree) is described in relation to how detailed a description of the original ancestor is required. Four methods are described for determining the position of the root of the tree or original ancestor. Each method depends upon some additional information to that used in constructing the basic network and the method chosen will depend on this additional knowledge.