Tree-building methods

Tree-building methods implemented in available software are discussed in detail in the literature (Saitou, 1996 Swofford et al., 1996 Li, 1997) and described on the Internet. This section briefly describes some of the most popular methods. Treebuilding methods can be sorted into distance-based vs. character-based methods. Much of the discussion in molecular phylogenetics dwells on the utility of distance-and character-based methods (e.g., Saitou, 1996 Li, 1997). Distance methods compute pairwise distances according to some measure and then discard the actual data, using only the fixed distances to derive trees. Character-based methods derive trees that optimize the distribution of the actual data patterns for each character. Pairwise distances are, therefore, not flxed, as they are determined by the tree topology. The 

Pairwise distance is calculated using maximum-likelihood estimators of substitution rates. The most popular distance tree-building programs have a limited number of substitution models, but PAUP 4.0 implements a number of models, including the actual model estimated from the data using maximum likelihood, as well as the log-det distance method. 

Unweighted Pair Group Method with Arithmetic Mean (UPGMA). 

Fitch-Margoliash (FM). The Fitch-Margoliash (FM) method seeks to maximize the fit of the observed pairwise distances to a tree by minimizing the squared deviation of all possible observed distances relative to all possible path lengths on the tree (Felsenstein, 1997). There are several variations that differ in how the error is weighted. The variance estimates are not completely independent because errors in all the internal tree branches are coimted at least twice (Rzhetsky and Nei, 1992). 

Minimum Evoiution (ME). Minimum evolution seeks to find the shortest tree that is consistent with the path lengths measmed in a manner similar to FM that is, ME works by minimizing the squared deviation of observed to tree-based distances (Rzhetsky and Nei, 1992 Swofford et al., 1996 Felsenstein, 1997). Unlike FM, ME does not use all possible pairwise distances and all possible associated tree path lengths. Rather, it fixes the location of internal tree nodes based on the distance to external nodes and then optimizes the internal branch length according to the minimum measmed error between these observed points. It thus purports to eliminate the nonindependence of FM measmements. 

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Various rate heterogeneity corrections are implemented in several tree-building programs. For nucleotide data, PAUP 4.0 implements both invariants and discrete gamma models for separate or combined use with time-reversible distance and likelihood tree-building methods and invariants in conjunction with the log-det distance method (see below). For nucleotide, amino acid, and codon data, PAML implements continuous, discrete, and autodiscrete models. For nucleotide and amino acid data, PHYLIP implements a discrete gamma model. 

Russo, C.A.M., Takezaki, N. and Nei, M. (1996) Efficiencies of different genes and different tree-building methods in recovering a known vertebrate phylogeny . Molecular Biology and Evolution, 13, 525-36. 

Character-state weight matrices have usually been estimated more or less by eye, but they can also be derived from a rate matrix. For example, if it is presumed that each of the two transitions occurs at double the frequency of each transversion, a weight matrix can simply specify, for example, that the cost of A-G is 1 and the cost of A-T is 2 (Fig. 14.5). (The parsimony method dictates that the diagonal elements of the matrix, or the cost of having the same base in different sequences, be zero. This proves to be a shortcoming of parsimony this will be discussed further below.) In the subsequent tree-building step, this set of assumptions will minimize the overall number of transversions and tend to cluster sequences differing mainly by transitions. 

The paralinear or log-det transformation corrects for nonstationarity (see Swofford et al 1996). In this method, which is applicable only to distance tree building, the numbers of raw substitutions of each type and in each direction are tallied for each sequence pair in a fom-by-fom matrix as shown in Figure 14.7. Each matrix has an algebraic determinant, the log of which becomes a factor in estimating sequence divergence, hence the name log-det. Pairwise comparisons of sequences having various and assorted patterns of base frequencies will yield a variety of matrix patterns, giving a variety of determinant values. Thus, each estimated pairwise distance will be affected by the determinant particular to each pair, which effectively... 

PAUP performs the nonparametric bootstrap for distance, MP, and ML, using all options available for tree building with these methods. When a bootstrap or jackknife with MP is under way, MAXTREES should be set between 10 and no more than... 

After importing the data file into MLC-i-i- and selecting gain-ratio as splitting method, the program builds the full tree shown in Fig. 4-16. The tree has 631 nodes, 316 leaves and 107 attributes. Attributes are molecular key features and leaves are CSPs. 

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