Weighted parsimony

Three different parsimony methods have been used for the analysis of restriction site data Wagner parsimony,25 Dollo parsimony,26 and weighted parsimony or generalized parsimony.27 As the names suggest, they all invoke a parsimony principle to select the best tree (or trees) from the set of all possible trees. Specifically, the trees selected are those that require the minimum amount of evolutionary change. The methods differ from one another in how the amount of evolutionary change is calculated. 

Weighted parsimony is intermediate between these two extremes. Each restriction site loss is counted as a single step, but each restriction site gain is counted as M steps, where M can be any positive number greater than 1. M can be estimated from an initial Wagner parsimony analysis that relates it to the observed probabilities of site gains and losses,29 or it may be chosen... 

Fitch, W.M. and Ye, J., Weighted parsimony does it work. Phylogenetic Analysis of DNA Sequences, Miyamoto, M.M. and Cracraft, J., Eds., Oxford University Press, New York, 1991, pp. 147-154. 

Hennig86 was written by James S. Farris (American Museum of Natural History, New York, NY 10024). It is a fast and effective parsimony program. It is often faster than PAUP but has many fewer features and options. However, Hennig86 does contain a routine for successive approximation a posteriori character weighting. 

A critical component of comodeling multiple outputs is the appropriate weighting of individual observations. The weights must be appropriate for small and large responses within an output and the relative weights must be appropriate between outputs. Failure of the former standard can lead to regions of systematic error in the fitted function and failure in the latter standard can cause some of the outputs to inappropriately dominate the determination of fitted parameters. However, error variance model selection, as for structural model development, should be guided by parsimony stay as simple as possible. 

Some of the first ideas on multi-way analysis were published by Raymond Cattell [1944,1952], Thurstone s principle of parsimony states that a simple structure should be found to describe a data matrix or its correlation matrix with the help of factors [Thurstone 1935], For the simultaneous analysis of several matrices together, Cattell proposed to use the principle of parallel proportional profiles [Cattell 1944], The principle of parallel proportional profiles states that a set of common factors should be found that can be fitted with different dimension weights to many data matrices at the same time. This is the same as finding a common set of factors for a stack of matrices, a three-way array. To quote Cattell ... 

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. 

Several phylogenetic analysis programs use a generalized parsimony method in which the user (Swofford 1990, Maddison and Maddison 1990) or the program (Williams and Fitch 1989) defines a matrix which describes the cost associated with a transition from state i to state j.. Modification of the cost matrix allows experimentation with different kinds of weighting. 

The conclusion from this reasoning is that cladistic application of the principle of parsimony implies an important first principle, namely that for equally weighted characters the probability of homology for each putative novelty should be the same for all characters. Only this justifies counting each change in the same way. The innate existence of this assumption in cladistics, and its methodical consequences, has been ignored in the past by many cladists. 

The principle of parsimony degenerates to numerical taxonomy, if characters are not weighted. (Remane, 1983)... 

The discussion between cladists and their critics is not new. Panchen reviewed the issues in 1982 (Panchen, 1982). He attacked the restriction to just parsimony, by the optimization of synapomorphies of cladograms, and pointed out that in the real world parallel evolution is common. What he did not offer was a theory that allows the classification of characters into those that are predisposed to parallelism or chance similarity and those that are not, and therefore he thought that cladists may have to admit the persistent intuitive element in classification. Today, intuition (in the sense of unfounded ad hoc assumptions) can be avoided in phylogenetic cladistics using objective criteria of character weighting. 

Haszprunar, G., Parsimony analysis as a specific kind of homology estimation and the implications for character weighting. Mol. Phylogenet. Evol, 9, 333—339, 1998. 

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