Maximum Parsimony (phylogenetics) - Analysis

Analysis

A maximum parsimony analysis runs in a very straightforward fashion. Trees are scored according to the degree to which they imply a parsimonious distribution of the character data. The most parsimonious tree for the dataset represents the preferred hypothesis of relationships among the taxa in the analysis.

Trees are scored (evaluated) by using a simple algorithm to determine how many "steps" (evolutionary transitions) are required to explain the distribution of each character. A step is, in essence, a change from one character state to another, although with ordered characters some transitions require more than one step. Contrary to popular belief, the algorithm does not explicitly assign particular character states to nodes (branch junctions) on a tree: the least number of steps can involve multiple, equally costly assignments and distributions of evolutionary transitions. What is optimized is the total number of changes.

There are many more possible phylogenetic trees than can be searched exhaustively for more than eight taxa or so. A number of algorithms are therefore used to search among the possible trees. Many of these involve taking an initial tree (usually the favored tree from the last iteration of the algorithm), and perturbing it to see if the change produces a higher score.

The trees resulting from parsimony search are unrooted: They show all the possible relationships of the included taxa, but they lack any statement on relative times of divergence. A particular branch is chosen to root the tree by the user. This branch is then taken to be outside all the other branches of the tree, which together form a monophyletic group. This imparts a sense of relative time to the tree. Incorrect choice of a root can result in incorrect relationships on the tree, even if the tree is itself correct in its unrooted form.

Parsimony analysis often returns a number of equally most-parsimonious trees (MPTs). A large number of MPTs is often seen as an analytical failure, and is widely believed to be related to the number of missing entries ("?") in the dataset, characters showing too much homoplasy, or the presence of topologically labile "wildcard" taxa (which may have many missing entries). Numerous methods have been proposed to reduce the number of MPTs, including removing characters or taxa with large amounts of missing data before analysis, removing or downweighting highly homoplastic characters (successive weighting) or removing wildcard taxa (the phylogenetic trunk method) a posteriori and then reanalyzing the data.

Numerous theoretical and simulation studies have demonstrated that highly homoplastic characters, characters and taxa with abundant missing data, and "wildcard" taxa contribute to the analysis. Although excluding characters or taxa may appear to improve resolution, the resulting tree is based on less data, and is therefore a less reliable estimate of the phylogeny (unless the characters or taxa are non informative, see safe taxonomic reduction). Today's general consensus is that having multiple MPTs is a valid analytical result; it simply indicates that there is insufficient data to resolve the tree completely. In many cases, there is substantial common structure in the MPTs, and differences are slight and involve uncertainty in the placement of a few taxa. There are a number of methods for summarizing the relationships within this set, including consensus trees, which show common relationships among all the taxa, and pruned agreement subtrees, which show common structure by temporarily pruning "wildcard" taxa from every tree until they all agree. Reduced consensus takes this one step further, by showing all subtrees (and therefore all relationships) supported by the input trees.

Even if multiple MPTs are returned, parsimony analysis still basically produces a point-estimate, lacking confidence intervals of any sort. This has often been levelled as a criticism, since there is certainly error in estimating the most-parsimonious tree, and the method does not inherently include any means of establishing how sensitive its conclusions are to this error. Several methods have been used to assess support.

Jackknifing and bootstrapping, well-known statistical resampling procedures, have been employed with parsimony analysis. The jackknife, which involves resampling without replacement ("leave-one-out") can be employed on characters or taxa; interpretation may become complicated in the latter case, because the variable of interest is the tree, and comparison of trees with different taxa is not straightforward. The bootstrap, resampling with replacement (sample x items randomly out of a sample of size x, but items can be picked multiple times), is only used on characters, because adding duplicate taxa does not change the result of a parsimony analysis. The bootstrap is much more commonly employed in phylogenetics (as elsewhere); both methods involve an arbitrary but large number of repeated iterations involving perturbation of the original data followed by analysis. The resulting MPTs from each analysis are pooled, and the results are usually presented on a 50% Majority Rule Consensus tree, with individual branches (or nodes) labelled with the percentage of bootstrap MPTs in which they appear. This "bootstrap percentage" (which is not a P-value, as is sometimes claimed) is used as a measure of support. Technically, it is supposed to be a measure of repeatability, the probability that that branch (node, clade) would be recovered if the taxa were sampled again. Experimental tests with viral phylogenies suggest that the bootstrap percentage is not a good estimator of repeatability for phylogenetics, but it is a reasonable estimator of accuracy. In fact, it has been shown that the bootstrap percentage, as an estimator of accuracy, is biased, and that this bias results on average in an underestimate of confidence (such that as little as 70% support might really indicate up to 95% confidence). However, the direction of bias cannot be ascertained in individual cases, so assuming that high values bootstrap support indicate even higher confidence is unwarranted.

Another means of assessing support is Bremer support, or the decay index (which is technically not an index). This is simply the difference in number of steps between the score of the MPT(s), and the score of the most parsimonious tree that does not contain a particular clade (node, branch). It can be thought of as the number of steps you have to add to lose that clade; implicitly, it is meant to suggest how great the error in the estimate of the score of the MPT must be for the clade to no longer be supported by the analysis, although this is not necessarily what it does. Decay index values are often fairly low (one or two steps being typical), but they often appear to be proportional to bootstrap percentages. However, interpretation of decay values is not straightforward, and they seem to be preferred by authors with philosophical objections to the bootstrap (although many morphological systematists, especially paleontologists, report both). Double-decay analysis is a decay counterpart to reduced consensus that evaluates the decay index for all possible subtree relationships (n-taxon statements) within a tree.