Maximum parsimony

In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes is to be preferred. Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains the data is considered best. The principle is akin to Occam's razor, which states that—all else being equal—the simplest hypothesis that explains the data should be selected. Some of the basic ideas behind maximum parsimony were presented by James S. Farris in 1970 and Walter M. Fitch in 1971. In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes is to be preferred. Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains the data is considered best. The principle is akin to Occam's razor, which states that—all else being equal—the simplest hypothesis that explains the data should be selected. Some of the basic ideas behind maximum parsimony were presented by James S. Farris in 1970 and Walter M. Fitch in 1971. Maximum parsimony is an intuitive and simple criterion, and it is popular for this reason. However, although it is easy to score a phylogenetic tree (by counting the number of character-state changes), there is no algorithm to quickly generate the most-parsimonious tree. Instead, the most-parsimonious tree must be found in 'tree space' (i.e., amongst all possible trees). For a small number of taxa (i.e., fewer than nine) it is possible to do an exhaustive search, in which every possible tree is scored, and the best one is selected. For nine to twenty taxa, it will generally be preferable to use branch-and-bound, which is also guaranteed to return the best tree. For greater numbers of taxa, a heuristic search must be performed. Because the most-parsimonious tree is always the shortest possible tree, this means that—in comparison to the 'true' tree that actually describes the evolutionary history of the organisms under study—the 'best' tree according to the maximum-parsimony criterion will often underestimate the actual evolutionary change that has occurred. In addition, maximum parsimony is not statistically consistent. That is, it is not guaranteed to produce the true tree with high probability, given sufficient data. As demonstrated in 1978 by Joe Felsenstein, maximum parsimony can be inconsistent under certain conditions, such as long-branch attraction. Of course, any phylogenetic algorithm could also be statistically inconsistent if the model it employs to estimate the preferred tree does not accurately match the way that evolution occurred in that clade. This is unknowable. Therefore, while statistical consistency is an interesting theoretical property, it lies outside the realm of testability, and is irrelevant to empirical phylogenetic studies. The maximization of parsimony (preferring the simpler of two otherwise equally adequate theorizations) has proven useful in many fields. Occam's razor, a principle of theoretical parsimony suggested by William of Ockham in the 1320s, asserted that it is vain to give an explanation which involves more assumptions than necessary. Alternatively, phylogenetic parsimony can be characterized as favoring the trees that maximize explanatory power by minimizing the number of observed similarities that cannot be explained by inheritance and common descent. Minimization of required evolutionary change on the one hand and maximization of observed similarities that can be explained as homology on the other may result in different preferred trees when some observed features are not applicable in some groups that are included in the tree, and the latter can be seen as the more general approach. While evolution is not an inherently parsimonious process, centuries of scientific experience lend support to the aforementioned principle of parsimony (Occam's razor). Namely, the supposition of a simpler, more parsimonious chain of events is preferable to the supposition of a more complicated, less parsimonious chain of events. Hence, parsimony (sensu lato) is typically sought in constructing phylogenetic trees, and in scientific explanation generally. Parsimony is part of a class of character-based tree estimation methods which use a matrix of discrete phylogenetic characters to infer one or more optimal phylogenetic trees for a set of taxa, commonly a set of species or reproductively isolated populations of a single species. These methods operate by evaluating candidate phylogenetic trees according to an explicit optimality criterion; the tree with the most favorable score is taken as the best estimate of the phylogenetic relationships of the included taxa. Maximum parsimony is used with most kinds of phylogenetic data; until recently, it was the only widely used character-based tree estimation method used for morphological data. Estimating phylogenies is not a trivial problem. A huge number of possible phylogenetic trees exist for any reasonably sized set of taxa; for example, a mere ten species gives over two million possible unrooted trees. These possibilities must be searched to find a tree that best fits the data according to the optimality criterion. However, the data themselves do not lead to a simple, arithmetic solution to the problem. Ideally, we would expect the distribution of whatever evolutionary characters (such as phenotypic traits or alleles) to directly follow the branching pattern of evolution. Thus we could say that if two organisms possess a shared character, they should be more closely related to each other than to a third organism that lacks this character (provided that character was not present in the last common ancestor of all three, in which case it would be a symplesiomorphy). We would predict that bats and monkeys are more closely related to each other than either is to an elephant, because male bats and monkeys possess external testicles, which elephants lack. However, we cannot say that bats and monkeys are more closely related to one another than they are to whales, though the two have external testicles absent in whales, because we believe that the males in the last common ancestral species of the three had external testicles. However, the phenomena of convergent evolution, parallel evolution, and evolutionary reversals (collectively termed homoplasy) add an unpleasant wrinkle to the problem of estimating phylogeny. For a number of reasons, two organisms can possess a trait not present in their last common ancestor: If we naively took the presence of this trait as evidence of a relationship, we would reconstruct an incorrect tree. Real phylogenetic data include substantial homoplasy, with different parts of the data suggesting sometimes very different relationships. Methods used to estimate phylogenetic trees are explicitly intended to resolve the conflict within the data by picking the phylogenetic tree that is the best fit to all the data overall, accepting that some data simply will not fit. It is often mistakenly believed that parsimony assumes that convergence is rare; in fact, even convergently derived characters have some value in maximum-parsimony-based phylogenetic analyses, and the prevalence of convergence does not systematically affect the outcome of parsimony-based methods.