Optimality criterion in which the shortest possible tree that explains the data is considered best
In phylogenetics and computational phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or minimizes the cost of differentially weighted character-state changes). 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. 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 sought 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 a hypothetical "true" tree that actually describes the unknown evolutionary history of the organisms under study—the "best" tree according to the maximum-parsimony criterion will often underestimate the actual evolutionary change that could have 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.
Alternate characterization and rationale.
In phylogenetics, parsimony is mostly interpreted as favoring the trees that minimize the amount of evolutionary change required (see for example ). 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 inferring phylogenetic trees, and in scientific explanation generally.
In detail.
Parsimony is part of a class of character-based tree estimation methods which use a matrix of discrete phylogenetic characters and character states 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 hypothesis 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.
Inferring 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 inferring phylogeny. For a number of reasons, two organisms can possess a trait inferred to have not been present in their last common ancestor: If we naively took the presence of this trait as evidence of a relationship, we would infer an incorrect tree. Empirical phylogenetic data may 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.
Data that do not fit a tree perfectly are not simply "noise", they can contain relevant phylogenetic signal in some parts of a tree, even if they conflict with the tree overall. In the whale example given above, the lack of external testicles in whales is homoplastic: It reflects a return to the condition inferred to have been present in ancient ancestors of mammals, whose testicles were internal. This inferred similarity between whales and ancient mammal ancestors is in conflict with the tree we accept based on the weight of other characters, since it implies that the mammals with external testicles should form a group excluding whales. However, among the whales, the reversal to internal testicles actually correctly associates the various types of whales (including dolphins and porpoises) into the group Cetacea. Still, the determination of the best-fitting tree—and thus which data do not fit the tree—is a complex process. Maximum parsimony is one method developed to do this.
Character data.
The input data used in a maximum parsimony analysis is in the form of "characters" for a range of taxa. There is no generally agreed-upon definition of a phylogenetic character, but operationally a character can be thought of as an attribute, an axis along which taxa are observed to vary. These attributes can be physical (morphological), molecular, genetic, physiological, or behavioral. The only widespread agreement on characters seems to be that variation used for character analysis should reflect heritable variation. Whether it must be directly heritable, or whether indirect inheritance (e.g., learned behaviors) is acceptable, is not entirely resolved.
Each character is divided into discrete character states, into which the variations observed are classified. Character states are often formulated as descriptors, describing the condition of the character substrate. For example, the character "eye color" might have the states "blue" and "brown." Characters can have two or more states (they can have only one, but these characters lend nothing to a maximum parsimony analysis, and are often excluded).
Coding characters for phylogenetic analysis is not an exact science, and there are numerous complicating issues. Typically, taxa are scored with the same state if they are more similar to one another in that particular attribute than each is to taxa scored with a different state. This is not straightforward when character states are not clearly delineated or when they fail to capture all of the possible variation in a character. How would one score the previously mentioned character for a taxon (or individual) with hazel eyes? Or green? As noted above, character coding is generally based on similarity: Hazel and green eyes might be lumped with blue because they are more similar to that color (being light), and the character could be then recoded as "eye color: light; dark." Alternatively, there can be multi-state characters, such as "eye color: brown; hazel, blue; green."
Ambiguities in character state delineation and scoring can be a major source of confusion, dispute, and error in phylogenetic analysis using character data. Note that, in the above example, "eyes: present; absent" is also a possible character, which creates issues because "eye color" is not applicable if eyes are not present. For such situations, a "?" ("unknown") is scored, although sometimes "X" or "-" (the latter usually in sequence data) are used to distinguish cases where a character cannot be scored from a case where the state is simply unknown. Current implementations of maximum parsimony generally treat unknown values in the same manner: the reasons the data are unknown have no particular effect on analysis. Effectively, the program treats a ? as if it held the state that would involve the fewest extra steps in the tree (see below), although this is not an explicit step in the algorithm.
Genetic data are particularly amenable to character-based phylogenetic methods such as maximum parsimony because protein and nucleotide sequences are naturally discrete: A particular position in a nucleotide sequence can be either adenine, cytosine, guanine, or thymine / uracil, or a sequence gap; a position (residue) in a protein sequence will be one of the basic amino acids or a sequence gap. Thus, character scoring is rarely ambiguous, except in cases where sequencing methods fail to produce a definitive assignment for a particular sequence position. Sequence gaps are sometimes treated as characters, although there is no consensus on how they should be coded.
Characters can be treated as unordered or ordered. For a binary (two-state) character, this makes little difference. For a multi-state character, unordered characters can be thought of as having an equal "cost" (in terms of number of "evolutionary events") to change from any one state to any other; complementarily, they do not require passing through intermediate states. Ordered characters have a particular sequence in which the states must occur through evolution, such that going between some states requires passing through an intermediate. This can be thought of complementarily as having different costs to pass between different pairs of states. In the eye-color example above, it is possible to leave it unordered, which imposes the same evolutionary "cost" to go from brown-blue, green-blue, green-hazel, etc. Alternatively, it could be ordered brown-hazel-green-blue; this would normally imply that it would cost two evolutionary events to go from brown-green, three from brown-blue, but only one from brown-hazel. This can also be thought of as requiring eyes to evolve through a "hazel stage" to get from brown to green, and a "green stage" to get from hazel to blue, etc. For many characters, it is not obvious if and how they should be ordered. On the contrary, for characters that represent discretization of an underlying continuous variable, like shape, size, and ratio characters, ordering is logical, and simulations have shown that this improves ability to recover correct clades, while decreasing the recovering of erroneous clades.
There is a lively debate on the utility and appropriateness of character ordering, but no consensus. Some authorities order characters when there is a clear logical, ontogenetic, or evolutionary transition among the states (for example, "legs: short; medium; long"). Some accept only some of these criteria. Some run an unordered analysis, and order