The parsimony criterion is one of the oldest and most widely used methods of constructing phylogenetic trees, having its roots in classical taxonomy based on morphological characters and later extended to molecular sequence data. The underlying principle of parsimony is that, among all possible explanations of the observed data, the simplest explanation — the one requiring the fewest evolutionary changes or the fewest arbitrary assumptions — should be preferred. In phylogenetics, this translates into selecting the tree topology that requires the smallest number of character-state changes to explain the distribution of characters observed among the species being studied.
Parsimony with Morphological Characters
Basic Principle
Parsimony was originally developed for use with morphological characters and has a long history in phylogenetic classification. The method states that the correct tree is the one that represents the simplest possible explanation of the data, that is, the explanation requiring the fewest arbitrary assumptions or the fewest independent evolutionary changes.
Binary Character States
Morphological parsimony is generally applied using binary character states, denoted as 0 and 1:
- State 0 represents the character state that is thought to be ancestral (the original, primitive condition).
- State 1 represents the character state that is thought to be derived (the newly evolved condition).
For example, the specialised bone structure found in a bird’s wing may be designated as the derived state (1), while the bone structure of the ancestral tetrapod forelimb, from which the bird wing evolved, is designated as the ancestral state (0). In actual practice, the morphological characters used for such analysis are far less obvious than this simplified example, and their correct identification requires the specialised expertise of trained anatomists and palaeontologists.
Example of Tree Selection Using a Single Character
Consider a situation in which species C and D possess a particular derived character that is absent in species A and B. Three alternative tree arrangements may be considered:
- Tree (a): The species are arranged such that the character needs to have evolved only once, on a single branch, to explain its presence in C and D and its absence in A and B.
- Tree (b): The species are arranged such that the character must have evolved once and then must have been lost once on a different branch — requiring two separate character-state changes.
- Tree (c): The species are arranged such that the character must have evolved independently, twice, once on the branch leading to C and once on the branch leading to D — again requiring two separate changes.
Since tree (a) requires only a single character-state change while trees (b) and (c) each require two changes, tree (a) represents the simplest, or most parsimonious, explanation of the data, and is therefore preferred under the parsimony criterion.
Limitation of a Single Character
A single character, by itself, can only ever divide the set of species into two groups — the “haves” (species possessing the derived character) and the “have-nots” (species lacking it). Such a character provides no information whatsoever about the branching order of species within each of these two groups. To reconstruct a complete and fully resolved tree, therefore, a large number of characters that evolved at different points in evolutionary history must be examined together.
Synapomorphy
A character state that is shared by two or more species because they inherited it from a common ancestor is called a synapomorphy (a shared derived character). In an ideal situation, a set of characters would be found in which the synapomorphies are “nested” one within another, with each character providing information about a different, successive branch point on the tree. If such an ideal set of characters were available, it would be possible to construct a tree on which each character requires only a single change of state.
Conflict Between Characters
In real data sets, conflicts frequently arise between different characters, each of which may support a different tree topology. For example, if one character (as in the earlier example) supports tree (a), a second character — say, one shared by species B and C but absent in A and D — might instead support tree (b). When such conflicting characters exist, it becomes impossible to find any single tree on which every character requires only one change; at least one of the conflicting characters must show more than one character-state change on whichever tree is finally chosen. Parsimony computer programs handle this by taking data from a large number of characters simultaneously and applying a heuristic tree-search algorithm to identify the topology for which the total number of character-state changes, summed across all characters, is as small as possible.
Weighting of Character Gain versus Loss
It is often biologically more plausible for a derived character to be lost in a lineage that no longer requires it (the “use it or lose it” principle) than for the same complex character to have originated independently more than once. To reflect this asymmetry, parsimony analyses can assign a higher weight to a character gain than to a character loss when computing the overall parsimony score.
Homoplasy
When the same character state evolves more than once independently — rather than being inherited from a single common ancestor — this phenomenon is called homoplasy. Characters affected by homoplasious change can be highly misleading when used in parsimony analysis, and in practice it is usually not possible to know, in advance, which particular characters in a data set are likely to show homoplasy.
Parsimony with Molecular Data
Application of Parsimony to Sequence Data
The parsimony method, originally developed by Fitch (1971), can be applied to molecular sequence data in a straightforward manner. Each column of a multiple sequence alignment is treated as an individual character, and each of the four possible nucleotide bases at that column represents a possible character state.
- A substitution event is defined as any change in the character state (that is, any change of the base present) at a given site.
- Since the identity of the true ancestral sequence is not known in advance, there is no distinction made between the gain and the loss of a particular character state at the molecular level — a change from one base to another is simply counted as a substitution, regardless of direction.
- Because there is no meaningful way to root the tree using this criterion alone, molecular parsimony algorithms operate on unrooted trees.
Example of an Informative Site
Consider a site (a single column of the alignment) that shows the base C in human, chimpanzee, and gorilla, but the base T in orangutan and gibbon. Comparing two candidate tree topologies:
- Tree (a) requires only a single substitution to explain this pattern of base distribution.
- Tree (b) requires two separate substitutions to explain the same pattern.
According to the parsimony criterion, tree (a) is therefore preferred over tree (b) on the basis of this particular site, since it requires fewer substitutions.
Informative and Non-Informative Sites
Not every site in a sequence alignment is useful for distinguishing between alternative tree topologies:
- A site that shows the same base in every species is obviously non-informative, since it provides no basis for preferring one topology over another.
- Less obviously, a site can also be non-informative even when it is variable. For example, a site that shows base Cin every species except the gibbon, which shows base T, is non-informative, because a single substitution on the branch leading to the gibbon can explain the data on any possible tree topology — the site therefore cannot help distinguish between alternative trees.
- The general rule is that, for a site to be informative under the parsimony method, it must contain at least two of the four possible bases, and each of these bases must be present in more than one species.
Application to the Primates Example
When the parsimony method was applied to a real data set of primate sequences, the most parsimonious tree obtained had exactly the same topology as the tree obtained independently by both the Neighbour-Joining (NJ) method and the Maximum-Likelihood (ML) method using the Jukes–Cantor (JC) model. Several alternative topologies were found to require only one or two additional substitutions compared with the best tree, and the question of how to statistically distinguish between such closely competing trees arises for parsimony in the same way that it does for maximum likelihood. In fact, the Kishino–Hasegawa (KH) test, originally developed for comparing log-likelihood values between trees, can be applied in an analogous way to compare parsimony scores between alternative trees. In this particular case, the alternative trees with only slightly more substitutions were found not to be significantly different from the single most parsimonious tree. Thus, for this data set, three independent methods — parsimony, NJ, and ML — converged on the same best topology, and they were also broadly in agreement regarding which parts of the tree were reliably determined and which parts remained poorly resolved. It is important to note, however, that parsimony and maximum likelihood do not always produce the same answer, since the two methods are based on fundamentally different criteria, and there is no theoretical guarantee that they will identify the same tree as optimal.
Comparison of Parsimony and Maximum-Likelihood Methods
Advantages of Parsimony
- Long track record: Parsimony has a much longer history of use in phylogenetics than maximum likelihood, and continues to be widely used.
- Computational speed: An efficient algorithm exists (Fitch 1971; Swofford et al. 1996) for calculating the parsimony score of any given tree topology very rapidly, whereas evaluating a tree under maximum likelihood requires the comparatively complex and time-consuming task of optimising both branch lengths and the parameters of the substitution-rate matrix for every candidate topology.
- Perceived model independence: Supporters of parsimony often criticise the explicit evolutionary models used in ML and distance-matrix methods, and argue that parsimony is superior because it does not require the analyst to assume any particular model of sequence evolution.
Hidden Assumptions in Parsimony
Despite this claim of model independence, parsimony analysis does, in practice, make implicit assumptions that are comparable to those made explicitly in ML. For instance, when standard (unweighted) parsimony is used, it is implicitly assumed that:
- All types of nucleotide substitution contribute equally to the parsimony score.
- Changes occurring at all sites in the alignment are weighted equally, regardless of how rapidly or slowly a given site is known to evolve.
These assumptions are directly comparable to the assumptions of equal substitution rates and equal rates across sites that are made when using a simple model such as the Jukes–Cantor (JC) model in ML or NJ analysis. It has been shown that using a more realistic model in ML — for example, the HKY model combined with variable rates across sites — can yield a significantly different tree from that obtained with the simpler JC model. In principle, the parsimony score could similarly be refined by weighting transitions and transversions differently, and by weighting changes at rapidly evolving sites less heavily than changes at slowly evolving sites; however, it is generally very difficult to determine, in an objective and justified manner, what the appropriate weighting values should be.
Advantage of Maximum Likelihood Over Parsimony
The maximum-likelihood framework offers a systematic way of improving the evolutionary model used in an analysis, because effects such as unequal substitution rates and rate variation across sites can be incorporated directly as explicit parameters within the model, and the optimum values of these parameters can then be estimated objectively from the data itself. Furthermore, ML provides a rigorous statistical procedure for testing whether the inclusion of each additional model parameter produces a significantly better fit to the observed data. Although no evolutionary model can ever be a perfectly exact description of the true underlying mechanism of sequence evolution, currently available models do account for many important evolutionary factors, and therefore incorporating them into the analysis is generally considered preferable to ignoring such factors altogether, as unweighted parsimony effectively does.
Neglect of Branch Lengths and the Long-Branch Attraction Problem
A fundamental limitation of the parsimony method is that it seeks to minimise only the total number of substitutions on a tree, without any regard to the actual branch lengths involved. Under parsimony, a substitution occurring on a long branch is counted with exactly the same weight as a substitution occurring on a short branch. Maximum-likelihood methods, in contrast, explicitly take branch length into account, recognising that substitutions are inherently more likely to occur on longer branches; where a branch is long, the occurrence of multiple substitutions along it is expected, and there is therefore no logical justification for trying to minimise the substitution count on such a branch.
This neglect of branch length information leads parsimony to suffer from a well-known and serious problem called long-branch attraction:
- If two branches on the true tree are long, due to genuinely rapid rates of evolution along each of them, tree-construction algorithms based on parsimony tend to erroneously group these two long branches together on the reconstructed tree.
- This can result in species being incorrectly grouped together in the reconstructed tree, based solely on the shared possession of a rapid evolutionary rate, even though the two species may otherwise have very little genuine evolutionary relationship or similarity.
- Long-branch attraction is a potential concern for several phylogenetic methods, but it is a particularly severeproblem for parsimony specifically.
- Critically, this is not merely a limitation arising from having too little sequence data to work with. It has been mathematically demonstrated (Felsenstein 1978; Swofford et al. 1996) that, in certain conditions, parsimony will converge on the wrong tree even as the length of the sequences used is allowed to increase without limit (that is, even in the limit of infinite sequence data).
When Parsimony Is Preferred
Parsimony is considered to be a particularly strong and appropriate method when it is applied to qualitative morphological characters, for which no good quantitative model of evolutionary change actually exists. For example, it does not make much practical sense to try to construct a detailed quantitative model for the “rate of evolution” of a structure such as a bird’s wing, because, as far as is currently understood, such a major morphological innovation represents a unique, one-off historical event rather than a process that recurs repeatedly in a statistically describable way.
By contrast, molecular substitutions occurring during sequence evolution take place repeatedly, many times over, in essentially the same manner across different lineages and sites. Because of this repeated, statistically regular nature of molecular change, it becomes meaningful and useful to construct quantitative models describing the rates of different types of substitution. Where such quantitative models are genuinely available and applicable — as is the case for molecular sequence data — likelihood-based methods such as maximum likelihood are generally considered preferable to parsimony.
Conclusion
The Parsimony Criterion builds evolutionary trees by selecting the topology that requires the fewest evolutionary changes.
- Strengths: It is computationally fast and does not require explicit evolutionary models (though it implicitly assumes all changes are weighted equally).
- Weaknesses: It ignores branch lengths, making it highly vulnerable to long-branch attraction (falsely grouping fast-evolving but unrelated lineages).
- Best Use: It is ideal for qualitative morphological data. For molecular sequence data, likelihood-based methods are generally preferred.
