Parsimony Methods

Abstract

Parsimony methods of phylogenetic reconstruction use an explicit criterion of optimality, the minimisation of evolutionary transformations. By doing so, parsimony also minimises instances of homoplasy (convergence or parallelisms) and maximises similarity due to a common descent (homology). Tree evaluation is done by an optimisation algorithm that calculates the length of each character over the tree; the global tree length is the sum of the individual character lengths. The Sankoff generalised algorithm allows for the optimisation of characters with any cost matrices; there are faster algorithms specific for unordered and additive characters. A problem with tree searches is the vast number of possible trees. There are exact solutions only for small datasets, but most real datasets require heuristic strategies. Measures of group support show the degree on which the data hold the conclusions, and sensitivity analyses help express the robustness of phylogenetic inferences on changes in parameters and conditions of analysis.

Key Concepts:

  • Phylogeny is the theoretical background for the classification of living organisms.

  • Parsimony methods for phylogenetic reconstruction use the minimisation of evolutionary transformations as the optimality criterion.

  • The parsimony criterion minimises instances of homoplasy (convergence or parallelisms) and maximises similarity due to common descent.

  • The optimisation of a character on a tree results in states assigned to hypothetical ancestors, implying the minimum number of transformations.

  • Tree searching is a complex problem, for which exact solutions are limited to the smaller datasets; most real datasets require heuristic solutions.

  • Differential transformation costs and character weights can be implemented in parsimony methods.

  • Measures of support and sensitivity can be used to express the robustness of phylogenetic inferences.

Keywords: parsimony; phylogenetics; optimisation; tree search; character weighting; group support; sensitivity analysis

Figure 1.

Optimisation and tree length. (a–d) There are many possible assignations of states to hypothetical ancestors on the same tree, each implying a different length; the parsimony criterion prefers the optimal reconstruction (a) over (b–d). (a, e, f) Different trees produce different tree lengths when optimised; Tree 1 is shorter than either Tree 2 or 3; the parsimony criterion prefers Tree 1. (g) A different assignation of ancestral states on Tree 3, producing the same length as in (f). (h) Optimisation of Tree 3, expressing all the states that can be optimally assigned on internal nodes, summarising the reconstructions (f) and (g).

Figure 2.

Matrices of transformation costs. (a) Unordered states, optimised with the Fitch algorithm. (b) Linearly ordered states, or additive, optimised with the Farris algorithm. (c) Symmetric cost matrix with transversions:transitions costs 5:2. (d) An asymmetric cost matrix, with gains (0–1) six times more costly than losses (1–0). (e) An extremely asymmetric cost matrix under Dollo's law, with cost of gains so high that convergences to state 1 will be forbidden in practice. Matrices (c–e) can only be optimised with the Sankoff algorithm.

Figure 3.

Rooting. (a) Tree 1 of Figure a can be rerooted by eliminating the root node, dragging the branch at the star and creating a new root node; all other ancestral assignments and the tree length remain the same, but the transformation changes direction, from T to A. (b) The rerooted Tree 1 can be drawn as Tree 4. For the parsimony criterion, they are equally optimal.

Figure 4.

(a) A data matrix of eight species scored for 16 binary characters, and the steps and homoplasy implied by the tree depicted in (b); the last three characters are uninformative. (b) One of the parsimonious trees, with character changes on branches; open circles are changes in homoplastic characters. (c) Two other optimal resolutions of clade (FGH). (d) Consensus of the three optimal trees, with Bremer/boostrap support values indicated below branches.

Figure 5.

Tree search strategies (see text for explanation). (a) The branch and bound sequence; whenever a subtree exceed the length of a previous complete tree, all deriving trees containing that subtree can be safely discarded. (b) In branch swapping by SPR a sectioned subtree is connected by its root to all the possible target branches (white circles); the rearrangement is kept if the tree becomes shorter. (c) Branch swapping by TBR works similarly, but the sectioned subtree is connected by all possible rerootings.

Figure 6.

Imaginary landscape of tree space, optimality values are higher on top. (a) In a tree space with a single peak, small optimality improvements by branch swapping will lead to the optimal tree. (b) In a complex landscape, branch swapping often gets stuck in local optima; one way of accessing the global optimum is using multiple replications with independent starting trees.

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References

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Further Reading

Felsenstein J (2004) Inferring Phylogenies. Sunderland: Sinauer.

Goloboff PA (2002) Techniques for analyzing large data sets. In: DeSalle R , Giribet G and Wheeler W (eds) Techniques in Molecular Systematics and Evolution, pp. 70–79. Basel: Brikhäuser Verlag.

Swofford DL , Olsen GL , Waddell PJ and Hillis DM (1996) Phylogenetic Inference. Molecular Systematics, 2nd edn. Sunderland: Sinauer.

Wheeler WC (2012) Systematics: A Course of Lectures. Sussex: Wiley‐Blackwell.

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How to Cite close
Ramírez, Martín J(Sep 2013) Parsimony Methods. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0005139]