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Minimum evolution

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Minimum evolution is a distance method employed in phylogenetics modeling. It shares with maximum parsimony the aspect of searching for the phylogeny that has the shortest total sum of branch lengths.[1][2]

The theoretical foundations of the minimum evolution (ME) criterion lay in the seminal works of both Kidd and Sgaramella-Zonta (1971)[3] and Rzhetsky and Nei (1993).[4] In these frameworks, the molecular sequences from taxa are replaced by a set of measures of their dissimilarity (i.e., the so called "evolutionary distances") and a fundamental result states that if such distances were unbiased estimates of the true evolutionary distances from taxa (i.e., the distances that one would obtain if all the molecular data from taxa were available), then the true phylogeny of taxa would have an expected length shorter than any other possible phylogeny T compatible with those distances.

Relationships with and comparison with other methods

Maximum parsimony

It is worth noting here a subtle difference between the maximum-parsimony criterion and the ME criterion: while maximum-parsimony is based on an abductive heuristic, i.e., the plausibility of the simplest evolutionary hypothesis of taxa with respect to the more complex ones, the ME criterion is based on Kidd and Sgaramella-Zonta's conjectures that were proven true 22 years later by Rzhetsky and Nei.[4] These mathematical results set the ME criterion free from the Occam's razor principle and confer it a solid theoretical and quantitative basis.

Maximum-parsimony criterion, which uses Hamming distance branch lengths, was shown to be statistically inconsistent in 1978. This lead to an interest in statistically consistent alternatives such as ME.[5]

Neighbor joining

Neighbor joining may be viewed as a greedy heuristic for the balanced minimum evolution (BME) criterion. Saito and Nei's 1987 NJ algorithm far predates the BME criterion of 2000. For two decades, researchers used NJ without a firm theoretical basis for why it works.[6]

Statistical consistency

The ME criterion is known to be statistically consistent whenever the branch lengths are estimated via the Ordinary Least-Squares (OLS) or via linear programming.[4][7][8] However, as observed in Rzhetsky & Nei's article, the phylogeny having the minimum length under the OLS branch length estimation model may be characterized, in some circumstance, by negative branch lengths, which unfortunately are empty of biological meaning.[4]

To solve this drawback, Pauplin[9] proposed to replace OLS with a new particular branch length estimation model, known as balanced basic evolution (BME). Richard Desper and Olivier Gascuel[10] showed that the BME branch length estimation model ensures the general statistical consistency of the minimum length phylogeny as well as the non-negativity of its branch lengths, whenever the estimated evolutionary distances from taxa satisfy the triangle inequality.

Le Sy Vinh and Arndt von Haeseler[11] have shown, by means of massive and systematic simulation experiments, that the accuracy of the ME criterion under the BME branch length estimation model is by far the highest in distance methods and not inferior to those of alternative criteria based e.g., on Maximum Likelihood or Bayesian Inference. Moreover, as shown by Daniele Catanzaro, Martin Frohn and Raffaele Pesenti,[12] the minimum length phylogeny under the BME branch length estimation model can be interpreted as the (Pareto optimal) consensus tree between concurrent minimum entropy processes encoded by a forest of n phylogenies rooted on the n analyzed taxa. This particular information theory-based interpretation is conjectured to be shared by all distance methods in phylogenetics.

Algorithmic aspects

The "minimum evolution problem" (MEP), in which a minimum-summed-length phylogeny is derived from a set of sequences under the ME criterion, is said to be NP-hard.[13][14] The "balanced minimum evolution problem" (BMEP), which uses the newer BME criterion, is APX-hard.[5]

A number of exact algorithms solving BMEP have been described.[15][16][17][18] The best known exact algorithm[19] remains impractical for more than a dozen taxa, even with multiprocessing.[5] There is only one approximation algorithm with proven error bounds, published in 2012.[5]

In practical use, BMEP is overwhemingly implemented by heuristic search. The basic, aforementioned neighbor-joining algorithm implements a greedy version of BMEP.[6] FastME, the "state-of-the-art",[5] starts with a rough tree then improves it using a set of topological moves such as Nearest Neighbor Interchanges (NNI). Compared to NJ, it is about as fast and more accurate.[20] Metaheuristics have also been used.[21]

See also

References

  1. ^ Catanzaro, Daniele (2010). Estimating phylogenies from molecular data, in Mathematical approaches to polymer sequence analysis and related problems. Springer, New York.
  2. ^ Catanzaro D (2009). "The minimum evolution problem: Overview and classification". Networks. 53 (2): 112–125. doi:10.1002/net.20280. S2CID 6018514.
  3. ^ Kidd KK, Sgaramella-Zonta LA (1971). "Phylogenetic analysis: Concepts and methods". American Journal of Human Genetics. 23 (3): 235–252. PMC 1706731. PMID 5089842.
  4. ^ a b c d Rzhetsky A, Nei M (1993). "Theoretical foundations of the minimum evolution method of phylogenetic inference". Molecular Biology and Evolution. 10: 21073–1095.
  5. ^ a b c d e Catanzaro, Daniele; Frohn, Martin; Gascuel, Olivier; Pesenti, Raffaele (July 2022). "A tutorial on the balanced minimum evolution problem". European Journal of Operational Research. 300 (1): 1–19. doi:10.1016/j.ejor.2021.08.004.
  6. ^ a b Gascuel O, Steel M (2006). "Neighbor-joining revealed". Mol Biol Evol. 23 (11): 1997–2000. doi:10.1093/molbev/msl072. PMID 16877499.
  7. ^ Desper R, Gascuel O (2005). The minimum evolution distance-based approach to phylogenetic inference in Mathematics of Evolution and Phylogeny. Oxford University Press, New York.
  8. ^ Catanzaro D, Aringhieri R, Di Summa M, Pesenti R (2015). "A branch-price-and-cut algorithm for the minimum evolution problem". European Journal of Operational Research. 244 (3): 753–765. doi:10.1016/j.ejor.2015.02.019. S2CID 1549028.
  9. ^ Pauplin Y (2000). "Direct calculation of a tree length using a distance matrix". Journal of Molecular Evolution. 51 (1): 41–47. Bibcode:2000JMolE..51...41P. doi:10.1007/s002390010065. PMID 10903371. S2CID 8619412.
  10. ^ Desper R, Gascuel O (March 2004). "Theoretical foundation of the balanced minimum evolution method of phylogenetic inference and its relationship to weighted least-squares tree fitting". Molecular Biology and Evolution. 21 (3): 587–98. doi:10.1093/molbev/msh049. PMID 14694080.
  11. ^ Vihn LS, von Haeseler A (2005). "Shortest triplet clustering: Reconstructing large phylogenies using representative sets". BMC Bioinformatics. 6: 1–14. doi:10.1186/1471-2105-6-1. PMC 545949. PMID 15631638.
  12. ^ Catanzaro D, Frohn M, Pesenti R (2020). "An information theory perspective on the Balanced Minimum Evolution Problem". Operations Research Letters. 48 (3): 362–367. doi:10.1016/j.orl.2020.04.010. S2CID 218998400.
  13. ^ Catanzaro D, Labbé M, Pesenti R, Salazar-González JJ (2009). "Mathematical models to reconstruct phylogenetic trees under the minimum evolution criterion". Networks. 53 (2): 126–140. doi:10.1002/net.20281. S2CID 17792339.
  14. ^ Catanzaro D, Aringhieri R, Di Summa M, Pesenti R (2015). "A branch-price-and-cut algorithm for the minimum evolution problem". European Journal of Operational Research. 244 (3): 753–765. doi:10.1016/j.ejor.2015.02.019. S2CID 1549028.
  15. ^ Aringhieri R, Catanzaro D, Di Summa M (2011). "Optimal solutions for the balanced minimum evolution problem". Computers and Operations Research. 38 (12): 1845–1854. doi:10.1016/j.cor.2011.02.020. hdl:2318/86826. S2CID 9514013.
  16. ^ Catanzaro D, Labbé M, Pesenti R, Salazar-González JJ (2012). "The balanced minimum evolution problem". INFORMS Journal on Computing. 24 (2): 276–294. doi:10.1287/ijoc.1110.0455.
  17. ^ Catanzaro D, Labbé M, Pesenti R (2013). "The balanced minimum evolution problem under uncertain data". Discrete Applied Mathematics. 161 (13–14): 1789–1804. doi:10.1016/j.dam.2013.03.012.
  18. ^ Catanzaro D, Pesenti R (2019). "Enumerating Vertices of the Balanced Minimum Evolution Polytope". Computers and Operations Research. 109: 209–217. doi:10.1016/j.cor.2019.05.001. S2CID 164835227.
  19. ^ Catanzaro D, Pesenti R, Wolsey L (2020). "On the Balanced Minimum Evolution Polytope". Discrete Optimization. 36: 100570. doi:10.1016/j.disopt.2020.100570. S2CID 213389485.
  20. ^ "ATGC: FastME". www.atgc-montpellier.fr.
  21. ^ Catanzaro D, Pesenti R, Milinkovitch MC (2007). "An ant colony optimization algorithm for phylogenetic estimation under the minimum evolution principle". BMC Evolutionary Biology. 7: 228. doi:10.1186/1471-2148-7-228. PMC 2211314. PMID 18005416.

Further reading

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