jueves, 31 de marzo de 2016

Equivalence Between Maximum Parsimony and Maximum Likelihood

The maximum parsimony method is based on choosing the tree with the fewest changes character states (Camin Sokal, 1965). The maximum likelihood method is based on choosing the tree most likely on the data (observations) (Sober 2004). The debate over which method is best for inferring phylogenetic relationships has been in force. One of the arguments to justify the maximum parsimony method as valid, is that under some models is equivalent to the method of maximum likelihood (Farris, 1983). Tuffley and Steel (1997) showed that under non common mechanism model, select the same tree likelihood that selects parsimony. In this work, we compare the topologies selected by the parsimony and likelihood under a symmetrical model.

For this, use a tree of 10 tips. From this, generate sequences 20.000 bp in seq-gen (Rambaut Grassly, 1997) under the JC model and use 20 replicas. Trees reconstructed using parsimony method in TNT (Goloboff et al 2008) and in PHYML likelihood method (Guindon S et al, 2010) under a fully symmetrical model. Finally I contrast trees using the metric of Robinson-Foulds (Robinson et al 1981) as a measure of distance. This is done with the function treedist of phangorn package R.

The analysis got that for 20 replicas that do, only in a distance between the tree generated likelihood and generated parsimony is 0 (Fig 1, Table 1).

table 1. Symetric di erence for 20 replicas

Fig 1. Diagram of the distance between the trees generated by ML and MP


This is not the expected result, however, several parameters that I not considered, could influence in the result. One of them and I consider that most affected was the result was the type of method to use in the analysis of parsimony. Tuffley and Steel in his work used Fitch parsimony, I use Wag-
ner parsimony. This affects the order of the characters because the characters wagner considered as additives, while Fitch are considered as non-additives. Therefore, it could not conclude that the maximum likelihood method is not equivalent to the maxim parsimony method.

References

Camin J.H., Sokal R.R. 1965. A method for deducing branching sequences in a phylogeny. Evolution. 19:311–326

Sober, E. (2004). The contest between parsimony and likelihood. Systematic biology, 53(4), 644-653.

Farris, J. (1983). The logical basis of phylogenetic analysis.

Tuffley, C. and Steel, M. (1997): “Links Between Maximum Likelihood and Maximum Parsimony

under a Simple Model of Site Substitution.” Bulletin of Mathematical Biology 59: 581-607.

Rambaut A, Grassly NC, Seq-Gen: an application for the Monte Carlo simulation of DNA sequence evolution along phylogenetic trees., Comput Appl Biosci, June 1, 1997

Goloboff, P. A., Farris, J. S. and Nixon, K. C. (2008), TNT, a free program for phylogenetic analysis. Cladistics, 24: 774–786. doi: 10.1111/j. 1096-0031. 2008.00217.x

New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0. Guindon S., Dufayard J.F., Lefort V., Anisimova M., Hordijk., Gascuel O. 2010, Systematic Biology, 59(3):307-321

Robinson, D., Foulds, L. R. (1981). Comparison of phylogenetic trees. Mathematical bioscienes, 53(1), 131-147.