Measure support branches

Gualdrón-Diaz J. C.

Once it has obtained cladograms; it is important to know how strong is the evidence that supports a node. There are different ways to interpret the support (Stability, confidence levels and reliability) and different methods to asses it; the most popular are the resampling methods such as Bootstrap and Jackknife and those linked to relative optimality values such as Bremer support (Wheeler, 2010). For this must be a clear distinction in some terms. According Goloboff et al. (2003); Brower (2006, 2010) support and stability are logically different, support for a given branch in a tree is a measure of the net amount of evidence that favors the appearance of that branch in a most parsimonious topology and stability is the persistence of a given branch in the face of the addition, deletion, or reweighting of characters, taxa, or both from the data matrix as in bootstrap and jackknife approaches. Likewise, strong statistical assumptions are necessary to interpret jacknife or bootstrap as confidence levels (Felsenstein, 1985). Another way to measure the support for individual branches of a cladogram is Bremer support, also referred as the “decay index”(Bremer, 1994). It is measured by comparing the fit of the data to optimal and suboptimal trees. This support measure two different aspects of group support. The absolute bremer estimated amount of favorable evidence (Bremer, 1994) and relative bremer (Goloboff and Farris, 2001) estimated the ratio between favorable and contradictory evidence (Goloboff et al., 2003). Both support and stability are attributes have proven to be particularly tricky to measure in a direct manner, due to the complexity of character interactions in homoplastic data (Goloboff and Farris, 2001). Nevertheless, these measure serves as a means to discern groups that are plausible from those that are dubious,and can act as a guide to the generation of additional data to refine and improve the hypothesis (Brower, 2006).

Jackknifing and bootstrapping sometimes produce incoherent results. Uninformative characters and characters irrelevant to the monophyly of a group can influence the values of support for Jacknife and Bootstrapp, to solve this Farris et al. (1996) proposed to assign equal probabilities of deletion to individual characters. Similarly Goloboff et al. (2003) suggest a Poisson-based sampling regime for bootstrapping that also alleviates this problem. One clear advantage of the jackknife over the bootstrap is that the values on branches are less affected when there are characters with homoplasy(Freudenstein and Davis, 2010). Another wrong conclusion with regard to support both for Jackknife and Bootstrapp is when some characters have differents weights or costs, producing either under or overestimations of the actual support (Goloboff et al., 2003).This influence of the weight can be eliminated by symmetric resampling, done that the probability of increasing the weight of the character equals the probability of decreasing it (Goloboff et al., 2003); so, given the above, this explains the differences in the error produced by jackknife and bootstrap.

Bremer support rather than being an estimate based on pseudoreplicated subsamples of the data (like bootstrapping and jackknifing) is a statistical parameter of a particular data set and thus is not dependent on the data matching a particular assumed distribution; an advantage of bremer support that it never hits a maximum value (such as 100%), and continues to increase as character support for a particular branch in the tree accumulates (Brower, 2006). A defect of that method is that it does not always take into account the relative amounts of evidence contradictory and favorable to the group. This problem is diminished if the support for the group is calculated as the ratio between the amounts of favorable and contradictory evidence (Goloboff and Farris, 2001). This method is known as relative bremer and its potential advantages are that their values vary between 0 and 1 and they provide an approximate measure of the amount of favorable/contradictory evidence. Under weighting methods the bremer supports may be hard to interpret, but the relative supports for different weighting strengths are directly comparable (Goloboff and Farris, 2001). A disadvantage of the relative supports is that the values of in different pairs of trees must be calculated carefully.

An important extension of bremer support was the discovery by Baker and DeSalle (1997) is Partitioned Branch Support (PBS). The PBS value for a particular branch for a given data partition is determined by subtracting the length of the data partition on the MP tree(s) from the length of the data partition on the MP anticonstraint tree(s) for that branch (Brower, 2006). Thus, given partition may contribute positively, be neutral or conflict with the weight of the evidence that supports a particular branch in combined analysis.PBS allows exploration of partition incongruence within a total evidence framework (Brower et al., 1996). This ability to localize incongruence to a single partition for a single branchs has the potential to reveal both interesting evolutionary processes, such as selection on a particular gene. Partitioning data is a potentially useful way to explore incongruence of signal among characters from different sources (Brower, 2006). PBS has the advantage that parameters calculated are using the complete data matrix and may be for any combination of partitions. One of the problems with PBS is that it is sensitive to missing data, and can shift dramatically among partitions as missing data are filled into the matrix (Brower, 2006). Much of the critism of support measures is focused upon their employment of reanalyses of data subsets or partitions as though they were separate sources of evidence, but as have pointed out Goloboff et al. (2003), no measure of clade quality yet developed is immune to certain cases conceivable.

According Brower (2006) there are no objetive means to set a criterion of rejection of support or stability for a particular branch in a particular cladogram. Nevertheless the support for the current data does not necessarily imply that this will be robust to addition of taxa and characters: support today is no guarantee of stability in the future. For this reason, measurements that imply a confidence interval like bootstrap values are potentially misleading; By contrast bremer support, because it has no upper bound, is more direct and way to document the accumulation of character support for a particular branch as additional data are incorporated in a particular phylogenetic hypothesis (Brower, 2006).

References

RH Baker and R DeSalle. Multiple sources of character information and the phylogeny of hawaiian drosophilids. 1997.

Kare Bremer. Branch support and tree stability. Cladistics, 10(3):295–304, 1994. ISSN 1096-0031. doi: 10.1111/j.1096-0031.1994.tb00179.x. URL http://dx.doi.org/10.1111/j.1096-0031.1994.tb00179.x.

A. V. Z. Brower, R. DeSalle, and A. Vogler. Gene trees, species trees, and systematics: A cladistic perspective. Annual Review of Ecology and Systematics, 27(1):423–450, 1996. doi: 10.1146/annurev.ecolsys.27.1.423. URL http://www.annualreviews.org/doi/abs/10.1146/annurev.ecolsys.27.1.423.

Andrew V. Z. Brower. The how and why of branch support and partitioned branch support, with a new index to assess partition incongruence. Cladistics, 22(4):378–386, 2006. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2006.00113.x. URL http://dx.doi.org/10.1111/j.1096-0031.2006.00113.x.

Andrew V. Z. Brower. Stability, replication, pseudoreplication, support and consensus a reply to brower. Cladistics, 26(1):112–113, 2010. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2010.00319.x. URL http://dx.doi.org/10.1111/j.1096-0031.2010.00319.x.

James S. Farris, Victor A. Albert, Mari KAllersjA¶, Diana Lipscomb, and Arnold G. Kluge.Parsimony jackknifing outperforms neighbor-joining. Cladistics, 12(2):99–124, 1996. ISSN 1096-0031. doi: 10.1111/j.1096-0031.1996.tb00196.x. URL http://dx.doi.org/10.1111/j.1096-0031.1996.tb00196.x.

Joseph Felsenstein. Confidence limits on phylogenies: An approach using the bootstrap. Evolution, 39(4):783–791, 1985. ISSN 00143820. doi: 10.2307/2408678. URL http://dx.doi.org/10.2307/2408678.

John V. Freudenstein and Jerrold I. Davis. Branch support via resampling: an empirical study. Cladistics, 26(6):643–656, 2010. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2010.00304.x. URL http://dx.doi.org/10.1111/j.1096-0031.2010.00304.x.

Pablo A. Goloboff and James S. Farris. Methods for quick consensus estimation. Cladistics, 17(1):S26–S34, 2001. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2001.tb00102.x. URL http://dx.doi.org/10.1111/j.1096-0031.2001.tb00102.x.

Pablo A Goloboff, James S Farris, Mari Kallersj, Bengt Oxelman, M J Ramirez, and Claudia A Szumik. Improvements to resampling measures of group support. Cladistics, 19(4):324–332, 2003. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2003.tb00376.x. URL http://dx.doi.org/10.1111/j.1096-0031.2003.tb00376.x.

Ward C. Wheeler. Distinctions between optimal pected support. Cladistics, 26(6):657–663, 2010. ISSN 1096-0031. doi: 10.1111/j.1096-0031.2010.00308.x. URL http://dx.doi.org/10.1111/j.1096-0031.2010.00308.x.

Branch Support: confidence, stability, credibility?

By Susana Ortiz

One way of assessing whether a clade present in a phylogenetic reconstruction really is part of the true configuration in the phylogeny, is evaluating its support, which may be established by estimating confidence intervals based on sampling methods (Bootstrap and Jackknife), and Bremer support, based on the length difference of trees as a stability measure. Even if, this approaches are not independent of the search strategy given that they are sensitive to its effectiveness (Freudenstein and Davis, 2010). Therefore a highly weighted clade, not necessarily means it is real, maybe is just the kind of response that fits to the resources used (e. g. search strategy). Posterior probabilities in Bayesian analyses have been used as a probabilistic measure of support (e. g. Goloboff et. al, 2003; Pickett and Randle, 2005), because it quantifies credibility, how likely a certain clade is to be correct, given the data, model and priors (Huelsenbeck et al., 2002). Comparision between Bayesian and nonoparametric Bootstrapping was proposed by Efron et al. (1996), where the bootstrap confidence level can be thought as the assessments of error for the estimated tree. However, posterior probabilities are sensitive to the prior for internal branch lengths (Yang Z., Rannala 2005), and are significantly higher than corresponding nonparametric bootstrap frequencies when the models used for analyses are underparameterized (Goloboff et. al, 2003). Despite have been several the attempts to come close the different approaches under certain conditions, this approaches are not freely assessable under all phylogenetic criteria given some restrictions not only methodological but conceptual.

Bootstrap and Jackknife are resampling techniques from the original data to infer variability of the estimate, in this case the phylogeny. The variation among trees provide an adequate indication of the uncertainty (Felsestein, 1985). Nevertheless, Bootstrap has also been proposed as a tool to assess robustness with regard to small changes in data (Holmes, 2003), it is not a test of how accurate is a topology but provides information about its stability, as well as to assess whether the data are adecuate to validate the topology (Berry and Gascuel, 1996). As for repeteability unless it is a perfectly Hennigian data set (Felsestein, 1985), is expected to have variations between replicas, so one might think that many replicates would mean a greater precition regarding the idea of which groups are monophyletic, but according to Pattengale et al. (2009), rather small number of Bootstrap replicates (typically after 100–500 replicates) producing support values that correlate at better than 99.5% with the reference values on the best ML trees.

This last, although the stopping criteria can recommend very different numbers of replicates for different datasets of comparable sizes. In the same way, the above does not mean that a clade is or is not monophyletic depending on its support, this just points out the certainty with which you can find a particular node in the topology. If this node are not in the Bootstrap consensus, it could means there is a polytomy due to multiple nodes’ resolutions maybe by incongruence between characters. Mort et al (2000), compared Bootstrap and Jackknife, their findings show the relation between the bootstrap’s values and the deletion proportion chosen in Jackknife. However, in favor of Jackknife, it has been proposed as a rapid and efficient method to identify strongly supported clades (Farris et al. 1996) and the assigment of equal deletion probabilities to characters, it reduces the problem of competition bewteen informative and noninformative characters (Freudenstein and Davis, 2010).

Bremer support (Bremer, 1984) is another alternative to measure support, although only under Parsimony criterion. This method measures the diference between the most parsimonious cladogram and suboptimal that lacks of interes clade (Grant and Kluge, 2008). So in Bremer a strongly supported branch means a large increment in the length of the suboptimal trees. The absolute (Bremer, 1984) and relative Bremer support (Goloboff and Farris, 2001) are variants depending on the type of evidence that it takes into account. The firts measures the absolute amount of favorable evidence, and second the ratio between favorable and contradictory evidence to the group, and both represent two aspects of support that can vary independently (Goloboff et al., 2003). Bremer support as a support measure has been interpreted as a stability measure, so independent to the influence to autapomorphies and lower frequencies for better supported groups, however, have raised objections to this vision, such that stability depends of the specific scenario as noted Goloboff et al. (2003) “a group stable under additions of characters may be very unstable under addition of taxa or under recoding of some charactes” but bremer as support only is based on the available evidence.

Homoplasy is another factor affecting the estimation of support, clades delimited by “unique and unreversed” or relatively less homoplastic character states are often considered more strongly supported (Grant and Kluge, 2008), although all support aproaches are not equally sensitive. According to Freudenstein and Davis (2010) The values on branches not affected by homoplasy are slightly higher for the bootstrap than the jackknife, but the addition of homoplastic characters caused support on branches affected by homoplasy to drop substantially more, as measured by the bootstrap than as measured by the jackknife different to Bremer support which takes the distribution of homoplasy into account (Sanderson, 1995). Incongruence between characters, the proportion of homoplastic characters versus homologous, additivity, and character weighing (in bootstrap) are key topics in the evaluation of support. Number of nonhomoplastic synapomorphies supporting a clade provides a numerical estimate of the support of a hypothesis but maybe it does not provide evidence than favor a hypothesis over some another alternative (Wilkinson et al. 2003). I agree with Grant and Kluge (2003) about support measures do not test phylogenetic hypotheses, they evaluate the relative degree or strength of evidence.

References

- Berry, V. and Gascuel, O. (1996). On the interpretation of bootstrap trees: Appropriate threshold of clade selection and induced gain. Molecular Biology and Evolution 13 999–1011.
- Efron B., Halloran E., and Holmes S. 1996. Bootstrap confidence levels for phylogenetic trees. Recherche, 93(14):7085–7090.
- Erixon, P B. Svennblad, T. Britton y B. Oxelman. 2003. Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylo- genetics. Systematic Biology 52: 665-673
- Farris, J.S., 1996. Jac. Computer Program Distributed by the Author. Moleky-larsystematiska laboratoriet, Naturhistoriska riksmuseet, Stockholm, Sweden.
- Felsestein, J. 1985. Confidence limits on phylogenies: An approach using the bootstrap. Evolution 39:783–791.
- Freudenstein J. V., Davis J., I. 2010 Branch support via resampling: an empirical study. Cladistics, 26:1–14.
- Goloboff P. A., Farris J. S., K Mari, J Ram, and C. A. Szumik. Cladistics Improvements to resampling measures of group support. Cladistics, 19:324–332, 2003. doi: 10.1016/S0748-3007(03)00060-4.
- Grant, T., Kluge, A. G. 2003. Data exploration in phylogenetic inference: scientific, heuristic, or neither. Cladistics 19, 379–418.
- Grant, T., Kluge A. G. 2008. Cladistics Clade support measures and their adequacy. Cladistics, 24:1051–1064, 2008.
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- Pickett, C.P Randle. 2005. Strange bayes indeed: uniform topological priors imply non-uniform clade priors, Molecular Phylogenetics and Evolution 34.
- Sanderson, M.J., 1995. Objections to bootstrapping: a critique. Syst. Biol. 44, 299–320.
- Wilkinson, M., Lapointe, F.-J., Gower, D.J., 2003. Branch lengths and support. Syst. Biol. 52, 127–130.
- Yang Z., Rannala B. 2005. Branch-length prior influences Bayesian posterior probability of phylogeny. Syst Biol 54(3), 455-70.

Bayesian Inference in Phylogenetic Analysis

The growing peak of Bayesian methods in phylogenetic inference in the last two decades is the result of the implementation of Markov chain Monte Carlo algorithms (MCMC; which include Monte Carlo method) and Metropolis-Hastings algorithm, on the estimation of posterior probability distributions and the exploration of more parameter-rich evolutionary models (Nylander, et, al. 2004). Statistically, the Bayesian inference calculates the probability that a hypothesis be true given the posterior probability based on priors probabilities and the likelihood under each hypothesis. Here the probability is used to represent uncertainty about the phylogeny and in the parameters of the model and not as expected frequency of occurrence like in classical or frequentist statistics (Yang, 2006). Under a philosophical context, the Bayesian and Maximum Likelihood approaches are inference methods, which are based in calculation of probabilities of evolutionary transformations of characters (for example, according to a nucleotide substitution model) instead of evaluation of possible synapomorphies, also any homologous characters (apomorphic and plesiomorphic) can be used for inferring phylogenies and they assume that evolution may be reticulated and not always dichotomous (Lukhtanov, 2010).

At present, is possible to identify six key topics related with Bayesian approach in phylogenetic reconstruction: (1) Integration of complex evolutionary models, (2) heterogeneity across the sites (3) heterogeneity across the data in analysis of combined data (Huelsenbeck et, al. 2001), (4) computational efficiency (Ronquist & Huelsenbeck, 2003), (5) posterior probability for a tree or clade has an easy interpretation(Yang, 2006) and (6) incorporation of priors values. The development of Bayesian MCMC algorithms is the associated cause with the increase in computational efficiency making possible to analyze more complex and realistic evolutionary models. This does not mean that parameters rich models are appropriated for all data set because we may make the mistake of overparameterization and more complex evolutionary models are associated with more topological uncertainty (Nylander, et, al. 2004). However, the interesting is that it open up the possibility of exploring more realistic models and complex (but a real model can be simple) to recognize heterogeneity across the sites and combined data.

In term of computational efficiency, although Maximum Likelihood analysis has gained ground with the improvement and development of new algorithms implemented in software such PhyML (Guindon and Gascuel, 2003) and RAxML (Stamatakis, 2007) and now is possible perform moderately fast and accurate bootstrapping to determine confidence, in Bayesian inference the interpretation of posterior probability is easier, it is the probability that the tree or clade is correct given the data, model and priors (Yang, 2006), whereas the interpretation of bootstrap although tend to be more conservative has been controversial specially with model misspecification and when the signal is only detectable at some sites (Ronquist and Deans, 2009). Despite the above, Bayesian posterior probability according to Yang (2006) can be spuriously high due to lack of convergence, poor mixing, misspecification of the likelihood substitution model and misspecification and sensitivity of the priors. About this last, it allows to incorporate prior knowledge about a particular hypothesis or to use vague or uninformative priors when the little information is available or do not want to build the analysis on any previous (Ronquist et, al. 2008). Since, priors can be subjective, is convenient to assess the influence of the priors on the posterior probability. Pickett and Randle (2005) pointed out that with a uniform prior the posterior probability of a clade depends on the both the size on the clade and the number of species.

Regarding to the lack of convergence and poor mixing in Bayesian approach them leading to spuriously high support for the trees visited in the chain (Yang & Rannala, 2005), multiple long chains from different starting points could be a possible solution when the data set is very large. However, Bayesian inference to face to another problem, this is inconsistency. Under Bayes´ criterion the tree topologies are estimated without estimating branch lengths this is integrating branch lengths for a given tree topology over a distribution of possible values (Goloboff & Pol, 2005), then statistical consistency can be lose and Bayesian inference is biased in favor of topologies that group long branches together, even when the true model and priors distributions of evolutionary parameters over a group of phylogenies are known. According to Kolaczkowski and Thornton (2009), this bias becomes more severe as more data are analyzed and sequences sites evolve heterogeneously and is relatively weak when the true model is simple. So, Bayesian inference is less efficient and less robust to the use of an incorrect evolutionary model than ML. Despite the above, Bayesian MCMC inference is a promising approach to phylogenetic analysis and computational biology that has been in progress with the development of algorithms, methods and software, nevertheless more research is needed on how to incorporate previous knowledge into appropriate informative priors and how to deal with complex models and large data sets without falling into inconsistency.

References

Goloboff P., Pol D. Parsimony and Bayesian phylogenetics. 2005. In: Albert V. (ed). Parsimony, phylogeny, and genomics. Oxford University Press. 210-266.

Guindon S., Gascuel O. 2003. PhyML: " A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood. Systematic Biology. 2003 52(5):696-704.

Huelsenbeck J. P., Ronquist F., Rasmus N., Bollback J. P. 2001. Bayesian Inference of Phylogeny and Its Impact on Evolutionary Biology. Science. 294 (5550) : 2310-2314

Kolaczkowski B., Thornton J. W. 2009. Long-Branch Attraction Bias and Inconsistency in Bayesian Phylogenetics. PLoS One. 4:e7891. doi:10.1371/journal.pone.0007891

Lukhtanov V. A. 2010. From Haeckel’s Phylogenetics and Hennig’s Cladistics to the Method of Maximum Likelihood: Advantages and Limitations of Modern and Traditional Approaches to Phylogeny Reconstruction. Entomological Review. Vol. 90(3) : 299-310

Nylander J. A. A., Ronquist F., Huelsenbeck J. P., Nieves-Aldrey J. L. 2004. Bayesian Phylogenetic Analysis of Combined Data. Syst Biol. 53(1) : 47-67

Pickett K. M., Randle C. P. 2005. Strange Bayes indeed: Uniform topological priors imply non-uniform clade priors. Mol. Phyl. Evol. 34:203-211

Ronquist F., Deans A. R. 2009.Bayesian Phylogenetics and Its Influence on Insect Systematics. Systematic Entomology 35 (3): 349-378.

Ronquist F., van der Mark P., Huelsenbeck J. P. 2009. Bayesian phylogenetic analysis using MrBayes. In: Lemey P., Salemi M., and Anne-Mieke V. (eds.) The Phylogenetic Handbook: a Practical Approach to Phylogenetic Analysis and Hypothesis Testing. Cambridge University Press. 219-236.

Stamatakis, A., Blagojevic, F., Nikolopoulos, D., Antonopoulos, C. 2007 Exploring New Search Algorithms and Hardware for Phylogenetics: RAxML Meets the IBM Cell. The Journal of VLSI Signal Processing. 48 : 271–286

Yang Z. 2006. Computational Molecular Evolution. Oxford University Press, Oxford, England

Yang, Z., and B. Rannala. 2005. Branch-length prior influences Bayesian posterior probability of phylogeny. Systematic Biology 54: 455-470.

MAXIMUM LIKELIHOOD AND MAXIMUM PARSIMONY UNDER A SIMPLE MODEL.

Jiménez- Silva C. L.
Universidad Industrial de Santander.
Laboratorio de Sistemática y Biogeografía

INTRODUCTION

Stochastic models for nucleotide substitution are becoming increasingly important as a foundation for inferring phylogenetic trees from genetic sequence data. Such models allow for tree reconstruction through either maximum likelihood-based approaches or the _tting of transformed functions of the data to trees (see Swo_ord et al. (Swo_ord et al., 1996) for a recent survey). The models are also useful for analysing the performance of other, more conventional tree reconstruction methods, which are not explicitly based on such models, such as the popular maximum parsimony method (Fitch, 1971). Maximum parsimony (MP) is a popular technique for phylogeny reconstruction. However, MP is often criticized as being a statistically unsound method and one that fails to make explicit an underlying ‘‘model’’ of evolution (Steel and Penny, 2000). Parsimony does not make explicit assumptions about the evolutionary process. Some authors argue that parsimony makes no assumptions at all and that, furthermore, phylogenies should ideally be inferred without invoking any assumptions about the evolutionary process (Wiley 1981). Others point out that it is impossible to make any inference without a model; that a lack of explicit assumptions does not mean that the method is ‘assumption-free’ as the assumptions may be merely implicit; that the requirement for explicit specification of the assumed model is a strength rather than weakness of the model-based approach since then the fit of the model to data can be evaluated and improved (e.g. Felsenstein 1973).

METHODS

In the analysis were simulated sequences of 1000 bp under JC69 model and all branches on the tree are assumed to have the same length, were 10 replicates of each simulation under Seq-Gen v1.3.2 program (Rambaut & Grassly, 1997). For different topologies, 3 taxa, 4 taxa, 6 taxa and 12 taxa. The sequences generated were analyzed in parsimony using TNT (Goloboff et. al, 2008) program and Winclada and NONA (Goloboff, 1999; Nixon, K. C. 1999) program to 3 taxa. Also, the sequences were analyzed in Maximum likelihood using PhyML (Guindon & Gascuel, 2005), to check an equivalence between parsimony and likelihood under a particular model, this is JC69. The nucleotide models evaluated were JC69 in PhyML, For each simulation was performed the same procedure and finally the topologies generated were compared with Tree C program (Arias & Miranda-Esquivel) assuming on equal an exactly equal nodes. It obtains eventually a total of 200 comparisons were made and the process was automated by constructing scripts in bash.

RESULTS

When, I compared the phylogenetic reconstructions, data showed equivalence between parsimony and likelihood under a JC69 model. Equivalence here means that the most parsimonious tree and the ML tree under the said model are identical in every possible data set. But, this result was only present with the data set of a few terminals, ie 3 and 4 taxa.

JC model was assumed for comparison because I refer to it, as the fully symmetric model since it makes no distinction between any of the character states and being with each sequence being 1000 nt long. As a first approximation, there is no selection at any of the sites, and therefore it is more ‘‘parsimonious’’ to assume one common mechanism for all sites rather than 1000 different mechanisms, one for each site.

That parsimony and likelihood trees used for working with the JC model, sometimes Called the Neyman model with four states. It assumes rates of evolution on the branch of the tree each freely Vary from site to site. In this case, we have some underlying constraints on the type of substitution model (ie, Jukes-Cantor type), but no constraints on the edge parameters from site to site. This is even more general than the type of approach considered by Olsen (see Swofford et al. 1996, p. 443) in which the rate at which a site evolves can vary freely from site to site, but the ratios of the edge lengths are equal across the sites. (Steel and Penny, 2000). On the methodology used in this work, a free parameters model was assumed. For this purpose, was assigned the custom model option in Phyml. When the custom model option was selected, also it is possible to Give to the program a user-defined nucleotide frequency distribution at equilibrium, where calculated parameters are given by the data. Based on this, it is proposed that this type of Underlying model Almost Certainly is too flexible, because it allows many new parameters for each edge. It might be regarded as the model one might start with if one knew virtually nothing about any common underlying mechanism

linking the evolution of different characters on a tree. (Steel and Penny, 2000).

For the data set of 6 and 12 taxa the results were different; between both methods they were obtained under three equal nodes. This difference of equal nodes based on the number of terminals, in concordance with Hendy and Penny (1989) showed that with four species and binary characters evolving under the clock, parsimony is always consistent in recovering the tree, although ML and parsimony do not appear to be equivalent under the model. With five or more species evolving under the clock, it is known that parsimony can be inconsistent in estimating the trees (Hendy and Penny 1989; Zharkikh and Li 1993). Thus it is not equivalent to likelihood.

While, you can consider parsimony and likelihood to be equivalent under the JC69 model, those studies often used small trees with three to six taxa. The cases for much larger trees are not known. However, it appears easier to identify cases of inconsistency of parsimony on large trees than on small trees (Kim 1996; Huelsenbeck and Lander 2003), suggesting that likelihood and parsimony are in general not equivalent on large trees.

REFERENCES

Arias J. S., Miranda-Esquivel D. M. 2007. Tree C.

W. M. Fitch. Toward de_ning the course of evolution: minimum change for a speci_c tree topology.Systematic Zoology, 20:406{416, 1971.

D. L. Swo_ord, G. J. Olsen, P. J. Waddell, and D. M. Hillis. Phylogenetic inference. In D. M. Hillis, C. Moritz, and B. K. Marble, editors, Molecular Systematics, chapter 11, pages 407{514. Sinauer Associates, 2nd edition, 1996.

Goloboff, P., 1999. NONA (No Name) ver. 2. Published by the author, Tucuman, Argentina

Felsenstein, J. 1973b. Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters. Syst. Zool. 22:240–249.

Hendy, M. D. and Penny, D. 1989. A framework for the quantitative study of evolutionary trees. Syst. Zool. 38:297–309.

Huelsenbeck, J. P. and Lander, K. M. 2003. Frequent inconsistency of parsimony under a simple model of cladogenesis. Syst Biol 52:641–648.

Kim, J. 1996. General inconsistency conditions for maximum parsimony: effects of branch lengths and increasing numbers of taxa. Syst. Biol. 45:363–374.

Nixon, K. C. 1999. Winclada (BETA) ver. 0.9.9 PUBLISHED BY THE AUTHOR, ITHACA, NY. I have become weary of Clados generated trees being published without citation. Please cite the program

M. Steel and D. Penny, Parsimony, likelihood and the role of models in molecular phyloge-netics. Molecular Biology and Evolution 17 839{850 (2000).

Wiley, E. O. 1981. Phylogenetics. The Theory and Practice of Phylogenetic Systematics. John Wiley & Sons, New York.

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Evaluation of topological congruence based on GTR model and different approaches to integrate the rate heterogeneity implemented under RAxML and PhyML

Introduction

The variation of substitution rates across nucleotide sites is a well-known process that can vary substantially for different positions in a sequence (Salemi & Vandamme). Accordingly, the rate of each sequence is modeled as a random variable drawn from a specified prior distribution, the most common empirical approach is to use a gamma density function to model the rate of distribution across sites (Mayrose et. al, 2005). However, is possible find opposing views for and against about implementing empirically this distribution especially with GTR model, some objections relate to the computational cost, memory consumption, rates not unimodals, etc. Innovative approaches have been raised to incorporate rate heterogeneity in programs such RAxML (Stamakis, 2006), nevertheless, the likelihood values produced can not be directly compared to likelihood values of other ML programs and little is known about the topological congruence when comparing its results. Given that, the objective of this study is to evaluate the topological congruence based on GTR model and different approaches to incorporates the rate heterogeneity under RAxML and PhyML programs.

Methods

In the analysis, sequences of 2000 bp were simulated under GRT and GTRGAMMA models under Seq-Gen v1.3.2 program (Rambaut & Grassly, 1997) in order to use GTR as control and avoid, a priori, a biased in favor of Γ. The sequences generated were analyzed in parsimony using TNT (Goloboff et. al, 2008) program and a topology was reconstructed. The parsimony´s topology and randomly selected topologies were used as starting trees in RAxML (Stamakis, 2006) and PhyML (Guindon & Gascuel, 2005) programs to determine if the initial topology influences the reconstruction of the phylogenetic relationships in both programs under the different models selected. The nucleotide models evaluated were GTRCAT, GTRMIX, GTRGAMMA and GTRCAT_GAMMA in RAxML versus GTR, GTRGAMMA in PhyML, also for each model was evaluated the number of categories to optimize the per-site individual rates in order to preclude the effect of over or subestimation, the categories defined were: 4, 10, 25, 35, 45, 50. For each simulation was performed the same procedure and finally the topologies generated were compared with Tree C program (Arias & Miranda-Esquivel) based on equal an exactly equal nodes. A total of 264 comparisons were made and the process was automated by constructing scripts in bash.

Results

The findings in this study indicate that RAxML with sequences simulated under GTR or GTRGAMMA recovered the shorter topology when it used the models GTRMIX, GTRGAMMA and GTRCAT_GAMMA from a random initial topology. However, if you provided a fixed starting tree (Maximum Parsimony topology) the topology recovered had an additional node (21 nodes). GTRCAT approximation was the only that recovered in both cases the same topology with 21 nodes coinciding with the GTR and GTRGAMMA models under PhyML. This implies, although GTRCAT approximation allows to computing trees under realistic approximation of nucleotide substitution (Stamakis, 2006), it do not perform the optimal topological inference based on the congruence between the nodes reconstructed. The analysis with distinct rate categories settings did not influence the tree recovered in PhyML, with one equal node and no node exactly equal in all cases, while, in RAxML the results are unstable between categories and did not follow a trend with increasing number of rate categories specified. Despite this, depending of the model selected, the number of equals nodes increases with specific categories, although the findings were variable under sequences simulated under GTR and GTRGAMMA (see table: http://dl.dropbox.com/u/16494208/Tabla.ods).

On the other hand, when the topologies estimated under different models implemented in PhyML and RAxML were compared (see appendix), the number or equal nodes recovered, from random starting tree, was better with the GTRMIX approximation in half the categories (10, 25, 50) and the worth scenario was obtained under GTRCAT with two equal nodes in 50 category. Additionally, topologies recovered from fixed starting tree (parsimony topology), showed a surprisingly high number of equal nodes (until 18 nodes) and exactly equal nodes (until 17 nodes) independently of the category analyzed.

Trees recovered with GTRGAMMA and GTRMIX models implemented in RAxML versus trees recovered with GTR/GTRGAMMA in PhyML, reconstructed the highest number of equal nodes followed by GTRGAMMA_CAT and GTRCAT, although the latter did not showed exactly equal nodes. The results found were exactly equals in the comparisons of the resulting trees under the models implemented in PhyML and the models used in RAxML in each simulation. But differences were detected when the comparision was performed under GTRAGAMMA simulation, because the behavior changed and the number of equal nodes increased in various categories under GRTCAT and GTRCAT_GAMMA followed by GTRGAMMA and GTRMIX versus GTR/GTRGAMMA in PhyML. Possibly, in this specific case, the rate heterogeneity described with gamma quantified from GRTCAT and GTRCAT_GAMMA approaches in RAxML is the closest to the response obtained with PhyML.

Conclusions

This study showed that the topological congruence in analysis using differents approaches to evaluate the rate heterogeneity in GTR is optimally treated with PhyML and RAxML, however PhyML is more stable and conservative also it is not strongly influenced by the number of categories. Contrary, RAxML is more sensible to the number of categories but it was not possible identify some type of trend or behavior to explain the changes. Additional findings, indicated that the topological congruence can be influenced by the starting tree in the analysis and by the model of simulation.

References

Arias J. S., Miranda-Esquivel D. M. 2007. Tree C.

Guindon S., Gascuel O. 2003. PhyML:"A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood."Systematic Biology. 2003 52(5):696-704.

Goloboff, P. A., Farris, J. S. and Nixon, K. C. 2008. TNT, a free program for phylogenetic analysis. Cladistics, 24: 774–786.

Mayrose I, Friedman N, Pupko T. 2005. A Gamma mixture model better accounts for among site rate heterogeneity. Bioinformatics. 21(Suppl. 2):ii151–ii158.

Rambaut, A. and Grassly, N. C. 1997. Seq-Gen: An application for the Monte Carlo simulation of DNA sequence evolution along phylogenetic trees. Comput. Appl. Biosci. 13: 235-238.

Salemi M., Vandamme A. M. (eds.). 2003. The Phylogenetic Handbook: a Practical Approach to Phylogenetic Analysis and Hypothesis Testing. 2nd Edition, 381-404, Cambridge University Press, Cambridge.

Stamatakis, A. 2006. RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models. Bioinformatics 22.

Annexes

Script for simulation of molecular sequences

#!/bin/bash

cd /home/andromeda/Seq-Gen.v1.3.2/source

for m in *.tree; do

for a in *.txt; do

echo "./seq-gen -mGTR -l2000 -n1 -z150 -op < $m > gtr$m$l.dat" >>gtr.txt

echo "./seq-gen -mGTR -g4 -l2000 -n1 -z150 -op < $m > gtrg$m$l.dat" >>gtrg.txt

chmod +x $a

./$a

done

done

mkdir gtr

mv gtr*.dat gtr

Script to run on PhyML and RAxML

RAxML:

#!/bin/bash

cd /home/andromeda/RAxML-7.0.4/

for s in *.datdo

for mod in GTRGAMMA GTRCAT GTRMIX GTRCAT_GAMMA;

do

for a in 4 10 25 35 45 50;

do

./raxml -f d -t parsi.tree -s $s -c $a -m $mod -n par$s$a$mod

done

done

done

mkdir parsi

mv RAxML_result.* parsi

PhyML

#!/bin/bash

cd /home/andromeda/PhyML_3.0/

for s in *.dat;

do

# categories

for a in 4 10 25 35 45 50;

do

echo "./phyml -i $s -d nt -q -n 1 -p -m GTR -c $a -a 1 -s BEST -o tlr --r_seed 12345 -- print_site_lnl --run gg$s$a" >> PHYML$s$a.txt

echo "./phyml -i $s -d nt -q -n 1 -p -m GTR -c $a -s BEST -o tlr --r_seed 12345 --print_site_lnl --run g$s$a" >> PHYML$s$a.txt

echo "./phyml -i $s -d nt -q -n 1 -p -m GTR -c $a -a 1 -s BEST -u parsi.tree -o tlr --r_seed 12345 --print_site_lnl --run ggp$s$a" >> PHYML$s$a.txt

echo "./phyml -i $s -d nt -q -n 1 -p -m GTR -c $a -s BEST -u parsi.tree -o tlr --r_seed 12345 --print_site_lnl --run gp$s$a" >> PHYML$s$a.txt

chmod +x PHYML$s$a.txt

./PHYML$s$a.txt

done

done

mkdir parsiphy

#mv RAxML_result.* parsi

Script to add header and change format

#!/bin/bash

for i in pargtrgarbol.tree.*; do

sed -i "1itread 'tree(s) from TNT, for data in e.nex'" $i

echo "proc-;" >>$i

done

Tree C´s script : comparison trees

#!/bin/bash

for i in gpgtrgarbol.tree.dat25.txt; do

for e in pargtrgarbol.tree.*; do

echo "./treec_linux -f $i -l $e -o sal$e$i.dat -t" >> treec.txt

chmod +x treec.txt

./treec.txt

done

done

mkdir comparison

mv *.dat comparison

Does the phylogenetic Species Category exist in virus?

Jiménez- Silva C. L.
Universidad Industrial de Santander.
Laboratorio de Sistematica y Biogeografia

Introduction

Phylogenetic specie is the smallest diagnosable group identified as an ancestor-descendant populations evolving separately from others (Cacraft, 1983). The species can be considered a species level, among all those available in the hierarhy Phylogenetic. Only monophyletic groups can be recognized and formally named taxa. This principle is based on the groups which include all the descendants of a single common ancestor are the only groups with real and natural existence in relation to the evolutionary process (De Luna and Mishler, 1996). The real existence of the species gives genealogical relationships with other group of organisms, their historical behavior, so it is considered that the species are different because they have diverged evolutionarily. Wiley (1978) supports this assertion by suggesting that the species is a single lineage of ancestral-descendant populations, they retain their identity from other lineages and have their own evolutionary tendencies and historical fate.

According to the above and the ontological status of phylogenetic species suggests that instead of viewing species as natural kinds we should think of them as individuals (Ghiselin, 1974 and Hull, 1978). Given the class/individual distinction, Ghiselin and Hull argue that species are individuals, not classes. Their argument assumes that the term ‘species’ is a theoretical term in evolutionary theory, so their argument focuses on the role of ‘species’ in that theory. Here is Hull's version of the argument, which can be dubbed the ‘evolutionary unit argument.’ Since Darwin, species have been considered units of evolution. The "individuals" can you discover connectors or space - time, ie, the status of "individual" at a time and place particle is linked to another state at another time and space site for historical connections (Dupré 2001, Reydon de 2003, y Crane 2004). From this concept and its ontological status is to intend whether the phylogenetic Species exist in virus Category.

The idea that species are individuals has a number of implications. For one, the relationship between an organism and its species is not a member/class relation but a part/whole relation. An organism belongs to a particular species only if it is appropriately causally connected to the other organisms in that species. The organisms of a species must be parts of a single evolving lineage (Hull, 1978). If belonging to a species turns on an organism's insertion in a lineage, then qualitative similarity can be misleading. Two organisms may be very similar morphologically, genetically, and behaviorally, but unless they belong to the same spatiotemporally continuous lineage they cannot belong to the same species.

Virus Species

The international Committee on taxonomy of viruses (ICTV) endorsed the following definition of virus species: a virus species is a polythetic class of viruses that constitutes a lineage of replication and occupies a particular ecological niche (Van Regenmortel & Mahy, 2004). This definition applies for viruses like units called "classes", in a biological classification scheme, an individual organism or a virus can be a member of several abstract classes like a species or a genus. Class membership must be distinguished from the so-called ‘‘part-whole’’ relationship which exists only between two concrete objects, one being a part of the other in the way, for instance, that cells and organs are parts of an organism. It is not possible for a concrete object like a virus to be ‘‘part’’ of an abstract entity like a species (similarly a thought cannot be part of an object). The mixing of logical categories has led to much debate in viral taxonomy (Bos, 2003; Van Regenmortel, 2003).

A class is defined by properties that are constant and immutable. This allows members of such a class to be recognized with absolute certainty since one or more property is necessarily present in every member of the class. Virus families, for instance, are universal classes because they consist of members, all of which share a number of defining properties that are both necessary and sufficient for class membership. Allocating a virus to a family is thus an easy task since a few structural or chemical attributes will suffice to allocate the virus to a particular family. (Van Regenmortel, 2006).

Classifying viruses consists in inventing taxonomic classes like particular families or species and allocating individual viruses to these classes in order to achieve some order whereby similar viral agents are grouped together. The failure to distinguish between real objects such as organisms and viruses and the mental constructions and abstractions needed to build up any classification system has been a fertile source of confusion in taxonomy (Van Regenmortel, 2003) Distinguishing between real, tangible objects like viruses (i.e. concrete individuals) and mental constructs like virus species and genera (i.e. classes) that exist only in the mind is a basic requirement for clear thinking. Although a taxonomic class is defined by properties possessed by concrete objects, it is an abstract, conceptualized collection, i.e. a mental construct.

Returning to the phylogenetic species concept, this raises the real Existence of the species Conceived as discrete units, ie, restricted in space and time. Inconsistent with the vision Referred to by (ICTV), Which Takes the virus species as a class being these, units exist independent and unrestricted that teporales or spatial boundaries. If we encuena that "classes" are abstractions, ie, a mental construct, missing reality. The concept proposed by De Luna and Mishler (1996), on the phylogenetic concept where raise the species as a group with real existence in relation to the natural evolutionary process. The virus species is not wonderful to hang phylogenetic species category and be closer to a nominalist concept (real missing) or phenetic.

References

Bos, L., 2003. Virus nomenclature; continuing topicality. Arch. Virol. 148, 1235–1246.

Crane, J. 2004, “On the Metaphysics of Species”, Philosophy of Science, 71: 156–173

Cracraft, J. 1983. Species concepts and speciation analysis. Current Ornithology, 1, 159–187.

Dupré, J., 2001, “In Defense of Classification”, Studies in the History and Philosophy of Biology and the Biomedical Sciences, 32: 203–219.

Ghiselin, M., 1974, “A Radical Solution to the Species Problem”, Systematic Zoology, 23: 536–544

Hull, D., 1978, “A Matter of Individuality”, Philosophy of Science, 45: 335–360
Reydon, T., 2003, “Species Are Individuals Or Are They?” Philosophy of Science, 70: 49–56.

Van Regenmortel, M.H.V. and Mahy, B.W.J., 2004. Emerging issues in virus taxonomy. Emerg. Infect. Dis. 10, 8–13.

Van Regenmortel, M.H.V., 2003. Viruses are real, virus species are man-made taxonomic constructions. Arch. Virol. 148, 2481–2488.

Van Regenmortel, M.H.V., 2006. Virologists, taxonomy and the demands of logic. Arch. Virol. 151, in press.

Wiley, E. O.,1978. The evolutionary species concept reconsideres. Syst. Zool., 27: 17-26.