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

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