Phylogenetic inference

Introduction

The 2020 LPSN user survey revealed at an early stage that many users were interested in a guide to phylogenetic inference and interpretation of trees. For this reason, this page was compiled to provide background information on the relationship between taxonomic classification and phylogenetic inference (theory) as well as hints on the inference, display, and interpretation of phylogenetic trees (practice).
Microbiology pioneered the broad application of sequence analysis in taxonomic classification and early on introduced mandatory 16S rRNA gene sequencing to accompany the publication of type strains of new species, a requirement has only much later on been approximated in other taxonomic disciplines (such as botany, mycology, zoology) in the course of DNA barcoding initiatives. Nevertheless, there may be some idiosyncrasies regarding the way microbial taxonomists apply phylogenetic inference and its taxonomic interpretation, if any. For instance, the preference for Neighbour Joining or the frequent use of too simplistic evolutionary models are peculiarities which the author has observed only in microbiology, but not in other areas of taxonomy such as botany, mycology and zoology. For this reason, the recommendations given here occasionally contradict current practice in microbial taxonomy. These deviations are intentional. Some habits may better be discontinued, and LPSN hopes to herewith contribute to their demise.
The author has regularly given university courses on phylogenetic inference and related topics since 2006. Some of the hints given below are based on this teaching experience. For instance, the interpretation of phylogenetic trees appears to be at least as important as the inference of phylogenetic trees. Software recommendations are given in the text. Literature references were selected that are either the original reference for a specific technology or other insight, or are recommended for further reading for other reasons. In particular, textbooks of interest and reviews of relevance that appeared as journal articles or book chapters are provided in the list of references. Suggestions for additions are welcome.
Phylogenetic resources on partner sites of LPSN include:

The role of phylogenies in taxonomic classification

Rules for nomenclature such as those constituting the International Code of Nomenclature of Prokaryotes (Lapage 1992) support taxonomic freedom, i.e. they do not determine how organisms are to be classified (Tindall 1999). However, a consistent research programme was developed in the literature on how to relate phylogenies and taxonomic classification, known as Phylogenetic Systematics (Wiley and Lieberman 2011), on which the following presentation is based.
The purpose of taxonomic classification is to provide a summary of the phylogeny of the classified organisms. If a taxonomic classification contains evidently non-monophyletic taxa according to the phylogenetic tree it is allegedly based on, then that classification contradicts this phylogeny. A summary, however, must never contradict the statements it summarizes. See Wiley et al. (1991) or Wiley and Lieberman (2011) and the references cited therein for details. The seminal work is the one of Hennig (1950, 1965, 1966) but Hull (1964) is also a crucial reference. Klenk and Göker (2010) and particularly Göker (2021) also elaborate on this issue and provide literature evidence. There is no principal difference between the purpose of taxonomic classification in microbiology and the purpose of taxonomic classification in other disciplines (the burden of proof lies with those who claim that there is a difference).
The term "phylogenetically coherent taxon" is often used in microbiology. We here explicitly discourage its use. If "phylogenetically coherent taxon" is supposed to mean "monophyletic taxon", then it is a superfluous later synonym. If "phylogenetically coherent taxon" is supposed to mean something else, then it is irrelevant or even misleading; the central importance of the monophyly criterion was explained above. A clade is by definition monophyletic, hence the expression "monophyletic clade" is a pleonasm. Consult Wiley et al. (1991), Wiley and Lieberman (2011) or Göker (2021) for details.
The term "phylogenetic data" is frequently used in microbiology in place of "sequence data". This usage is highly misleading and strongly discouraged (Göker 2021). As long as a phylogeny is not involved, data are not phylogenetic. Sequence data are not innately phylogenetic, and many kinds of other data, such as phenotypic data, are not innately non-phylogenetic (Wiley et al. 1991, Berger and Stamatakis 2010, Wiley and Lieberman 2011, Goloboff and Catalano 2016). As one can well choose to not infer a phylogeny from sequence data, why call them phylogenetic data? Equating "phylogenetic data" with "sequence data" is as inappropriate as equating "horse" with "mount": there are horses that are not used as mounts and there are mounts that are not horses.
While popular in microbiology, it makes not much sense to talk about "members" of a taxon. Epistemologically, taxa are logical individuals rather than logical classes (because taxa have a beginning in time and an end in time). But whereas logical classes have members, sets have elements, and individuals have parts. For instance, Felis silvestris is a part of the genus Felis, not its member. Among the vast body of literature on this issue you might consult Wiley and Lieberman (2011) for details. Again, there is no principal difference between taxonomic classification of bacteria and taxonomic classification in other disciplines. The International Code of Nomenclature of Prokaryotes (Lapage 1992) is inconsistent regarding this aspect of taxonomic terminology; see Tindall (1999) for the relationship between classification and nomenclature in general. One could also use the neutral term "representative" instead of "member", "element" or "part". Moreover, a phrasing such as "members of the genus Phaeobacter have frequently been isolated from sea water" is just an unnecessarily clumsy expression for "the genus Phaeobacter has frequently been isolated from sea water" or even better "Phaeobacter has frequently been isolated from sea water", since the category is often implicit in a taxon name. Make it short!
Polyphasic taxonomy was originally linked to phenetics, a competing school of taxonomy (Klenk and Göker 2010, Göker 2021). Inconsistencies are generated if on the one hand trees are inferred using phylogenetic methods but on the other hand single characters, such as phenotypic ones, are interpreted using phenetic principles (Montero-Calasanz et al. 2017, Nouioui et al. 2018, García-López et al. 2019, Hördt et al. 2020). These inconsistencies can lead to false conclusions about the suitability of taxonomic markers (Nouioui et al. 2018, Göker 2021). The problem can be solved by interpreting single characters, too, using the principles of Phylogenetic Systematics (Wiley et al. 1991, Wiley and Lieberman 2011).

Inferring trees

Sequence data are not the only kind of data that can be used to infer phylogenies (Wiley and Lieberman 2011, Göker 2021). But if they are used in conjunction with one of the common ways to infer phylogenies, nucleotide or amino-acid sequences need to aligned. It is strongly suggested to use more recent and more sophisticated multiple sequence alignment algorithms (Lee et al. 2002, Grasso and Lee 2004, Morgenstern 2009) over popular ones such as ClustalW/ClustalX (Higgins et al. 1992, Thompson et al. 1997). For instance, both MAFFT (Katoh et al. 2002, Katoh et al. 2005) and MUSCLE (Edgar 2004) are faster and more accurate than ClustalW/ClustalX. Consult their literature references for according benchmarking studies. In contrast to pairwise sequence alignment (Needleman and Wunsch 1970), multiple sequence alignment cannot exactly be solved, even if a optimal set of parameters (Gu and Li 1995) is at hand.
For phylogenetic inference itself, it is here suggested to prefer Maximum Likelihood (ML) over other phylogenetic inference methods such as Neighbour Joining (NJ), Maximum Parsimony (MP) or Bayesian Inference whenever possible. This holds even though NJ (Saitou and Nei 1987) and MP (Camin and Sokal 1965, Farris et al. 1970, Farris 1977, Fitch 1971, Sankoff 1975) are computationally much faster than ML (Felsenstein 1981). If you already have an ML tree, it is here recommended to use MP to conduct a second phylogenetic inference. Comparisons of inference methods are provided in the next three sections. In any case bootstrapping (Felsenstein 1985, Felsenstein 1988) should be used to obtain branch support values. Göker (2021) discusses bootstrapping when applied to data matrices covering several to many genes; see also Siddall (2010) and Simon et al. (2017). The bootstrapping used for obtaining branch support values is nonparametric; do not confuse this with parametric bootstrapping (Huelsenbeck et al. 1996).
Parametric methods such as ML are based on an statistical model about how the data from which a tree is to be inferred were evolving (Hasegawa et al. 1985, Kimura 1980, Tamura and Nei 1993, Le and Gascuel 2008, Whelan et al. 2001). Do not use a too simplistic evolutionary model for phylogenetic inference and explicitly state the model you were using. The Jukes-Cantor model (Jukes and Cantor 1969) is usually too simplistic, and rate heterogeneity should almost always be accounted for using a gamma distribution (Yang 1993, Yang 1996, Goldman and Whelan 2000). Model selection (Akaike 1974, Schwarz 1978) is possible in phylogenetics by comparing the likelihood of a preliminary tree under distinct models (Posada and Crandall 1998, Posada and Crandall 2001, Posada and Buckley 2004, Posada 2008). In many situations, one can well use most complex nucleotide substitution model, GTR (Lanave et al. 1984), in many situations. A too complex model is often less problematic than a too simplistic model, and high-performance inference algorithms may be optimized for the complex model. For example, this used to be the case with the RAxML software (Stamatakis 2006, Stamatakis 2014). Heuristic methods (Swofford and Olsen 1990, Swofford et al. 1996, Nixon 1999) are needed in most situations because the number of possible tree topologies is too high to be exhaustively examined (Felsenstein 1978a). If you estimate a gamma distribution, you need not also estimate a proportion of invariant sites (Hasegawa et al. 1985), as the gamma distribution already distinguishes between sites with distinct rates of evolution. See Felsenstein (2004) for an overview on evolutionary models.
Note that none of the phylogenetic inference methods, such as ML, MP, NJ, unweighted least squares (Cavalli-Sforza and Edwards 1967), weighted least squares (Fitch and Margoliash 1967), minimum evolution (Kidd and Sgaramella-Zonta 1971), BIONJ (Gascuel 1997), balanced minimum evolution (Desper and Gascuel 2002, Gascuel and Steel 2006), and Bayesian Inference (Huelsenbeck and Ronquist 2001, Huelsenbeck et al. 2001, Ronquist and Huelsenbeck 2003, Huelsenbeck et al. 2004), presuppose a molecular clock. This is their major advantage over clustering approaches such as UPGMA (Sokal and Michener 1958). The latter are not phylogenetic methods; see Göker (2021) for the difference in perspective. Phylogenetic methods always yield an unrooted tree although a rooted tree is needed for drawing taxonomic conclusions, a topic that will be covered in more detail below.

ML versus other inference methods

It is obvious that NJ is still a very popular method in microbial taxonomy. NJ is, however, not only much less popular in other areas of taxonomy (e.g., botany, mycology), but also regularly outperformed in empirical and simulation studies by character-based methods such as maximum likelihood (Huelsenbeck 1995a, 1995b). It has already been noted by Penny (1982) that there is an inherent loss of information when distance matrices are inferred from character matrices (which is a necessary step before starting the proper NJ algorithm). A similar comment on the less efficient use of information by distance methods such as NJ is made on p. 175 in Felsenstein (2004).
Sometimes distances methods need to be used. But even if only distance-based methods are considered, NJ is slightly outperformed by the Fitch-Margoliash method (Kuhner and Felsenstein 1994) and more clearly by newer alternatives such as balanced minimum evolution as implemented in FastME (Desper and Gascuel 2004, Lefort et al. 2015). Indeed, that NJ can be regarded as a crude approximation of ML (if the distances are inferred using appropriate models) is exemplified by the use of NJ to calculate starting trees in the maximum-likelihood software PhyML (Guindon and Gascuel 2003, Guindon et al. 2005). It thus seems that NJ should have a place only in situations in which distance methods must be used (because, e.g., character matrices are not generated) or as an emergency solutions in cases where authors lack access to software that implements more appropriate algorithms. But there are also instances in which approaches that are hybrids between ML and a distance method (Price et al. 2010) yield results that may be comparable to ML (Liu et al. 2011).
Bayesian inference (Huelsenbeck and Ronquist 2001, Huelsenbeck et al. 2001, Ronquist and Huelsenbeck 2003, Huelsenbeck et al. 2004), compared to ML and MP, was frequently shown in the literature to overestimate branch support (Cummings et al. 2003, Douady et al. 2003, Erixon et al. 2003, Lewis et al. 2005, Pickett and Randle 2005, Simmons et al. 2004, Suzuki et al. 2002, Taylor and Piel 2004) although not all studies agreed in this regard, see, e.g., Alfaro et al. (2003) and Huelsenbeck and Rannala (2004). Be that as it may, it is obvious that higher support does not mean better results: rather, the support values must be realistic, given the data.
The literature does not appear to indicate in general that MP is more severely affected by compositional biases than parametric methods such as ML, Bayesian inference or distance methods. For instance, in the study by Phillips et al. (2004), MP as well as ML inferred the correct tree whereas minimum evolution, a distance method, was affected by a G+C content bias. This was observed even when LogDet distances (Lake 1994, Lockhart et al. 1994) were used, an approach that was introduced to deal with compositional heterogeneity. Rosenberg and Kumar (2003) found that ML performed best under heterogeneity of nucleotide frequencies but MP was not outperformed by any of the distance methods. In the study by Jermiin et al. (2004), MP performed as well as ML with respect to compositional heterogeneity, and both were outperformed by LogDet distances. Felsenstein (2004) discusses LogDet distances on pp. 211-213. Relative performance of inference methods in situations with heterotachy was also controversially discussed in the literature (Kolaczkowski and Thornton 2004, Steel 2005).
Instead of distortion by compositional bias and heterotachy the artefact usually associated with MP is long-branch attraction (Felsenstein 1978b, 1988), yet this problem also negatively impacts compatibility analysis (Le Quesne 1974) and parametric methods with misspecified models (Bergsten 2005), and affects Bayesian inference more than ML (Kolaczkowski and Thornton 2009). Hence the difference between MP and parametric models is more a gradual one than an absolutely strict one. The mathematical links between MP and ML were explored by Tuffley and Steel (1997) and Steel (2002). For the traditional justification of MP see Farris (1983) and for a justification of MP in general and with respect to evolutionary models see Goloboff (2003), but note that this issue remains controversial in the literature (Siddall and Whiting 1999, Swofford et al. 2001). However, leading providers of ML phylogenetic inference software such as the RAxML authors (Stamatakis 2006, Stamatakis 2014, Pattengale et al. 2010) also implemented high-performance MP programs like the Parsimonator. The fastest MP software is most likely TNT (Goloboff et al. 2008, Goloboff and Catalano 2016).

Displaying and describing trees

Among file formats specifically developed for storing phylogeny-related information, Newick and NEXUS (Maddison et al. 1997) are probably the most well-known. The Newick format was developed for storing phylogenetic trees; see p. 590 in Felsenstein (2004), which includes a historical explanation of the name. NEXUS can, in principle, store any kind of phylogeny-related data, including trees. Software packages for drawing phylogenetic trees, such as FigTree, make use of these formats. A server-based application for visualising trees is iTOL (Letunic and Bork 2016).
A phylogenetic tree must be shown with branch support values, preferable those obtained by bootstrapping (Felsenstein 1985, Pattengale et al. 2010). Mere tree topologies are as inappropriate as claiming a significant difference between two treatments without conducting a statistical test. Phylogenetic inference will always yield a tree, no matter whether there is any support in the data for a certain branch, let alone for the entire tree. Without support values, any part of the topology might as well be occurring by chance alone. Show the support values from additional bootstrapping analyses, if any, on the first tree. Topological agreement between several trees alone is of limited interest, as it only demonstrates that the outcome is not due to a particular method, but does not demonstrate whether there is real support in the data for a certain branch.
A cladogram only shows the branching order (topology). Do not confuse the depiction of, e.g., an MP tree as a cladogram with a tree with real branch lengths (phylogram). Branch lengths obtained from a parametric method such as ML are scaled in terms of the expected number of substitutions per site; they do not represent raw sequence dissimilarity. Branch lengths from MP, if any, represent the minimum number of changes. However, distinct methods for calculating branch lengths under MP can yield the same overall parsimony score. (Search for the best tree under the MP criterion does not calculate branch lengths for reasons of efficiency. Obtaining branch lengths for the final tree requires an extra step.) Methods for calculating MP branch lengths (Wiley et al. 1991, Wiley and Lieberman 2011) include ACCTRAN, i.e. accelerated transformation (Farris 1970), and DELTRAN, i.e. delayed transformation (Swofford and Maddison 1987); both are available in PAUP* (Swofford 2002). If MP branch lengths are shown, the character-state reconstruction method in use for calculating these lengths must be explicitly stated. Better resolution means higher branch support. Branch lengths have no direct connection to resolution; for instance, longer branches do not mean that the tree is better resolved.
Explicitly explain how the tree was rooted. Phylogenetic inference methods result in an unrooted tree. If the software you were using yielded a rooted tree, an extra step must have been conducted (unless you have accidentally chosen clustering method such as UPGMA, which yields a rooted tree). This step would need to be made explicit, or the rooting modified. For instance, it seems that MEGA (Tamura et al. 2007), which implements several phylogenetic inference algorithms, automatically roots trees if they have branch lengths but the author observed several times that this rooting step is not made transparent. One can well use midpoint rooting instead of outgroup rooting in many cases (Hess and De Moraes Russo 2007). Indeed, strongly differing outgroups render a phylogenetic analysis susceptible to long-branch attraction because the branch between ingroup and outgroup is usually a relatively long one (Bergsten 2005). It may make sense to assess distinct ways to root a phylogenetic tree, including the application of software that detects the rooting that yields the least distortion of the data under a molecular clock (Simon et al. 2017).

Interpreting trees

Whereas trees might well topologically differ from each other, those topological differences might be due to branches that are unsupported anyway. In such cases there is no evidence of a conflict in the data. Conversely, lack of well-supported conflicting branches is not an indication of no conflict between two trees; the adequate assessment for this issue is a one-sided paired-site test under the chosen optimality criterion (Felsenstein 2004). To properly check for a conflict between some data and an existing taxon, run an unconstrained phylogenetic analysis of these data and an analysis constrained for the monophyly of that taxon. Then conduct a paired-site test. If this test shows the constrained tree to be significantly worse than the unconstrained tree, then the data reject the taxon at the given level of alpha. In the case of non-monophyletic taxa, correctly distinguish between polyphyletic and paraphyletic ones (Farris 1975). The most important criterion when establishing a new taxon is that there is sufficient support for it being monophyletic (Vences et al. 2013). This means the taxon must correspond to a clade and that clade must show a sufficient degree of branch support in a rooted tree. The purpose of branch support values such as bootstrap values is not to distinguish between identical and non-identical sequences. Two sequences may well belong to the same well-supported subtree but nevertheless be significantly different.
When discussing phylogenetic trees, keep in mind that the purpose of ML, MP, NJ and Bayesian inference, and of any other proper phylogenetic method, is not to place more similar (less distant) organisms more closely together (Felsenstein 2004). This might well happen, but it is not what the algorithms aim at, and it happens in some region of the tree only if this region of the tree is not too strongly deviating from a molecular clock. In fact, more similar organisms are not necessarily more closely related. The most closely related organisms in a tree are not necessarily those with the highest pairwise similarity. Relatedness can only be inferred from a rooted topology, and any uncertainty due to low branch support must also be taken into account. Interpreting tree topologies can and should be trained. Wiley et al. (1991) and particularly Baum et al. (2005) provide a quiz that can be used to exercise the interpretation of phylogenetic trees. See Gregory (2008) for explanations of the most common misinterpretations of trees found in the literature. Krell and Cranston (2004) as well as Crisp and Cook (2005) treat a specific case: among two sister groups, one of them cannot be more basal than the other one.
When dissecting a tree into a partition of selected clades for the purpose of discussing it, make sure these clades are not arbitrarily assigned. Quite a few published studies claim to have "recognized" a certain set of clades in a phylogenetic tree although the shown tree could as well be dissected into a different set of clades. Arbitrary decisions by authors do not become less arbitrary if these authors fail to make them explicit. One useful method to assign clades is to choose the best supported ones and, in case of ties between a clade and its subclade, to choose the larger clade, yielding the overall lowest number of clades (Simon et al. 2017). For instance, if a clade had 96% support and its two immediate subclades had 95% and 100% support, respectively, the subclades would be preferred because their average support is higher. If they had 95% and 97% support, respectively, their parent clade would be preferred. But other methods to assign clades are certainly possible.
Even though quite popular in microbiology, it does not normally make sense in phylogenetic terms to "define" taxonomic ranks using thresholds for pairwise distance or similarities. The first reason is the one given above: More similar (less distant) organisms are not necessarily more closely related. Second, a threshold alone does not yield a clustering if more than two organisms are involved. Pairwise thresholds should only be applied in situations for which it has been proven that the deviations from a molecular clock are negligible. For instance, Meier-Kolthoff et al. (2014) confirmed this for the GGDC. Moreover, some methods used in the literature to estimate thresholds are dubious. For instance, using the minimum within-taxon similarity of all taxa of a certain rank in an empirical data set is not an approach that minimizes the discrepancies to the existing classification. See Göker et al. (2009) for an alternative and Göker (2021) for an in-depth discussion of this topic.

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