One model (monism) or many (pluralism) to study evolution?
Philosophers have often debated whether one model or many ought to be used in science, identifying schematically two positions among scientists: the monists and the pluralists. Those who are inclined to use a single model to account for all of their data, however complex these might be, are traditionally called monists. The remainder are pluralists. In its simplest description, monism designates a commitment to one model to which all other evidence and interpretations must be subordinated [38, 39]. For instance, in physics, monism is justified by the appeal for a single system of fundamental laws that could explain all physical phenomena. Searching for a unified explanation is seen as the essence of good scientific practice, since in that context hypotheses are rigorously applied, evidence interpreted consistently, and all findings coherently unified by fundamental principles into one overarching theoretical framework. In evolutionary biology, this approach would be relevant, for instance, if evolution were a thoroughly homogeneous, structurally simple process. Then it might be that we should look at the understanding of evolution as, in effect, a single question, calling for a single mode of analysis. And this is, essentially, the assumption implicit in much neo-Darwinist thinking. Furthermore, monism comes in general with an ontological commitment to a particular class of entities as the organizing theoretical focus. Typically, in the case of traditional phylogenetics, these chief objects of study would be the species. Whether species history is being traced by genes, genome composition or something else, the traditional role of phylogeny is to recover their relationships. Consistent with that approach, traditional phylogeneticists consider that species evolution follows a tree, and processes such as LGT are theorized as supplementary and thus unthreatening. From that standpoint, even if all individual prokaryotic gene trees disagree, there is still some universal species tree. In that sense, it seems that scientists exclusively committed to the reconstruction of one single universal tree (the tree of species or tree of life) embrace or are inspired by a monistic perspective on the process of evolution, in which lateral processes are not admitted at all or play only a secondary role. In the rest of this manuscript, we will call this position tree-monism.
However, there are objections to a monistic approach, and not only in biology. Pluralism opposes monism. Pluralism in philosophy of science (and political philosophy) means the conviction that different models may be legitimate to analyze a phenomenon, and that conflict between them need not be seen as invalidating one or more alternative approaches [38, 39]. Many pluralists would justify their pluralism with the claim that the world itself is not carved up in a way that is conducive to the application of one approach only, and that a richer understanding of the phenomena can be gained with the application of more than one approach. Pluralism should be unsurprising for biologists since they are dealing with thoroughly complex objects. Thus their scientific models, to provide any possibility of insight and understanding, must focus only on specific and limited aspects of this complex reality. One should then anticipate that different questions should best be addressed using different concepts or models. This has important bearing on our practice of evolutionary biology. Once it is accepted that different classes of biological entities are evolving to some extent in different ways (as do prokaryotes and eukaryotes, for instance), then it is a wholly empirical question to what extent the same processes will be equally significant in explaining evolutionary histories. It is also an entirely empirical question whether the perspective best fitted to gaining insight into one class of objects or processes (e.g. the eukaryotes) will be the same as that most appropriate to another (e.g. the prokaryotes) and, indeed, whether any single perspective will adequately illuminate a particular class of objects or processes. With regard to the tree of life, the pluralistic position has thus been regularly advanced by microbial phylogeneticists who have emphasized the diversity of evolutionary processes and entities at play in the microbial world [40, 41]. This group prefers to model evolution as a diverse set of processes acting on the histories of diverse kinds of entities generating, finally, a diversity of overlapping and cross-cutting patterns, corresponding to different evolutionary outcomes. For such pluralists, depending on the approach taken (e.g., the choice of sequence, the choice of the reconstruction method, the taxa of interest), a different evolutionary pattern may be generated (e.g. a reticulated network rather than a vertical tree). Embracing this latter view, we will now argue that using a single tree-like model to describe all life evolution is no longer the most scientifically productive to hold. In other words, we should approach the study of prokaryote genome evolution openly, and no longer subordinate our approaches to the study of microbial evolution to the preconceived notion of a tree.
Limits of traditional tree-monism
In addition to its limits in accounting for the different evolutionary processes emphazised by the prokaryote/eukaryote divide, there are many methodological and epistemological reasons why tree-monism may not be any longer the most scientifically fruitful position from which to study microbial evolution. We will examine some of these issues in order to show how tree-monism falls short in many ways.
Problem 1: The circularity and arbitrariness of tree methods
The most traditional tree of life hypothesis, ignoring LGT, predicts that trees of single-copy genes (orthologs) from a common taxonomical sampling should be congruent with one another and with the species tree. Thus, the goal of the phylogenetic analysis has long been to reconstruct this common topology. No gene tree alone can fully resolve the entire species tree of all life forms , so genes are often combined into a single analysis under the tree-monistic assumption that they all share the same vertical history. In doing so, the aim is to reduce effects of small sample size (stochastic errors) in phylogenetic calculations, thereby reinforcing the true phylogenetic signal [42, 43]. Unfortunately for this assumption, LGT means that there is no a priori guarantee that a common tree is really present in the molecular data. Worse, it is currently not possible to provide positive evidence that the roughly three dozen genes that have been claimed to save the concept of a universally shared core from extinction [44, 45] actually do share a common history . Hence, there is a high risk that the traditional approach produces circular phylogenetic analyses, in which assumptions of a common tree are supported by assumptions about how the data should be represented. As noted by Avise, "any comparative dataset can be used to reconstruct a phylogenetic tree when a tree provides the suppositional metaphor for the data analysis. Even inanimate entities (such as different kinds of chairs or cars) can be grouped into tree-like depictions based on their similarities or differences" . A typical example of such an arbitrary tree is Cicarelli et al.'s tree of life , which is based on 34 concatenated orthologs. When tree assumptions are removed, their data reveals a great deal of LGT and many genes whose history is simply unknown .
Problem 2: Underestimation of phylogenetic incongruence; exaggeration of congruence
To avoid the arbitrary issues associated with combining genes into a single tree, statistical tests attempt to examine whether different gene-tree topologies could be due to chance . In those tests (e.g., character congruence tests such as the incongruence length difference test  and variants, or likelihood based tests), the null hypothesis (H0) is "that the same tree underlies all of the dataset partitions" . The alternative hypothesis, H1, proposes that some of the genes being compared have undergone a different history. It is then statistically incorrect to say that when "genes do not significantly reject the consensus tree" (H0), that "agreement seems to be the rule" . First, in purely statistical terms, this failure to reject does not mean that they support the consensus tree, and that they have evolved according to this very topology . Second, individual genes with a weak phylogenetic signal will always fail to reject the consensus tree.
Fortunately, the critical power (and relevance) of such simple congruence tests can be illustrated by studying an increasing number of independent test topologies, "supported" or "rejected" by individual genes. To do this, the Shimodaira-Hasegawa or Approximately Unbiased tests [52, 53], which hold the null hypothesis that all the trees tested are equally good explanations of the data (and the H1 hypothesis that some trees are better explanation of the data), can be used . In particular, testing independent topologies leads to the identification of genes that simultaneously fail to reject many different trees. If the failure to reject one tree meant straightforwardly that this tree should be accepted as representing the true phylogenetic history, then one would have to assume that a gene simultaneously failing to reject multiple incompatible topologies evolved to produce many incompatible phylogenetic histories. A more realistic explanation is that such a gene contains too weak a phylogenetic signal, given the assumed substitution model, to decide what its history was.
Shi and Falkwoski's work illustrates one approach of how to critically study genes with a weak phylogenetic signal, without claiming that data are congruent with one tree when there is no genuine support for it : First, they built phylogenetic trees for 682 orthologous protein families from 13 cyanobacterial genomes and did not observe any predominant, unanimous topology that represents a large number of orthologs. The maximum number of orthologs that share a particular topology accounts for only 1.9-2.1% of the orthologous datasets . Then, they reconstructed five test topologies: the consensus tree, the ML and NJ supertrees, and the ML and NJ concatenated trees for these alignments. They observed that almost all (97.5 to 99.6%) of the molecular datasets supported the five topologies at the 95% confidence level, suggesting a lack of resolution of single gene phylogenies. Had they only tested the agreement of the individual gene phylogenies against one of these five candidate trees of cyanobacteria, they could have mistakenly concluded that they had found The Tree of Cyanobacteria.
Problem 3: Large-scale exclusion of conflicting data
Methods that search for a single universal tree often involve steps of data exclusion in which lateral gene transfer is conceived as noise. The use of such eliminative criteria allows these phylogeneticists to ignore LGT, but also leaves them without any trustworthy genes with which to study prokaryote evolution. Soria-Carrasco and Castresana's "Estimation of phylogenetic inconsistencies in the three domains of life"  is a good example of this logic. These authors compared the level of incongruence in proteobacterial genes and eukaryotic genes to test whether the proportion of vertical/lateral signal significantly varied between these taxa. They argued that if these levels were comparable between eukaryotes and proteobacteria, LGT could not be considered a major evolutionary process in these bacteria. Through recurring steps of data exclusion, they removed as much conflicting data as possible to guarantee that no phylogenetic difference could be found between the eukaryotic and proteobacterial data.
First, they retained only ubiquitous "core" genes, thus throwing out of the analysis the majority of the prokaryotic data in order to avoid taxonomical patchiness. The disagreement between these individual "core" gene trees and the "species tree" (i.e. the concatenated gene tree) was, however, higher for prokaryotes than for eukaryotes. Consequently, in a second step, the authors excluded all genes for which there was more than one copy per species. The aim was to exclude duplicated genes both from the eukaryotic and prokaryotic datasets, due to a suspicion that the large amount of incongruence observed in bacteria could be due to excessive duplications and losses. Yet, such a procedure obviously excluded the paralogs as well as any multiple copies resulting from lateral gene transfers in prokaryote genomes. Only 127 genes could be retained for proteobacteria, as opposed to 346 for eukaryotes.
Nevertheless, prokaryotic gene trees continued to show more disagreement with the concatenated gene tree than eukaryotic genes did, and this prompted a third exclusion step. Biases in gene length were corrected, since proteobacterial sequences were smaller on average than eukaryotic sequences (214 aa versus 251 aa). All genes were trimmed to an identical length of 182 unambigously aligned positions. Based on this reduced dataset, the AU test indicated that 46.5% of the individual proteobacterial genes were incompatible with the "species tree" as opposed to only 23.4% of the eukaryotic alignments. The authors then dismissed these results by arguing that the gene lengths were now too short to conclude anything about the impact of LGT. So, in a final step of "good" gene selection, they removed all markers shorter than 300 aa and retained only 88 eukaryotic genes and 20 proteobacterial ones for their comparative analysis. But even in this heavily curated dataset, the AU test demonstrated a higher level of incongruence within the proteobacterial dataset (25% incongruence) than within the eukaryotic dataset (14.8% incongruence).
Even though the "purified" data now amounted to a mere 0.8% of the size of a bacterial genome, and are obviously unrepresentative of the evolution of the rest of the proteobacterial genome, the authors surprisingly concluded that overall no more LGT could be observed in proteobacteria than in Eukaryotes. According to them, such a study "opens the way to obtain the tree of life of bacterial and archaeal species using genomic data and the concatenation of adequate genes, in the same way as it is usually done in eukaryotes."  From a pluralistic point of view, however, it is striking that a great majority of the bacterial data have to be excluded to achieve the reconstruction of a so-called "universal" tree. In other words, almost none of the data that Soria-Carrasco and Castresana examined fit the metaphor of a tree, but they nonetheless filtered their observations to sieve out only those that were compatible with their preconceived notion that the evolutionary process is tree-like in both groups. The result is that this forced them to disregard most of the data they initially wished to explain evolutionarily.
Problem 4: Deprioritizing conflicting data
For those who take a monistic approach, sidelining or deprioritizing data that conflicts with the model of a single tree may appear to be a less extreme alternative than large-scale data exclusion. One such example is Daubin and Galtier's recent proposal to build a tree of life by dismissing the plethora of incongruences in molecular data. For them, "the existence of incongruences is not sufficient to dismiss the notion of a species tree, nor to preclude its reconstruction. [...] In our view, the species tree could still be a useful concept even if incongruent with every gene tree" . They argued that from a statistical point of view, rejecting the species tree because of the existence of conflicts between gene trees means refusing to calculate the mean of a distribution because its variance is non-zero, which appears too extreme a policy . They claim that the species tree can be recovered even when the variance in phylogenetic signal is extensive, as long as transfers occur randomly. Furthermore, they assert that one could interpret the mean and variance in phylogenomics differently: the mean signal corresponding to speciations/extinctions, and the variance to LGT and other non-vertical processes .
Daubin and Galtier are suggesting that calculations of the mean phylogenetic signal of incongruent genes are the best way to build a tree of life because it integrates (in reality, averages) a large amount of incongruent data. Under their assumptions, "a supertree method (which essentially returns the "average" estimated gene tree) recovers the true species tree with strong accuracy from phylogenomic data simulated under a model incorporating LGT, even when the amount of LGT is such that two random gene trees share only 50% of their internal branches, on average" . Although it is curious that anyone would summarize such a reticulated pattern with a tree, a deeper problem with such claims is that lateral gene transfer does not in fact occur randomly. It is strongly influenced by the selective processes operating in organismal environments.
For example, the bacteria Salinibacter ruber displays many genes linked to adaptation for life in hypersaline environments. These genes have their closest homologs in the genomes of co-habitating halophilic archaea . A similar example can be found in the archaeal genera Sulfolobus and Thermoplasma. Despite belonging to different phyla, 17% of their genes are each other's closest homologs . This mutuality can be explained by extensive lateral gene transfer between these organisms, as they evolve to thrive in the same types of environments (high temperature and low pH). Furthermore, vertical and lateral evolutionary signals are entangled with one another in molecules, such that it becomes difficult to distinguish them through simple tree-centred approaches. If we really want to understand evolutionary process and pattern, it seems clear that simply deprioritizing lateral signal will be a mistake.
Problem 5: Ambiguities in tree of life patterns
Several observations question the validity of equating the consensus or average phylogenetic pattern with a bifurcating evolutionary organismal history, or with the tree-like evolutionary history of the species [58–61]. At least some of the consensus signal found in core genomes  might reflect not a shared history but instead, artefactual phylogenetic reconstruction. Many phylogenomic studies have produced a "reference tree" that is an aggregate constructed from many individual genes. Using 16S rDNA trees as an explicit or implicit comparative criterion, these aggregate trees have been claimed  or used in practice [62–64] as a vertical scaffold onto which LGT events can be mapped. Whether constructed using a supermatrix, supertree or other approaches, it is often possible (and always desirable) to attach estimates of statistical significance to features of such aggregate trees. Supermatrix-derived phylogenies can be subjected to bootstrap or jackknife analyses in the same manner as single-gene phylogenies, while other approaches such as supertrees can be resampled using techniques that are appropriate to the underlying data, e.g., bipartitions in a supertree constructed using the Matrix Representation with Parsimony [65, 66] method, and other support indices .
Such measures of statistical support can be extremely misleading, however. It is widely known, for instance, that support values such as the bootstrap proportion or posterior probability can strongly support an incorrect split in a tree due to model violations or multiple phylogenetic histories within a data set . It is therefore necessary to test whether strong support for a given split in an aggregate tree is found consistently in all or a majority of the contributing entities (i.e., single-gene alignments or individual phylogenetic trees). In one such supertree , a sister relationship between Aquifex aeolicus and Thermotoga maritima was reconstructed as the earliest-diverging group within the bacterial supertree. A total of 120 trees in the input data set yielded a 'strong conclusion' about this relationship, either resolving A. aeolicus and T. maritima as sisters with strong Bayesian posterior support (PP ≥ 0.95), or displaying an alternative relationship in which the two were placed with other partners, again with strong support. Only 20 out of the 120 trees supported the pairing of these two taxa. Furthermore, analysis of alternative relationships showed many distinct partners for A. aeolicus, including several branches within the Proteobacteria, as well as both the Euryarchaeotes and the Crenarchaeotes, and the genus Clostridium (which includes the thermophile Thermoanaerobacter tencongensis). Similarly, T. maritima showed strong affinities for several Gram-positive lineages (especially T. tengcongensis), Pyrococcus and Chlorobium tepidum. While more than 30 trees supported a relationship between Aquifex and basal Proteobacteria, the A. aeolicus/T. maritima pairing was nonetheless favoured by the MRP algorithm. It is thus highly debatable as to whether this latter relation should be considered as the true vertical signal.
Another example can be found in analyses of Thermoplasma, which is a genus of hyperthermophilic euryarchaeotes that often branches near the base of the Archaea in aggregate trees [69, 70]. However, concatenated informational protein phylogeny places Thermoplasma within the euryarchaeal methanogens. Analysis of the quartet relationships between Thermoplasma acidophilum, the euryarchaeotes Methanopyrus kandleri and Pyrococcus horikoshii, and the thermoacidophilic crenarchaeote Sulfolobus tokodaii from the Beiko et al. (2005)  dataset yielded 22 quartets that placed T. acidophilum with S. tokodaii, consistent with the reference supertree. 22 other quartets supported a sister relationship between T. acidophilum and M. kandleri (consistent with the informational protein phylogenies of another study ), and another 21 supported T. acidophilum with P. horikoshii. Quartet analyses with T. acidophilum and other triplets of genomes yielded relatively weak support for the basal positioning of Thermoplasma in the Archaeal part of the supertree. Instead, two alternative placements within the Euryarchaeota and Crenarchaeota were supported. Furthermore, it is noteworthy that most supertree methods can produce novel clades not supported by any of the source trees .
Even though simulated random LGT regimes tended to diminish statistical support for more-ancient relationships rather than offering strongly supported alternatives in average trees, phylogenetic approaches have been shown, in theory and in practice, to favour one topology even if the input data are generated equally on two or more trees [73, 74]. Compositional or rate effects may be sufficient to give strong statistical support to a grouping of branches that should in fact be unresolved . Indeed, systematic biases in residue composition have been shown to influence large, concatenated phylogenies such as those of eight species of yeast . Likewise, most phylogenetic reconstructions methods to-date assume a time-reversible model, while compositional bias in fact changes during evolution. The assumptions of this model are thus frequently violated, especially if different genera, families, or even phyla are included in the same reconstruction. Likewise, when data are simulated under biased regimes of LGT and a genome phylogeny approach, the recovered tree displays neither the complete vertical history, nor that of any significant pathway of LGT .
Furthermore, gene transfer can create patterns indistinguishable from those created by vertical inheritance, as was first recognized when the extent of gene transfer among bacteria became visible in comparative genome analyses [78–80]. It is reasonable to assume that the rate of successful transfers relates to overall similarity (use of the same transfer machinery, phages that infect both organism, similar machineries for transcription and translation, and similar signals functioning in replication and genome organization ). Gene transfer biased towards similar partners reinforces the similarity that leads to more gene transfer. The transfers thus create a signal that groups organisms together, such that we consider them to be closely related. In some instances these gene transfers might reinforce a signal due to shared ancestry, but in other instances all of the signal that we detect today might have been created by gene transfer itself. The claim that the consensus tree recovered in some molecular phylogenies is based on shared ancestry hitherto remains an unproven assumption. What remains are two processes, vertical inheritance and gene transfer, both of which contribute to recovered trees in ways that can be difficult to distinguish using only one model.
Consequently, any statistically well-supported tree recovered from a phylogenomic analysis should not be construed uncritically as a 'tree of life' unless hybrid signals and model violation effects are considered and rejected as potential confounding factors.
Beyond these methodological issues, adherence to the traditional tree of life raises substantial epistemological issues, about the very nature of the knowledge generated.
Problem 6: What are trees of life really trees of?
As discussed above, the simplest tree-of-life rescue strategy currently used is to group some genes, including those which might have different histories, and calculate the "average" tree-like history of these genes . The analyst lumps together a great deal of data that did not evolve by a common tree-like process, analyzes it with methods that deliver only trees as their result (as opposed to more-general models such as networks), obtains a tree, and then asserts that this exercise provides evidence in favour of the existence of a tree. A second tree-rescue strategy is to select some smaller set of "core" genes and come up with a tree based on their divergence. A final tree-rescue strategy is to view a "variable core" as defining the tree of life. Known as supertrees, these trees do not represent the histories of even a small set of genes, but instead reflect the inheritance of different genes at different nodes . What these strategies have in common is a commitment to uncovering tree-like inheritance patterns in the complexity of microbial inheritance. The question is whether they really do result in a hierarchy that corresponds to the tree of species, or whether they are in fact teaching us something else altogether about prokaryote evolution.
Consider first the averaging strategy. A species is composed of organisms, and those organisms are composed of parts whose histories differ. Some genes might have been transmitted "vertically" through much of their histories, while others might have been transferred from closely or distantly related taxa at various past times. If we average these histories, what does the resulting tree represent? The simple problem is that the historical branch-points on such a tree do not necessarily represent past species. We don't have a species history here at all. Even Galtier and Daubin admit that not even a single gene might have followed the path represented by the average tree. No real species would necessarily correspond to these averages. Averaging the tree signal would be akin to asking about the 'geographic average' destination of an American business traveller, which would probably be (i) somewhere in Iowa, and (ii) would not convey much meaningful information. Such a central tendency tree should thus be critically interpreted by biologists, and not conflated with the universal species tree.
In the second tree-rescue strategy, the search for a core, a scientist attempts to separate the wheat (vertically transferred genes) from the chaff (genes that underwent LGT). Such methods do, of course, yield tree-representations. Proponents thus claim that if there is such a set of core genes, "a tree of bacterial species remains possible" . Yet, the main difficulty with the claim that the history of the core genes represents the species history is that all we can safely conclude from the history of the core genes is simply knowledge of the history of the core genes. A species--and the organisms that comprise it--have histories that are not exhaustively explained by the histories of a few of their parts. To maintain that the history of the core genes "represents" the species history requires some argument that the history of these parts is somehow "essential" to a species' genealogy. But post-Darwinian biologists are generally loath to attribute any special essentialist status to either genes or species. If they fail to essentialize (which should be expected), then any such core-gene tree, which might well be an interesting and at times scientifically fruitful representation, cannot be considered to represent the species history.
Finally, in the supertree strategy, the transmission of individual genes is not used to create a tree-scaffold, but instead different genes in different parts of the tree of life are combined. More precisely, different markers, presenting very little overlap in their taxonomical samplings, are used to reconstruct different parts of the tree. It is assumed they all fit on a common tree, despite the fact that there is little or none support in such a patchwork of data for many inner nodes. This strategy can appear to increase the size of the core, since the genes that persist across a speciation event, or even a series of such events, will not be whittled away merely because those same genes are transferred in some other part of the tree. But does this strategy represent a species tree? Again, the problem is one of representation. There is certainly some pattern in nature which answers to this description. Perhaps a supertree representation accurately reflects the history of cell division. However, to call this a species tree is to claim that all important species characteristics are inherited along these lines - a claim that is exceedingly hard to justify.
Because none of the options described above accurately reflects species trees, we should instead strive to describe prokaryote evolution as it is in nature. That may require a departure from analytical methods that only operate in the language and mathematics of trees. Networks, for example, offer an alternative mathematical framework, albeit one that is not necessarily compatible with a tree-monistic concept of inheritance or speciation.
Problem 7: Tree monism no longer provides the ideal comparative evolutionary framework
In the time before genome sequences, when there was bona fide reason to "hope" that prokaryote genomes would uncover vast evidence for common ancestry, the goal of obtaining a universal tree of life promised to serve three highly desirable purposes. First, it would provide a natural classification of living organisms, by identifying all the extant descendants of a given ancestor forming a natural group. Knowing the tree of life would thus conveniently define a hierarchical classification of Life, the "groups within groups" proposed by Darwin. Second, this tree could provide insights into the shared properties of organisms belonging to the same group, and allow generalizations about the natural groups. Third, this tree could be seen as a time machine. Knowing its topology, and the properties of the extant organisms, to a certain extent one could infer the properties of the ancestors (i.e. achieving retrodiction) by assigning properties that are common among all descendants to ancestral nodes. For all these reasons, the universal tree seemed the best possible comparative framework for evolutionary biology, and ribosomal RNA was occasionally referred to as "the ultimate chronometer" .
Today however, if embracing a monist perspective to describe microbial evolution, the question is not to ask whether the tree model still represents the best framework to infer and depict evolutionary relationships, but rather to ask which of the competing approaches already available is best suited to produce the most satisfactory tree. A wide array of methods have been developed not only to address LGT, but also to deal with gene conversion, recombination or hybridization (for reviews, see [84–88]). All of these so-called reticulation events are the product of various biological processes that violate the universal tree model. Consequently, they directly challenge its utility for classification, generalization, and for retrodiction, since any attempt to treat evolution as a tree-like process is insufficient even if partially useful .
Consider the analogy of the origins of organelles via endosymbiosis in eukaryote evolution. It vividly demonstrates that the notion of a generalized tree of life is not the most productive position to hold. It highlights an important manifestation of the discrepancy that arises between hierarchical classification using the structure of a tree on the one hand and evolutionary process on the other hand, when the evolutionary process is not tree-like to begin with. Plastids arose from cyanobacteria, and mitochondria (including their anaerobic and non-ATP-producing forms, hydrogenosomes and mitosomes) from proteobacteria. Both organelle types (usually) still possess their own genome, and both symbioses entailed gene transfers from those endosymbionts to the nucleus during the evolutionary transition in which those endosymbionts became organelles [36, 89]. Moreover, some current views have it that the origin of mitochondria was contemporaneous with the origin of eukaryotes themselves [90–92], that the host for the origin of mitochondria stems from within the archaebacteria , and that the origin of photosynthetic eukaryotes was contemporaneous with the origin of plastids [35, 94]. Although there are still some controversies around this scenario, the main point is that the endosymbiotic origin of plastids and mitochondria does not conform to the tree paradigm. Both eukaryotes in general and plants in particular represent genetic mergers in evolution, cellular marriages consummated by the genetic integration afforded by endosymbiotic gene transfer and protein import by organelles.
Thus, any tree of life that makes the effort to link prokaryotes and eukaryotes in a manner that reflects the underlying evolutionary process would need to include archaebacterial-eubacterial lineage mergers at the origin of mitochondria/eukaryotes and eukaryote-cyanobacterial mergers at the origin of plants. Similar mergers occur in the origin of algae that possess secondary plastids . But if we force the metaphor of a bifurcating (or multifurcating) tree onto the evolutionary process linking prokaryotes and eukaryotes, then we have to decide whether to put the eukaryotes on the host lineage or on the mitochondrial lineage, and we have to decide whether to put the plants on the cyanobacterial lineage or on the eukaryote lineage, when in fact the endosymbiotic origin of these organelles ends up putting the resulting organisms on both branches at once.
The discrepancy is even greater between a hierarchical classification of prokaryotes and lateral evolutionary processes. When Cicarelli et al. attempted to identify (by hand, ultimately, even though the paper advertised an automated method in the title) all the genes that had not been lost or transferred among genomes representative of all life, they ended up with 31 genes, corresponding to about 1% of the genes in a typical prokaryote genome. The authors assumed that those genes tended to produce congruent trees, rather than demonstrating that they actually do. In other words, at face value they found that about 1% of any genome at best might tend to fit the working hypothesis of a tree. Any reasonable account of scientific method would suggest that when a working hypothesis can only account for about 1% of the data, a true scientist would start looking for a better working hypothesis. The current retention by many evolutionary biologists of a strict tree metaphor for prokaryotes, despite its inability to account for the observations, presents a serious barrier to our understanding of prokaryotic evolution and is hard to square with most accounts of how science should be done.
On the other hand, despite their differences, all the evolutionary processes listed above can be modelled and represented simultaneously by phylogenetic networks better than by trees, if a unique representation is desired. It thus seems both prudent and pragmatic to explore alternative mathematical representations of microbial evolution. Adoption of network strategies does not constitute rejection of significant bifurcating patterns in the history of life. Instead, it requires the denial that tree-patterns are the only possible patterns. Leaving aside the specific methods to detect LGT [69, 96], recombination , gene conversion , hybridization  and other reticulation events , different algorithms have now been proposed to build phylogenetic networks or to represent the non-tree component, such as weak hierarchies, split decomposition, netting, statistical parsimony, minimum spanning networks, reticulograms, median networks, median-joining networks, union of parsimony trees, and neighbor-net [101–109]. Consensus methods for assembling incompatible trees into networks and supernetworks are also available .
In light of all these approaches, algorithms and software already published (and still being developed), the search for optimal trees could be advantageously replaced by the search for optimal networks. Because trees are special types of networks, the tree model is most properly understood as embedded in the network-model of evolution . The paradigmatic shift from a monistic to a pluralistic understanding of the evolutionary processes is thus echoed by a graph-theoretical shift, from trees (i.e, connected acyclic graphs) to networks (i.e., connected graphs which may contain reticulations). Indeed a good network approach will always return a tree if the underlying data have a tree-like structure (for distance data, the four-point condition has to be satisfied). However, if significant conflicting signals are present in a data set, then suitable network methods should be able to depict reticulation events that a strictly tree-based approach cannot. Although network methods have limitations , they should nonetheless permit progress towards more accurate representations of the process of microbial evolution as it occurs in nature, as opposed to depicting how some of us think it might occur by extrapolation from observations and experience in the study of vertebrates.
With so many methods available, the real problem is to assess the relative performance of the competing approaches with simulated data [77, 86, 113–115] as well as in real-case applications . The problem of identifying the minimum number of reticulations in a graph is NP-hard , such that most recent developments in this field have been to develop good algorithms to approximate the optimal solution [118, 119]. If it is accepted that networks are the best model to study LGT and microbial evolution, the next problems arise of how to assess the likelihood  and robustness of such networks , and to compare networks or determine when a network is significantly more informative than a tree . Although methodological and algorithmic limitations may have precluded the use of phylogenetic networks in the past, a few steps have been taken in this direction . It is time to show much more of the evolutionary process.
Process pluralism and its implications for taxonomy
Many of the above limitations associated with a tree-monistic approach in reconstructing the tree of life could easily be dealt with by assuming a more pluralistic approach to describe microbial evolution. We already know that microbial evolution and the tree of life are distinct in process and pattern, and we simply have to admit it more openly and take measures in our research to accommodate that state of affairs. Not only do we recognize the multi-level nature of selection in biology, and that an exclusive focus on any higher level of organisation (e.g. cell or organism) will inevitably conceal divergent underlying processes at the genetic level, but we also have begun to acknowledge the diversity of evolutionary processes in action (between eukaryotes and prokaryotes, and within prokaryotes). For prokaryotes, there is an increasing agreement that whenever LGT is frequent enough, trees of genes, genomes, cells, organisms, and perhaps of higher level entities as well, will inevitably diverge. Consequently, as further evidence accumulates, evolutionary biologists will, of necessity, increasingly divorce themselves from traditional tree-monism, even though the monistic principle of descent with modification persists. In practice, we are already studying a diversity of evolutionary processes and considering these as natural, regardless of whether or not our classificatory system consists of only one kind of evolutionary unit (clades). Typically, phylogeneticists are now dealing with a plurality of units in microbial evolution. We need to realize that many of our present "phylogenies of life" correspond to diverse mappings that sometimes represent the history of genes, groups of genes, or perhaps even other categories of entity (for example, processes such as change in genomic G+C content). These different histories do not have to map exclusively or entirely on to one another, but can be acknowledged as evidence of the complexity and richness of microbial evolutionary processes. In that sense, many current tree-rescue efforts are fully consistent with a pluralistic diagnosis. What is not consistent though is the claim that such a tree pattern, when it is found, is a species tree , and that it corresponds to the whole of microbial evolution.
All the above has important implications for the "species" notion as well. Rather than working under a single unified concept, microbiologists already accept many different pragmatic definitions of prokaryotic species. They have no species concept that would be relevant for all of life (eukaryotes, let alone prokaryotes) that would justify the reconstruction of a universal species tree. Doolittle and Zhaxybayeva (2009) showed that due to various genetic, population ecological, and evolutionary processes, not all prokaryotes belong to genomically and phenotypically cohesive clusters that biologists could be defined as "species" . In some instances, life-defining processes work together and generate groups of related organisms, sufficiently like one another to be called species. However, the evolution of such coherent clusters is not the general outcome in the prokaryotic world. Rather, various prokaryotic species taxa are defined in nature (and throughout the literature) based on many different criteria, such as global genetic distance (Average Nucleotide Identity, DNA-DNA hybridization experiments) and the presence of some cohesion mechanism (e.g., recombination rates assessed by Multi Locus Sequence approaches, the exploitation of some ecological niche characterized by ecotypes, some phylogenetic inertia). Based on such criteria it is the case that there are multiple correct ways to classify the organic world, and a single organism may be classified in more than one manner depending on the aims of classification.
For instance, two species concepts proposed for prokaryotes are a recombination concept fashioned after the Biological Species Concept [126, 127] and the ecotype concept suggested by Cohan . A recent study of the genus Thermotoga shows that the same group of organisms forms a single species according to the recombination approach but consists of multiple species according to the ecological approach . Thus each organism in this group belongs to two different types of species (a recombination species and an ecotype species) and those species are not coextensive (having the same spatial and temporal location). In this example, nature imposes a plurality of species concept upon us. The occurrence of lateral gene transfer is also a source of taxonomic pluralism. The recombination concept provides an example. For some microbes, different parts of a single prokaryote genome recombine with different genomes. That is, there is no whole genome recombination in these organisms. The consequence is that by the standards of the recombination concept, the same genome belongs to different species . Similar considerations apply to a phylogenetic approach to classifying microbes. Because of lateral gene transfer (and, as we have noted, due to endosymbiosis in eukaryotes), different parts of an organism's genome often have different evolutionary histories [40, 130]. Phylogenetically based classifications for the same group of genomes vary, depending on which clusters of genes in those genomes are chosen. For instance, ribosomal components group the Thermotogales within the bacterial domain as a "basal" branching lineage. If only an unrooted bacterial phylogeny is considered, as seems reasonable because possible outgroups are on very long branches, the Thermotogales appear as a sister group to the Aquificales. In whole-genome phylogenies, the Thermotogales are frequently found to group with Clostridia and Bacilli . Nelson et al.  detected many archaeal genes in the genome of Thermotoga maritima, a finding supported by the recent analysis of several genomes from members of the Thermotogales . This analysis of five Thermotogales genomes finds that the ribosomal components group Thermotogales with Aquificae. About 8% of the genes group with homologs from Archaea, but the vast majority of genes group with Clostridia homologs. Hence a prokaryote or a part of a prokaryote can belong to more than one classificatory unit and those units do not form a nested hierarchy of inclusive units.
An implication of this discussion is that prokaryotes probably belong to overlapping rather than inclusive hierarchies. In theory, this plurality of definitions of microbial taxa could open the way to multiple classification schemes (i.e., taxonomic pluralism) instead of a single universal hierarchy, often seen as the holy grail of traditional phylogenetics. What are evolutionary microbiologists to make of such pluralism? Should they reject it out of hand given the Linnaean ideal that an organism belongs to only one species and has only one placement in an inclusive hierarchy? Interestingly, the debate over whether to adopt pluralism has already been played out in the general debate of how to define 'species' given the plethora of eukaryote species concepts [134, 135]. It shows that adopting a pluralistic approach to microbial taxonomy is not as radical as one might think.
One concern critics of pluralism have is that pluralism lacks a means for distinguishing legitimate from illegitimate classifications [136, 137]. They worry that pluralism is too liberal an approach to science because it accepts any suggested classification. That is not the approach being advocated here. Taxonomists stipulate that to be allowed as legitimate, a classification must meet standard scientific criteria [134, 138]. And at least one philosopher of taxonomy stipulates that microbial species must be the result of a common type of causal process or be causally efficacious in a similar way [134, 138]. For example, if we classify microbes by ecotypes, we need to empirically test whether evolutionary processes cause groups of stable and genetically coherent ecotypes. The same goes for a recombination approach to microbial taxa. If both approaches are empirically confirmed and they cross-cut the world of microbes, then we should allow a plurality of classifications. If one approach is empirically successful and the other fails, then only one of those approaches to microbial classification should be accepted. Taxonomic pluralism is not an a priori conjecture but a hypothesis vulnerable to empirical tests.
Another concern with pluralism is whether it leads to inconsistent classifications. As Hennig (1966, 165) writes, "if systematics is to be a science it must bow to the self-evident requirement that objects to which the same label is given must be comparable in some way."  If some microbes are grouped according to a recombination species concept and others according to an ecological species concept, then those species are not comparable units. The answer to this concern should not be surprising. Classifications need to be internally consistent, but classifications of different types of entities need not be consistent with one another. Recombination species and ecotype species are different types of entities, bounded by different causal processes, so we should not expect them to be comparable. However, within a particular taxonomic study, if we say there are four species within a genus and three species in another genus, then we had better be comparing like to like. An analogy may help clarify this point. Genera in different phyla (for example, bacterial genera and mammalian genera) are considered very different types of entities. But within a particular classification, genera should be constructed according to the same parameters and thus be comparable.
This still leaves Hennig's concern that a single label is applied to different types of entities. The worry is that the ambiguity of 'species' implied by pluralism leads to semantic confusion . If classifications are constructed according to different parameters and that information is not evident, then we will not know what sorts of entities and relations are represented by a classification. There are two ways to address this concern. One is to get rid of ambiguous terms and replace them with more accurate terms for the different types of units classified. Following the debate over eukaryote species concepts, we might call recombination species 'biospecies,' ecotype species 'ecospecies' and phylogenetic species 'phylospecies.' But the replacement of 'species' with new terms will only go so far once the differences between prokaryote and eukaryote evolution are considered. There are different kinds of ecospecies and biospecies (for example, eukaryotic biospecies whose genomes are involved in whole genome recombination versus prokaryotic biospecies whose genomes recombine in a piecemeal fashion). A more practical approach to avoiding semantic confusion is not to reform our language but to be clear about what type of units are being categorized in a particular classification. For a classification of species, we should say which species approach is being used and how it is being applied (for example, whole genome recombination, or partial genome recombination and which part of the genome). Doing so will avoid semantic confusion and ensure that comparable units are classified within a particular classification.
Stepping back from these details we see that whether or not one should adopt taxonomic pluralism at the species level is largely an empirical question. If nature is cross-cut by significant evolutionary processes, then we should recognize the different types of resultant evolutionary units, whether they are called 'species' or something else. So if we want to accurately describe the species of the microbial world and learn about the processes of microbial evolution, it might be compelling to adopt taxonomic pluralism rather than to stick by default to a single hierarchy.