The basic steps for a mega-phylogeny include (1) designating the clade of interest, (2) identifying the gene region(s) of interest, (3) recording the extent of molecular diversity of the gene region in the clade of interest, (4) recording the threshold of coverage and identity to be used for orthology tests, (5) narrowing the possible sequences with a very broad term search [optional], (6) remove all potential sequences that are not members of the clade of interest, (7) testing orthology by BLASTing each potential sequence to each gene region identified for the breadth and removing those sequences that differ by more than the established threshold, (8) identifying sequences that should be reverse complemented, (9) removing sequences for duplicate taxon names, keeping the sequence with the best coverage and identity, and (10) test for saturation. If the sequences are saturated, subdivide them using the next available subclade and perform additional tests of saturation (step 10). Finally, once all of the sequences are in an alignment or exist as singletons (i.e. are not found to be contained in any subdivisions), profile each alignment to a master alignment. This can be repeated an arbitrary number of times for each gene region of interest. If multiple gene regions are used, these are then concatenated into a large matrix and the phylogeny inferred.

We implemented this pipeline in Python (vers. 2.5) with the BioPython (vers. 1.48) module and using the BioSQL (vers. 1.0.1) database schema. Each mega-phylogeny matrix assembly analysis presented here was run on a Linux laptop with 1 GB RAM and a 2.4 Ghz dual-core processor. The phylogenetic analyses were conducted on an eight-way SMP Linux computer with 2.4 Ghz processors and 32 GB of RAM using RAxML (vers. 7.0.4; 8). The steps that are novel for matrix assembly are described briefly below.

Determining whether sequences are orthologous is a challenge for large tree construction. Supermatrix methods have attempted to overcome this problem by identifying orthologous sets of sequences using clustering techniques 24, but these can be time consuming and are typically not developed with the goal of large phylogeny assembly [e.g., 28]. Here, we determine orthologous sequences using designated sequences representing the breadth of variation observed in the gene region of interest across the clade of interest. We BLAST all of the potential sequences from the database against these designated sequences and other potential sequences that are determined to match with a certain threshold (i.e. according to both coverage and identity). At this stage, reverse complements are corrected by determining which direction best matches the designated regions of interest. Instead of N × N comparisons between each potentially useful sequence, only N × n comparisons are necessary, where n is the number of example sequences used to represent the region. This dramatically shortened the run time of the algorithm as well as generally produced denser matrices.

One major problem for large matrices using broadly sampled sequences or smaller matrices with quickly evolving sequences is that multiple sequence alignments become more challenging as sequences become more divergent 2829. Almost all multiple sequence alignment algorithms build a phylogeny during the estimation procedures 30. The phylogenies built for multiple sequence alignment are often based on model-corrected or raw pair-wise distances. These methods are susceptible to problems with saturation (i.e. multiple mutations at the same site for the same organism) and are therefore much less accurate for large and broadly sampled alignments that are likely to contain very distantly related sequences. The quality of multiple sequence alignments can have a dramatic impact on the accuracy of the phylogenies produced [e.g., 313233]. As a result, other supermatrix methods sidestep multiple sequence alignment by employing clustering techniques to determine "alignable regions." Such clustering techniques have allowed for the assembly of very large matrices of sufficiently similar sequences 2434. This approach can be dramatically affected by the parameters used during clustering, sometimes resulting in multiple informative clusters for slower gene regions (e.g. two large rbcL clusters for Ericales in Phylota).

We combine the analysis of sequence saturation with recent advances in multiple profile-to-profile alignment methodology. A profile alignment is an algorithmic approach to identifying structural elements that are highly conserved between different alignments 343536. To accomplish this, separate alignments are aligned together while preserving the columns in the individual alignments. Newer profile alignment programs allow for more flexibility in profile alignment procedures (e.g. MAFFT; 37). In our case, we separate sequences into subgroups of aligned sequences based on the degree of sequence saturation. For example, if the algorithm determines that the most inclusive group of sequences is saturated, then the group is broken up into less inclusive groups using the next level in the taxonomic hierarchy. In a Linnaean taxonomic system, if an "order" is found to be saturated, it would be broken into "families". Each smaller subset of sequences is then re-aligned and the saturation reassessed. This process continues iteratively to less inclusive groups until sequences no longer appear saturated and these alignments are then stored. We note, however, that the taxonomic groups used in this procedure need not correspond to ranks in the Linnaean hierarchy, but should simply be hierarchically nested (as in the NCBI taxonomy). Grouping using a rank-free classification (PhyloCode; 38) could be used and will be possible once a database of phylogenetic names is implemented and usable. After every sequence has been either placed in an alignment or placed as a "singleton," the individual alignments are then profiled to a larger alignment. The order of the profiling can be random, optimized to find the best order, or aided by a hierarchical "guide" tree (e.g. first aligning more closely related matrices). Currently, we employ highly conservative guide trees based on published studies to carry out profile alignments.

We introduce a simple method based on dispersion statistics to rapidly detect saturation across a set of sequence data. Dispersion (an indicator of spread) is assessed on the one-dimensional Euclidean distance between the raw pair-wise sequence distances and those corrected according to a Jukes-Cantor model of molecular substitution. A one-dimensional Euclidean distance is the absolute difference between two points. Our measure of dispersion is based on the median and is commonly referred to as the median absolute deviation (MAD) and given by

MAD = 1.4826 × Med (| x_i - Med (x)|),

where the median is estimated from the residual variation about the median of all pair-wise Euclidean distances. The constant 1.4826 is used to make MAD consistent for the standard deviation 39. Thus, in our use, the larger the MAD the larger the overall spread in the Euclidean distances – that is, above a certain value the assumed nucleotide substitution model is no longer adequately accounting for the rate variation exhibited by pair-wise distances among species.

We performed a simple simulation study to explore the behavior of MAD. First, we wanted to determine a threshold for subdividing sequences into smaller alignments. In addition, we wanted to compare MAD with alternative measures of dispersion based on the sample mean (i.e. mean square error, MSE; root mean square, RMSE). Sequence data were simulated across randomly constructed 20- and 100-tip phylogenies. Different rates of molecular evolution were simulated by incrementally scaling the total tree length by a factor of 0.10, starting from 0.10 and stopping at 2.0. All molecular simulations were carried out using Seq-gen (Ver 1.3.2; 40).

The results from these simulations clearly highlight the utility of MAD. First, unlike MSE or RMSE, MAD does not require an underlying Gaussian distribution, which is useful as the distribution of Euclidean distances becomes skewed as the degree of sequence divergence increases. A second advantage, and perhaps the most critical, is that MAD appears stable when sequence divergence is unrealistically high (e.g. tree length scaled by a factor of 2; Figure 1). This situation is also analogous to the presence of outliers that have well-known influences on dispersion statistics based on the mean. Because MAD does not require an explicit distribution and is the 50^th percentile of the residual variation, it has the inherent property of being robust to outliers (Figure 1G, H). Finally, our simulations indicate that a MAD exceeding ~0.01 provided a conservative indication of a saturation level necessitating a profile alignment scheme.

Nearly 10% of all angiosperms are contained within the Asterales; a clade that is mainly comprised of 12 recognized families with a majority of the diversity being attributed to just two families, Asteraceae (e.g. sunflowers, thistles) and Campanulaceae (e.g. Lobelia and relatives). The monophyly of Asterales is well supported despite uncertainty in its position within the more inclusive Campanulidae clade 41. There are roughly 5200 species of Asterales represented in GenBank, or roughly 20% of the entire clade. However, aside from studies of carefully selected exemplar taxa representing major lineages of Asterales 414243444546, a comprehensive phylogeny has never been produced for this clade. Here we apply our mega-phylogeny approach to the Asterales to reconstruct the most complete phylogeny of the group to date.

Our Asterales sequence matrix was comprised of rbcL, matK, trnL-F, trnK, ndhF, and ITS. The combined matrix of 12,033 sites was comprised of 90.959% gaps or missing sequence. However, the individual gene regions were more variable in gap or missing sequence composition: 98.043% in ETS, 36.348% in ITS, 98.188% in matK, 90.338% in ndhF, 92.597% in rbcL, 98.002% in trnK, and 81.445% in trnL-F. Of the five gene regions sampled, ITS was the best represented taxonomically (with 4242 species) and was the only region identified by our procedure as requiring profile-to-profile alignments. The MAD score indicated that the degree of ITS saturation varied among groups, but within-group alignments were never carried out above the traditional "tribal" level. This resulted in 180 separate within-group alignment files of differing hierarchical level.

As an efficient means to direct the profile-to-profile alignments, we assembled a "guide" tree by compiling and grafting together published phylogenies (sensu 47). Briefly, we first obtained a backbone phylogeny from Winkworth et al., 41 and Lundberg and Bremer 44 for the major lineages of Asterales. We then grafted trees based on more focused studies into the backbone tree. We started this process with the most inclusive clade and proceeding "inwards", adding more and more detailed analyses of included clades. Our final grafted tree was pruned down to correspond to the 180-alignment files output from our saturation analysis (see Additional file 1). This guide tree was then traversed in a post-order fashion, performing profile-to-profile alignments starting at the "terminals" and working recursively back to the root. The phylogeny was then inferred using RAxML (vers. 7.0.4; 8), partitioning for each gene region using the GTR+GAMMA model of rate substitution.

Our final phylogeny includes 4954 tips with the branching within and among "families" being mostly consistent with previously published results (Figure 2). One exception concerns the early branching lineages of Asterales, involving the placement of Rousseaceae+Carpodetaceae, Campanulaceae, and Pentaphragmataceae. The current consensus recognizes a basal trichotomy among these three clades (48; but see 4144). Our analysis recovered Rousseaceae+Carpodetaceae as the sister groups of all other Asterales, within which Campanulaceae (including Lobeliaceae) is sister to the rest (Figure 2). This result has been recovered before 44, but other studies have suggested a basal split between Rousseaceae+Carpodetaceae plus Campanulaceae 4144 and all the rest. Our analysis shows Pentaphragmataceae as sister to a clade comprising Stylidiaceae, Alseuosmiaceae, Argophyllaceae, Phellinaceae, Menyanthaceae, Goodeniaceae, Calyceraceae, and Asteraceae (Figure 2). A recent combined analysis of chloroplast and nuclear genes found strong support for this relationship 41.

Relationships within Asteraceae coincide well the subfamilial classification of Panero and Funk 46. However, we note that our phylogeny does not support the monophyly of Wunderlichioideae, Stifftioideae, Mutisioideae, or Gochnatioideae (sensu 46). Instead we found these groups to be broken into smaller successive sister clades to the rest of Asteraceae.

Several relationships, within major clades, are worth noting as they highlight the utility of our method. Based on the NCBI taxonomy, the profile-alignment portion of our algorithm assumed that Campanula was monophyletic. However, the MAD score detected extreme sequence variation that required profile alignments among species. This variation is an indication of extreme molecular differentiation, and in the case of Campanula, paraphyly, which is consistent with more focused systematic studies of Campanulaceae 4950. In several cases we also assumed sister relationships where the primary literature suggested low nodal support. For example, we profiled the genus Doronicum and the tribe Senecioneae as sister clades within the more inclusive Asteroideae, though there is generally low confidence in this hypothesis 51. The resulting tree showed these two clades to be more distantly related, as Doronicum is placed near the early branching lineages of Asteroideae (Figure 2). Taken together, these results show that even though we assume some phylogenetic relationships at the outset in doing the profile alignments, our results need not recover the same relationship within the final phylogenetic tree.

The green plants (Viridiplantae) contain more than 350,000 species including green algae, liverworts, mosses, ferns, and seed plants, including the flowering plants. The early branches of the entire clade and of each major group of green plants have attracted extensive molecular work 52535455. Two large clades of living green plants are supported: Streptophyta and Chlorophyta 52. Charophytes (stonewarts) have been supported as the sister group to land plants based on the inclusion of six genes 5355. Despite the large number of molecular studies that have focused on deep relationships within green plants, few studies with very large numbers of taxa have been conducted.

Here, we create a mega-phylogeny of the chloroplast ribulose-bisphosphate carboxylase (rbcL) gene for all green plants. This well sampled gene has been extensively examined in smaller studies throughout plants, especially in flowering plants [beginning with 5]. Despite the widespread use of rbcL, the addition of other genes has generally been necessary to confidently reconstruct many relationships. Here, our goal was to construct the largest rbcL phylogeny for green plants while simultaneously accommodating saturation across the alignment.

Over 16,000 rbcL sequences were found to be orthologous to the designated sequences sampled throughout flowering plants. Our final matrix with duplicate taxa removed consisted of 13,533 tips and 1401 nucleotide sites with 4.6238% of the matrix consisting of gaps. Our saturation analysis recognized 15 separate aligned subgroupings: Chlorophyta (486 sp.), Zygnesnophyceae (131 sp.), Coleochaetophyceae (21 sp.), Charophyceae (34 sp.), Marchantiophyta (462 sp.), Bryophyta (570 sp.), Anthocerotophyta (56 sp.), Lycopodiopsida (48 sp.), Isoetopsida (101 sp.), Equisetophyta (18 sp.), Marattiopsida (59 sp.), Ophioglossopsida (29 sp.), Filicopsida (1624 sp.), Psilotophyta (3 sp.), and Spermatophyta (9900). These aligned subgroups were combined using profile alignments across a guide tree based on Donoghue 56 and Cantino et al. 38 (see additional file 2). The phylogeny was constructed using RAxML (vers. 7.0.4; 8) using the GTR+GAMMA model of rate substitution.

A recent analysis by Qiu et al. 55 compiled the most comprehensive dataset to date, using six genes and 193 species to resolve relationships of the four major land plant lineages: liverworts, hornworts, mosses, and vascular plants. They recover, with strong support, a resolution of successive sister clades starting with liverworts, then mosses, then hornworts, and vascular plants. Our maximum-likelihood tree of more than 13,000 species recovers this same relationship with the use of rbcL alone (Figure 3). However, within vascular plants, our trees differ in the placement of lycophytes. In the Qiu et al. 56 tree, monilophytes are more closely related to seed plants than lycophytes and these relationships are well established based on other evidence (e.g., morphology 57, gene order and gene losses 5859). We find the lycophytes to be more closely related to seed plants, which is likely to be mistaken and reflects an artifact in the evolution of rbcL.

Our much larger phylogeny resolves some relationships by including more data in the form of more species instead of more genes. This has been documented previously but has rarely been tested on such a large scale 6061. With the inclusion of more taxa other broad evolutionary patterns emerge [cf. 27]. For example, in this case, the ferns appear to have faster rates of evolution than the other vascular plants. Further study is required to quantify this pattern and its important, as the timing and rate of evolution of ferns has been interpreted in light of angiosperm evolution 62. With more taxa sampled, rate heterogeneity can become more apparent, raising an important issue about the possible effects of clade-specific rates on divergence-time estimates 27. Unfortunately, accurate estimates of divergence times using tens of thousands of species remain impractical.

Another important result is that rbcL appears to be saturated across green plants. That is, despite the conservative nature of this coding region, when looking very broadly there are likely to be multiple mutations at sites throughout the gene causing either less accurate multiple sequence alignments or causing clustering methods to break up the matrix into smaller sections. Broad analyses of green plants will need to take this into account. Our analysis also demonstrates the limitations of conventional computers for analyzing large phylogenies. The matrix manipulation, tree construction, and tree rerooting required at least 8 GB of memory and were conducted on an 8 CPU machine. To build even larger matrices, more memory and faster machines will be essential.

The mega-phylogeny method is inherently modular, making each step easily extensible. For example, instead of using BLAST comparisons for sequence orthology tests, another test could be used. In fact, a modified clustering method, as is typically found in supermatrix construction, could be utilized. Additionally, instead of the MAD measurement for saturation, other measures could be devised. Concomitantly, any number of different taxonomic databases can be used when saturation is detected. We have relied on the NCBI hierarchical taxonomy, but increased precision might eventually be obtained by using a system containing many additional levels. The modularity of the mega-phylogeny approach encourages its longevity when better methods and approaches become available to address specific procedures underlying mega-phylogeny matrix creation.

Modularity is especially important with respect to the guide trees involved in profile alignment, where the results from different guide trees (or no guide tree) can be compared. For example, there may be a published study of broadly sampled taxa included in the clade of interest for the mega-phylogeny approach. A profile alignment using this tree could easily be compared to one that consists only of basal polytomies, which will be profiled randomly. The use of guide trees for this step highlights the need for available definitive bifurcating trees for profile alignments, especially broadly sampled trees. From this perspective, the compilation of large-scale trees from published phylogenies (e.g., available on TreeBASE, http://www.treebase.org) becomes a highly relevant endeavor, not only from the standpoint of the initial guide tree but also as a basis for the comparison of results. Important differences could then highlight areas in special need of attention. For example, further attention is needed to the signal in rbcL that places lycophytes with seed plants.

A key element of our mega-phylogeny method is its reliance on prior knowledge of phylogenetic relationships when performing profile-to-profile alignments. We assume that each group being aligned is monophyletic, which is potentially a problem once saturation is detected and less inclusive multiple sequence alignments are employed. However, despite such assumptions, our saturation analysis using the MAD statistic is not irreversibly susceptible to outliers and can detect extreme variation when, for example, it is not monophyletic as demonstrated with Campanula within our Asterales matrix. In this case, the MAD score suggested that the assumption of monophyly for Campanula was violated, and it emerged as paraphyletic in the final tree. Even though the assumption of monophyly is a potential problem, it is not always detrimental. Further work is needed to explore the sensitivity of the results to such assumptions. In the meantime, the approach highlights the need for taxonomic databases to most accurately reflect current best knowledge of phylogenetic relationships.

Various problems identified in supermatrix construction may also pertain to the mega-phylogeny method. For example, there are problems with database-enabled phylogenetics that are hard or impossible to avoid, such as misidentification or mislabeling in GenBank 4. Sequence orthology tests can help identify such problems, however outliers are likely to still cause difficulties in some matrices. Additionally, there are potential problems with "rogue taxa" that can lower resolution and support throughout the tree. However, the problem of rogue taxa continues to also be a problem for supermatrices and therefore the development of solutions will likely benefit both methods.

It may be possible to incorporate diversity estimates for each taxonomic group, such that large clades represented by single (or a few) species for a particular gene could be excluded. This would likely reduce problems associated with rogue taxa. Although this information is not currently readily available, its inclusion could greatly increase the efficacy of the mega-phylogeny approach.

Our method can also be extended to deal with the problem of sequence outliers. Unfortunately, the size of the matrices that can be constructed makes checking for outliers by hand impractical. But saturation statistics could be extended to identify these outliers in the individual gene regions. Although the orthology tests and reverse complement procedures identify the vast majority of problematic sequences, the MAD statistic has the potential to cleanse the datasets further, allowing for almost complete automation of large tree construction.

Finally, the mega-phylogeny procedure can be parallelized. Many of the procedures related to sequence-to-sequence comparisons (e.g., orthology tests, reverse complements) can be easily distributed on multiple CPU's or computers. This is also true of some of the multiple sequence alignment calculations. Parallelizing these procedures would yield even faster the mega-phylogenic analyses.