The TIGR Gene Indices Database provided 172,900 Tentative Consensus (TCs) sequences for the seven focal taxa (Table 1). After discarding sequences for which there was no open reading frame (ORF) at least 500 nucleotides (nt) in length, 105,453 TCs remained. These were trimmed to their longest ORF, producing sequences with average length of 1094 nt (336 nt shorter, on average, than the original TCs).

Clustering of sequences implemented with BLAST and single-linkage clustering produced a wide diversity of cluster sets (Table 2) depending on how we set the minimum hit fraction, which is the set union of the sets of locally aligned sites (hits) reported by BLAST. With this minimum value set to zero, nearly 40,000 clusters were assembled, some 4423 of them phylogenetically informative. However, the largest contained 6565 sequences, and the sequences in it were extremely heterogeneous in length, sequence, and annotation, and were not homologous to any level that would be useful in phylogenetic inference. Clearly the stringency of overlap set by the minimum hit fraction was too low. When we increased the minimum hit fraction the size of the largest cluster was reduced and the data became more fragmented, as reflected in the increasing number of clusters (Table 2), but also more homogeneous within clusters. Ultimately we selected a hit fraction of 0.7 in an effort to maximize the amount of information retained while attempting to minimize within-cluster heterogeneity (see also e.g. Schlueter et al. 48; who impose analogous requirements, although on fractional overlap of an entire hit rather than the set union of hits, as we do).

The chosen cluster set contained 88,864 clusters, only 577 of which were potentially phylogenetically informative; that is, they had at least four sequences and at least three taxa (most contained just a single sequence or a single taxon: Table 3 and Table 4). Fifty-nine clusters contained sequences from all seven taxa. The largest informative cluster contained 94 sequences, including several from each of the seven taxa. On the other hand, an extraordinarily large number of clusters, 79,122, were singletons (only one sequence). The contributions of each taxon to the final data sets ranged widely: from 315 to 1065 TCs and membership in 159 to 538 clusters (Table 1). The number of sequences excluded due to insufficiently long ORFs also varied tremendously across taxa (Table 1). In the end only 4536 TC sequences of the original 105,453 found their way into phylogenetic analysis (4.3%). This was about one tenth of the sequences produced by the least stringent clustering requiring 0% hit fraction overlap, but those clusters were largely unusable because of their heterogeneity as described above.

The collection of gene trees reconstructed using parsimony (henceforth "parsimony gene trees") was quite similar to that reconstructed under likelihood ("likelihood gene trees"). In fact, 354 of the clusters produced the same tree topology or same set of equally optimal tree topologies. In 34 other clusters the set of ML trees was a proper subset of the set of MP trees, and in one cluster the reverse was true. Finally, in 187 clusters, the set of MP trees and the set of ML trees were disjoint. Not surprisingly, these tended to be the clusters with more sequences (mean 12.4 sequences, whereas the mean across all 577 clusters was 7.9 sequences).

The distribution of the number of clusters inferred to have a given number of duplications is highly skewed for both parsimony and likelihood gene trees with many clusters having zero duplications but the maximum number of duplications in any cluster still being quite large (Table 5).

On the accepted species tree, the inference method affected the number of duplications inferred for 154 clusters but had no effect on the other 323 clusters. Of those for which it made a difference, in 87 clusters the likelihood gene trees fit the accepted species tree better i.e. with fewer duplications, and in 67 clusters the parsimony trees fit better.

The optimal species trees differed slightly depending on whether the parsimony or likelihood gene trees were used. Based on the likelihood gene trees, the optimal tree was exactly the accepted species tree, with an (out-) duplication score of 779.0 (Fig. 3A). Based on the parsimony gene trees, the optimal species tree was very similar to the accepted tree, except for a rearrangement within the legumes (Fig. 3B). Its score was 771.9 (out-) duplications. The duplication score of the accepted species tree based on the parsimony gene trees was 796.3 and it was ranked fourth among all species trees. Fractional scores reflect weighting of multiple equally parsimonious or equally likely gene trees within a cluster. Note also that the rankings and relative scores are the same when counting all duplications as when counting out-duplications only. As they are restricted to only a single species, in-duplications are akin to autapomorphies in being phylogenetically uninformative.

Because of the exhaustive enumeration algorithm we could obtain the entire distribution of duplication scores for the two analyses (Fig. 4). The duplication scores for the likelihood trees ranged from 779.0 – 1152.0, whereas those for the parsimony trees ranged from 771.9 – 1165.9. Both distributions were highly skewed with a long tail of low scoring trees, suggesting the presence of phylogenetic signal, at least by analogy to skewness indices that have been used to study parsimony score distributions 49.

Bootstrap I values could only be calculated for the parsimony gene tree collection because of computational limits (100 maximum likelihood searches on 557 data sets was prohibitive). Support was >95% for all nodes in the species tree derived from the parsimony gene trees except for the rosid clade, which was only supported at 48% (Fig. 3). Bootstrap II support values were also moderate for the Rosid clade in both parsimony and likelihood gene tree analyses (71% and 68% respectively). In addition, the relationship within the legumes, which conflicts between the two optimal species trees (Glycine + Lotus versus Medicago + Lotus), is weakly supported (66%) in the likelihood analysis, but strongly supported (99%) in the parsimony analysis.

Because our analyses supported two different trees depending on which collection of gene trees was used, we examined whether these two trees were statistically distinguishable on the basis of the data at hand. Let T_L be the optimal species tree found based on the likelihood gene trees (identical to the accepted tree) and T_P be the optimal tree found with the parsimony gene trees. We examined the difference in support for these two trees based on either the likelihood gene tree collection or the parsimony gene tree collection using the analog of the paired-sites test described in the Methods. Based on the parsimony gene trees, there was weak but significant support (P = 0.04) for a difference between T_L and T_P. Of the 577 gene trees, 403 showed no difference in unrooted duplication scores between the two trees; 101 had better (lower) scores for T_P compared to T_L; 77 had better scores for T_L. On the other hand, there was no significant difference in support (P = 0.36) based on the likelihood gene tree collection for a difference between T_L and T_P. Of the 577 gene trees, 408 showed no difference in unrooted duplication scores between the two trees; 85 had better (lower) scores for T_P compared to T_L; 84 had better scores for T_L. These results are congruent with the bootstrap II comparisons in that they suggest the parsimony gene tree collection makes a more decisive claim about the difference in the species trees than does the likelihood gene tree collection.

Phylogenomic data sets, whether derived from whole genome sequencing 15, database mining 18, or EST assemblies 2027 have yet to combine into one analysis more than a few hundred clusters of sequence homologs ("loci"). The reasons for this are many, but a primary one is the tradeoff between completeness of a data set and lack of homology that eventually limits cluster construction. Sanderson and Driskell 50 and Driskell et al. 18 illustrated this graphically by showing the low density of concatenated data matrices assembled from GenBank data mining approaches. Density can be defined as the fraction of sequences present in a "data availability matrix" consisting of all taxa in an analysis by all clusters. The reason why phylogenetic data matrices derived from whole genome analyses do not include all the genes in the genome is partly because lack of homology between sequences in these taxa limits how many taxa actually share the gene in common (either due to gene loss or excessive divergence). Clusters used in phylogenetic analysis are sometimes explicitly constructed to have all taxa or a minimum fraction of such taxa 51, thus keeping data density above a threshold, but also greatly limiting the eventual size of the data matrix.

EST-based studies also seem to fit into this same paradigm. For example, using small EST libraries to identify orthologous clusters of ESTs, Hughes et al. 20 constructed supermatrices with 71% missing data, and this was after exclusion of most of the data because of extensive paralogy. In our data, for the cluster set used for most analyses, we identified 88,864 clusters for the seven taxa. However, 79,122 of these were singleton clusters, meaning that a whopping 75% of the original 105,453 TCs did not pass our minimal homology threshold. Moreover, as only 577 of the remaining clusters were actually potentially phylogenetically informative, the final density in the phylogenetic data availability matrix could not possibly exceed 577/88,864 or 0.6%. Higher densities are possible if the cluster assembly stringency is relaxed, but as we have seen, this leads to very heterogeneous clusters with few regions of homology – presumably engendering downstream problems in subsequent phylogenetic analysis.

This very small fraction of the EST data that appear to be potentially useful for phylogenetic studies raises questions about the relative costs and benefits of obtaining EST data for phylogenetic work 20. However, several other factors are important to consider. First, using available EST libraries as tools to screen for loci useful for phylogenetic inference may justify their expense in a small number of pilot taxa. Primers can be developed for later use in extensive taxon surveys (e.g. 52). Second, as local alignment tools (e.g. 53) and phylogenetic inference algorithms improve, it should be possible to assemble clusters with more heterogeneity and distant homologies, and hence exploit more of the original data. Finally, it may be necessary to view the problem as one that will eventually be overcome by improvements in technology and reductions in expense. After all, for many single loci sequenced in conventional phylogenetic analysis, most sites are conserved and uninformative. The only factor that makes this palatable is the (now) relative inexpensiveness of sequencing technology.

Among the 577 phylogenetically informative clusters, most showed evidence of gene duplication by conflicting with the accepted species tree. Even if we conservatively regard inparalogs as multiple alleles or multiple accessions of the same locus, there are 351 clusters that show at least one out-duplication when reconciled against the species tree using the likelihood gene trees. If we take a more liberal view, counting all duplications, then 535 of the clusters show evidence of duplication. Similar numbers obtain if the parsimony gene trees are used. Since duplications are minimized across all rootings of the gene trees, our estimated number of duplicated loci is probably somewhat lower even than the true value. On the other hand, the fact that the gene trees themselves have error is unaccounted for by our methods, and, failing to take uncertainty into account may inflate the inferred number of duplications 13. Regardless of these considerations, the fraction of the phylogenetically useful data in clusters that are locked up in gene families in plants, as opposed to single-copy genes, seems to be extremely high. To exploit the nuclear genome in plants to build species trees therefore seems to require methods that can handle extensive duplication (and gene loss or failure to sample), such as GTP or alternative frameworks 1154.

Despite the extensive heterogeneity in the data themselves, and the complex informatics pipeline that ultimately filtered out most of the original data, remarkably strong signal for the accepted species phylogeny was evident in the GTP analysis. The GTP analysis of the likelihood gene trees yielded the correct "accepted" species tree. The analysis of the parsimony gene trees yielded a species tree close to the accepted tree (which was ranked fourth out of 945). We find these results both surprising and promising for three reasons. First, gene families are subject to a variety of processes that can destroy the hierarchical signature of phylogenetic history, such as gene conversion between paralogs. Methods are available to detect such events 5556 and to incorporate them into phylogenetic inference 57, but the latter are still in their infancy.

Second, the EST data themselves were "messy" compared to other data sets we have examined 18. EST tentative consensus sequences, which formed the start of our analysis, are themselves assembled from individual short EST sequences using complex and assumption-laden informatics protocols 30. Among the factors that these assemblies contend with are filtering contaminants, correct assembly of pieces of the same paralog in gene families, and handling of alternative splicing, all in the presence of the usual issues raised in local and global homology algorithms. Though EST data have been widely used in evolutionary studies (e.g. of whole genome duplications: 48), they have rarely been used en masse in phylogenetic analysis of any taxon 2051, and it was reasonable to think that one cause for this was that these complexities overcame any underlying signal. Apparently this is not the case.

Finally, GTP has only been used to build species trees in a few studies. Although a few issues have been raised in criticism of GTP (see below), one cannot help but think that GTP has not been used more either because of lack of software tools, or lack of data. Although many implementations of gene tree reconciliation are available 134054, few tools for GTP itself have been available except for Page's COMPONENT 38 and later GeneTree programs 39. Neither of these is set up to handle large numbers of loci easily or is scriptable, a necessity for much high throughput informatics work. Moreover, the search strategies rely only on branch swapping from random starting trees. If GTP is as difficult an optimization problem as maximum parsimony, with as messy data, experience suggests that this heuristic is not likely to perform very well. However, we have not solved that particular problem either. Instead, we avoided it by implementing an exact exhaustive enumeration possible only because of the small species tree in our problem.

Another reason for the lack of GTP studies may be the lack of available gene family data for many taxa. Phylogeneticists have done their best to filter out gene families in the search for single-copy "magic bullets" that are easily sequenced by direct PCR, and to avoid cloning, Southern blots, or other labor-intensive techniques that are often necessary to initially identify paralogous copies of loci 58. However, large databases of protein families exist and have been relatively underexploited for species tree inference (except see Cotton and Page's 12 analysis of the HOVERGEN database). For many taxa that phylogeneticists find interesting, however, such data are simply not available. The taxa are not model species by and large, and there has been no compelling reason to seek a diversity of loci in relatively obscure taxa. This will probably change as more and more sequencing projects and EST libraries build bridges to nonmodel taxa.

Criticisms of GTP are numerous 59, and many reflect the same concerns as have been raised about supertree analysis 60 – in particular, that by taking a set of trees as the input, information about the uncertainty in those trees is lost (and hidden information within each data set cannot synergistically emerge). Certainly some number of duplications are inferred incorrectly simply because the gene tree is wrong 13. To address this, relative clade support scores can be incorporated when reconciling gene trees with species trees 13. However, the sheer volume of gene trees used here apparently overcame the errors associated with any one incorrect gene tree, implying a lack of systematic bias in the gene tree estimates, at least when likelihood was used to infer the gene trees. A more niggling issue is that the standard GTP algorithms all still require binary input trees. Chang 61 has developed an algorithm that solves this problem, but it is not yet implemented. Both of these problems can be addressed at least partly through bootstrap procedures 12, which, when constrained to generate binary gene trees, sample across much of the diversity that is entailed by multifurcations arising from either lack of data for that node or conflicting signals.

Currently the main factor limiting the application of GTP to species tree inference seems to be a paucity of implemented tree search heuristics. Three related algorithmic challenges remain in this arena. First, gene tree uncertainty has to be integrated more directly into the tree reconciliation calculations. Durand et al. 13 developed algorithms to calculate improved duplication scores in the presence of gene tree uncertainty and demonstrated the dramatic reduction in estimated score that can ensue. These or similar approaches must ultimately be imbedded in GTP algorithms. Second, multifurcations in the gene tree and species tree have to be accommodated 61. Finally, to address the growing size of data sets, it will be necessary to integrate these aspects of the GTP problem with whatever tree search heuristics are developed, so that redundant re-calculation of scores for subtrees are avoided.

On the data analysis side, the size and taxonomic diversity of EST libraries will continue to grow, and our results suggest that these will be useful sources of data in the future for inferences about phylogeny. However, much work remains on the pre-processing side of the analysis, prior to gene tree construction and GTP analysis. The assembly of ESTs is a computationally and biologically challenging problem, especially in light of the high frequency of duplication in plant genomes, and the not infrequent occurrence of alternative splicing 30. Perhaps the greatest challenge will be to develop methods that properly account for ascertainment bias: the failure to sample all paralogs in a gene family for some or all taxa. Although model-based approaches (e.g. 54) to gene tree reconciliation offer a direct route to incorporate models of sample bias into the problem, these are computationally expensive methods, and it may be possible to use faster weighting schemes in some modification of the GTP framework.

Finally, the ubiquity of whole genome duplications (e.g. 562) has important implications for inferring species trees from gene families. Page and Cotton 63 looked for clustering of episodes of duplication in vertebrate gene families but found little evidence for it based solely on the phylogenetic position of the duplications. Subsequently 64 they added to their phylogenetic approach inferred duplication times and then found support for an ancient round of accelerated duplication rates in vertebrates, though not the recent episode that has been reported elsewhere 65. Their approach complements a much more widely used approach of examining the distribution of duplications ages for peaks at different points in time (e.g. 66). In addition to providing insights into genome evolution, these approaches suggest that supplementing the GTP inference problem with divergence time information to constrain its structure may be profitable, if only the accuracy of such information can be assured.

We downloaded EST data for seven plant taxa, including six angiosperms (Oryza sativa, Solanum tuberosum, Arabidopsis thaliana, Glycine max, Lotus japonicus, Medicago truncatula) and one conifer, Pinus (Fig. 2) to serve as an outgroup. Data were obtained from the TIGR Gene Indices Database 6768 (Table 1). Initial data analysis protocols were similar to those reported in 48. We extracted all TCs (tentative consensus sequences) for each taxon and used the EMBOSS program getorf 69 to find open reading frames of at least 500 nt in length in the sense direction. Default settings were used (ORF defined as a region between stop codons according to the standard genetic code). These filtered TCs were then used in subsequent analyses.

Clusters of homologous TCs were obtained using all-by-all BLAST nucleotide similarity searches 70 on the filtered and trimmed TCs (low-complexity filter DUST turned on; maximum Expect (E) value of 1.0e-10). BLAST was undertaken on nucleotide sequences despite the high level of divergence at third codon positions because of the possibility of mistaken amino acid translations based on incorrect ORF identifications in these data in which alternative splicing was not uncommon. Single-linkage clustering was used to assemble clusters based on BLAST output (program blink available at MJS's web site 71; additional utility scripts available from authors). High levels of within-cluster heterogeneity among sequences can lead to severe alignment problems 72. Therefore, a pair of sequences was considered as a hit if it was reported as a BLAST hit and it surpassed a minimum "hit fraction" of 0.70 for each sequence, i.e., at least 70% of each sequence must align to the other sequence with E values lower than the threshold – though not necessarily in a single contiguous hit. The threshold was imposed symmetrically for both query and target sequence. The value 0.70 was experimentally determined by simultaneously attempting to maximize the number of sequences assigned to clusters and minimizing the heterogeneity, both in terms of sequence divergence and length differences, of the resulting clusters.

Resulting clusters were screened for potential phylogenetic informativeness. To provide potential information in a GTP analysis, which fundamentally requires a rooted species tree and one or more rooted gene trees, the gene trees and the clusters used to construct them must consist of three or more sequences from three or more species. However, because we are not using external evidence to root the gene trees but rather are examining all duplication scores across all possible rootings, our gene trees must have at least four sequences. If a gene tree with three sequences only is rerooted, it will be congruent with all rooted species tree for some gene tree rooting, and therefore it will not provide any information to discriminate among species relationships in the GTP analysis. If on the other hand, the gene trees were rooted using a molecular clock or midpoint rooting, for example, then clusters with only three sequences could potentially incur duplication scores that differed from species tree to species tree.

Once the clusters were screened for informativeness (with specific regard to gene tree parsimony), we used the global alignment program Clustal W 73 to align nucleotide sequences within the clusters. A sample of alignments was checked manually for obvious alignment mistakes, none were found, and consequently the alignments were not edited further. Gene trees were reconstructed for each cluster using heuristic maximum parsimony and maximum likelihood implemented in PAUP* 4.0b10 74. Because only binary trees may be used in available algorithms for gene tree parsimony, zero-length branches were not collapsed in either method. Heuristic parsimony searches consisted of simple-addition sequences with tree-bisection-reconnection branch swapping, keeping a maximum of 10000 equally parsimonious trees (which was never exceeded). Heuristic maximum likelihood searches used a neighbor-joining starting tree followed by TBR branch swapping, time-limited to 6 hours, using an HKY85 + Γ model of evolution in which all parameters were estimated from the data. All phylogenetic analyses were conducted on a dual Xeon 2.80 Ghz CPU with 3 GB of RAM or on a 35 node Linux cluster, in which the head node is a dual Xeon 2.66 ghz CPU with 3 GB RAM and each node is a dual AMD 1.4 Ghz CPU with 1 GB RAM.

To construct a confidence set of trees for each cluster in parsimony analyses, we bootstrapped the sequence data (100 pseudoreplicates, saving each gene tree, or set of trees, each weighted by the inverse of the number of trees found for that particular replicate). Searches were conducted with the same settings as for searches on the original clusters. The computational overhead was too high to do the same for maximum likelihood (worst case running time: six hours × 100 replications × 557 data sets).

To reconcile the gene trees to species trees by minimizing the number of duplication events, we implemented the algorithm of Zmasek and Eddy 32 in a C program available from MJS at his web site 71. This algorithm runs, under the rarely expected worst case, in O(n²) time 32, but its average behavior is much better, as shown both by Zmasek and Eddy's experimental results 32 and our experience with the present data set. We implemented their algorithm in C to run quickly for the large numbers of gene trees and species trees analyzed in this paper: each gene tree parsimony analysis had to reconcile 557 gene trees under all possible rootings for each of 945 species trees. Although Durand et al.'s 13 recently released NOTUNG 2.1 program is quite full featured and would have been an appropriate tool for this task, its Java implementation and requirement that it be re-executed for each species tree/gene tree pair made it too slow for this problem.

Other criteria can be used to reconcile gene trees to species trees such as the sum of duplications plus losses or, for recently diverged lineages, coalescent depth 75. We chose not to incorporate the number of losses into the optimality criterion because the data sets for the current study, largely derived from ESTs, are exceptionally prone to incomplete sampling, and a true evolutionary loss is therefore difficult to distinguish from mere ascertainment bias. Moreover, adding losses to the optimality criterion introduces the difficult problem of weighting the relative importance of duplications, losses due to evolutionary deletion, and "losses" due to sampling omissions. The duplication score alone is expected to be a more robust indicator of gene family diversity in these circumstances 12.

Reconciliation of a gene tree to a species tree requires that both trees be rooted 8. The species tree of angiosperms is rooted with an outgroup to angiosperms among seed plants, the conifer, Pinus. However, outgroup rooting is not possible for the gene trees, because, for example, a gene tree might have two paralogs from Pinus in different parts of the tree, leaving the position of the root uncertain. Occasionally, the root may be inferred in simple scenarios in which a single duplication has occurred prior to all taxa in the analysis and the root is clearly between the two paralog trees, but in general, this will not be the case. Therefore, as suggested previously 1332, we reconciled the species and gene tree by evaluating the duplication score for all possible roots of the gene tree, selecting the root(s) that minimize the number of duplications inferred. Some EST clusters produced multiple equally parsimonious trees. In these cases an average duplication score was constructed across the set of equally parsimonious trees.

Because clusters lacking duplications are of special significance to species level phylogenetics, e.g. they can potentially be concatenated in "supermatrix" analyses, we estimated their occurrence in the data. A cluster was scored as lacking duplications if all equally parsimonious trees for that cluster had an unrooted duplication score of zero. These values are reported both for all duplications and for only out-duplications.

Because of the relatively small size of the species tree, gene tree parsimony searches for the optimal species tree were implemented by exhaustively enumerating all 945 species trees (rooted with Pinus), and calculating the summed gene duplication scores across all gene trees for each of these species trees. This procedure was repeated for both parsimony and likelihood collections of gene trees. This strategy obviously would not be feasible for species trees much larger than this. A benefit of exhaustive enumeration is that it provides the exact distribution of GTP scores across all the species trees. This allowed, among other things, a ranking of all species trees according to GTP score and a comparison of the relative position of the optimal GTP tree and the true tree.

Little work has been done to develop confidence assessments in GTP analyses, per se, although several authors have taken a bootstrap approach to identification of orthologs with gene tree reconciliation 32. Cotton and Page 12 suggested a bootstrap analysis to account for gene tree uncertainty, in which each of k data sets used to generate the k gene trees is bootstrapped N times, generating a set of k bootstrap profiles. Then a higher level GTP bootstrap analysis is done by taking the ith tree from each of the k profiles and performing a complete GTP search for the species tree, generating species tree i, and repeating this for i = 1, ..., N. The collection of N species tree then forms a confidence set of species trees, and majority rule consensus is used to summarize support, as in conventional bootstrapping 76. We refer to this as Bootstrap I.

An alternative bootstrap procedure uses the gene trees themselves as the sampling unit. In a single bootstrap replicate, a set of k gene trees is assembled by sampling from the original set of k gene trees randomly with replacement. Then a species tree is built by GTP, and the process is repeated N times. Again a majority rule tree can be constructed. We refer to this as Bootstrap II.

Finally, because the optimal species tree may be different from the accepted species tree in Figure 2, it is useful to test whether there is a significant difference in support from the gene duplication data. For this, we propose a simple analog to paired sites tests used extensively for parsimony and likelihood tree inference (reviewed in 77). For each gene tree, we calculate the duplication score on tree 1 and tree 2. Under the null hypothesis of equal support for the two trees, the mean difference in score of these across sites should be zero. A paired t-test provides a test of significance taking the variance into account. As is now well known however, if one of the two trees is the optimal tree (as it will be here), the test is one-sided and the P-value must be the appropriate one-sided version 77. Additional analogous tests presumably could be constructed to account for multiple test issues that might arise if we examined many trees 78.