After an extensive screen of rice genome sequences, we identified and sequenced 142 single-copy genes that were most likely free of the paralogy problem for reconstructing the phylogeny of all diploid genome types of Oryza (Table 1; see Materials and methods for details of gene screening). These genes are distributed throughout the 12 rice chromosomes and represent a genome-wide sampling of phylogenetic markers (Additional data files 1 and 2). After removing regions with ambiguous alignment, we concatenated the 142 genes into a data matrix of 124,079 bp, with exons accounting for 43% of the total sequence. The concatenated alignment contained 26,838 (21.6%) variable sites, of which 6,753 (5.4%) were phylogenetically informative (Additional data file 2).

Phylogenetic analyses of the concatenated sequences using maximum likelihood (ML), maximum parsimony (MP) and Bayesian inference (BI) all yielded a single fully resolved tree with high bootstrap support or Bayesian posterior probability (PP) for all internal branches (Figure 1). We labeled these branches as I, II, III, and IV. The relationships between A-, B-, and C-genomes are finally resolved, with the sister relationship between A- and B-genomes supported by 99-100% bootstrap support or PP. The F-genome, which jumped all over the previously reported phylogenies, is firmly placed between the basal G-genome and the rest of the genome types.

Because the increase in sequence length or the number of sampled genes does not guarantee the elimination of systematic errors 283435, it is necessary to investigate the potential impact of systematic bias on our phylogenetic reconstruction. First, we tested homogeneity of base composition across species for total, intron, exon, and three codon sites of the concatenated data set. The results indicated that four nucleotide bases occurred in almost equal proportions and the GC content varied little among species for all data partitions (χ² tests, P = 0.346-1.0; Additional data file 3). The potential compositional bias was also examined with analysis using log-determinant (LogDet) distance 36. This yielded the same topology as ML, MP, and BI (Table 2). These tests suggest that the concatenated data set did not contain compositional signals that could have biased the phylogenetic reconstruction.

Second, we analyzed rate constancy among lineages using Tajima's relative rate test 37. When the concatenated sequences were considered, results showed that the null hypothesis of rate constancy was rejected in almost all pairs of contrasts (P < 0.01). It is noteworthy that the F-genome evolved at a faster rate and the G-genome evolved at a slower rate than other genomes (Additional data file 4). To explore the potential impact of rate heterogeneity on tree reconstruction, we adopted the RY-coding strategy that discards fast-evolving transitions and consequently makes phylogenetic reconstructions less susceptible to uneven occurrence of multiple hits among lineages 3438. The tree obtained from the re-coded data set was topologically identical to that shown in Figure 1 (Table 2). To further test the potential long-branch attraction effect of the fast-evolving F-genome, we identified genes that evolved more rapidly in the F-genome than in the A-, B-, and C-genomes. We calculated the ratio of the mean distance between the F-genome and each of A-, B-, and C-genomes to the mean distances among A-, B-, and C-genomes for each gene. We then progressively excluded fast-evolving genes of the F-genome in a decreasing order of the ratios. The topology based on the remaining genes did not change until more than 50 genes were excluded (Additional data file 5). These suggest that rate heterogeneity was not severe enough to cause significant systematic bias.

Third, to examine the potential systematic errors caused by model misspecification 303235, we applied a series of homogeneous and mixed models in BI and evaluated the relative merits of competing models by Bayes factors. Although Bayes factor comparisons showed that all mixed models outperformed the homogeneous models significantly (Additional data files 6 and 7), analyses with all 14 alternative models, including ones incorporating the covarion model, which accounts for heterotachous signal, yielded the same topology as shown in Figure 1, with all internal branches supported by 100% PP. Taken together, the above analyses indicate that the phylogeny inferred from the concatenated gene sequences was not biased by systematic errors.

We next tested whether the resulting phylogeny could have been influenced by a subset of the genes. A gene bootstrap analysis was performed with 1,000 replicates 27. For each replicate, we randomly drew 142 genes with replacement from the entire pool. The sampled genes were concatenated and analyzed using ML. The results strongly supported the topology shown in Figure 1 (Table 2), indicating that the phylogenetic reconstruction was not dominated by a subset of the 142 genes.

Finally, we investigated whether within-genome sampling would influence the phylogenetic reconstruction. Because the A- and C-genomes have more than one species, while each of the remaining genomes has only one species 1913, we sequenced 62 genes for an additional A-genome species, O. barthii, and two additional C-genome species, O. rhizomatis and O. eichingeri (Table 1). Sequences of cultivated rice, O. sativa, belonging to the A-genome were also retrieved from the BGI-RIS Database 39 and added to the data set. Phylogenetic analyses of the 11 species generated the same inter-genome relationship as the one shown in Figure 1 (Figure 2). This indicates that one species sampled from each genome was sufficiently representative for the reconstruction of the genome relationships.

When phylogenetic analyses were done for each of the 142 genes separately, more than 40 different optimal trees were generated, indicative of extensive incongruence among gene phylogenies. To gain insight into the extent of incongruence, we constructed consensus networks from ML trees of the 106-gene data set without missing data. Figure 3a shows the network at a threshold of 0.15, which presents branches appearing at a frequency of 15% or higher of all gene trees. Two boxes are evident in the network, indicating that topological incongruence is concentrated on branch I involving the relationships between A-, B-, and C-genomes and branch IV involving the relationships between the F-genome, G-genome, and the rest of the genome types (R). We also explored the features of consensus networks by increasing the threshold from 0.05 and found that the boxes were collapsed when the threshold reached 0.3 and it ended up with the topology identical to that shown in Figure 1 (Additional data file 8). These results further support the phylogenetic relationships revealed by the concatenated data set and highlight the incongruence involving branches I and IV.

In the first box, the length of parallel edges supporting split AB|CEFGL is longer than those supporting splits AC|BEFGL and BC|AEFGL (Figure 3a), suggesting that a higher proportion of consensus signal groups A and B together. This is in agreement with the result that a larger number of gene trees (53%) support the sister relationship of A and B than those supporting the alternative sister relationship between B and C (26%) or between A and C (21%) (Figure 3b). For the second box, the length of parallel edges supporting split ABCEF|GL is longer than those supporting the two alternative splits. This is also consistent with the result that 45% of gene trees support the sister relationship between R and F while 30% and 25% of gene trees support the sister relationships between R and G or between F and G, respectively (Figure 3b).

To further explore the incongruence among gene trees, we performed the incongruence length difference (ILD) test based on two partitioning strategies and found that there was no significant incongruence between any pair of the process partitions (intron and three codon positions; Additional data file 9). In contrast, significant heterogeneity was found among gene partitions, including tests among all gene partitions as a whole (P < 0.01) and between pairwise comparisons and between each gene and the remaining genes combined (Additional data file 10). These results were consistent with the distributions of bootstrap support for alternative topologies at the two boxes (Figure 3b). For each box, there is a substantial proportion of high bootstrap support for alternative topologies, suggesting that the competing topologies are well supported on the respective gene trees. Remarkably, genes supporting any given topology are distributed randomly among the 12 chromosomes (χ² test, P = 0.233-0.823), indicative of a genome-wide incongruence (Figure 3c).

To address the question of whether the incongruence among genes is attributed to different evolutionary histories of genes or merely systematic errors 4041, we conducted tests for systematic bias for each of the 142 genes. The Chi-square test revealed that there was no heterogeneity of base composition for any gene. However, rate heterogeneity was detected for some genes by the relative rate test. We then conducted phylogenetic analyses for each gene using different strategies, including ML, MP, RY-coding, and LogDet distance. The comparison of bootstrap 75% majority-rule consensus trees showed that only 4 out of 142 genes yielded incompatible topologies between different methods of analyses (Additional data file 11). This indicates that there are few systematic errors involved in individual genes and the incongruence among gene partitions is governed mainly by different evolutionary histories of genes.

Different evolutionary histories of genes can be attributed to three major factors, including paralogy, hybridization, and lineage sorting 40. We have largely ruled out the potential effect of paralogy by carefully screening gene markers (see Materials and methods). The pattern of incongruence also does not support hybrid speciation because hybridization would have led to two major incongruent topologies rather than the presence of a leading topology with two alternative topologies occurring at nearly equal frequencies for both clades I and IV. The random distribution on chromosomes of the genes that support a given topology (Figure 3c) does not support the hybridization hypothesis either because related or linked loci should share gene trees if the species have a history of introgression or hybridization 42. Therefore, we are left with the hypothesis of lineage sorting as the primary explanation for the incongruence.

Population genetic theory suggests that lineage sorting is more likely to occur at an internal branch of a species tree that is short (few in generations) and wide (large in effective population sizes) 4344. Based on estimation by the ML method, branches I and IV were the shortest internal braches on the concatenation tree and obtained relatively low support values in analyses with different methodologies (Figure 1 and Table 2). For branch I, there is a sufficient amount of published data that allow us to estimate the probability to obtain the species tree from a given gene. That is, P = 1 - 2/3exp(-t) under the coalescent model, where t is the time between two speciation events in the unit of generations/2Ne and Ne is the effective population size 43.

Using the previously reported nucleotide diversity at silent sites (θ_sil = 0.0038-0.0095) for the A- and C-genome species 4546 and a substitution rate for grasses (5.9 × 10^-9 substitutions per synonymous site per year) 4748, we estimated that the effective population sizes of these Oryza species ranged from 1.6 × 10⁵ to 4.0 × 10⁵. A speciation model test on three C-genome species suggested that their ancestral population sizes were approximately ten-fold larger than those of each species 45. Thus, the ancestral population size of A-, B-, and C-genomes (Ne) should be at least 1.6 × 10⁶. Because the A-genome species began to diverge approximately 2 Mya 49 and divergence between B- and C-genomes occurred approximately 3.8 Mya 45, the time between two speciation events should be less than 1.8 million years. Given the generation time of 1-2 years in wild rice species 50, the number of generations between the two speciation events is at most 1.8 × 10⁶. The estimated upper limit of generations together with the lower limit of Ne led to the calculation of the upper limit of P as 0.62. This implies that there is less than a 62% chance for any given gene tree to be the same as the species tree or less than 62% of gene trees from the sampled genes will be congruent with the species tree. Our finding that 53% of gene trees support the sister relationship of A- and B-genomes agrees with the theoretical expectation (Figure 3b), which further supports the lineage sorting hypothesis.

For branch IV, the divergence happened at greater depth in the tree and thus homoplasy resulting from mutational saturation might be a factor to cause incongruent gene phylogenies 3351. However, analyses of saturation plots did not reveal any mutational saturation for the concatenated data set (Additional data file 12), suggesting that lineage sorting is still the most plausible explanation for the incongruence.

To assess how much of the data set might be needed to resolve such short branches, we explored the relationship between the number of genes or nucleotide sites and the proportion of gene trees that support the topology or clades shown in Figure 1. The results demonstrated that the probability of getting identical topology or clades as in Figure 1 steadily increased with the number of genes or sites sampled, regardless of methods used, although ML generally performed better than MP (Figure 4). Using 95% of identical gene trees or clades in 500 replicates as a criterion, about 120 genes were needed for both ML and MP methods to resolve branch I and more than 80 (ML) and 120 (MP) genes were needed to resolve branch IV. Additionally, 120 (ML) or more genes (MP) were needed to resolve both branches simultaneously (Figure 4 and Additional data file 13).

When nucleotide sites rather than genes were the unit of resampling, about 40 kb of nucleotides were sufficient to resolve branch I with both methods. This is equivalent to 46 sampled genes in length given the average length of 874 bp per gene. It took approximately 40 kb and 80 kb (approximately 92 genes) for ML and MP, respectively, to resolve branch IV. A total of 50 kb (approximately 57 genes) for ML and 80 kb for MP were sufficient to resolve both branches simultaneously (Figure 4 and Additional data file 13). These results indicate that random sampling of unlinked nucleotides has a higher power of phylogenetic resolution than sampling contiguous nucleotides such as those within a gene.

We used the BGI-RIS Database 39 for gene screening. Similar to the strategy used by Yu et al. 64, we extracted the protein sequences with nr-KOME cDNA 65 evidence and then conducted extensive searches against the genomic sequences of indica rice (93-11) in all six reading frames using TBLASTN at E-values of 10^-7. To ensure that single-copy genes were used in our analysis, we applied a stringent similarity criterion of 50% in our searches; that is, only protein-coding genes that have no counterpart over 50% similar to themselves in the rice genome were selected for further analyses. Excluding those sequences without syntenic counterparts in the japonica (Nipponbare) genome 2, we got a total of 943 genes as candidates for phylogenetic markers. Using coding sequences of these candidates, we performed BLAST searches against the GenBank database to obtain the gene counterparts from barley, maize, sorghum, wheat, or other species of Poaceae as targets for primer design. On this basis, we designed 162 pairs of primers for amplifying orthologous segments from Oryza species and the outgroup Leersia tisserantti. Finally, 118 genes were kept according to the following criteria: they were sampled randomly from all the 12 rice chromosomes; the amplifying length ranged from 0.5-2.0 kb with an intron length of 30-70% so that adequate information is available at different taxonomic levels; and clear and strong amplified fragments were obtained from the Oryza species and the outgroup. Moreover, we sequenced 24 additional genes that were single copies demonstrated by previous studies (Additional data file 2). All the 142 genes used in this study were mapped onto the chromosomes of indica rice (93-11) (Additional data file 1).

We sampled six Oryza species, representing all six diploid genomes in the genus, and one Leersia species (L. tisserantti) as outgroup because Leersia is most closely related to Oryza 1253. Information on the materials used in this study is listed in Table 1. Primers for PCR of all 142 genes are listed in Additional data file 14. Missing or partial sequences of some genes were present in some species because of the amplifying difficulty (Table 1). However, missing data in our case did not impact the tree constructions no matter what methods were used because our data set contained sufficient information, consistent with previous computer simulation and empirical investigation 212566.

PCR amplifications and purification of the products were performed by standard methods. Purified products were sequenced either directly or after cloning into pGEM T-easy vectors (Promega, Madison, WI, USA) if the direct sequencing failed. Sequencing was carried out on an ABI 3730 automated sequencer (Applied Biosystems, Foster City, CA, USA). All sequences obtained in this study have been deposited in the GenBank database (accession numbers EF577518 to EF578433, and EU503348 to EU503533; Additional data file 14).

Individual genes were aligned using T-Coffee 67 and then manually adjusted. Phylogenetic trees were reconstructed by ML, MP and BI methods. ML and MP were implemented with PAUP 4.0b10 68 and the branch-and-bound algorithm was used for tree searching. A non-parametric bootstrap strategy 69 was used for assessing tree reliability, with 1,000 replicates for MP analysis and with 100 and 500 replicates for ML analysis of the concatenated sequence and single genes, respectively.

BI was attempted with MrBayes 3.1.2 70. Given the sensitivity of the Bayesian method to model misspecification, we explored a series of homogeneous models by combining model components in different ways, including substitution rates among nucleotides (Nst = 1, 2, 6), rate variations across sites (Rates = Equal, Gamma, Propinv, Invgamma), and rate variations across the tree (Covarion = Yes, No) (Additional data file 6). Furthermore, we explored mixed models that accommodate heterogeneity across data partitions by specifying partition-specific substitution models 70. We applied mixed models to our partitioned data by two schemes (see 'Analysis of systematic bias and congruence tests' below). Mixed models were implemented with separate models for each data partition selected by the program Modeltest 3.7 71 and model parameters separately estimated, and a rate multiplier (ratepr = variable) was also employed to allow the overall rate to be different across partitions. In all the BI analyses, three independent Markov Chain Monte Carlo runs were executed, each starting with randomly choosing topologies for the four simultaneous chains, one cold and three incrementally heated. The four chains were run for at least 1,000,000 generations until stationarity in Markov chains was achieved, sampling trees every 100 generations with the first 10% of trees sampled discarded as burn-in, and then the posterior probabilities were calculated from the remaining samples.

We used Bayes factors 72 to evaluate the relative merits of two competing models, with the intention of detecting the effect of model components on our data. This method does not require alternative models to be hierarchically nested, and so it makes possible the comparison of any pair of distinctly different models. A Bayes factor in favor of one model (model 1) over another model (model 0) was calculated as the ratio of their marginal likelihoods and the natural logarithm of marginal likelihood can be approximated by the harmonic mean of the likelihoods of Markov Chain Monte Carlo samples with MrBayes 73. We calculated twice the natural logarithm of the Bayes factors for the competing model pairs, and interpreted the results according to the rule suggested by Kass and Ratery 72, which states that a result of 2 to 6 is 'positive' evidence in favor of model 1, a result of 6 to 10 is 'strong' evidence, and a result of >10 is 'very strong' evidence; conversely, a result of <0 provides evidence in favor of model 0.

To combine evidence from different loci without losing the information on independent gene histories, which might be drowned out by suppressing them into a bifurcating tree, several phylogenetic network approaches have been proposed and proven to be useful alternatives when using multi-gene data sets 747576. Consensus network, which is applied to multiple trees with the same set of taxa, is one commonly used network approach and can display simultaneously the conflicting evolutionary hypotheses based on multiple loci in a network fashion 7476. Such conflict or uncertainty might arise from stochastic errors, systematic bias, or biological processes 75. Therefore, phylogenetic networks provide a more inclusive approach than analysis of the concatenated data set because weak or conflicting signals are hidden when genes are concatenated before phylogenetic analysis 76.

In the consensus network, areas where all trees have compatible splits (that is, a split is a bipartition of the taxa) will be tree-like (that is, a single branch); in contrast, areas with incompatible splits will be represented by bands of parallel edges, thus forming a potentially hyper-dimensional graph. The degree of denseness of boxes in networks reflects the intensity of contradictory evidence for grouping certain taxa, and the length of an edge is determined by the weight assigned to it 7475. The phylogenetic networks can range from one extreme, a structure of high-dimensional hypercubes in the absence of any common phylogenetic patterns among gene trees, to the other extreme, a unique bifurcating tree in the absence of stochasticity associated with bifurcating evolutionary process 75. By employing the threshold value, we can reduce the visual complexity of resulting graphs by using only the splits that occur in more than a given proportion of all trees.

In the present study, we constructed consensus networks from optimal ML trees for a 106-gene data set in which sequences of all six diploid genomes and the outgroup were available and included in our consensus network all splits that occurred above a threshold value ranging from 0.05-0.3. In our case, branch lengths were not considered when using optimal ML trees as source trees because we were only interested in the conflict between topologies of gene trees. Thus, edge lengths in the final network are proportional to the number of trees in which a particular split appears. Consensus network was performed by the method described by Holland 76, in which Python scripts (kindly offered by BR Holland) was first implemented to create Nexus files and then the resulting network was visualized by Spectronet 77.

Systematic errors such as compositional signal, rate signal and heterotachous signal might be reinforced as more and more data are considered 35. We first tested the compositional bias resulting from the heterogeneity of nucleotide compositions among lineages by Chi-square test. The LogDet distance 36 was also used to account for compositional bias with the neighbor-joining method. Then Tajima's relative rate test 37 was employed with each pair of Oryza species, using L. tisserantti as outgroup, to test rate constancy. Sequence data were also analyzed under the RY-coding strategy (A and G = R, C and T = Y), which maintains only transversions and thus efficiently reduces saturations by excluding more frequently occurring transitions 3138. In addition, the effect of heterotachous signal was explored by implementing a covarion model in BI.

Substitutional saturation of the data set was evaluated by plotting observed pairwise distance (uncorrected P-distance) for transitions and transversions against the ML pairwise distances for each pair of taxa. Saturation plots were constructed for total, exon, intron and third codon positions, respectively. Second order polynomial regression lines were fitted to all saturation plots and if the slope of this regression line was zero or negative, the data were considered saturated 78.

The ILD test 79, a character-based test for homogeneity, was used to explore the difference in phylogenetic signal between data partitions. We partitioned the data set by two schemes: four process partitions including intron and each codon positions 80; and 142 gene partitions along gene boundaries, which may reveal variation in allelic histories that the concatenated data might obscure 2676. Then, we performed three kinds of ILD tests for each type of partition: a test among all partitions simultaneously; a test between all possible pairwise partitions; and a test between single partitions and the rest of the data set combined.

To explore the relationship between the number of genes or nucleotides in a sample and the probability to infer the species tree in our case, we drew random samples of different sizes from the original 142-gene data set without replacement and concatenated each sample for phylogenetic analyses. When sampling genes, we generated samples consisting of 20, 40, 60, ..., 120 genes each for 500 replicates. Similarly, samples with randomly sampled sites in a total length of 10, 20, 30, ...100 kb were generated each for 500 replicates. ML and MP methods were used to determine whether or not the sampling results were affected by reconstruction methods. The branch-and-bound search was used in both methods, with the General Time Reversible (GTR)+Γ model for ML. The proportion of trees (or clades) identical to that in Figure 1 was calculated as the probability that a correct phylogenetic hypothesis will be obtained at a specific data size 63.