dataesr/scientific-paragraphs-categorization huggingface dataset:
3 ). In both cases, the durations between speciation events at the base of Ochrophyta are very short (on the left of Fig. 3 ). In the Plastid-Correct (PC) hypothesis (Fig. 3A ), the long branch length of E+SSC is genuine in the plastid dataset (due to an increased evolutionary rate), hence a large λ E +SSC (cp), increasing the amount of phylogenetic signal per position. In addition, as both E and SSC evolved faster, LBA generates a positive non-phylogenetic signal for this grouping, which leads to the correct topology being inferred with very high bootstrap support. In contrast, in the nucleus tree, Pinguiophyceae and SSC evolved faster than E and PXR. Therefore, LBA between Pinguiophyceae and SSC creates a non-phylogenetic signal in favor of the erroneous groupings P+SSC and E+PXR. In the Nucleus-Correct (NC) hypothesis (Fig.
3B ), E and SSC evolved much faster than the other ochrophytes in the plastid dataset, generating a strong LBA artifact (and thus a very negative value of NPS P +SSC (cp | LG 4 X )) that exceeds the genuine P+SSC signal. The nucleus tree was easier to infer, because the fast evolving taxa (P and SSC on one hand and PD and BB on the other) are in this case sister groups, so LBA reinforces the genuine phylogenetic signal. Since both hypotheses imply an erroneous branching due to a high amount of non-phylogenetic signal, distinguishing between them requires estimating whether the unavoidable model violations are sufficient to generate erroneous trees with the plastid or the nucleus datasets. Evidence for the presence of model violations First, we evaluated the impact of major variations of the taxon sampling.
The rationale was to reveal a possible artefact of the tree reconstruction method (i. e. , model violations sufficiently important to make the non-phylogenetic signal stronger than the genuine phylogenetic signal) through the discovery of incongruence between phylogenies inferred from different subsets of species. We investigated two strategies: (1) use of only a distant outgroup (to increase LBA by creating a long unbroken branch) and (2) independant removal of highly supported ochrophyte lineages. We selected the six clades that were strongly supported by the three datasets: Eustigmatophyceae (E), Pinguiophyceae (Ping), SSC clade (represented by SC in the plastid), PXR clade, PD clade and BB clade. Since the phylogenetic signal is more accurately extracted with many taxa, we focus on the analyses with complete (albeit different, see above) taxon sampling.
Taxon sampling variations of the plastid dataset revealed that model violations of LG4X sometimes produced LBA artifacts. This suggested that the non-phylogenetic signal generated by this combination of model and dataset did not often dominate the phylogenetic signal, suggesting that the hypothesis NC may be correct. Yet, it is important to notice that the grouping E+SSC was always observed. Variations of the taxon sampling in the nucleus dataset showed more incompatibilities with the tree inferred from all species (10, in boldface in Table  2 , corresponding to 6 alternative groupings) than in the plastid (only 3). The incompatibilities were more complicated to understand, as the six clades evolved at a more homogeneous rate in the former than in the latter (Fig. 1B-C ). Pinguiophyceae appeared to be the most unstable clade: they emerged as the sister-group to the remaining ochrophytes (BS=100%) when using the distant outgroup, as the sister-group to BB (BS=95%) when removing SSC, and as the sister-group to SSC (BS=100) when removing BB.
Pinguiophyceae were only represented by two closely related species (Phaeomonas and Pinguiococcus), leaving a long unbroken branch at their base (Fig. 1C ). As BB and SSC are the fastest evolving clades in the nuclear dataset, the placement of Pinguiophyceae can be explained by a LBA with the longest branch available in each of the three cases, i. e. , the outgroup, BB, and SSC, respectively. The limited support for Ping+SSC (BS=68%) when using the complete dataset could then result from an average among these contradictory attractions, all the more so that the competing bipartition (32%) is BB+Ping. The removal of PXR, a relatively slowly evolving clade, had the most dramatic effect, all the deep relationships becoming incongruent. It may have allowed the grouping of E+SSC (BS=91%), hence reducing the attraction between SSC and Pinguiophyceae, the latter being then attracted by BB (BS=88%).
Interestingly, E+SSC was also recovered P D F P r o o f : M o l. B i o l. E v o l. through the removal of Pinguiophyceae (BS=56%). Altogether, these results suggest the presence of a high amount of non-phylogenetic signal under the LG4X model and/or a limited genuine phylogenetic signal in the nuclear dataset, thereby supporting hypothesis PC (Fig. 3A ). While taxon sampling variations of the nuclear dataset argued in favor of hypothesis PC, as E+PXR and Ping+SSC groupings failed to be robustly recovered, the plastid dataset also showed incongruence that may instead argue in favor of hypothesis NC. The higher number of incompatibilities observed with the nucleus than the plastid (10 versus 3) indicates an amount of non-phylogenetic signal that is lower in the plastid and/or an amount of genuine phylogenetic signal that is lower in the nucleus dataset (i.
e. , NPS B (nu| LG 4 X)> NPS B (cp | LG 4 X ) and/or λ B (nu)<λ B (cp)), which yields a less reliable tree. For instance, whereas plastid taxon samplings consistently recovered two high-level clades (E+SSC and BB+PD), the nuclear dataset failed to recover any such clade consistently. However, the main result of taxon sampling variations was the evidence for a major impact of model violations with LG4X, especially for the nuclear compartment. These observations are in agreement with the sensitivity to LBA of models that do not fully incorporate the heterogeneity of the substitution process across sites  (Lartillot et al. 2007; Philippe et al. 2011 Philippe et al. , 2019;; Simion et al. 2017). They further suggest that neither the PC nor the NC hypothesis is correct and that we need to use a better model to get insights into the ochrophyte radiation.
Impact of using a better fitting model of sequence evolution We tested two site-heterogeneous models that have been shown to be less sensitive to LBA  (Lartillot et al. 2007 ): the CAT+Γ model implemented in the Bayesian framework  (Lartillot and Philippe 2004 ) and the C20+LG+Γ model, an empirical version of the CAT+Γ model implemented in the maximum likelihood format  (Le et al. 2008). We first compared LG4X to C20+LG+Γ using ModelFinder  (Kalyaanamoorthy et al. 2017 ) from IQ-TREE  (Nguyen et al. 2015) , which showed C20+LG+Γ to be better than LG4X with both the plastid and the nuclear datasets (Supplementary Table  2 ). Second, cross-validation demonstrated CAT+Γ to have a better fit than C20+LG+Γ for both datasets (plastid: likelihood difference between CAT+Γ and C20+LG+Γ of 370 +/-152; nucleus: 488 +/-141).
Consequently, the combination of these two tests showed CAT+Γ to have a better fit than LG4X and C20+LG+Γ for our datasets. Even if CAT+Γ is computationally very demanding (e. g. ,  Philippe et al. 2019) , we were able to compute CAT+Γ bootstrap support for the complete plastid dataset given its moderate size (63 x 21,692). In contrast, this computationally expensive model could not be used on the much larger nuclear dataset (124 x 209,105). To make the analysis tractable, we resorted to a gene jackknife approach instead  (Delsuc et al. 2008). We chose to generate datasets of ~50,000 positions and to run 50 replicates. In the case of LG4X, we verified that the jackknife supports (JS) were comparable with BS, despite being based on ~4 times less positions: as expected, JS values were lower than BS values (Supplementary Table  3 ).
2007 ). In contrast, the topology inferred from the nucleus supermatrix using CAT+Γ (Fig. 4B ) was different from that inferred with LG4X (Fig. 1C ): only the monophyly of BB+PD (JS=76%) was common among the high-level relationships observed between the six major clades. In the CAT+Γ tree, SSC was sister of Eustigmatophyceae (E+SSC; JS=54%) instead of Pinguiophyceae, while the latter group was sister of BB+PD (JS=56%). Finally, PXR was weakly grouped with BB+PD+Ping (JS=32%). Overall, the use of a better fitting model, which likely reduces the nonphylogenetic signal, allows the common recovery of the relationship between Eustigmatophyceae and SSC (E+SSC) by both the plastid and the nucleus datasets, a relationship key to distinguish between the two hypotheses explaining the conflicts observed between the two compartments when using the LG4X model (Fig.
In contrast, the plastid dataset has never recovered BB+PD+Ping. Despite the use of fewer sites (50,000) than LG4X (i. e. , increased stochastic error), CAT+Γ thus turned out to be more robust to taxon sampling variations, thereby demonstrating its success in reducing the amount of non-phylogenetic signal. We then estimated the performance of the computationally more efficient, but more poorly fitting, site-heterogeneous model C20+LG+Γ. As expected from its intermediate fit between LG4X and CAT, the impact of taxon sampling (Supplementary Table  4 ) was intermediate: 4 incongruences for the plastid and 3 for the nucleus with C20+LG+Γ (to compare with 3 and 10 for LG4X and 1 and 4 for CAT). Importantly, only one grouping, BB+PD, was consistently recovered in all experiments. While E+SSC was always recovered by the plastid dataset, the nucleus dataset found it in only one case (after removal of PXR) and generally grouped Eustigmatophyceae with PXR and SSC with Pinguiophyceae.
The heterogeneities of the functional constraints across sites in phylogenomic datasets are probably too important for being handled by only tens of categories. As a result, although C20/C60+LG+Γ are the best fitting models under ML and can be used with the complete dataset, the CAT+Γ model appeared as the most suitable to accurately address the difficult question of the Ochrophyta radiation. Reducing the non-phylogenetic signal favored one facet of hypothesis PC (Fig. 3A ), i. e. , the grouping of Eustigmatophyceae and SSC is correct and more highly supported in the plastid than in the nucleus compartment because of an acceleration of the substitution rate (and thus of λ E +SSC (cp)) in the branch at the base of E+SSC in plastid loci. First, E+SSC was always recovered by the two compartments for sixteen (2*8) different taxon sampling variations.
Second, this relationship is also supported by a common split of the plastid encoded gene clpC, which is involved in the protein degradation pathway mediated by the ClpP protease  (Ševčíková et al. 2015). Third, we observed five common losses of plastid genes in these two clades (ATP synthase CF1 delta subunit, hypothetical protein Ycf39/Isoflavone reductase, PSI reaction center subunit XII, hypothetical protein Ycf35 and cytochrome b6-f complex subunit 6/petL; data not shown), although we cannot exclude convergence since the plastid genome is reduced in both cases. Overall, our experiments proved that decreasing the non-phylogenetic signal through selection of a better fitting model reduced incongruence and increased robustness to taxon sampling variations. Although only two (BB+PD and E+SSC) high-level relationships out of four were consistently recovered in the case of Ochrophyta, the use of the CAT+Γ model demonstrated the key importance of adequately handling the non-phylogenetic signal when trying to resolve ancient radiations.
However, testing the potential of such an approach is possible by assuming the knowledge of the correct phylogeny. More precisely, we can estimate branch lengths for each gene, constrained to a candidate topology, and select those displaying the longest (or shortest) length for the branch of interest. Finally, we can infer a phylogeny using a concatenation of the resulting set of markers and compare it to the phylogeny obtained without such a selection to study the effect of filtering the dataset by the signal of interest. We applied this protocol, using the LG4X model, to the nucleus dataset by selecting the 200 genes with the longest internal branch at the base of E+SSC, yielding a supermatrix of 47,386 positions (LONGnu) and, as a negative control, the 200 genes with the shortest internal branch, yielding a supermatrix of 39,867 positions (SHORTnu).
Not surprisingly, the phylogeny inferred from SHORTnu with the LG4X model (Supplementary Figure  5A ) did not recover E+SSC, but strongly grouped Pinguiophyceae and SSC (BS=96%) and Eustigmatophyceae and PXR (BS=100%), in agreement with the topology observed with the full dataset (Fig. 1C ). In the absence of a strong genuine phylogenetic signal (for E+SSC), the misleading non-phylogenetic signal dominated, and the apparent phylogenetic signal for two erroneous groupings (P+SSC and E+PXR) increased, despite the use of a much smaller dataset (BS rose from 68/81 to 96/100, respectively). Note that a zero branch length might also be due to the fact that a locus has a different history (e. g. , due to hybridization or ILS), amounting to the branch being non-existent. When the time separating two nodes is very short, the probability to observe at least one substitution in the corresponding branch is proportional to the size of the genes.
We therefore expect the genes having a very short branch length to be shorter in terms of positions than the ones with a long branch. This prediction is fulfilled (200 versus 238 positions on average, Mann-Whitney test p-value of 0. 017), suggesting that rate variation and short gene length rather than different history are the main causes of the observed short branch lengths. In contrast, the phylogeny inferred from LONGnu with LG4X (Supplementary Figure  5B ) strongly supported E+SSC (BS=100%) with the same complete taxon sampling. This suggests that the genuine phylogenetic signal was now stronger than the non-phylogenetic signal created by the serious violations affecting this model, thereby leading to a strong apparent signal in favor of E+SSC. As the full dataset did not support E+SSC, under the assumption that the non-phylogenetic signal per site generated by the use of LG4X is the same for all genes, the non-phylogenetic signal produced over 209,105 positions is probably stronger than the corresponding signal in the 47,386 positions of the LONGnu set of genes.
This protocol cannot be used to resolve radiations, because it assumes the species phylogeny to be known, but it can be used to reveal the contradictory attractions present in a large dataset (here SSC attracted either by Pinguiophyceae or Eustigmatophyceae), these attractions stemming either from model violations or from the genuine (historical) signal. More importantly, it validates the idea of looking for innovative methods to detect genes with a high signal for internal nodes of a species phylogeny, disregarding the global topologies of the gene trees. Such approaches could be another avenue to alleviate the impact of model violations when trying to resolve radiations, without designing ever-more complex evolutionary models.
Towards resolving the Ochrophyta phylogeny Our analysis showed that the resolution of the deep ochrophyte relationships was extremely difficult, because of short internal branches and serious model violations. Interestingly, the small plastid dataset appeared to contain a relatively large amount of phylogenetic signal, in particular because of its high value of λ E +SSC (cp). Since the CAT+Γ model did not show evidence of a strong non-phylogenetic signal for the nucleus or the plastid, it should be interesting to combine the high number of positions of the nucleus and the high λ of the plastid to increase the apparent phylogenetic signal of the ochrophyte radiation. Indeed, by combining the plastid and nuclear datasets, we should lengthen at least one of the difficult branches, i. e. , λ E +SSC (nu+ cp)> λ E+ SSC ( nu), thus making the problem easier to resolve for any method of phylogenetic inference.
However, there are potential drawbacks to this approach, such as the fact that combining those datasets would reduce the taxon sampling down to 23 common species, along with the potential introduction of additional model violations (in particular branch length heterogeneity across compartments) (Kolaczkowski and Thornton 2004). Nevertheless, reducing the number of species allowed us to use more sites (80,000) with the best fitting model (CAT). Such a combined phylogeny inferred with the nu+cp supermatrix using the CAT+Γ model (Fig. 5 ) showed a much higher support for deep ochrophyte relationships: BB+PD (JS=100%), BB+PD+Ping (JS=100%), E+SSC (JS=99%) and E+PXR+SSC (JS=90%). Interestingly, the nu+cp phylogeny (Fig. 5 ) is different from both the plastid (Fig. 4A ) and the nucleus (Fig. 4B ) trees.
Studies are thus needed to evaluate what are the best compromises between the number of species and the complexity of models to optimize the reduction of the non-phylogenetic signal. The reduction of model violations achieved when dropping LG4X in favor of the CAT+Γ model allowed us to reduce the incongruence revealed by taxon sampling variations and improve the resolution of the ochrophyte radiation, especially for the nucleus dataset. However, the CAT+Γ model is still far from perfect. For instance, it does not take into account the genetic code to weigh amino acid substitutions (see  Rodrigue et al. 2010) , and it assumes that the evolutionary process is the same all over the phylogeny (e. g. , ignoring compositional biases, heterotachy or heteropecilly). These simplifications are bound to result in model violations that could lead to an incorrect phylogeny.
In addition to the number of positions and the reduction of model violations, the strength of the apparent phylogenetic signal is also dependent on branch length. The length of a given branch is variable across loci, e. g. , being longer at a locus that underwent reduced purifying selection or directional selection. In the case of the plastid dataset, we were lucky to have had a large number of loci that underwent a substitution rate acceleration in the E+SSC basal branch. This acceleration likely explains the observation that the small plastid dataset (21,692 positions) is able to strongly recover the monophyly of this clade otherwise very difficult to resolve, whereas the large nuclear dataset (209,105 positions) cannot. The difference was more pronounced with the LG4X model than with the CAT+Γ model, probably because the long branches of Eustigmatophyceae and SSC were further artifactually attracted.
This "lucky" rate acceleration suggests a new approach to resolve ancient radiations: searching for loci having accelerated in the short internal branches of interest, so as to facilitate extraction of a signal that is scarce for other, more regular, loci. Finally, combining the nuclear and plastid datasets, along with the use of the CAT+Γ model, helped us to simultaneously increase n and λ and decrease model violations, leading to a well-supported tree, robust to taxon sampling variations. Given the difficulties to resolve the ochrophyte radiation, this phylogeny needs to be confirmed with a richer taxon sampling and/or with a better model. It nevertheless constitutes a working hypothesis to understand in which order the remarkably diverse phenotypes of Ochrophyta emerged, from the picoplanktonic Nannochloropsis to the silica frustule-bearing diatoms and to giant marine kelps.
Creation of phylogenomic datasets For each compartment, we assembled the datasets following a semi-automatic protocol similar to the one described in our previous phylogenomic studies  (Simion et al. 2017 , Irisarri et al. 2017). In summary (see Figure  1  of  Simion et al. for an overview and https://github. com/psimion/SuppData_Metazoa_2017/blob/master/utilities_src. tgz f o r software availability), we used protein annotations obtained from genomic data to define orthologous groups with OrthoFinder version 1. 4  (Emms and Kelly 2015). Sequence similarity matrices were computed with BLAST for mitochondrial and plastid datasets and with USEARCH  (Edgar 2010)  for the nuclear dataset (e-value threshold = 1e-5) before being divided with the MCL algorithm using the default inflation value (1.
5). We filtered the resulting orthogroups for minimal taxonomic representation before validating their orthology relationships. Then we improved their taxon sampling by adding species from transcriptomic and genomic data using Forty-Two (https://metacpan. org/dist/Bio-MUST-Apps-FortyTwo). Detailed description for each compartment, as well as on the computational treatments undertaken to remove paralogous and xenologous sequences from the multiple sequence alignments, can be found in the Supplementary Information. In particular, we used the Branch Length Correlation (BLC) method  (Simion et al. 2017 ) to detect and remove outlier genes. Finally, our analyses focused on the three datasets summarised in Table  1  and available at https://doi. org/10. 6084/m9. figshare. 7680395. v2.
Phylogenetic inferences All supermatrices used in our analyses were concatenated using SCaFoS  (Roure et al. 2007). We inferred phylogenetic trees using RAxML version 8. 2  (Stamatakis 2014)  with the LG4X mixture model  (Le et al. 2012 ) using 100 fast bootstrap replicates. Inferences under the C20+LG+Γ and C60+LG+Γ models were carried out using IQ-TREE 1. 6. 8 (Nguyen et al. 2015). Inferences under the CAT+Γ mixture model  (Lartillot and Philippe 2004)  were carried out using PhyloBayes-MPI version 1. 8  (Lartillot et al. 2013) , either on bootstrap replicates for mitochondrial and plastid datasets or on gene jackknife replicates for the nucleus dataset. Preliminary analyses demonstrated that convergence was not reachable for a dataset of 124 species and 209,105 amino-acid positions with the current implementation of PhyloBayes-MPI.
VLB analyses We reduced each dataset to an ingroup taxon sampling of 22 comparable species (21 for the mitochondrion as one out of four Pelagophyceae species was missing), i. e. , identical or closely related (Supplementary Table  8 ). For the outgroup, we used Guillardia theta for the plastid and Phytophthora sojae for the mitochondrion and Phytophthora parasitica for the nucleus. We used distinct species to have a similar branch length leading to the outgroup in each compartment, whereas using the same species (e. g. , G. theta) would have generated a much longer branch in the mitochondrion/nucleus than in the plastid. Out of the three resulting supermatrices, we drew 1000 variable length bootstrap (VLB) replicates of different sizes  (100, 250, 500, 1000, 1500, 2000, 2500 sites)  and 100 replicates of 5000 sites using seqboot from the PHYLIP package  (Felsenstein 1989 ).
Model comparison AIC, AICc and BIC between LG4X and GTR+Γ4 models were computed using ModelFinder  (Kalyaanamoorthy et al. 2017 ) from IQ-TREE version 1. 6. 8 (Nguyen et al. 2015) , with the constrained topology previously obtained under the LG4X model with RAxML. Crossvalidations between GTR+Γ4 and CAT+Γ4 were carried out using PhyloBayes version 4. 1. For both plastid and nuclear datasets, ten training datasets of 10,000 positions were used, and likelihoods were computed on ten test datasets of 2,000 positions. F P r o o f : M o l. B i o l. E v o l. P D F P r o o f : M o l. B i o l. E v o l.
Acknowledgments We thank  Zehra Çebi  for growing up algal strains and for extraction of DNA, and  Paul Simion  and  Rik Verdonck  for critical reading of the manuscript. Sequencing was carried out by the  Cologne Center for Genomics (CCG). Computations were performed on the supercomputers Mp2 and Ms2 from the  Université de Sherbrooke , managed by  Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the  Canada Foundation for Innovation (CFI) , the  ministère de l'Économie, de la science et de l'innovation du Québec (MESI) , and the  Fonds de recherche du Québec -Nature et technologies (FRQ-NT). This work was supported by the  TULIP Laboratory of Excellence  ( ANR-10-LABX-41 ).