Adrián A Davín

Eric Tannier

Tom A Williams

Bastien Boussau

Vincent Daubin
email: vincent.daubin@univ-lyon1.fr

Gergely J Szöllősi

Gene transfers can date the Tree of Life

Biodiversity has always been predominantly microbial and the scarcity of fossils from bacteria, archaea and microbial eukaryotes has prevented a comprehensive dating of the tree of life. Here we show that patterns of lateral gene transfer deduced from the analysis of modern genomes encode a novel and abundant source of information about the temporal coexistence of lineages throughout the history of life. We use new phylogenetic methods to reconstruct the history of thousands of gene families and demonstrate that dates implied by gene transfers are consistent with estimates from relaxed molecular clocks in Bacteria, Archaea and Eukaryotes. An inspection of discrepancies between transfers and clocks and a comparison with mammal fossils show that gene transfer in microbes is potentially as informative for dating the tree of life as the geological record in macroorganisms.

Until Zuckerkandl and Pauling put forth the "molecular clock" 1 hypothesis, the geological record alone provided the timescale for evolutionary history. Their demonstration that distances between amino acid sequences correlate with divergence times estimated from fossils demonstrated that information in DNA can be used to date the Tree of Life. Since then, the theory and methodology of the molecular clock have been developed extensively, and inferences from clock analyses (such as the diversification of placentals before the demise of dinosaurs [START_REF] Dos Reis | Phylogenomic datasets provide both precision and accuracy in estimating the timescale of placental mammal phylogeny[END_REF][START_REF] O'leary | The placental mammal ancestor and the post-K-Pg radiation of placentals[END_REF] ) hotly debated. Despite these controversies, combining information from rocks and clocks is now widely accepted to be indispensable [START_REF] O'leary | The placental mammal ancestor and the post-K-Pg radiation of placentals[END_REF][START_REF] Donoghue | Rocks and clocks: calibrating the Tree of Life using fossils and molecules[END_REF][START_REF] Yang | Dating species divergences using rocks and clocks[END_REF] : state-of-the-art estimates of divergence times rely on sequence based relaxed molecular clocks anchored by multiple fossil calibrations. This approach provides information on both the absolute timescale and the relative variation of the evolutionary rates across the phylogeny (Fig. 1a). Yet, because most life is microbial, and most microbes do not fossilize, major uncertainties remain about the ages of microbial groups and the timing of some of the earliest and most important events in life's evolutionary history [START_REF] Knoll | The Fossil Record of Microbial Life[END_REF][START_REF] Knoll | Paleobiological perspectives on early eukaryotic evolution[END_REF] .

In addition to leaving only a faint trail in the geological record, the evolution of microbial life has also left a tangled phylogenetic signal due to extensive lateral gene transfer (LGT). LGT, the acquisition of genetic material potentially from distant relatives, has long been considered an obstacle for reconstructing the history of life [START_REF] Doolittle | Phylogenetic Classification and the Universal Tree[END_REF] , because different genetic markers can yield conflicting estimates of the species phylogeny. However, it has been previously shown that transfers identified using appropriate phylogenetic methods carry information that can be harnessed to reconstruct species history [START_REF] Abby | Lateral gene transfer as a support for the tree of life[END_REF][START_REF] Szöllősi | Phylogenetic modeling of lateral gene transfer reconstructs the pattern and relative timing of speciations[END_REF][START_REF] Williams | Integrative modelling of gene and genome evolution roots the archaeal tree of life[END_REF][START_REF] Huang | Ancient gene transfer as a tool in phylogenetic reconstruction[END_REF][START_REF] Huang | The presence of a haloarchaeal type tyrosyl-tRNA synthetase marks the opisthokonts as monophyletic[END_REF][START_REF] Wolfe | Tunneling through time: Horizontal gene transfer constrains the timing of methanogen evolution[END_REF] . This is possible because different hypotheses of species relationships yield different LGT scenarios and can thus be evaluated using phylogenetic models of genome evolution [START_REF] Maddison | Gene Trees in Species Trees[END_REF][START_REF] Szöllősi | Modeling Gene Family Evolution and Reconciling Phylogenetic Discord[END_REF][START_REF] Sjöstrand | A Bayesian method for analyzing lateral gene transfer[END_REF][START_REF] Szöllősi | The Inference of Gene Trees with Species Trees[END_REF][START_REF] Daubin | Horizontal Gene Transfer and the History of Life[END_REF] . But in addition to carrying information about the relationships among species, transfers should also carry a record of the timing of species diversification because they have occurred between species that existed at the same time [START_REF] Gogarten | Horizontal gene transfer: pitfalls and promises[END_REF][START_REF] Szöllősi | Phylogenetic modeling of lateral gene transfer reconstructs the pattern and relative timing of speciations[END_REF][START_REF] Szöllősi | Lateral Gene Transfer from the Dead[END_REF] . As a consequence, a transfer event can be used to establish a relative age constraint between nodes in a phylogeny independently of any molecular clock hypothesis: the ancestor node of the donor lineage must predate the descendant node of the receiving lineage (Fig. 1b, Fig. S8). Below we show that the dating information carried by transfers is consistent with molecular clock based estimates of relative divergence times in representative groups from the three domains of life.

Figure 1. Gene transfers, like fossils, carry information on the timing of species divergence: a)

The geological record provides the only source of information concerning absolute time: the age of the oldest fossil representative of a clade provides direct evidence on its minimum age, but inferring maximum age constraints (e.g. dashed line for the red clade), and by extension the relative age of speciation nodes, must rely on indirect evidence on the absence of fossils in the geological record [START_REF] Yang | Dating species divergences using rocks and clocks[END_REF][START_REF] Dufresne | Accelerated evolution associated with genome reduction in a free-living prokaryote[END_REF][START_REF] Benton | Paleontological evidence to date the tree of life[END_REF][START_REF] Dos Reis | Bayesian molecular clock dating of species divergences in the genomics era[END_REF] . b) Gene transfers, in contrast, do not carry information on absolute time, but they do define relative node age constraints by providing direct evidence for the relative age of speciation events: the gene transfer depicted by the black arrow implies that the diversification of the blue donor clade predates the diversification of the red clade (i.e. node D is necessarily older than node R). c) Sequence divergence (here measured in units of expected number of nucleotide substitutions along a strict molecular clock time tree, see supplementary materials) for 36 mammals 2 is correlated (Pearson's R 2 =0.664, p<10 -2 ) with age estimates based on the fossil record (ages corresponding to the time of divergence in million years). d) A similar relationship can be seen for gene transfer based relative ages by plotting the sequence divergence (measured similar to part c) against the relative age of ancestral nodes for 40 cyanobacterial genomes (Spearman's rank correlation rho=0.741, p<10 -6 ) inferred by the MaxTiC (maximal time consistency) algorithm [START_REF] Chauve | MaxTiC: Fast Ranking Of A Phylogenetic Tree By Maximum Time Consistency With Lateral Gene Transfers[END_REF] .

We examined genome-scale datasets consisting of homologous gene families from complete genomes in Cyanobacteria (40 genomes [START_REF] Szöllősi | Genome-scale phylogenetic analysis finds extensive gene transfer among fungi[END_REF] ), Archaea (60 genomes [START_REF] Williams | Integrative modelling of gene and genome evolution roots the archaeal tree of life[END_REF] ) and Fungi (60 genomes [START_REF] Nagy | Latent homology and convergent regulatory evolution underlies the repeated emergence of yeasts[END_REF] ). For each gene family we used the species tree-aware probabilistic gene tree inference method ALE undated [START_REF] Szöllősi | Genome-scale phylogenetic analysis finds extensive gene transfer among fungi[END_REF][START_REF] Szöllősi | Efficient exploration of the space of reconciled gene trees[END_REF] to sample evolutionary scenarios involving events of duplication, transfer and loss of genes conditional on a rooted species phylogeny and the multiple sequence alignment of the family. The undated reconciliation method does not impose any constraint on possible donor-recipient branch pairs aside from forbidding transfers to go from descendants to parents (Fig. S9). For putative gene transfer events, we recorded the donor and recipient branches and used the frequency with which they occurred among the sampled scenarios to filter transfers and weigh the relative age information they imply. Because the reference species tree is not dated, individual transfers can imply conflicting information about the relative age of speciation nodes (Fig. S11). To extract a maximal subset of transfers consistent with each other, we used the newly developed optimization method MaxTiC [START_REF] Chauve | MaxTiC: Fast Ranking Of A Phylogenetic Tree By Maximum Time Consistency With Lateral Gene Transfers[END_REF] (maximal time consistency, see also supplementary text). A maximal subset of consistent transfers specifies a time order of speciation events in the species tree. For instance, using MaxTiC on the 4816 transfers that correspond to relative age constraints (see Figs 1b, S8, S10) in the 5322 gene families considered for Cyanobacteria, we identified a maximal subset of 3322 (69%) transfers that are consistent (Table S1). This maximal subset of transfers implies a time order of speciations that correlates with the distance between amino acid sequences of extant organisms (Spearman's ρ = 0.741; p < 10 -6 ; Fig. 1d,S9). A similar correlation (Fig. 1c) can be observed if, following Zuckerkandl and Pauling 1 , we compare fossil dates and sequence divergence in mammals 2 (10 time points, Pearson's R 2 =0.664; p = 0.0025 and Spearman's ρ = 0.83; p = 0.0056).

We observed a strong correlation between time estimates from MaxTiC and molecular clocks in all our datasets (p<10 -3 -Fig S14 -S16). This suggests that LGT indeed carries information on the relative age of nodes in all three domains of life. However, it is not conclusive because part of the correlation trivially results from the fact that parent nodes are necessarily both older and more distant to extant sequences than their direct descendants [START_REF] Felsenstein | Phylogenies and the Comparative Method[END_REF] . To control for this effect, we compared the relative time orders of speciation events inferred from transfers to dates obtained using molecular clocks in the absence of calibrations. We used Phylobayes 32 on a concatenate of nearly universal gene family alignments to sample chronograms (i.e., dated trees) under four different uncalibrated molecular clock models [START_REF] Lartillot | PhyloBayes 3: a Bayesian software package for phylogenetic reconstruction and molecular dating[END_REF] (the strict molecular clock, the autocorrelated lognormal, the uncorrelated gamma and the white-noise model). As a control for the shape of the tree, we measured the random expectation by sampling chronograms from the prior on divergence times but keeping the species phylogeny fixed (without any sequence information). To compare the dating information from transfers to the information conveyed by fossils, we used the same uncalibrated approach on the same mammalian dataset as above [START_REF] Dos Reis | Phylogenomic datasets provide both precision and accuracy in estimating the timescale of placental mammal phylogeny[END_REF][START_REF] Lepage | A General Comparison of Relaxed Molecular Clock Models[END_REF] and derived relative node age constraints from fossil calibrations (see supplementary text). For the prokaryotic and fungi datasets, we derived relative node age constraints from the maximal consistent subsets of transfers obtained using MaxTiC [START_REF] Chauve | MaxTiC: Fast Ranking Of A Phylogenetic Tree By Maximum Time Consistency With Lateral Gene Transfers[END_REF] . For both fossil-and transfer-based constraints, we then measured the fraction of constraints that are in agreement with each chronogram. As Fig. 2 shows, both fossil-and transfer-based constraints agree with uncalibrated molecular clocks significantly more than expected by chance. The observed agreement is robust to the choice of different clock models (Fig. 2), priors on divergence time and models of protein evolution (Figs. S17-S19). This result demonstrates the presence of genuine and substantial dating signal in gene transfers.

Figure 2. Agreement between transfer based relative ages and molecular clocks: a)

Relative ages derived from 12 fossil calibrations from a phylogeny of 36 extant mammals were compared with node ages sampled from four different relaxed molecular clock models implemented in Phylobayes and with node ages derived from random chronograms, keeping the species phylogeny fixed. b-d) Relative ages derived from gene transfers using the MaxTiC algorithm were compared with estimates from the same 5 models as in a). For each model and each sampled chronogram we calculated the fraction of relative age constraints that are satisfied. On each plot, we show the distribution of the fraction of relative age constraints satisfied by 5000 sampled chronograms. The blue distribution corresponds to chronograms drawn from the prior with the 95% confidence interval denoted by dashed lines, orange to the strict molecular clock, purple to the autocorrelated lognormal, green to the uncorrelated gamma and grey to the white-noise models.

Interestingly, molecular clock models show differences in their agreement with relative time constraints. As expected, the strict molecular clock model generally explores a narrow range of dated trees compared to relaxed clocks. However, on average, chronograms based on the strict molecular clock agree less with relative time constraints than those based on relaxed clock models. This is particularly clear in mammals, where the median fraction of satisfied constraints falls within the 95% confidence interval of the random control (Fig. 2a). This is caused, in large part, by the accelerated evolutionary rate in rodents being interpreted (in the absence of fossil calibrations) as evidence for an age older than that implied by fossils (Fig. S4). The lognormal model is best suited to recover such autocorrelated (e.g. clade specific) rate variations along the tree, and indeed exhibits a median of 100% agreement with fossil based relative age constraints. The uncorrelated gamma model performs

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Fraction of relative age constraints satisfied Archaea (60 genomes, Williams) second best, perhaps because it is, in fact, autocorrelated along each branch [START_REF] Lepage | A General Comparison of Relaxed Molecular Clock Models[END_REF] . Consistent with this idea, the completely uncorrelated white noise model fares worst (Fig. 2a-d). This is in agreement with previous model comparisons in eukaryotes, vertebrates and mammals [START_REF] Lepage | A General Comparison of Relaxed Molecular Clock Models[END_REF] . A similar pattern is apparent when considering LGTderived relative age constraints in Cyanobacteria, Archaea and Fungi, suggesting strong autocorrelated variation of evolutionary rates in these groups that are best recovered by the lognormal model (Fig. 2b-d).

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The motivating principle of the MaxTiC algorithm is that transfers from the maximum consistent set carry a robust and genuine dating signal, while conflicting transfers are likely artefactual. Two lines of evidence suggest that this is indeed the case: first, the agreement of relative time constraints derived from transfers excluded by MaxTiC with the node ranking inferred by uncalibrated molecular clocks tends to be lower than random (Fig. S12). Second, while the average sequence divergences for donor clades tend to be higher than for corresponding recipient clades in the set of self-consistent transfers (p < 10 -8 one sided T-test for difference greater than zero, see Fig. 3.), they are lower for those discarded by MaxTiC (p < 10 -8 one sided T-test for difference lower than zero, cf. Fig. 3).

Figure 3. For genuine

LGTs, the donor lineage must be at least as old as the recipient. As one proxy to investigate whether this was the case for transfers retained by our MaxTiC algorithm, we calculated clade-to-tip distances (see methods) for the inferred donor and recipient clades for LGTs that were retained and discarded by MaxTiC. (a) In all three datasets, transfers retained by MaxTiC (in red above) have the property that donor clades are further from the tips of the tree than recipient clades, but the opposite pattern is observed for conflicting transfers rejected by MaxTiC (green above), consistent with the idea that MaxTiC distinguishes genuine LGTs from phylogenetic artifacts.

One obvious difference between fossil-and transfer-based relative ages in Fig. 2 is that the level of agreement is patently lower for the latter. While in mammals approximately half of the chronograms proposed by the lognormal model agree with 100% of relative constraints, for other datasets no model reaches 80% agreement. This means that some relative constraints derived from LGT consistently disagree with uncalibrated molecular clock estimates. These disagreements are difficult to interpret because both molecular clocks and our transferbased inferences may be subject to error; simulations suggest that spurious gene transfer inferences do occur with ALE, albeit at a low rate (Chauve et al. [START_REF] Chauve | MaxTiC: Fast Ranking Of A Phylogenetic Tree By Maximum Time Consistency With Lateral Gene Transfers[END_REF] , Fig. S23). Nonetheless this low error rate on simulations

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Cyanobacteria Archaea Fungi d[donor]-d[recipient] d=clade-to-tip divergence

Retained Discarded

Cyanobacteria

Archaea Fungi

d donor d recepient [subs. per site]
suggests that at least some transfers contradicting the molecular clocks are genuine. This yields the exciting idea of a new source of dating information, independent of and complementary to the molecular clock.

To gain further insight into the robustness of these transfer-based estimates, we evaluated their statistical support from the data. Since MaxTiC yields a fully ordered species tree, the relative age constraints derived from its output are potentially overspecified and include constraints with relatively low statistical support. To ascertain the extent of overspecification, we evaluated the statistical support of relative constraints by taking random samples of 50% of gene families and reconstructing the corresponding MaxTiC 1000 times (Figs. S20-S22). We then counted the number of times a constraint was observed. In all datasets, a large majority of constraints were highly supported (found in at least 95% of the replicates) and among these, a significant number (between 20% and 32%) consistently disagreed with molecular clock estimates (see Table S2). These strongly-supported transfer-based constraints that disagree with the clocks could result from the inability of uncalibrated molecular clock estimates to recover the correct timing of speciations in groups with large variations in the substitution rate over time.

Specifically, LGTs provide strong support for the relatively recent emergence of the Prochlorococcus -Synechococcus clade in Cyanobacteria (blue clade in Fig. 4a), irrespective of uncertainty in the root of Cyanobacteria (see Supp. Mat.). Although the Prochlorococcus -Synechococcus clade is inferred to be ancient by three of the four uncalibrated molecular clock models in our study, previous analyses using relaxed molecular clock methods with more extensive species sampling and several fossil calibrations, including fossils dating akinete forming cyanobacteria at ~2.1 Gya 36 (green in Fig. 4.a) have consistently dated this clade as younger than most of the rest of cyanobacterial diversity [START_REF] Blank | Timing of morphological and ecological innovations in the cyanobacteria â a key to understanding the rise in atmospheric oxygen[END_REF][START_REF] Shih | Crown group Oxyphotobacteria postdate the rise of oxygen[END_REF] . Prochlorococcus have a known history of genome reduction and evolutionary rate acceleration [START_REF] Dufresne | Accelerated evolution associated with genome reduction in a free-living prokaryote[END_REF] , which may lead to artifactually ancient age inferences under uncalibrated molecular clock models, as for rodents above. This demonstrates that relative time orders implied by LGT can, like fossils, provide a consistent dating signal that is independent of the rate of sequence evolution. LGT-based constraints were sampled per data set (a: Cyanobacteria, b: Archaea, c: Fungi). The black line corresponds to the consensus chronogram. Red shading represents the spread of node orders within the sample: nodes are in bright red if there is little or no uncertainty on their order according to LGT, in a light red smear if there is high uncertainty on their order. Clades discussed in the text are labelled and shaded. Supplementary Figures S1,S2 and S3 provide the same consensus chronograms with species names at the tips.

Euryarchaeota

In Archaea, patterns of LGT suggest that several nodes within the Euryarchaeota including cluster 1 and 2 methanogens (blue and purple clades in Fig. 4) are older than both the TACK+Lokiarchaeum clade (red clade in Fig. 4, the clade uniting Thaumarchaeota, Crenarchaeota, Aigarchaeota, Korarchaeota and Lokiarchaeum) and the DPANN Archaea (grey in Fig. 4, a genomically diverse group with small cells and genomes, with reduced metabolism suggestive of symbiont or parasite lifestyles). The relative antiquity of methanogens is consistent with evidence of biogenic methane at a very early stage of the geological record (~3.5 Gya 39 ), and with another recent analysis that used a single LGT to place the origin of methanogens before the radiation of Cyanobacteria 14 . These relationships are not recovered by any of the molecular clock models, and suggest that LGT-derived constraints may be highly informative for future dating studies.

The relative order of appearance of archaeal energy metabolisms corresponds to increasing energy yield, with methanogenesis evolving before sulphate reduction, and the oxidative metabolisms of Thaumarchaeota and Haloarchaea evolving most recently. In addition, we find that Ignicoccus hospitalis branches before its obligate parasite Nanoarchaeum (cf. Fig. S2), despite the early divergence of the DPANN clade from other Archaea.

In Fungi, we recover LGTs that provide information on the order of some of the deepest splits. In particular, among crown groups, LGTs indicate that Zoopagomycota 40 (blue in Fig. 4) diverged earlier than Mucoromycotina, Basidiomycota and Ascomycota (purple, grey and green in Fig. 4). Note that some inferred

LGTs could result from processes such as hybridisation or allopolyploidisation, and that these processes contribute dating information that can be treated in the same way as LGTs. On a wider scale, between Eukaryotic groups, LGTs suggest that Amoebozoa (the outgroup, yellow in Fig. 4) diversified earlier than Opisthokonta and Apusozoa (the ingroup). This indicates that LGTs could strongly reduce the uncertainty associated with the divergence of the major eukaryotic clades [START_REF] Eme | On the age of eukaryotes: evaluating evidence from fossils and molecular clocks[END_REF] .

Our demonstration that clocks and transfers contain complementary and compatible dating signals casts the phylogenetic discord of LGT in a new light. This calls for the development of new methods to combine relative age constraints derived from transfers with molecular clocks and fossils calibrations. In principle, such a method can be developed by extending current Bayesian relaxed molecular clocks to include a prior on relative age constraints, as is now done with fossil calibration priors. An alternative approach would be to jointly infer a dated species tree together with thousands of dated and reconciled gene trees in the context of a hierarchical probabilistic model [START_REF] Szöllősi | The inference of gene trees with species trees[END_REF] ; this approach would be theoretically superior, but likely computationally prohibitive at the present time [START_REF] Szöllősi | The inference of gene trees with species trees[END_REF] .

The geological record of microbial life is sparse, and its interpretation is fraught with difficulty. Our results show that there is abundant information in extant genomes on dating the Tree of Life waiting to be harvested from the reconstruction of genome evolution. This signal mostly contains information on the relative timing of diversification of groups that have exchanged genes through LGT, but we foresee several strategies to relate this relative timing to the broader history of life on Earth. First, gene transfers between bacteria and multicellular organisms that have left a trace in the fossil record will allow the propagation of absolute time calibrations to the microbial part of the Tree of Life [START_REF] Wybouw | A gene horizontally transferred from bacteria protects arthropods from host plant cyanide poisoning[END_REF] . Similarly, the signal of coevolution between hosts and their symbionts, such as in the gut microbiome of mammals [START_REF] Groussin | Unraveling the processes shaping mammalian gut microbiomes over evolutionary time[END_REF] , could also be used to propagate absolute dating information from the host to the symbiont phylogeny. Finally, geochemistry can provide major constraints on early evolution [START_REF] Knoll | Life: the first two billion years[END_REF][START_REF] Wolfe | Tunneling through time: Horizontal gene transfer constrains the timing of methanogen evolution[END_REF] : for example, LGT events to the ancestors of bacteria capable of oxygenic photosynthesis, i.e. Oxyphotobacteria [START_REF] Soo | On the origins of oxygenic photosynthesis and aerobic respiration in Cyanobacteria[END_REF] , imply that the donor lineages must be older than the oxygenation of Earth's atmosphere at approximately 2.3 Gya [START_REF] Knoll | Life: the first two billion years[END_REF][START_REF] Wolfe | Tunneling through time: Horizontal gene transfer constrains the timing of methanogen evolution[END_REF] . Phylogenetic models of genome evolution have the potential to turn the phylogenetic discord caused by gene transfer into an invaluable source of information on dating the tree of life.

Figure 4 .

 4 Figure 4. The order of speciations according to LGT. 5000 chronograms with a speciation time order compatible withLGT-based constraints were sampled per data set (a: Cyanobacteria, b: Archaea, c: Fungi). The black line corresponds to the consensus chronogram. Red shading represents the spread of node orders within the sample: nodes are in bright red if there is little or no uncertainty on their order according to LGT, in a light red smear if there is high uncertainty on their order. Clades discussed in the text are labelled and shaded. Supplementary FiguresS1, S2and S3 provide the same consensus chronograms with species names at the tips.

36 species, Dos Reis)

		Mammals (
	Fraction of relative age constraints satisfied	7 0.8 0.9 1.0

Acknowledgements

G.J.Sz. received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No. 714774. This project was supported by the French Agence Nationale de la Recherche (ANR) through grant no. ANR-10-BINF-01-01 'Ancestrome'. Computations were made using the Curie supercomputer thanks to PRACE project 2013081661 and the computing facilities of the CC LBBE/PRABI. T.A.W. is supported by a Royal Society University Research Fellowship. We thank N. Lartillot, T. Warnow, M. Paris, I. Derényi and J. Miguel Blanca Postigo for useful discussions, comments on the manuscript and further computing resources.


Yves Laprie
email: yves.laprie@loria.fr

Benjamin Elie L2s
email: benjamin.elie@loria.fr

Centralesupélec

Anastasiia Tsukanova
email: anastasiia.tsukanova@loria.fr

Pierre-André Vuissoz
email: pa.vuissoz@chru-nancy.fr

Centerline articulatory models of the velum and epiglottis for articulatory synthesis of speech

Keywords: Speech, Articulatory models, MRI, Deformable objects

This work concerns the construction of articulatory models for synthesis of speech, and more specifically the velum and epiglottis. The direct application of principal component analysis to the contours of these articulators extracted from MRI images results in unrealistic factors due to delineation errors. The approach described in this paper relies on the application of PCA to the centerline of the articulator and a simple reconstruction algorithm to obtain the global articulator contour.

The complete articulatory model was constructed from static Magnetic Resonance (MR) images because their quality is much better than that of dynamic MR images. We thus assessed the extent to which the model constructed from static images is capable of approaching the vocal tract shape in MR images recorded at 55 Hz for continuous speech. The analysis of reconstruction errors shows that it is necessary to add dynamic images to the database of static images, in particular to approach the tongue shape for the /l/ sound.

I. INTRODUCTION

The numerical acoustic simulations of the vocal tract have seen recent progress in the possibility of taking into account the complexity of the vocal tract geometry [START_REF] Mokhtari | Singlematrix formulation of a time domain acoustic model of the vocal tract with side branches[END_REF], [START_REF] Elie | Extension of the single-matrix formulation of the vocal tract: consideration of bilateral channels and connection of self-oscillating models of the vocal folds with a glottal chink[END_REF], the specificities of vocal fold vibrations [START_REF] Story | Voice simulation with a bodycover model of the vocal folds[END_REF], [START_REF] Lous | A symmetrical two-mass vocal-fold model coupled to vocal tract and trachea, with application to prosthesis design[END_REF] and production of consonants [START_REF] Elie | Acoustic impact of the gradual glottal abduction on the production of fricatives: a numerical study[END_REF] or other complex speech sounds as trills [START_REF]Simulating alveolar trills using a two-mass model of the tongue tip[END_REF]. These advances rely on numerical models that are more faithful to the acoustics of speech, but also on articulatory data that are more precise and accurate thanks to the emergence of Magnetic Resonance Imaging (MRI).

In order to exploit these advances within the framework of articulatory synthesis it is necessary to provide a sufficiently precise geometric description of the vocal tract shape given as an input of aero-acoustical simulations. Precision should be good especially at the place of articulation, i.e. the place where the distance between both walls of the vocal tract is minimal.

Many efforts have been dedicated to the main articulators [START_REF] Maeda | Compensatory articulation during speech: Evidence from the analysis and synthesis of vocaltract shapes using an articulatory model[END_REF]- [START_REF] Laprie | A curvilinear tongue articulatory model[END_REF], i.e. the mandible which corresponds to the jaw opening, the tongue which controls the distribution of the back and front cavities in the vocal tract, and lips which give the vocal tract aperture and the length of the front cavity via their protrusion. However, less voluminous articulators are likely to change the acoustics quite profoundly and should therefore also receive a great deal of attention. This is the case of the velum which controls the velopharyngeal port and fine adjustments of the balance between back and front cavities. Similarly, the epiglottis located in the larynx region may change the resonance at the lower part of the vocal tract, and can also be used to articulate some phonemes.

This work is dedicated to the development of articulatory models for these two articulators and their link with the delineation of the contours of these articulators in MR images. We already developed a 2D articulatory model of the vocal tract from X-ray [START_REF] Laprie | A curvilinear tongue articulatory model[END_REF] and then MR images. The choice of a 2D model is motivated by two issues. First, the main geometrical feature from an acoustic point of view is the distribution of cavities and the places where constrictions occur. Taking the third dimension into account does not bring much [START_REF] Ericsdotter | Detail in vowel area functions[END_REF]. Second, the development of a complete 3D model from 3D MR volumes requires efforts of delineation which are often prone to errors. Indeed, the distinction between air and tissues is often problematic and depends on the operator who analyzes the image or supervises semi-automatic tools provided by itk-SNAP [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability[END_REF] or MITK [START_REF] Nolden | The medical imaging interaction toolkit: Challenges and advances[END_REF].

Our approach uses data analysis methods, i.e. Principal Component Analysis (PCA), to identify articulator deformation modes. The weakness of this approach is that the model is strongly linked to a speaker. To a certain extent the model can be quite easily adapted to another speaker in terms of size and main anatomical parameters including palate shape [START_REF] Laprie | Construction and evaluation of an articulatory model of the vocal tract[END_REF]. Similarly, the up/down or front/rear movements, and the rounding of the tongue are common to all speakers, ensuring that the model can be used without risk of major errors. On the other hand, finer speaker articulatory strategies escape this adaptation.

The underlying assumption for using PCA to build an articulatory model is that the magnitude of actual deformations modes, i.e. PCA factors, is greater than those due to delineation errors. From a practical point of view this means that the variance explained by those factors is stronger than those of delineation errors. This assumption is fully verified for the tongue which occupies an important place on the MR midsagittal image of the vocal tract, but not for smaller articulators like the epiglottis and the velum. On the mid-sagittal image the epiglottis is a filiform object whose two edges are separated by only a few pixels.

This means that the PCA factors resulting from delineation errors can mix with or even dominate the true deformation factors. The situation is quite similar for the velum which is a small object which does not present a strong contrast on the image and whose edges cannot be delineated easily. A deeper reason is related to the intrinsic form and nature of these organs. The epiglottis appears as a filiform object on the image and it makes little sense to look for transverse deformation factors. Sections II and III are dedicated to the description of these models.

The main advantage of a model derived from vocal tract images is to ensure that the model produces vocal tract shapes similar to those that the speaker realized during the acquisition. X-ray images used to construct articulatory models until the late 1990s were extracted from films and correspond to continuous speech. The main difficulty encountered during the construction of these models was the poor quality of the images on which several contours are superimposed. This is due to the nature of images obtained from X-rays that cross the speaker's head and projects all contours on the same image. In particular, teeth and fillings often hide the tongue contour which was poorly detected.

Models constructed from MR images mainly correspond to static images. Subjects are asked to position their articulators as if they were producing the sound for vowels. They must keep the position without moving during the acquisition which lasts approximately ten seconds. For consonants, they are asked to place their articulators as if they were going to produce the consonant in a particular vocalic context. Each consonant acquisition thus corresponds to a CV and in order to limit the number of acquisitions the vowels are often the cardinal vowels /i,a,u/. The main reason of using static images is that the availability of dynamic MR imaging is recent (in the late 2000s), very limited and of poor quality and resolution (less than 100x100 for the whole vocal tract in most cases). Conversely, static images offer the advantage of covering the complete volume of the vocal tract with a resolution of 1mm or slightly below, and a good contrast between air and tissues, which makes the delineation process easier. The risk of using static images is that the model cannot generate vocal tract shapes that correspond to continuous speech. This issue is addressed in section IV.

In this work we exploited 99 MR static images recorded by a male speaker corresponding to 14 vowels, 72 blocked consonant-vowel articulations for /f,s,S,p,t,k,l,m,n,K/ followed by a cardinal vowel and other vowels in some cases, plus 3 reference images (used to register the dental cast). The data were collected with a GE Signa 3T machine with an 8-channel neurovascular coil array. The protocol consisted in a 3D volume of the vocal tract acquired with a custom modified Enhanced Fast Gradient Echo (EFGRE3D, TR 3.12 ms, TE 1.08 ms, matrix 256x256x76, with spatial resolution 1.02x1.02x1.0 mm3). The mid-sagittal slice was used to construct the models for each of the articulators of the vocal tract.

In addition we also exploited dynamic MR data recorded at Max Planck Institute in Göttingen by using the real-time MRI reconstruction algorithm [START_REF] Niebergall | Real-time MRI of speaking at a resolution of 33 ms: Undersampled radial FLASH with nonlinear inverse reconstruction[END_REF]. This database comprises 200 phonetically balanced sentences and spontaneous speech. The sampling frequency is 55 Hz and each image (189x189 pixels) is a 8 mm slice located at the mid-sagittal plane.

II. CENTERLINE MODEL OF THE VELUM

In [START_REF] Laprie | 2D articulatory velum modeling applied to copy synthesis of sentences containing nasal phonemes[END_REF] PCA was applied directly to the velum contours extracted from a X-ray film. Even if this model rendered the velopharyngeal opening correctly, it fails to render complex forms observed in some recently acquired MR images where the velum rolls up on itself as illustrated by Fig. 1.a which corresponds to the static articulation of /Ka/. As it can be seen on Fig. 1.b, the rolling of the velum on itself is confused with swelling. Coupled with delineation errors this gives unrealistic first PCA factor, which corresponds to the swelling of the velum as shown in Fig. 2. The variance explained by this first factor is 58.2%, while that explained by the second factor, i.e. the actual opening and closing movement of the velopharyngeal port by the velum, is only 32.6%.

Hence the idea of a model construction that reduces the impact of delineation errors, and a model that is capable of representing the rolling movement, and more generally the pendulum movement, when the velum closes the velopharyngeal port. Instead of being applied to the exterior contours of the velum, PCA is applied on the centerline of the velum as illustrated by Fig. 3. The centerline is represented as a regularly sampled curve whose upper extremity is fixed. The PCA input vector is the sequence of segments that define this curve. Since one extremity of the curve is fixed, each segment is entirely determined by the angle it forms with the previous segment. The input vector of PCA is thus formed by the sequence of angles and the total length of the centerline. Actually, to ensure the homogeneity of the input vector each segment is represented by its length and the angle it forms with the previous segment. The integration of the length into the input vector is intended to account for the small elongation of the velum and also the fact that the upper extremity may not be completely fixed.

Since the global articulatory model requires the knowledge of the velum shape and not only the velum centerline a reconstruction algorithm was designed. Its principle consists of reconstructing both edges of the velum from the fixed extremity. The distance of each edge point with respect to the centerline is an affine function of the index of the corresponding center-point. The mobile extremity is represented as an ellipse which connects both edges. The widths of the edges at both extremities were adjusted by hand on a reference image. The algorithm takes into account the high curvature configurations where two segments orthogonal to the centerline, and corresponding to two consecutive centerpoints, cross. This time, the first factor explains 43.4 % of the variance (see Fig. 4 left) and corresponds to the real lowering/raising movement of the velum. The second factor (15.6% of the variance) corresponds to the rolling deformation, and the third factor captures the slight change in length, whether due to a real lengthening effect (possibly explained by the movement of the anchor point) or delineation errors. Even if the variance explained relates to the overall contour in one case and the central line in the other, we can note that the weight of the first factor, which is now relevant, is less important in this new model. More importantly, the velum is now adequately represented by the PCA factors, and the effect of delineation errors is pushed beyond the fourth factor.

III. MODEL OF THE EPIGLOTTIS

As the velum, the epiglottis can be modeled from its centerline. But unlike the velum, which is largely independent of other articulators, the epiglottis is strongly influenced by the tongue (and therefore the jaw) and larynx.

As a matter of fact, the centerline was determined after delineation of all the epiglottis contours, and the width was set as the average width of all these contours in the upper part where the two epiglottis edges are clearly visible (see Fig. 5). The height of the upper part (where both contours are visible) is adjusted by hand to fit the contours extracted from images. The centerline is approximated as a B-spline and represented by its control points P l (0 ≤ l < M where M is the number of control points) in the form of a two-coordinate vector, and the reconstruction of the epiglottis from the centerline amounts to a line at a distance of half the width from the centerline.

In order to take into account the influences of the jaw, larynx and tongue, we applied multiple linear regression [START_REF] Rao | Linear Models and Generalizations[END_REF] on the control points P l (0 ≤ l < M ) of the epiglottis contour:

P l = jaw 0,l B 0 + j=T -1 j=0 tg j,l C j + lx 0,l D 0 + E l
where jaw 0,l is the control factor of the first linear component of the jaw in the global articulatory model and B 0 the twocoordinate regression vector for the jaw, tg j,l the control factors of the T first linear components of the tongue and C j the corresponding regression vector, lx 0,l the first control factor of the larynx component and D 0 the corresponding regression vector, and E l is the residue vector.

Actually, since the centerline is represented by the M control points, each centerline occurrence is represented by a 2 × M vector formed by the coordinates of the M points. Each of the N occurrences of the epiglottis is represented by a 2×M vector named P i with 0 ≤ i < N . These contour vectors P i are the observations, and the control factors of the jaw jaw 0,i , tongue tg j,i and larynx lx 0,i are the input explanatory variables. For the jaw and larynx we kept only the first factor (jaw 0 , resp. lx 0 ), which is in both cases the most informative one. For the tongue, which is in front of the epiglottis, we kept the first six deformation factors tg 0..5 . All the variables are centralized and therefore the intercept can be ignored.

By grouping all the explanatory factors jaw 0 , tg j , and lx 0 , in a vector of K = T + 2 coordinates which are named X j , the previous equation is

P i = j=K-1 j=0 b j X i + e i
or in a matrix form P = XB + E, where P is the N × 2M matrix of the observations, i.e. the control points of the centerlines, X is the N × K matrix of the explaining articulatory factors, B is the K × 2M regression matrix and E is the N × 2M matrix of residue not explained by jaw, tongue and larynx. B is given by B = (X t X) -1 X t Y .

Then, the contributions of the jaw, tongue and larynx can be subtracted from the observations of the epiglottis, i.e. P -XB, and PCA can be applied to the residue E. Given the nature of epiglottis, i.e. a cartilage, the number of relevant linear components should be small.

We applied this analysis scheme to two sets of data: that of mid-sagittal slice of 3D MRI images presented in the introduction and a corpus of 1021 mid-sagittal images from an X-ray film made of short sentences recorded by a female speaker [START_REF] Sock | DOCVACIM an Xray database and tools for the study of coarticulation, inversion and evaluation of physical models[END_REF] explained by the articulators influencing the epiglottis and that two linear components are enough to approximate the epiglottis fairly accurately. The regression stage enables most of the extrinsic influences exerted on the epiglottis to be removed before PCA. It should be noted that these influences explain as much variability as the intrinsic components.

Fig. 5 shows that the first factor corresponds to a vertical movement, and the second corresponds to a horizontal movement in the lower and mid part of the epiglottis which contributes to the constriction of the whole laryngeal vestibule. This retraction is not explicitly used in French which is the mother tongue of the two speakers but plays a determining role in the production of glottal consonants in Arabic or Hebrew [START_REF] Laufer | The function of the epiglottis in speech[END_REF], [START_REF] Esling | Glottal stop, glottalized resonants, and pharyngeals: A reinterpretation with evidence from a laryngoscopic study of nuuchahnulth (nootka)[END_REF].

IV. FITTING THE ARTICULATORY MODEL TO DYNAMIC

IMAGES

The main reason of using static MR images of the vocal tract is to provide a much better image quality than that of real-time MR images, and to allow the retrieval of the third dimension. The latter crucial feature can be exploited directly by developing a complete 3D articulatory model, or by utilizing machine learning techniques to automatically restore the area function from the 2D sagittal model. It is this latter avenue that we will use in the future.

However, it is not guaranteed that the articulatory model derived by PCA from static MR images can capture vocal tract shapes of continuous speech. We have included in our database a sufficient number of phonetic contexts to cover most of the articulatory variability of the target language, here French. Despite these precautions it is possible that the blocked articulation of a consonant in a vocalic context, for example /k/ followed by the vowel /a/, does not reflect real dynamic articulations. Of all the articulators the tongue shape is most likely not to be approached correctly. Indeed, it has the greatest variability. Moreover, most consonants require an effort to make and maintain the contact between the tongue and the palate or teeth, during the MR acquisition. To investigate this question we randomly selected a series of 64 real-time MR images. All the articulator contours were carefully delineated by hand and the model constructed from images of static articulatory configurations was fitted to these contours. We found that the model approached most images correctly but failed for some images, especially those corresponding to the /l/ sound (see Fig. 6). The average reconstruction error was 1.57 mm (σ = 3.02mm). Since the errors mainly concerned the tongue shape for /l/ sounds, we added 3 real-time MR images of /l/ for the vowels /i, a, u/ to the images used to build the model. The average reconstruction error then dropped to 1.33 mm (σ = 2.52mm).

V. CONCLUDING REMARKS

The construction of an articulatory model is a key stage in the development of articulatory synthesis because it enables the vocal tract shape to be defined with a small number of parameters. These parameters are associated to deformation modes of the speech articulators. The strategy of using centerline models accompanied by simple reconstruction algorithms turned out to guarantee that the deformation modes, corresponding to principal factors, are more relevant for the velum and epiglottis than those directly obtained by applying PCA to global contours. The second lesson of this work is that it is necessary to associate dynamic images with a static MRI image database in order to obtain a model that can correctly approach all vocal tract shapes that a speaker can produce. Even if the dynamic MR images are of a lower quality, they can cover shapes that are difficult to achieve by keeping articulators immobile.

Fig. 1 .

 1 Fig. 1. (a) MRI sagittal image of /Ka/ (left), (b) Velum (solid blue curve) approximated by the PCA model (middle), (c) Velum and velum centerline (solid blue curves) approximated by the centerline PCA model.

Fig. 2 .

 2 Fig. 2. Nomograms of the first three factors of the standard PCA velum model. The yellow curve is the average configuration. The green and yellow curves are ±σ. The blue curves (for the second and third factor) are ±2σ.

Fig. 3 .

 3 Fig. 3. Centerline velum model. The red cross is the anchor point of the centerline.

Fig. 4 .

 4 Fig. 4. Nomograms of the first three factors of the centerline velum model. The red curve is the average configuration. The green and yellow curves are ±σ.

Fig. 5 .

 5 Fig. 5. Epiglottis and its centerline (left), first two deformation modes of the epiglottis for the male speaker. The green line is the neutral position (middle), and the complete articulatory model in red approximating the vocal tract for the articulation /sø/ (right)

Fig. 6 .

 6 Fig. 6. Vocal tract contours reconstructed by the model constructed from static images (left), and by the model extended with dynamic images (right). The thin yellow lines are the contours delineated by hand. The red line is the reconstructed vocal tract used for acoustic simulations.

TABLE I STANDARD

 I . Tab. I shows that most of the variance is DEVIATIONS IN MILLIMETER OF THE EPIGLOTTIS: TOTAL, AFTER SUBTRACTING THE INFLUENCE OF OTHER ARTICULATORS, AFTER SUBTRACTING 1 st , 2 nd AND 3 rd LINEAR COMPONENTS.

	σ in mm	male (static) female (dynamic)
	total	8.44	14.32
	regression	5.08	6.51
	PCA 1st	2.66	3.17
	PCA 2nd	1.33	1.73
	PCA 3rd	0.78	0.93

ACKNOWLEDGMENT

This work is supported by an ANR Grant ArtSpeech to the Speech Group LORIA CNRS UMR7503 Nancy France 2015-2019.