Many viroids and RNA viruses have genomes that exhibit secondary structure, with paired nucleotides forming stems and loops. Such structures violate a key assumption of most methods of phylogenetic reconstruction, that sequence change is independent among sites. However, phylogenetic analyses of these transmissible agents rarely use evolutionary models that account for RNA secondary structure. Here, we assess the effect of using RNA-speciﬁc nucleotide substitution models on the phylogenetic inference of viroids and RNA viruses. We obtained data sets comprising full-genome nucleotide sequences from six viroid and ten single-stranded RNA virus species. For each alignment, we inferred consensus RNA secondary structures, then evaluated different DNA and RNA substitution models. We used model selection to choose the best-ﬁtting model and evaluate estimated Bayesian phylogenies. Further, for each data set we generated and compared Robinson–Foulds (RF) statistics in order to test whether the distributions of trees generated under alternative models are notably different to each other. In all alignments, the best-ﬁtting model was one that considers RNA secondary structure: RNA models that allow a nonzero rate of double substitution (RNA16A and RNA16C) ﬁtted best for both viral and viroid data sets. In 14 of 16 data sets, the use of an RNA-speciﬁc model led to signiﬁcantly longer tree lengths, but only in three cases did it have a signiﬁcant effect on RFs. In conclusion, using RNA model when undertaking phylogenetic inference of viroids and RNA viruses can provide a better model ﬁt than standard approaches and model choice can signiﬁcantly affect branch length estimates. Key words: RNA virus, viroid, RNA secondary structure, phylogenetics. Introduction strand. Among the 16 possible base-pairings that can poten- Many tasks in modern molecular systematics rely upon the tially occur, only six (the Watson–Crick pairs AU, UA, GC, CG, use of nucleotide (or codon or amino acid) substitution mod- and the “wobble” pairs GU and UG) are stable enough to form els. Substitution models facilitate the statistical testing of mo- actual base-pairs (the remaining base-pairings are called mis- lecular evolutionary hypotheses and improve the estimation of matches, MM). RNA structures play important roles in many genetic distances among taxa by accounting for unobserved viruses and viroids, whose genomes are encoded in RNA. For evolutionary changes. However, these models make several example, RNA structures are involved in viral/viroid replication assumptions about the process of molecular evolution, for (Hutchins et al., 1986; Damgaard et al., 2004), translation example, whether nucleotides differ in relative frequency, or (Pelletier and Sonenberg, 1988), and immune evasion (Tellam whether substitution rates vary among nucleotides (Posada et al., 2008). Nucleotide changes that disrupt the most stable and Crandall, 2001) or codon positions (Shapiro et al., 2006). Watson–Crick pairs are often deleterious, and therefore, RNA The existence of RNA secondary structure, such as stems secondary structures can impose strong evolutionary con- (also called hairpins), is likely to violate a key assumption of straints on sequence evolution. In order to maintain RNA struc- most methods of phylogenetic reconstruction, that evolution- ture, a base of a pair must in many cases be matched by a ary changes occur independently among sites (Nasrallah et al., complementary nucleotide. One consequence of this evolution- 2011). Stems are comprised of nucleotide sequences that form ary constraint is that the amount of nucleotide evolution esti- base-pairings with complementary regions within the same mated from unpaired sites is expected to be higher than that The Author(s) 2018. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Genome Biol. Evol. 10(2):657–666. doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 657 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 ~ Patino Galindo et al. GBE from paired sites (Nasrallah et al., 2011). An association be- full-genome sequences from RNA viruses and viroids. tween the presence of complementary base pairing and amino Further, we measure the degree to which phylogenetic infer- acid conservation has been reported for HIV-1 (Sanjuan and ence is affected, in terms of estimated branch lengths and Borderıa, 2011; Snoeck et al., 2011). tree topologies, when an RNA-speciﬁc model is used to de- In order to accommodate the evolutionary correlations scribe the evolution of paired sites in the genomes of these among-sites that are imposed by RNA secondary structure, infectious agents. various types of RNA-speciﬁc substitution models for phylo- genetic inference have been developed. The 6-state (RNA6A- Materials and Methods E) models discard all mismatched sites from analysis, whereas Data Sets and Alignments the 7-state (RNA7A-G) models group all mismatched sites into a single state (Tillier and Collins, 1998). The 16-state models Full-genome nucleotide sequences from six viroid species [to- (RNA16A-F, I-K) take into account all 16 possible pairs that the mato apical stunt pospiviroid (TASVd), citrus exocortis viroid four nucleotides could form (Scho ¨ niger and Von Haeseler, (CEVd), columnea latent viroid (CLVd), grapevine yellow 1994; Muse, 1995). RNA16models canbe classiﬁedinthree speckle viroid (GYSVd), Australian grapevine viroid (AGVd), different types: 1) “all pairs” models (RNA16A, B, I, J, and K), potato spindle tuber viroid (PSTVd)], and ten single-stranded in which each of the 16 dinucleotides has its own equilibrium RNA virus species [hepatitis delta virus (HDV), Sudan- frequency; 2) “stable sets” models (RNA16D, E, and F), in ebolavirus (SUDV), dengue virus (DENV), hepatitis C virus which the equilibrium frequencies of mismatched pairs, (HCV), human immunodeﬁciency virus (HIV), foot and mouth Watson–Crick pairs, and wobble pairs, are different; and 3) disease virus (FMDV), measles virus (MeV), rabies virus (RV) “stable pairs” model (RNA16C), which can be considered to rubella virus (RuV), and mumps virus (MuV)] were down- be an extension of an RNA7 model, in which the ten possible loaded in April, 2015. Viroid and HDV sequences were down- mismatched pairs have a single equilibrium frequency (Savill loaded from GenBank; viral genomes were obtained from the et al., 2001; Allen and Whelan, 2014). Virus Pathogen Database and Analysis Resource, VIPRBRC Previous studies of ribosomal RNA (rRNA) genes have con- (http://www.viprbrc.org). Only full genome sequences that cluded that RNA-speciﬁc models outperform standard nucleo- included untranslated regions were considered. Alignments tide substitution models when describing the evolution of for each species were generated using MAFFT (using the structured RNA sequences (Savill et al., 2001; Kosakovsky “align- G-ins- 1” progressive method strategy) (Katoh and Pond et al., 2007), as assessed by statistical model comparison Standley, 2013) and positions with a high proportion of using the Akaike Information Criterion (AIC) (Linhart and gaps were removed with TrimAl (Capella-Gutie´rrez et al., Zucchini, 1986). The use of RNA models in rRNA phylogenetic 2009). Given that “gappy” positions were rare and repre- inference has been associated with an improvement in accuracy sented rare insertions that were absent in most taxa, exclud- (the distance between the real and the reconstructed tree) and ing them had no inﬂuence on the inferred consensus RNA robustness (as measured by bootstrap support values) (Keller secondary structures for each species. et al., 2010). In agreement with these studies, Allen and Whelan (2014) compared different nucleotide and RNA models for 287 human RNA gene families, most of them microRNAs RNA-Secondary Structure Inference and snoRNAs, and concluded that RNA models outperformed nucleotide substitution models in most cases, because the for- For each species, RNA minimum free-energy (MFE) consensus mer yielded the lowest corrected AIC (AICc) values. secondary structures were predicted using RNAalifold, as Conserved RNA secondary structures have been reported implemented in the Vienna Package 2.0 (Lorenz et al., to exist in the genomes of many linear RNA viruses, for ex- 2011). The folding temperature was set to 25 and 37 C ample, species of the Flaviviridae family (Thurner et al., 2004; for viroids and viruses, respectively, which, according to Mauger et al., 2015)and HIV-1 (Watts et al., 2009). Hepatitis Sanjuan et al. (2006), corresponds to the temperatures at Delta Virus (HDV) and viroids, which exist as circular RNA which these pathogens replicate. RNA molecules were as- genomes, present exceptionally highly structured genomes sumed to be circular for HDV and viroids. Because the large and>70% of the nucleotide sites in their genomes form size of RNA viruses with linear genomes (at least 8,000 nt) can base-pairs (Wang et al., 1986; Sanjuan et al., 2006). Despite hinder the inference of RNA secondary structure, the this, phylogenetic reconstructions of RNA viruses (including RNAalifold analyses of these data sets were performed using HDV) and viroids have not been generated using RNA models, segments of 1,000 nt. Analyses of HIV and HCV were also and thus potentially ignore the constraints that these struc- performed using the RNA structures obtained experimentally tures impose on genome evolution. using approaches based on SHAPE reactivity, as reported by The goal of this study is to investigate whether RNA- Siegfried et al. (2014) and Mauger et al.(2015), respectively. speciﬁc substitution models outperform standard nucleotide Arc diagrams of the obtained structures, which display the substitution models when applied to different sets of locations of base-paired nucleotides along each genome, 658 Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Effect of RNA Substitution Models GBE were plotted with the R4RNA package for R (Lai et al., 2012; PHASE-3.0. This program allows the inference of a phyloge- R core team, 2015). netic tree under a “mixed model,” in which a DNA substitu- The conservation of RNA secondary structure within each tion model is assigned to unpaired positions and an RNA data set was tested using RNAz (Gruber et al., 2007)by cal- substitution model is assigned to paired positions. For each culating the Structure Conservation Index (SCI). An SCI¼ 0 data set, two different phylogenetic trees were estimated, indicates that RNAalifold did not ﬁnd a consensus structure, using either 1) the best-ﬁtting model (which in our study whereas a SCI 1 reﬂects a set of perfectly conserved struc- was always a mixed model) or 2) a DNA-only model. At least tures (Washietl et al., 2005). Consequently, only those data two independent MCMC runs, each with>1,000,000 states, sets with an overall SCI 0.70 were retained for further anal- were computed, and a 10% burn-in was removed from each ysis, in order to ensure that the RNA secondary structures run before analysis. The prior distribution used for branch under investigation were evolutionary conserved. length estimation was an exponential distribution with rate In order to assess the order-dependency of the inferred parameter¼ 10. This is the default prior in PHASE-3.0. RNA secondary structures, a sequence randomization method After combining the output of both MCMC runs, conver- (Simmonds et al., 2004; Davis et al., 2008) implemented in gence was checked visually by plotting sampled values of the the SSE 1.1 package (Simmonds, 2012) was appliedtoeach likelihood, posterior and priors. After convergence was con- data set. This method evaluates the difference between the ﬁrmed, an extended majority rule consensus phylogenetic MFE of the inferred secondary structure from 1) real sequen- tree was obtained for each data set using the program ces from each alignment and 2) the same sequences after “mcmcsummarize” from the PHASE package. The phylogeny their sites have been randomly reordered. The sequence ran- obtained under the best-ﬁtting model (which, for all the data domization is undertaken in a manner that preserves dinucle- sets, was the mixed model) was then used as a ﬁxed topology otide frequencies. For viroids and HDV, these MFE differences to estimate branch lengths, by running mcmcphase with ei- (MFED) were calculated in windows of size 300 nt, and a ther the DNA or the mixed substitution model. sliding-step of 30 nt, under the constraint of a circular ge- Next, sites in each sequence alignment were partitioned nome. For the RNA viruses with linear genomes, MFED into two separate data sets that included only paired or un- were calculated for each 1,000-nt long segment. In all cases, paired sites, respectively. Branch lengths were estimated sep- MFEDs were calculated under both sense and antisense ori- arately from these two partitions, using the same ﬁxed entations. A positive MFED indicates that the MFE of the RNA topology as above. A DNA substitution model was used for structure derived from the real sequence alignment is lower the unpaired sites partition, and either the best-ﬁtting DNA (and thus more stable) than that from the randomized se- substitution model or the RNA substitution model was used quence alignment, and thus is a conservative test of the pres- for the paired sites partition. ence of a signiﬁcantly structured genome. Comparison of Branch Lengths and Tree Topologies Model Selection and Phylogenetic Analyses Tree lengths (the sum of all branch lengths in a phylogeny) For each data set, the best-ﬁtting substitution model for phy- were calculated from the consensus trees that were estimated logenetic reconstruction was chosen using a Perl script in- from the complete alignments. Tree lengths obtained from cluded in the package PHASE-3.0 (“model_selection.pl”; paired sites (either under a DNA or RNA substitution model) Allen and Whelan, 2014). The inputs to this analysis were 1) and unpaired sites (always under a DNA substitution model) the sequence alignment, 2) the inferred secondary structure, were calculated in the same way. To determine if branch and 3) an initial neighbor-joining tree, estimated under the lengths estimated under the DNA and mixed substitution Tamura-Nei model, using Mega version 5 (Tamura et al., models were different, they were compared using paired 2011). The Perl script compares an array of different models: Wilcoxon tests. two DNA substitution models (HKY and GTR), 16 different To assess the effects of model choice on inferred tree to- RNA substitution models (seven RNA7 and nine RNA16 mod- pologies, we computed distributions of Robinson–Foulds (RF) els), and the inclusion or exclusion of a gamma distribution distances. The RF distance between two tree topologies is a model of among-site rate variation. The best-ﬁtting model measure of how different they are (Robinson and Foulds, was identiﬁed as that with the lowest value of the corrected 1981). For each data set we computed three different distri- Akaike Information Criterion (Akaike, 1974; Burnham and butions of RF distances: 1) distances between pairs of topol- Anderson, 2002): AICc¼ln(L)þ 2kþ 2k(kþ 1)/(n k 1), ogies that were sampled from the same posterior distribution, where k is thenumberofparameters, L is the likelihood, and generated using a RNA-speciﬁc substitution model, 2) distan- n is sample size. ces between pairs of topologies sampled from the same pos- Phylogenetic trees were estimated using the Bayesian terior distribution, generated using a standard DNA Monte Carlo Markov Chain (MCMC) approach implemented substitution model, and 3) distances between a tree from in the program mcmcphase, which is part of the package the posterior used in (1) and a tree from the posterior used Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 659 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 ~ Patino Galindo et al. GBE in (2). In total, 18,000 trees were sampled from each posterior genotypes, etc.). For HDV, we found 46% of paired sites distribution. For cases (1) and (2), trees were sampled without along the genome were conserved among the eight HDV replacement, to prevent MCMC states being compared with genotypes in the virus, each with SCI> 0.70 separately. For themselves. All RF distances from a given data set were nor- HCV, HIV-1, DENV, and RV, it was necessary to analyze a less malized according to the number of taxa (by dividing the RF diverse sub-genomic taxonomic unit (speciﬁcally, subtype 1 b value by 2n-6, where n is the number of taxa to be analyzed). for HCV, genotype 1 for DENV, subtype B for HIV-1, and Distributions (1) and (2) represent the degree of statistical lineage C1 for RV). All these genotype/subtype data sets uncertainty in tree topologies arising from inference under a had SCI> 0.70 and were therefore analyzed further. Arc dia- given substitution model, whereas distribution (3) represents grams representing the RNA minimum free-energy consensus the difference in tree topologies obtained by inference under secondary structures obtained with RNAalifold for each data the two different models. Thus, a comparison of distribution set with SCI> 0.70 are shown in supplementary ﬁgure S1, (3) with distributions (1) and (2) indicates whether the effect Supplementary Material online. The percentage of nucleoti- on tree topology of using an RNA-substitution model is des forming base-pairs in the alignments that were further greater or less than estimation uncertainty alone. analyzed ranged between 23% (HIV, structure obtained ex- We assessed whether distributions (1) and (22) were sig- perimentally using SHAPE by Siegfried et al., 2014)and 78% niﬁcantly different from distribution (3) by performing 9,000 (AGVd) (table 1). pairwise comparisons between RF distances randomly sam- The median MFED values we obtained for viroids and HDV pled from distributions (1) or (2) and from distribution (3). The ranged between 2.6% (HDV) and 15.4% (CLVd) and, in al- probability that the two distributions are different is com- most all cases, were higher than those obtained for viruses puted as the number of instances in which the RF distance with linear RNA genomes. Only FMDV and HCV-1 b pre- from (3) is larger than that from (1) or (2), divided by the total sented median MFED values higher than 2%; in most viruses number of comparisons (Abecasis et al., 2009). P-values this value was close to zero (table 1). obtained from the same virus/viroid were then corrected with the false discovery rate method (FDR; Benjamini and Model Selection and Phylogenetic Analyses Hochberg, 1995). The distributions of normalized RF distances and their statistical comparisons were computed using an R For each data set analyzed, the best-ﬁtting model (i.e., the script (available from https://github.com/juanangel87/GBE_ model with the lowest AICc value) was a mixed model, which 2017) that utilizes the phangorn package for R (Schliep, assigned a DNA substitution model (either GTR or HKY) to 2011). unpaired sites and a RNA16 substitution model to paired sites In order to assess whether the joint prior was having undue (table 1). inﬂuence over the estimated posterior distributions for branch Phylogenies were estimated for each data set using lengths and RF distances, we computed one of the data sets mcmcphase (part of the PHASE-3.0 package). To examine (HCV-1b) without data, such that the MCMC sampled from the effect of including a RNA substitution model in the anal- the prior distribution only, for all the models implemented in ysis, we estimated branch lengths on a ﬁxed topology under PHASE-3.0 (GTR, HKY, RNA6A-E, RNA7A-G, and RNA16A-F, two different substitution models: ﬁrst, using the best-ﬁt I-K). Using the comparison approach described above, we model (which, as noted above, was always a mixed model), then compared the branch lengths and tree topologies in- and second, using the best-ﬁtting DNA substitution model. ferred from the HCV-1b data set (under the GTR and Tree lengths (the sum of all branch lengths) obtained under RNA16A models) to those obtained without data. the two abovementioned models (termed L(mixed) and L(DNA)) were compared using paired Wilcoxon tests. We also calculated ratios of the tree lengths obtained under the two models (i.e., L(mixed)/L(DNA)) (see table 2). Although the Results effect on branch length estimates of using a mixed model was RNA Secondary Structure Inference near to zero for PSTVd and AGvd (ratios ¼ 0.99 and 1.00, Structure Conservation Index (SCI) values were calculated for respectively; P values> 0.05), for the other viral and viroid each data set. Values of SCI 0.70 were found in only ﬁve data sets there was a signiﬁcant increase in tree length (P viral data sets: HCV (SCI¼ 0.40), DENV (0.40), HIV-1 (0.66), values< 0.05). The largest effects were observed for TasVd, RV (0.66), and HDV (0.66). These data sets include ﬁve of the CLVd, and GYSVd, whose L(mixed)/L(DNA) ratios were 6.5, seven data sets with the largest average pairwise genetic dis- 2.8, and 2.7, respectively. tances (table 1). For genetically diverse viruses such as these, We also compared the estimated tree lengths obtained evolutionary conservation of RNA secondary structure will be from the separate data sets comprising unpaired and paired greater at the sub-genomic level. Therefore, for DENV, HIV-1, sites. The L(paired)/L(unpaired) ratios obtained under the RV, and HDV we attempted to infer RNA secondary structures DNA model reported in table 2 are consistent with the hy- for taxonomic units below the species level (i.e., subtypes, pothesis that base-pairing imposes a signiﬁcant evolutionary 660 Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Effect of RNA Substitution Models GBE Table 1 Summary Statistics of Each Viroid and Virus Data Set Analyzed, Including Size (number of taxa and sequence length), Overall Mean Genetic Distance, Structure Conservation Index (SCI), Estimate Percentage of Base-Paired Nucleotides, Median MFED Value, and Best-Fitting Evolutionary Model of Each Viroid and Virus Data Set Analyzed n Taxa Sequence Mean P SCI % (paired %(Median Best-Fitting Model D AICc (overall best-ﬁtting Length (nt) Distance nucleotides) MFED) model vs. best-ﬁtting DNA-only model) Viroids TASVd 22 374 0.036 0.91 68 14.30 HKY_CþRNA16C_C 338 CeVd 178 369 0.041 0.92 70 8.40 GTR_CþRNA16E_C 258 CLVd 14 379 0.061 0.88 68 15.40 GTR_CþRNA16A_C 352 GYSVd 24 352 0.128 0.84 65 8.30 GTR_CþRNA16C_C 336 AGVd 27 368 0.02 0.91 78 11.40 HKY_CþRNA16C 295 PSTVd 88 356 0.019 0.97 69 12.80 HKY_CþRNA16A_C 220 Viruses a b HDV 121 1,543 0.204 0.66 46 2.60 GTR_CþRNA16D_C 2,237 Sudan Ebolavirus 7 18,875 0.032 0.9 64 1.40 GTR_CþRNA16A >1,000 DENV 23 10,733 0.263 0.40 NC NC NC NC DENV-1 20 10,733 0.061 0.81 60 ()1.3 GTR_CþRNA16A_C >1,000 HCV 42 9,605 0.292 0.40 NC NC NC — HCV-1b (RNAalifold) 20 9,605 0.087 0.82 66 3.80 GTR_CþRNA16A_C >1,000 HCV-1b (SHAPE reactivity) 20 9,605 0.087 0.82 51 3.80 GTR_CþRNA16A_C >1,000 HIV-1 18 9,173 0.126 0.64 NC NC NC — HIV-1B (RNAalifold) 33 9,173 0.056 0.74 57 0.50 GTR_CþRNA16D_C >1,000 HIV-1B (SHAPE reactivity) 33 9,173 0.056 0.74 23 0.50 GTR_CþRNA16D_C 674 FMDV 19 8,192 0.135 0.75 60 3.90 GTR_CþRNA16D_C >1,000 Measles 20 15,893 0.042 0.89 63 0.10 GTR_CþRNA16A_C >1,000 Rubella 35 9,758 0.06 0.9 65 1.20 GTR_CþRNA16A_C >1,000 Mumps 20 15,355 0.045 0.86 61 ()0.8 GTR_CþRNA16A_C >1,000 Rabies 26 11,923 0.111 0.66 5 NC NC NC Rabies C1 20 11,923 0.088 0.74 63% ()0.3 GTR_CþRNA16A_C >1,000 NOTE.—NC, not computed. SCI (Structure Conservation Index) below 0.70. Percentage of nucleotides forming base pairing, after obtaining a consensus structure comprising paired-sites that are present in>75% of genotypes/subtypes within a species. The RNA secondary structure only includes the 15 regions along the HIV-1B genome, reported by Siegfried et al. (2014), that have both SHAPE reactivity values and low Shannon entropies, thus being considered as well deﬁned structures. constraint. With the exception of CeVd, PSTVd, and HIV-1B the mixed model (HDV: P value¼ 0.016; HIV-1B: P val- (SHAPE) tree lengths estimated from paired sites were>29% ue¼ 0.002). For HCV, shorter RF distances were obtained shorter than those estimated from unpaired sites. However, when comparing topologies sampled under the DNA model when an RNA model was used for paired sites, the L(paired)/ with those obtained by comparing different posterior distri- L(unpaired) ratios increased and, in most cases, paired sites butions (P value¼ 0.018). For HDV, the consensus phyloge- under an RNA model yielded remarkably larger tree lengths netic tree obtained under the mixed model presented more than unpaired sites (AGVd,HDV,MeV,SUDV, DENV-GT1, highly supported nodes (deﬁned by posterior node proba- HCV-1b-SHAPE-, HIV-1B-SHAPE-, FMDV, MeV, RuV, MuV, bilities 0.90) than those obtained under a DNA-only model: RV) (table 2). 82 (mixed model) versus 68 (DNA model). The same effect For each data set analyzed, three different RF distance was observed in HIV-1B (RNAalifold): 21 well supported nodes distributions were obtained as described above. The results (mixed model) versus 15 (DNA model), but the differences are shown in ﬁgure 1. The randomization tests showed that, were reduced when using the SHAPE-derived secondary after FDR correction of P values, only for HDV, HCV-1b structure (17 well-supported nodes using the mixed model, (SHAPE), and HIV-1B (RNAalifold) did we obtain a signiﬁcantly and 15 using the DNA model). In the case of HCV-1b, using different distribution of RF distances when comparing topol- the secondary structure derived from RNAalifold had no effect ogies sampled from the same posterior than when comparing on the number of well-supported clades (14 under both mod- topologies from the two different posterior distributions. For els). However, the use of the experimentally derived structure both HDV and HIV-1B we observed shorter RF distances under led to a lower number of well-supported clades (from 14, Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 661 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 ~ Patino Galindo et al. GBE Table 2 Comparisons of Tree Lengths (L) Estimated under DNA and Mixed Models, for All Sites, Paired Sites, and Unpaired Sites L (DNA L (mixed Ratio P value L (unpaired L (paired sites, L (paired sites, Ratio (paired- Ratio (paired- model) model) (mixed/ log(DNA sites) DNA model) RNA model) DNA model/ RNA model/ DNA) vs. mixed) unpaired) unpaired) Viroids TASVd 0.47 3.07 6.532 <0.001 3.05 0.51 1.82 0.167 0.597 AGVd 4.91 4.93 1.004 0.341 0.55 0.31 1.13 0.563 2.055 CeVd 30.41 33.81 1.111 <0.001 34.18 33.4 31.42 0.977 0.919 CLVd 0.44 1.23 2.795 <0.001 1.36 0.74 1.01 0.544 0.743 GYSVd 0.77 2.06 2.675 <0.001 2.11 0.88 2.21 0.417 1.047 PSTVd 17.28 17.05 0.989 0.14 17.22 17.17 17.13 0.997 0.995 Viruses HDV 9.09 12.15 1.337 <0.001 12.44 7.5 15.35 0.603 1.234 Sudan Ebolavirus 0.07 0.1 1.408 <0.001 0.1 0.05 0.13 0.555 1.322 DENV-1 0.46 0.55 1.196 <0.001 0.55 0.42 0.92 0.764 1.673 HCV-1b (RNAalifold) 1.16 1.73 1.495 <0.001 1.73 0.89 1.84 0.513 1.064 HCV-1b (SHAPE) 1.17 1.4 1.191 <0.001 1.4 0.98 1.9 0.7 1.357 HIV-1B (RNAalifold) 1.48 2.21 1.493 <0.001 2.21 0.92 2.2 0.416 0.995 HIV-1B (SHAPE) 1.48 1.51 1.02 <0.001 1.52 1.5 2.59 0.987 1.704 FMDV 2.01 2.48 1.234 <0.001 2.52 1.48 2.72 0.587 1.079 Measles 0.33 0.42 1.273 <0.001 0.42 0.3 0.78 0.714 1.857 Rubella 0.71 1.04 1.465 <0.001 1.04 0.6 1.33 0.577 1.277 Mumps 0.35 0.48 1.371 <0.001 0.42 0.32 0.86 0.761 2.048 Rabies C1 0.94 1.16 1.234 <0.001 1.16 0.86 2.07 0.741 1.784 P value obtained from comparing the branch length distributions using paired Wilcocon tests, after a logarithm transformation. The RNA secondary structure only includes the 15 regions along the HIV-1B genome, reported by Siegfried et al. (2014), that have both SHAPE reactivity values and low Shannon entropies, thus being considered as well deﬁned structures. Topology could not be ﬁxed for branch lengths inference due to unresolved bipartitions, and a Wilcoxon rank sum test was performed instead of a paired test. using the DNA model, to 10, using the mixed model) (supple- models that are widely used to study viral evolution. In all data mentary ﬁg. S2, Supplementary Material online). The RF dis- sets the best-ﬁt model was a mixed model that uses a nucle- tances obtained when comparing the consensus trees (DNA otide model for unpaired sites and a RNA model for paired vs. mixed model) of these data sets were 0.22 for HDV, 0.24 sites. These mixed DNA/RNA models outperformed models in for HCV-1 b (RNAalifold), 0.35 for HCV-1 b (SHAPE), 0.37 for which unpaired and paired sites were partitioned and repre- HIV-1B (RNAalifold), and 0.33 for HIV-1B (SHAPE). sented by different DNA models. It is important to note that For all data sets, branch lengths obtained by sampling only 16-state RNA substitution models outperformed 7-state RNA from the joint prior distribution were signiﬁcantly longer than models in all instances. The main difference between these those obtained by sampling from the data-informed marginal families of RNA models is that 7-state models pool all mis- posterior distribution with empirical data (all P values< 0.001) matches (pairs of nucleotides that do not form stable base (supplementary table S1, Supplementary Material online). pairs) in a single state while 16-state models consider each Similarly, RF distributions from the marginal posterior were mismatch as separate state. A special case is RNA16C, in signiﬁcantly shorter than those obtained by sampling only which the ten different mismatched pairs have the same tran- from the prior (all P values< 0.001) (supplementary ﬁg. S3, sition probabilities, and is thus considered an extension of an Supplementary Material online). Thus, under the different RNA7 model (Savill et al., 2001). models implemented in PHASE-3.0, the empirical data are For most of the viroids we studied, the RNA16C model was informative and the joint prior appears to have limited inﬂu- the best-ﬁtting model, whereas for the RNA viruses, RNA16A ence on the estimated posterior distributions. was the best-ﬁtting model in most cases. RNA16A and RNA16C have been reported previously to ﬁt well when ap- plied to noncoding RNA data sets because, unlike other Discussion RNA16 models, they allow a nonzero rate of double substi- We assessed the effect of RNA substitution models on the tutions, and thus they count complementary changes as a inference of genetic distances and phylogenies for viroids and single step (Savill et al., 2001). Allen and Whelan (2014) RNA viruses using complete genome sequences. We ﬁrst in- assessed best-ﬁtting models for the analysis of the evolution vestigated whether using an RNA-speciﬁc model provides a of human noncoding RNAs and found that, for the majority of better ﬁt to the data than the conventional DNA substitution RNA types, “stable pairs” models (RNA7A-G and RNA16C) 662 Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Effect of RNA Substitution Models GBE FIG.1.—Density plots representing, for each data set, the distribution of RF distances obtained by comparing topologies from the same posterior distribution (either including or excluding the RNA model) versus the distribution of RF distances obtained by comparing topologies from two different posterior distributions. The results of the randomization tests are shown as the proportion of comparisons for which an RF distance obtained through comparing states from the same posterior (blue¼ under mixed model; red¼ under DNA model) was lower than the RF distance obtained by comparing states from the two different posterior distributions (black¼ mixed vs. DNA models). Signiﬁcant values after FDR correction are labeled with “*.” Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 663 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 ~ Patino Galindo et al. GBE and “stable sets” models (RNA16D, E, F) ﬁtted the best for HIV-1B (RNAalifold), the RF distance distribution obtained such data. They concluded that the former were usually se- from the posterior distribution generated under the RNA lected when applied to data sets in which few evolutionary model was less bimodal than the other distributions. In this changes occurred, whereas the latter were selected when the case, the topological uncertainty under the mixed model was consensus secondary structure contained higher proportions substantially reduced, as also reﬂected in improved node sup- of paired sites. Our results suggest that models that allow for port values. In the consensus tree, the number of well- nonzero rates of double substitutions ﬁt best for viroid and supported branches increased from 15 (DNA-only model) to virus genome data sets. 21 (mixed model). This, however, did not occur when using Bayesian phylogenies were estimated using the best-ﬁtting the RNA structure obtained with SHAPE. Indeed, in the case mixed model and using a DNA substitution model. This of HCV-1b, the RF distance distribution obtained from the allowed us to assess the differences in estimates of branch posterior distribution generated under the DNA-only GTR lengths and trees topologies when an RNA model is included model was lower and less bimodal than the other distribu- in the phylogenetic analysis. In all data sets (except PSTVd and tions. Thus, although RNA models for phylogenetic inference AGVd) the use of a RNA model led to trees with substantially have been previously associated with an increase in branch longer branch lengths. Among those data sets where the use support values (Keller et al., 2010), using an RNA model may of an RNA model led to a signiﬁcant increase in branch also lead to higher topological uncertainty for some data sets lengths, the increase in total tree length ranged between (e.g., HCV-1b in our study). This could be due to the higher 2% (HIV-1B, SHAPE structure) and 653% (TASVd). Under a number of parameters to be estimated in RNA models. DNA model, tree lengths estimated from paired sites were One of the limitations that may hamper the use of RNA always much shorter than those estimated from unpaired models for phylogenetic inference is the lack of reliable and sites, and such differences were reduced when the RNA representative RNA structures at the taxonomic unit under model was applied to paired sites. A lower number of sub- investigation. In this study, we used consensus RNA structures stitutions at paired sites, compared with unpaired sites, is inferred by computational approaches. The accuracy of these expected due to the likely stronger evolutionary constraints RNA structures used could in theory be improved by using at paired sites (Nasrallah et al., 2011). However, in some data experimental approaches, such as RNAse mapping or SHAPE sets tree lengths estimated from paired sites under a RNA reactivity (Wilkinson et al., 2006). Although the bioinformatic model were considerably larger than those estimated from tools used in this study (speciﬁcally RNAz and RNAalifold) unpaired sites (especially in AGVd, measles, mumps, and ra- showed the presence of ample conserved RNA secondary bies virus; table 2). These results suggest that, in such cases, structures in the genomes analyzed, subsequent analyses RNA models may overestimate the number of substitutions that compared MFEs between true and randomized sequen- along the inferred tree. It is important to note that PHASE-3.0 ces suggest weaker support for some of these structures, at estimates branch lengths in units of expected number of sub- least for linear RNA viruses. However, the randomization test stitutions per nucleotide, even when a RNA model is included may be statistically conservative and further experimental (and not the number of substitutions per base-pair). We rec- analyses are needed. Indeed, although HCV-1b and HIV-1B ognize the beneﬁt of this parameterization, because it allows presented negative MFED values, well deﬁned and large scale us to directly compare branch lengths estimated under differ- RNA secondary structures for these viruses have been identi- ent models (Allen and Whelan, 2014). ﬁed experimentally (Watts et al., 2009; Siegfried et al., 2014; In our analysis, viroid phylogenies exhibited larger RF dis- Lavenderet al., 2015; Mauger et al., 2015). However, further tances between trees sampled from posterior distributions analyses are necessary to assess the biological importance of than did the virus phylogenies, regardless of the evolutionary such experimentally found structures. model used. This suggests a greater degree of uncertainty in To date very few secondary structures of complete viral estimated viroid phylogenies, possibly reﬂecting lower phylo- genomes have been obtained experimentally and, further, genetic signal in viroid alignments. Furthermore, the compar- they have been obtained from single genome sequences and isons of RF distributions show that, with the exception of thus do not capture the diversity in RNA secondary structures HCV, HIV, and HDV, the use of a mixed model to infer viral that is known to exist, even below the species level (Tuplin and viroid phylogenies has no signiﬁcant effect on estimated et al., 2004; Mauger et al., 2015). Because of this lack of rep- tree topologies. For HCV, HDV, and HIV-1, including an RNA resentative experimental RNA secondary structures, we used model was associated with an increase in the number of well- the computational method implemented in RNAalifold, which supported branches in the resulting consensus tree. allowed us to infer a consensus structure from alignments of The RF distance distributions for SUDV, HCV-1b (SHAPE), different, yet related, RNA sequences. This method can im- and HIV-1B (RNAalifold and SHAPE) were bimodal. For SUDV prove the prediction of secondary structures compared with this is likely because there were comparatively few sequences, those obtained only with individual sequences, and can provide that is, RF distances were zero or very low because sampled a representative structure for the analyzed data set (Hofacker tree topologies were identical or very similar. In the case of et al., 2002; Bernhart et al., 2008). Furthermore, in our analyses 664 Genome Biol. Evol. 10(2):657–666 doi:10.1093/gbe/evx273 Advance Access publication January 9, 2018 Downloaded from https://academic.oup.com/gbe/article-abstract/10/2/657/4794727 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Effect of RNA Substitution Models GBE we only included those data sets that represented taxonomic Acknowledgments levels showing evolutionarily conserved structures, in order to This work was funded by the European Research Council un- ensure that the structures we inferred ﬁtted well for each data der the Unions Seventh Programme (FP7/2007-2013)/ set. However, it is important to note that, in vivo, the same European Research Council grant agreement number primary sequence can fold into alternative structures (Schultes 614725-PATHPHYLODYN to O.G.P., and by project and Bartel, 2000). Consequently, differences between RNA BFU2014-58656-R from Ministerio de Economıa y structures in vivo and computationally inferred structures are Competitividad (Spanish Government) and project expected to exist, and such differences are likely to be larger PROMETEO/2016/122 from Generalitat Valenciana to F.G.C. for viruses with linear RNA genomes than for HDV or viroids, J.A.P.G. was recipient of a FPU fellowship (FPU-AP2010-0561) which tend to form simpler, rod-like structures. For this rea- from Ministerio de Educacion y Ciencia (Spain). son, our in silico results should be interpreted with some cau- tion, but will hopefully serve as a starting point for subsequent Literature Cited in vitroor invivoresearch. For HIV-1B andHCV-1bwe also Abecasis AB, Vandamme A-M, Lemey P. 2009. Quantifying differences in undertook analyses using an experimentally determined RNA the tempo of HIV-1 subtype evolution. 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