Taxonomy-aware, sequence similarity ranking reliably predicts phage–host relationships

Background Characterizing phage–host interactions is critical to understanding the ecological role of both partners and effective isolation of phage therapeuticals. Unfortunately, experimental methods for studying these interactions are markedly slow, low-throughput, and unsuitable for phages or hosts difficult to maintain in laboratory conditions. Therefore, a number of in silico methods emerged to predict prokaryotic hosts based on viral sequences. One of the leading approaches is the application of the BLAST tool that searches for local similarities between viral and microbial genomes. However, this prediction method has three major limitations: (i) top-scoring sequences do not always point to the actual host; (ii) mosaic virus genomes may match to many, typically related, bacteria; and (iii) viral and host sequences may diverge beyond the point where their relationship can be detected by a BLAST alignment. Results We created an extension to BLAST, named Phirbo, that improves host prediction quality beyond what is obtainable from standard BLAST searches. The tool harnesses information concerning sequence similarity and bacteria relatedness to predict phage–host interactions. Phirbo was evaluated on three benchmark sets of known virus–host pairs, and it improved precision and recall by 11–40 percentage points over currently available, state-of-the-art, alignment-based, alignment-free, and machine-learning host prediction tools. Moreover, the discriminatory power of Phirbo for the recognition of virus–host relationships surpassed the results of other tools by at least 10 percentage points (area under the curve = 0.95), yielding a mean host prediction accuracy of 57% and 68% at the genus and family levels, respectively, and drops by 12 percentage points when using only a fraction of viral genome sequences (3 kb). Finally, we provide insights into a repertoire of protein and ncRNA genes that are shared between phages and hosts and may be prone to horizontal transfer during infection. Conclusions Our results suggest that Phirbo is a simple and effective tool for predicting phage–host relationships. Supplementary Information The online version contains supplementary material available at 10.1186/s12915-021-01146-6.


Background
Viruses infecting bacteria (phages) are the most abundant entities across all habitats and represent a vast reservoir of genetic diversity [1].Phages mediate horizontal gene transfer and constitute a major selection pressure that shapes the evolution of bacteria [2].Bacterial viruses also affect biogeochemical cycles and ecosystem dynamics by controlling microbial growth rates and releasing the contents of microbial cells into the environment [2,3].Moreover, phages play a key role in shaping the composition and function of the human microbiome in health and disease [4][5][6].Recently, there has been renewed interest in phage therapy and phage-based biocontrol of harmful bacteria [7,8] in medical treatment [9,10] and the food industry [11,12].Hence, characterizing phage-host interactions is critical to understanding the factors that govern phage infection dynamics and their subsequent ecological consequences [13].
The scope of phage-host interactions is poorly understood, although it has been hypothesized that all bacteria fall prey to viral attacks [1].Methods for studying phage-host interactions primarily rely on cultured virus-host systems; however, recent in silico approaches suggest a much broader range of hosts may be susceptible to viral infections [14,15].These methods predict bacterial hosts based on sequence composition [16,17], direct sequence similarity between phages and hosts [14,15], analysis of CRISPR spacers or tRNAs [13,18], and machine-learning approaches that integrate several sequence-based methods [19,20].
Despite significant progress in phage-host predictions, the classic BLAST [21] algorithm is currently the leading non-machine-learning method for identifying phage-host interactions [14,16].Depending on the data set, the tool finds the correct genus level host for 40-60% of phages [14,16].The task of finding a host for a given phage using BLAST is conceptualized as obtaining the host sequence with the highest similarity to the query phage sequence.However, restricting host predictions to the first topscored bacterial sequence has three limitations.First, the true host may not be the top-scoring match in the BLAST results.Second, mosaic phage genomes may match to many, typically related, bacteria.Although phages are generally host-specific, some may infect multiple host species [22,23].Finally, many distantly related bacterial species may obtain a comparable BLAST score for a query phage due to spurious alignments.These ambiguous host predictions require further manual curation of the taxonomic or phylogenetic relationship between the top-scored prokaryotic species to select the true host(s).
We have addressed these issues by developing a simple extension to BLAST, named Phirbo, that exploits the information contained in the full BLAST results, rather than its top-ranking matches.Phirbo improved the accuracy of finding hosts, beyond what is found from the best BLAST match, by relating phage and host sequences through intermediate, common reference sequences that are potentially homologous to both phage and host queries.Subsequent quantification of the overlapping signals allows for the reliable prediction of phage-host interactions without the need for direct comparisons between the phage and host sequences and without any prior knowledge of their phylogenetic or taxonomic context.

Phirbo algorithm overview
Our algorithm is based on the assumption that the degree of similarity between phage and host sequences is proportional to the overlap between ranked similarity matches of each sequence to the same reference data set of prokaryotic sequences.Specifically, to compare a pair of phage (P) and host (H) sequences, we first perform two independent BLAST searches against the reference database of prokaryotic genomes (D)-one BLAST search for phage and the other for the host query (Fig. 1a).The two lists of BLAST results (Fig. 1b), P → D and H → D, contain prokaryotic genomes ordered by decreasing sequence similarity (i.e., bit-score).To avoid a taxonomic bias due to multiple genomes of the same prokaryote species, we rank prokaryotic species according to their first appearance in the BLAST list (Fig. 1c).In this way, both lists represent phage and host profiles consisting of the ranks of top-score prokaryotic species.
The properties of these lists (Fig. 1c) can be characterized by four features: (i) species listed at the top of each ranking are more important (similar) to the query than those listed at the bottom; (ii) the lists may not be conjoint (some species may appear in one ranking but not in the other); (iii) the ranking lists may vary in length (BLAST may return few prokaryotic matches in response to virus sequences in contrast to thousands of matches in cases of multiplespecies prokaryotic families); (iv) two or more species from the database may achieve the same BLAST score and, therefore, occupy the same position on the ranking list (Fig. 1c).A recently introduced similarity measure used for comparing the rankings of Web search engine results [24], the Rank-Biased Overlap (RBO), satisfies these four conditions.The RBO algorithm starts by scoring the overlap between the sublist containing the single top-ranked item of each list.It then proceeds by scoring the overlaps between sublists formed by the incremental addition of items further down the original lists.Each consecutive iteration has less impact on the final RBO score as it puts heavier weights on higher-ranking items by using geometric progression, which weighs the contribution of overlaps at lower ranks (see the "Methods" section).An overall RBO score falls between 0 and 1, where 0 signifies that the lists are disjoint (have no items in common) and 1 means the lists are identical in content and order.Our results indicate that the extent of the phage-host relationship can be estimated by the application of an RBO measurement to the ranking lists generated from BLAST results (Fig. 1d).

Phirbo differentiates between interacting and noninteracting virus-host pairs
To assess the discriminatory power of Phirbo to recognize virus-host interactions, we used two published reference data sets: Edwards et al., which contains 2699 complete bacterial genomes and 820 phages with reported hosts [14,25], and Galiez et al. that has 3780 complete prokaryotic genomes and 1420 viral genomes [17,26].For each data set, we compared the distribution of Phirbo scores between all known virushost interaction pairs and the same number of randomly selected non-interacting virus-prokaryote pairs (Additional file 1: Figure S1).The scores obtained by Phirbo in both data sets separated the interacting from non-interacting virus-host pairs more than the BLAST scores.The median Phirbo score across interacting virus-host pairs was nearly 1500 times greater than for non-interacting pairs, while the median BLAST score was three times higher for interacting pairs than noninteracting pairs (Additional file 2: Table S1).Both methods differentiated between interacting and noninteracting virus-host pairs with higher accuracy than WIsH-the state-of-the-art, alignment-free, host prediction tool [17].
Fig. 1 Calculation of the interaction score between phage and host sequences.(a) The BLAST search of phage and prokaryote sequences against a reference data set result in (b).Two BLAST lists containing prokaryote matches ordered by decreasing similarity (i.e., bit-score).(c) BLAST lists were converted into rankings of prokaryote species.The ranked lists differ in content: Yersinia rohdei and Y. ruckeri are present in the first ranking list but absent in the second list, while Shigella dysenteriae and Erwinia toletana are only present in the second list.Two species, Y. rohdei and Y. ruckeri, from the first BLAST search have the same scores and are consequently tied for the same rank.(d) An interaction score was calculated between two ranking lists using rank-biased overlap To further examine the discriminatory power of Phirbo across all possible virus-prokaryote pairs, we used receiver operating characteristic (ROC) curves (Fig. 2a, b).The area under the ROC (AUC), which measured the discriminative ability between interacting and non-interacting virus-host pairs, was higher for Phirbo (AUC = 0.95) in the Edwards et S2).Using the same BLAST lists, Phirbo evaluated 99% of the interacting virus-hosts pairs.This high coverage indicated that nearly every pair of virusprokaryote sequences could be related by at least one common prokaryotic sequence detectably similar to both the virus and host sequences.

Phirbo has the highest host prediction performance
To evaluate host prediction performance, we used precision-recall (PR) curves, which provide more reliable information than ROC when benchmarking imbalanced data sets for which the non-interacting pairs vastly outnumber the interacting pairs [27,28].Accordingly, we plotted PR curves for Phirbo, BLAST, and WIsH predictions obtained from the Edwards et al. (Fig. 2a) and Galiez et al. (Fig. 2b) data sets.Overall, Phirbo performed better at host prediction at the species level than BLAST and WIsH, regardless of the data set.The area under the PR curve (AUPR), which summarized overall performance, was higher in Phirbo by 25 percentage points (AUPR = 0.56-0.65)than in BLAST (AUPR = 0.33-0.41).
Phirbo also reported the highest F1 score (an average of precision and recall [see the "Methods" section]) in the Edwards et al. and Galiez et al. data sets (Fig. 2a, b).Specifically, the precision and recall of Phirbo in predicting interacting virus-host pairs were 59-65% and 57-64%, respectively, while BLAST had precision and recall in the range of 28-43% (Fig. 2a,  b).When setting a score cut-off that maximized the F1 score of each tool, Phirbo recalled 27-28% more interacting virus-host pairs than BLAST and 34-44% more pairs than WIsH.Phirbo found the correct host at the species and genus levels for 38-50% and 55-60% of the analyzed viruses, respectively (Fig. 2c, d).These results represent a 10% and 20% improvement over BLAST in the prediction of hosts at the species and genus levels, respectively.

Phirbo preserves BLAST top-ranked host predictions
We further evaluated the host prediction accuracy of Phirbo by selecting a top-scored prokaryotic sequence for each virus without thresholds on score values [14,16,17,19].Briefly, host prediction accuracy is calculated as the percentage of viruses whose predicted hosts have the same taxonomic affiliation as their respective known hosts (if multiple top-scoring hosts are present, the prediction is scored as correct if the true host is among the predicted hosts).Phirbo restored all hosts predicted by BLAST in the data sets by Edwards et al. and Galiez et al., achieving the same prediction accuracy as BLAST across all taxonomic levels (Table 1).Of note, BLAST found multiple different host species with equal scores for 14 phage genomes.This was observed in phages infecting bacteria from the Enterobacteriaceae family and the Rhodococcus and Bacillus genera.However, Phirbo assigned the highest score to the correct host species (Additional file 2: Table S3).Additionally, it refined the host prediction for the Cronobacter phage ENT39118 sequence, which BLAST assigned to the Escherichia coli genome.Phirbo revealed Cronobacter sakazaki as the primary host species, as the BLAST list of the Cronobacter phage is more similar in content and order to the BLAST list of C. sakazaki (Phirbo score = 0.50) than E. coli (Phirbo score 0.48) (Additional file 1: Figure S2).
As Phirbo links virus to host through common sequences, the content of the sequence database was the main factor defining host prediction quality.Since the similarity between viruses may indicate a common host [19,29], we expanded the two BLAST databases of prokaryotic sequences obtained from Edwards et al. and Galiez et al. by viral sequences (n = 820 and n = 1420, respectively), and recalculated Phirbo scores between every virus-prokaryote pair.The virus-host linkage through homologous prokaryotic and viral sequences increased the host prediction accuracy of Phirbo at all taxonomic levels, allowing correct identification of hosts at the genus level for 56-63% of viruses (Table 1).Specifically, Phirbo refined BLAST mis-predictions for 55 phage genomes and showed which sequences demonstrated low similarity to the sequences of their host species.The direct BLAST alignments of these phage sequences, and the sequences of their corresponding hosts, obtained significantly lower scores than alignments obtained by the other known phage-host pairs (P = 1.9 × 10 −45 , Mann-Whitney U test).Notably, Phirbo also assigned correct host species for 18 phages whose hosts were not reported in the BLAST results, mainly Chlamydia species, Vibrio cholerae, and the opportunistic pathogen, Acinetobacter baumannii.kb, 5 kb, 3 kb, and 1 kb) with 10 replicates.Host prediction accuracy was calculated as the mean percentage of viruses whose predicted hosts had the same taxonomic affiliation as their respective known hosts (Fig. 3).Although Phirbo achieved equal host prediction accuracy with BLAST across all contig lengths, it had substantially higher overall performance in terms of AUC and AUPR (Fig. S3; P < 10 −5 , Wilcoxon signed-rank test).Surprisingly, BLAST-based methods obtained higher host prediction accuracy across all contig lengths compared to WIsH, a tool designed to predict the hosts of short viral contigs (Fig. 3).
The host prediction accuracy of Phirbo was examined using the expanded BLAST database of both prokaryotic and viral full-length sequences.To ensure fairness, for each tested viral contig, we removed its corresponding full-length sequence from the BLAST database and recalculated Phirbo scores between the viral contig and every prokaryotic sequence.This approach outperformed BLAST at every contig length across all taxonomic levels in both data sets (Fig. 3).Generally, the host prediction accuracy of Phirbo improved by 5-11 percentage points compared to the BLAST results.For example, when the contig length was 3 kb, the prediction accuracy of Phirbo was 8-11% higher than BLAST at the family level and 8-17% higher than WIsH (Fig. 3; Additional file 2: Table S4).Phirbo also achieved the highest AUC and AUPR scores when discriminating between interacting and non-interacting virus-host pairs (Additional file 1: Figure S3).

Phirbo uses multiple protein and non-coding RNA signals for host prediction
We investigated the sequence information used by BLAST and Phirbo for host prediction.For each virus that was correctly assigned to the host species by both tools (n = 485), we calculated the fraction of the viral genome that was included in the segments aligned with prokaryotic sequences (sequence coverage).This analysis revealed that our tool used three times more viral sequence (median sequence coverage 35%) than BLAST (12%) (Additional file 1: Figure S4; P < 10 −15 , Wilcoxon signed-rank test).This increased sequence coverage indicates that different genome regions of the viruses map to the genomes of prokaryotic species other than the host species.For 249 of the 485 phages, more than one third of their genomes were aligned to genomes of their    host species (Additional file 2: Table S5).Such large regions of homology are likely prophages or phage debris left by large-scale recombination events during phage replication.The observed high sequence coverage points to the virus taxa, known for their temperate lifestyle and frequent recombination with host genomes (i.e., Siphoviridae family as well as the Peduovirinae and Sepvirinae subfamilies).
To further examine the properties of sequences that may be exchanged between a phage and its host, we selected a population of phages with sequence coverage below 30% (n = 236).These phages, which are less likely to represent complete prophages, belong to 16 viral families (Additional file 2: Table S6).Next, we re-annotated the genomic sequences of the phages to find putative protein and non-coding RNA (ncRNA) genes.Phage sequence regions used by Phirbo for host predictions were significantly enriched (P < 10 −5 ) in 82 protein families of known or probable function.In contrast, only half of the protein families were used in BLAST-based host predictions (Additional file 2: Table S7).The protein families used by Phirbo covered most of the processes of the viral life cycle including DNA replication, cell lysis, recombination, and packaging of the phage genome (Fig. 4).In contrast to BLAST, Phirbo also exploited the information contained in phage ncRNAs while assigning phages to host genomes.The vast majority of these ncRNAs (>90%) were tRNAs, which showed significant overrepresentation in the phage sequence fragments used by Phirbo (P = 4 × 10 −13 ) (Additional file 2: Table S8).The remaining ncRNAs belonged to group I introns (3%), RNAs associated with genes associated with twister and hammerhead ribozymes (1%), skipping-rope RNA motifs (1%), and eight less abundant RNA families.

Phirbo has higher precision and recall than VirHostMatcher-Net and PHP
We tested Phirbo against two machine-learning host prediction tools, VirHostMatcher-Net [19] and Prokaryotic virus Host Predictor (PHP) [20].VirHostMatcher-Net predicts phage-host interactions using multiple virus-host and virus-virus sequence similarity features including BLAST.PHP utilizes a Gaussian model based on differences of k-mer frequencies between viral and host genomic sequences.We benchmarked Phirbo, VirHostMatcher-Net, and PHP using the Wang et al. data set of 1462 viruses (W) and 62,493 candidate prokaryotic hosts [19,30].Analogously, we calculated host prediction accuracy for each tool by selecting a topscored prokaryotic sequence for each virus (Table 2).Phirbo was outperformed by PHP at the levels from order to phylum, and it had lower prediction accuracy than VirHostMatcher-Net at taxonomic levels from up to the class level.
Although VirHostMatcher-Net and PHP were trained and tested on mutually exclusive sets of viruses [19,20], both data sets contained viruses that have high sequence similarity and infect the same host species.To minimize the effect on the benchmark results of these potentially crossmatching sequences, we performed a more stringent test that gradually separated the testing viral sequences from the training data set.Specifically, we assembled three subsets (W species , W genus , and W family ) from the Wang et al. virus set (1,462 phages).W species consisted of all viruses for which host specificity at the species level was different than for viruses in the original training set.Correspondingly, W genus and W family sets had different host genera or families, respectively.
Across the three data sets, Phirbo achieved the highest host prediction accuracy at all taxonomic levels; for example, it recalled the correct host genus for 56-62% of The highest accuracies among the methods for each data set and taxonomic level are in bold viruses-outperforming VirHostMatcher-Net (n = 34-51%) and PHP (n = 25-34%) (Table 2).Phirbo was also markedly robust in regard to data set heterogeneity, as predictions across all four data sets varied significantly less, particularly at the species, genus, and family levels (standard deviation = 2-4%), than results of VirHostMatcher-Net (11-14%) and PHP (4-11%).

Implementation and availability
Predicting hosts from phage sequences using BLAST is accomplished by querying phage sequences against a database of candidate hosts.However, Phirbo also uses information about sequence relatedness among prokaryotic genomes.Therefore, it requires ranked lists of prokaryote species generated by BLAST for the virus and host genomes.The computational cost of querying every host sequence against the database of all candidate hosts using BLAST may still be a limiting factor.However, for mass host searches, the computational cost of all-versus-all host comparisons becomes marginal, as it must be done only once.After the relatedness among host genomes is established, the time required for Phirbo host predictions is negligibly higher than the time for typical BLASTbased host predictions.For example, running Phirbo between ranked lists of host species for 1462 viruses and 62,493 candidate hosts from Wang et al. (resulting in ~91 million phage-host comparisons) took 2 h on a 16-core 2.60GHz Intel Xeon.
As Phirbo operates on rankings, BLAST can be replaced by an alternative sequence similarity search tool to reduce the time to estimate homologous relationships between host genomes.For instance, Mash [31] computed host relationships in 2 h for the Wang et al. data set that encompassed 62,493 bacterial and archaeal genomes (see the "Methods" section).The host prediction performance of Phirbo using BLAST-based rankings for viruses and Mash-based rankings for host genomes is comparably high to the performance of Phirbo predictions using BLAST rankings for both viral and host genomes (Additional file 2: Table S9).
We envisage Phirbo as a natural extension to standard BLAST-based host predictions.The Phirbo tool is

Discussion
The identification of similar sequence regions between host and phage genomes using BLAST has been a baseline for the identification of putative virus-host connections in numerous metagenomic projects [13,[32][33][34].However, a BLAST search requires regions with significant similarity between the query phage and host [14,16,17].Yet, many viral and host sequences lack sufficient similarity and escape detection with standard BLAST searches.To tackle this issue, alignment-free tools have been developed to predict prokaryotic hosts from viral sequences [14,16,17,35].The rationale behind these tools is based on the observation that viruses tend to share similar patterns in codon usage or short sequence fragments with their hosts [14,16,17].As virus replication is dependent on the translational machinery of its host, some viruses adapt their codon usage to match the availability of tRNAs during viral replication in the host cell [36][37][38].Similar oligonucleotide frequency use may be driven by evolutionary pressure on the virus to avoid recognition by host restriction enzymes and CRISPR/Cas defense systems [37,39].Although state-of-the-art alignment-free tools (i.e., WIsH [17] and VirusHostMatcher [16]) can rapidly assess sequence similarity between any pair of virus and prokaryote sequences, they are less accurate for host prediction than BLAST [14,16].The relatively high accuracy of BLAST suggests that localized similarities of genetic material may be a stronger indication of virushost interactions than global convergence of their genomic composition.This evidence comes in the form of protein-coding DNA fragments and non-coding RNAs.The latter group is dominated by tRNA genes, which are strongly over-represented in direct BLAST alignments between phages and their hosts and are even more prevalent among indirect connections used by Phirbo.This may be important, as previous studies have shown that not all phage tRNA genes come directly from their hosts.Some appear to be derived from genomes of other, often distantly related, bacteria and may be the result of earlier evolutionary events [40].For proteincoding genes, a more diverse picture emerges.Proteins rich in phage-host BLAST alignments can be assigned into different functional categories including phage virion components, replication-related proteins, regulatory factors, and proteins involved in the metabolism of the host.The transfer of some over-represented families in phages and/or prophages has been previously reported (e.g., lytic proteins, DNA replication and recombination proteins, and enzymes involved in nucleotide and energy metabolisms [41]), and some of these genes are connected with the phage-host range [42,43].However, no clear pattern emerges after analyzing the functions of the remaining, over-represented proteins.
In this study, we attempted to expand the information content of a single local alignment of virus and host sequences by incorporating the results of multiple alignments between a viral sequence and different prokaryotic genomes.This approach may more closely resemble a manual assignment of virus-host pairs, where an expert analyst not only considers a top-ranked matching prokaryote in the BLAST results, but also uses the information contained in other, less significant, matches and their sequence and taxonomic similarity.Through a taxonomically aware stratification scheme, this approach tracks the multilateral dynamics of horizontal gene transfer.This dynamics is reflected by the fact that BLAST lists obtained by querying a database of prokaryotic genomes with viral sequences tend to cover more taxa than similar lists based on prokaryoteprokaryote comparisons (Additional file 1: Figure S5).This observation points to the phages as the hot-spots of horizontal gene transfer between evolutionary and ecologically related species.Therefore, we propose to relate virus and host sequences through multiple intermediate sequences that are detectably similar to both the virus and host sequences.By linking virus and host sequences through similar sequences, Phirbo achieved a more comprehensive list of virus-host interactions than BLAST.Simultaneously, Phirbo was capable of assessing almost all virus-host pairs, bringing the method closer to alignment-free tools, which compute scores between all possible virus and host pairs.Thus, our approach can be directly applied to different virus and prokaryote data sets without training or optimizing the underlying RBO algorithm.

Conclusions
Our results show that expanding the information obtained from plain similarity comparisons by incorporating taxonomically grounded measurements of phagehost similarity leads to improved precision and recall of phage-host predictions.The Phirbo method provides the phage research community with an easy-to-use tool for predicting the host genus and species of query phages, which is usable when searching for phages with appropriate host specificity and for correlating phages and hosts in ecological and metagenomic studies.

Virus and prokaryotic host data sets
The data sets analyzed in this study were retrieved from three previously published virus-host studies [14,17,19].The first set [14] contained 2699 complete bacterial genomes obtained from NCBI RefSeq and 820 RefSeq genomes of phages for which the host was reported.The data set encompassed 16,757 known virus-host interaction pairs and 2,196,424 pairs for which interaction was not reported (non-interacting phage-host pairs).The second data set [17] contained 3780 complete prokaryotic genomes of the KEGG database and 1420 viruses for which host species were reported in the RefSeq Virus database.The data set consisted of 26,024 interacting-and 5,341,576 non-interacting virus-host pairs.The third data set [19] included 1462 viruses and 62,493 candidate prokaryotic hosts encompassing 113,250 interacting-and 91,251,516 non-interacting virus-host pairs.

Phirbo score
The interaction score for a given virus-host pair was calculated using the ranked-biased overlap (RBO) measure.RBO [24] is a measurement of rank similarity that compares two lists of different lengths (giving more attention to high ranks on the lists).RBO ranges from 0 to 1, where a greater value indicates greater similarity between lists.Equation 1 was used for the calculation of the RBO value between two ranking lists, S and T.

RBO S; T
where the parameter p (0 < p < 1) determines how steeply the weight declines (the smaller the p, the more top results are weighted).When p = 0, only the topranked item is considered, and the RBO score is either 0 or 1.In this study, we set p to 0.75, which assigned ~98% of the weight to prokaryotic species at the first 10 ranks.A(S, T, d) is the Jaccard index, which measures overlap between the two ranking lists, S and T, up to rank d, calculated by Eq. 2. n is the number of distinct ranks on the ranking list.

Host prediction tools
The host prediction tools BLAST [21], WIsH [17], and Phirbo were run separately on the Edwards et al. and Galiez et al. data sets.For each tool, sequence similarity scores were calculated across all combinations of virusprokaryote pairs.BLAST 2.7.1+ [44] was run with default parameters (task: blastn, e-value threshold 10) to query each virus sequence against a database of candidate host genomes.For each BLAST alignment, the highest bit-score between every virus-host pair was reported (for virus-host pairs that were absent in the BLAST results, a bit-score of 0 was assigned).For RBO host prediction, an additional BLAST search was performed to establish ranked lists of genetically similar host genomes.Specifically, a nucleotide BLAST was run with default parameters to query each host sequence against a database of candidate host genomes.As an alternative to BLAST, Mash 2.1 [31] was used with default parameters (k-mer size = 21, sketch size = 1000) to establish ranked lists for each host by comparing its sequence against the database of candidate host genomes.RBO scores were calculated between all pairwise combinations of virus and host ranking lists.WIsH 1.0 [17] was used with default parameters to calculate loglikelihood scores between all pairwise combinations of virus-host sequences.To have comparable values between different phages, log-likelihood scores returned by WIsH were converted into z-scores.VirHostMatcher-Net 1.0 [19] and Prokaryotic virus Host Predictor (PHP) [20] were run using default parameters.

Evaluation metrics
The metrics of host prediction performance were calculated using sklearn (i.e., AUC, AUPR, recall, precision, specificity, and accuracy) [45].Optimal score thresholds to calculate recall, precision, specificity, and accuracy were computed as maximizing the F1 score, an accuracy metric, which is the harmonic mean of precision and recall.Host prediction accuracy was evaluated analogous to previous studies [14,17,19].Specifically, for each query virus, the host with the highest score to the query virus was selected as the predicted host.In cases where multiple hosts were predicted with equal score, the prediction was scored as correct if the correct host was among the predictions.The prediction accuracy was calculated at each taxonomic level as the percentage of viruses whose predicted hosts shared a taxonomic affiliation with known hosts.

Phage genome annotation
To define phage genes potentially exchanged between phage and host genomes, we re-annotated 485 phage genomes that were correctly assigned to host species by both Phirbo and BLAST.The genes were classified into predefined pVOGs (prokaryotic Virus Orthologous Groups) [46] and RNA families [47].Briefly, open reading frames (ORFs) in the analyzed 485 phage genomes were identified using Transeq from EMBOSS [48].The ORFs were then assigned to the respective orthologue group by HMMsearch (e-value < 10 −5 ) against the database of hidden Markov models (HMMs) created for every of 9518 pVOG alignments using HMMbuild of HMMER v3.3.1 [49].Non-coding RNAs (ncRNAs) were predicted in the phage genomes (e-value < 10 −5 ) using Rfam covariance models v14.3 [47] and the Infernal tool v1.1.3[50].We counted the number of times each pVOG and Rfam term was present in phage sequences used by BLAST and Phirbo during host prediction.To determine whether the observed level of pVOG/Rfam counts was significant within the context of all the terms within the phage genome, we calculated the p-value using the hypergeometric distribution implemented in Scipy [51].

(
See figure on previous page.)Fig. 2 Host prediction performance of Phirbo, BLAST, and WIsH.The performance is provided by receiver operating characteristic (ROC) and precision-recall (PR) curves and statistical measures (i.e., F1 score, precision, and recall) separately for (a) Edwards et al. and (b) Galiez et al. data sets.ROC curves and the corresponding area under the curve (AUC) display the classification accuracy of virus-host predictions across all possible virus-prokaryote pairs.Dashed lines represent the levels of discrimination expected by chance.Dashed lines in the PR curve plots represent the levels of discrimination expected by chance.Score cut-offs for each tool were set to ensure the highest F1 score.(c), (d) Number of correctly predicted virus-host interactions (%) in the Edwards et al. and Galiez et al. data sets, respectively.Bars indicate the number of viruses for which a correct host was predicted at the species (blue bars) and genus (red bars) levels out of all phages in Edwards et al. (n = 820) and Galiez et al. (n = 1,420)

Fig. 3
Fig. 3 Host prediction accuracy over virus contig length.Prediction accuracy is provided separately for (a) Edwards et al. and (b) Galiez et al. data sets.Each complete virus genome was randomly subsampled 10 times for different sequence lengths (i.e., 20 kb, 10 kb, 5 kb, 3 kb, and 1 kb).Hosts were predicted on each subsampling replicate by selecting a prokaryotic sequence with the highest similarity to the query viral sequence.Points indicate the average of the resulting accuracies for all the viruses at a given subsampling length and host taxonomic level (i.e., species, genus, and family).An extended version of this figure containing host prediction accuracy values is provided in Additional file 2: TableS4

Fig. 4
Fig. 4 Functional classification of phage coding sequences used by Phirbo for host prediction.Protein families (pVOGs) were classified into 15 functions (e.g., DNA replication, transcription).Numbers in the dark circles indicate the number of different pVOGs related to a given function.An extended version of this figure containing the list of pVOGs is provided in Additional file 2: TableS7

Fig. 5
Fig. 5 Host prediction performance of Phirbo, VirHostMatcher-Net, and PHP on the Wang et al. data set.The performance was evaluated using (a) precision-recall (PR) curves and (b) receiver operating characteristic (ROC) curves

A
S; T ; d ð Þ¼ S :d ∩T :d j j S :d ∪T :d j j where S :d and T :d represent the elements present in the first d ranks of lists S and T, respectively.

Table 1
[17] prediction accuracies (%) for virus and host genomes from the data sets by Edwards et al.[14]and Galiez et al.[17] The highest accuracies among the methods for each taxonomic level are in bold a Phirbo scores were calculated using rank-biased overlap (RBO) between BLAST lists containing prokaryotic sequences.Specifically, the BLAST database contained 2699 sequences of bacterial genomes in theEdwards etal.data set and 3780 sequences of bacterial and archaeal genomes in the Galiez et al. data set b Phirbo scores were calculated using RBO between BLAST lists containing both prokaryotic and viral sequences

Table 2
[19] prediction accuracies (%) for virus and host genomes from the Wang et al.[19]data set