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Design parametersA new type of Debris-flow grille dam is proposed to be built with a height of 8 m. Column section 500 mm × 700 mm, spacing 5000 mm. The cross section of the beam is 400 mm × 300 mm, and the spacing is 4000 mm. The section steel adopts I-steel 45a, the spacing is 250 mm. The counterfort wall is 300 mm thick and 6500 mm high. Pile foundation adopts manual digging pile, pile by 1000 mm, 5000 mm deep. The concrete is C30; Stressed bar is HRB335; Stirrups is HRB300; Stay Cable is 3 (emptyset) s15.2. The design size of the anchor piers is shown in Fig. 12. In the Figure where (T = 2 times 10^{5} N); (L_{l} = 8500;{text{mm}}); (E_{l} = 1.95 times 10^{5} ;{text{N/mm}}^{2}); (A_{l} = 420;{text{mm}}); (D_{e} = 1000;{text{mm}}); (L_{m} = 1200;{text{mm}}); (E_{e} = 3.0 times 10^{4} ;{text{N/mm}}^{2}); (H = 1000;{text{mm}}); (mu = 0.2); (E = 20;{text{N/mm}}^{2}). The parameter of gully bed soil is shown in Table 1.Figure 12The parameters of anchor piers.Full size imageTable 1 The parameters of gully bed soil.Full size tableAnalysis of results(1) The effect of the elastic modulus and Poisson’s ratio of the surrounding soil on the displacement deformation of the anchor-pulling system.The elastic modulus (E) and Poisson’s ratio (mu) are important parameters for calculating the displacement deformation of soil. They have something to do with both the properties of materials and the stress level. To analyze the effect of the physical parameter variation of the surrounding soil on the displacement deformation of the anchor-pulling system, we can study changing the elastic modulus and Poisson’s ratio. The variation range of the elastic modulus is 15–45 N/mm2, and the variation range of Poisson’s ratio is 0.15–0.25.Figure 13 shows the variation curve in which the displacement deformation increases with the elastic modulus of the soil around the anchor pier. We can see that as the elastic modulus of the soil around the anchor pier increases, the displacement deformation decreases gradually. When the elastic modulus is in the range of 15–35 N/mm2, the curve is steep, and the decrease in deformation is apparent. After 35 N/mm2, the curve becomes smooth, and the decrease in deformation tends to be stable.Figure 13The effect of the elastic modulus E(15–45 N/mm2) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageIn Fig. 14, the displacement deformation increases linearly with Poisson’s ratio of the soil around the anchor pier. However, the total impact is not large. From calculation, the variation of elastic modulus of the soil around the anchor pier has nothing to do with elastic deformation of the stayed cable ((S_{1} )), but mainly influences relative shear displacement between anchor piers and the surrounding soil ((S_{2} )) and the compression performance of the soil on the front of anchor piers ( (S_{3} )). where ((S_{2} )) accounted for 89% and (left( {S_{3} } right)) accounted for 11%. When the Poisson ratio increases, the displacement deformation also increases. Poisson’s ratio has the greatest influence on the relative shear displacement ((S_{2} )) of the anchor pier and soil, accounting for approximately 96.4%. The design parameters should be selected correctly during design. The influence of parameters on the deformation of anchor system is analyzed by using control variable method. The influence of a single variable on the results can be intuitively obtained. However, the elastic modulus E and Poisson ‘ s ratio (mu) of rock and soil are not independent. Therefore, Matlab is used to analyze the influence of the two aspects on the deformation of the tensile anchor system, and the results are shown in Fig. 15. It can be seen from Fig. 15 that the influence of elastic modulus E on the deformation of tensile anchor system is much greater than that of Poisson’s ratio (mu). And the variation of the curve is basically the same, so the interaction between the two is weak.Figure 14The effect of Poisson’s ratio (mu)(0.15–0.26) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageFigure 15Influence of elastic modulus E (15–45 N/mm2) and Poisson’s ratio (mu left( {0.15 – 0.26} right)) on deformation of anchor system.Full size image(2) The effect of the design parameters of anchor piers on the displacement deformation of the anchor-pulling system.The design parameters of anchor piers include the equivalent width (D_{e}), length (L_{m}) and height (H). Different design parameters have varying effects on the displacement deformation of the anchor-pulling system. Keep other parameters unchanged and let ( D_{e} ) vary in 0.5–1.5 m, (L_{m}) vary in 0.6–2.0 m, and (H) vary in 0.5–1.5 m. Analyzing their effect on the displacement deformation of the anchor-pulling system, the results are shown in Figs. 16 and 17.Figure 16The effect of equivalent width (D_{e})(500–1500 mm) on the displacement of the anchor-pulling system.Full size imageFigure 17The effect of equivalent length (L_{m})(600–2000 mm) on the displacement of the anchor-pulling system.Full size imageAs illustrated in Figs. 16 and 17, the effects of the design parameters of the anchor piers on the displacement deformation of the anchor-pulling system are almost the same. As the size increases, the displacement deformation gradually decreases, and the front section decreases quickly, while the rear section becomes gradually smooth. Here, the equivalent width (D_{e}) and length (L_{m}) mainly affect the compression performance of the soil on the front of anchor piers (left( {S_{3} } right)). The anchor piers can be seen as rigid bodies where horizontal displacement takes place. Increasing the size means increasing the contact area between the anchor pier and soil body. With this increase, the compression performance of the soil on the front of the anchor piers decreases. However, the effect of the height (H) on the displacement deformation of the anchor-pulling system is the contribution to the relative shear displacement between the anchor piers and the surrounding soil ((S_{2} )). When (H) grows, ((S_{2} )) grows accordingly. However, theoretically, the larger the effect of the size, the better it is. Because of the constraint of topographic conditions, construction conditions and economic benefits in practical engineering, it is necessary to choose the best size. the anchor pier provides enough anchor force and saves all kinds of resources. The best design dimensions suggested are (D_{e}) = 1.2 m–1.8 m, (L_{m}) = 1.5 m–2.5 m, and (H) = 1.0 m–1.6 m.It can be seen from Fig. 18 that the width (D_{e}) and the height (L_{m}) of anchor pier influence each other greatly. When (D_{e}) is 600 mm, with the increase of (L_{m}), the deformation of tension anchor system will first decrease and then increase. When (D_{e}) is greater than 800 mm, with the increase of (L_{m}), the deformation of tension anchor system will continue to decrease. And with the increase of (L_{m}), the decreasing trend is more obvious. When (L_{m}) is 500 mm, with the increase of the height of the anchor pier (D_{e}), the deformation of the anchor system will increase first. When (L_{m}) is greater than 800 mm, with the increase of (D_{e}), the deformation of the anchor system will continue to decrease. But the decreasing trend is not much different.Figure 18Influence of Anchor Pier Width (D_{e} left( {500 – 1500;{text{mm}}} right)) and Anchor Pier Height (L_{m} left( {600 – 2000;{text{mm}}} right)) on Deformation of Anchorage System.Full size imageThe numerical validationThe establishment of the finite element modelWhen the finite element model of the anchor-pulling system and surrounding soil is created, the constitutive model of the surrounding soil uses the Mohr–Coulomb elastoplastic model. The anchor pier and surrounding soil use eight nodes as oparametric elements, such as solid45, of which the basic grid unit is cubic units. When the grid is divided, the grid between the anchor pier and the surrounding soil contact is dense. The LINK10 unit is used to simulate cables, which have a bilinear stiffness matrix. It can simulate not only tensile bar units but also compressed bar units. For example, when the pull-up option is used alone, if the unit is under pressure, its stiffness disappears, so it can be used to simulate the relaxation of cables or chains. This feature is very significant for the static problem of wire rope, which uses a unit to simulate the entire cable. It can also be used for dynamic analysis with inertial or damping effects when the needed relaxation unit should pay attention to its performance rather than its movement. The soil is homogeneous. The soil physical parameters and structure design parameters are consistent with the theoretical calculation parameters mentioned above. The tensile force of the cable is exerted on the nodes as a force. The top surface of the model is free, and the normal displacements of the remaining faces are constrained such that the displacements are zero. The contact of the anchor pier and surrounding soils is a rigid-flexible surface-to-surface contact element to reflect the interaction. The surface of the anchor pier is regarded as the “target” surface, and the surface of the soil body is regarded as the “contact” surface. The coefficient of friction and normal penalty stiffness are 0.35 and 0.15, respectively. The scope of interaction between the anchor pier and the surrounding soil in the model is taken as 15 m × 11 m × 12 m, referring to past experience in engineering and the research data of the effect scope that the related anchors have had on the soil. The values of the model geometric parameters and physical and mechanical parameters are the same as in “Design parameters” section. The finite element model is shown in Fig. 19.Figure 19Finite element model of the anchor-pulling system and surrounding soil.Full size imageResearch on finite element model gridIn order to verify the convergence of numerical simulation, the soil was divided into three different mesh sizes. Condition 1 is fine finite element meshing. The stress nephogram of condition 1 is shown in Fig. 20. Condition 2 is medium finite element mesh. The stress nephogram of condition 1 is shown in Fig. 21. Condition 3 is coarse finite element mesh. The stress nephogram of condition 1 is shown in Fig. 22. See Table 2 for specific grid division.Figure 20Condition 1 stress cloud diagram.Full size imageFigure 21Condition 1 stress cloud diagram.Full size imageFigure 22Condition 1 stress cloud diagram.Full size imageTable 2 Mesh size of three working conditions.Full size tableIt can be seen from the stress nephogram of the three working conditions that the thicker the grid is, the greater the displacement of the anchor system is. The maximum displacement difference between condition 2 and condition 3 is 2.6%; the maximum displacement of condition 1 is 17% different from that of condition 2. The finer the mesh, the more accurate the numerical simulation results. But with the increase in computing time. It can be seen from Table 2 that the maximum iteration of condition 1 is 10 times, and the result will converge. The maximum iterations of condition 2 and 3 only need 7 times, and the results can converge.The calculation resultsFigure 23 and Fig. 24 are the displacement nephograms of the soil around the anchor piers for 100 kN and 400 kN, respectively. The soil displacement increases with increasing load, the affected area will increase and become uniform, and the area under load will also increase. The soil within the range of 1–3 m around the anchor pier is greatly affected, accounting for 80% of the total force. The soil around the anchor pier should be reinforced, and the anchoring force should be enhanced in the design.Figure 23Displacement fringe of soil around the anchor piers for 100 kN.Full size imageFigure 24Displacement fringe of soil around the anchor piers for 400 kN.Full size imageIn order to further study the influence of anchorage pier size on the displacement and deformation of anchorage system, finite element models with different sizes are established by finite element method. The stress nephogram is shown in Figs. 25, 26 and 27.Figure 25Top 800 mm, bottom 800 mm anchor pier stress nephogram.Full size imageFigure 26Top 1000 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFigure 27Top 800 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFrom Figs. 25, 26 and 27, it can be seen that when the anchor pier is rectangular, the deformation of the tensile anchor system decreases with the increase of the size of the anchor pier, but the degree is small. When the anchor pier is trapezoidal, the material is small, but the deformation is more ideal than the rectangular. It can be seen that reasonable selection of anchor pier size is crucial, not blindly increase the size of anchor pier.Figure 28 shows that the displacement of the soil around the anchor pier increases with increasing load, and the added value is obvious at approximately 2–3 mm. Figure 29 shows that the increase in load has a great effect on the soil in front of the anchor pier. As the load increases, the compressive deformation of the soil gradually increases. As the distance from the anchor pier increases, the displacement of the soil decreases, and the scope of influence gradually decreases. The displacement of the soil tends to be stable beyond 4–5 m from the anchor pier.Figure 28The displacement of soil around anchor pier.Full size imageFigure 29The horizontal displacement of soil along cable axis.Full size imageComparison of theoretical calculation and numerical simulation results at the time of load variationTo verify the correctness of the theoretical calculation, we compare the theoretical calculation with numerical simulation results of displacement deformation of anchor-pulling system under different pulling force of stayed cable. The results are shown in Fig. 30, see Table 3 for data.Figure 30Comparison of theoretical calculation and numerical simulation results.Full size imageTable 3 Comparison between theoretical calculation and numerical simulation.Full size tableAs seen from Fig. 30, the theoretical and numerical simulation results are consistent, showing a linear growth trend. The slope difference of the two straight lines is approximately 5%, which meets the accuracy requirements of geotechnical engineering. As the restraint effect of the surrounding soil on the anchor pier is not fully considered, the theoretical calculation result is too large. The deformation of anchor (left( {S_{1} } right)) in displacement deformation is the same, and the relative shear displacement (left( {S_{2} } right)) of the anchor pier and the soil and the compressive deformation ((S_{3} )) of the soil at the front end of the anchor pier are 1.25 times and 1.08 times the numerical simulation results, respectively. The change in (left( {S_{2} } right)) in the calculation results is large and should be taken into account in the design. More

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Detection and validation of high-quality jumbo phage binsDue to the large size of jumbo bacteriophage genomes, it is likely that they are present in multiple distinct contigs in metagenomic datasets and therefore require binning to recover high-quality metagenome-assembled genomes (MAGs) [28]. This has been shown for large DNA viruses that infect eukaryotes, where several recent studies have successfully employed binning approaches to recover viral MAGs [2, 3, 30]. Here, we used the same 1545 high-quality metagenomic assemblies [31] used in a recent study to recover giant viruses of eukaryotes [3], but we modified the bioinformatic pipeline to identify bins of jumbo bacteriophages. These metagenomes were compiled by Parks et al. [31] and included available metagenomes on the NCBI’s Short Read Archive by December 31, 2015 (see Parks et al. [31]). This dataset includes a wide variety of marine metagenomes (n = 469) including many non-Tara metagenomes (n = 165). We focused our benchmarking and distribution analyses on Tara data [29] because of the well-curated metadata and size fractions in this dataset. We first binned the contigs from these assemblies with MetaBat2 [32], which groups contigs together based on similar nucleotide composition and coverage profiles, and focused on bins of at least 200 kilobases in total length. We subsequently identified bins composed of bacteriophage contigs through analysis with VirSorter2 [33], VIBRANT [34], and CheckV [35] (see Methods for details).The occurrence of multiple copies of highly conserved marker genes is typically used to assess the level of contamination present in metagenome-derived genomes of bacteria and archaea [36]. Because bacteriophage lack these marker genes [37], we developed alternative strategies to assess possible contamination in our jumbo phage bins. Firstly, we refined the set of bins by retaining those with no more than 5 contigs that were each at least 5 kilobases in length to reduce the possibility that spurious contigs were put together. Secondly, we assessed the possibility that two strains of smaller phages with similar nucleotide composition may be binned together by aligning the contigs in a bin to each other. Bins that had contigs with high sequence similarity across the majority of their lengths were discarded (Supplementary Fig. 1). Thirdly, we discarded bins if their contigs exhibited aberrant co-abundance profiles in different metagenomes (see Supplementary Methods). To generate these co-abundance profiles, we mapped reads from 225 marine metagenomes provided by Tara Oceans [29] onto the bins. Coverage variation between contigs was benchmarked based on read-mapping results from artificially-fragmented reference genomes present in the samples (See Methods for details). Only bins with coverage variation below our empirically-derived threshold were retained. Using this stringent filtering, we identified 85 bins belonging to jumbo bacteriophages. These bins ranged in length from 202 kbp to 498 kbp, and 31 consisted of a single contig, while 54 consisted of 2–5 contigs (Supplementary Fig. 2).To assess global diversity patterns of jumbo bacteriophages, we combined these jumbo phage bins together with a compiled database of previously-identified jumbo phages that included all complete jumbo Caudovirales genomes on RefSeq (downloaded July 5th, 2020), the INPHARED database [14], a recent survey of cultivated jumbo phages [6], the Al-Shayeb et al. study [4], and marine jumbo phage contigs from metagenomic surveys of GOV 2.0 [26] (60 jumbo phages), ALOHA 2.0 [38] (8 jumbo phages), and one megaphage MAG recovered from datasets of the English Channel [39]. Ultimately, we arrived at a set of 244 jumbo phages, including the 85 bins, that were present in at least one Tara Oceans sample (min. 20% genome covered, see Methods) or deriving from a marine dataset (i.e. ALOHA, GOV 2.0) which we analyzed further in this study and refer to as marine jumbo phages. Statistics on genomic features can be found in Supplementary Dataset 1.Marine jumbo phages belong to distinct groups with diverse infection strategiesBecause bacteriophages lack high-resolution, universal marker genes for classification, such as 16S rRNA in bacteria, phages are often grouped by gene content [40, 41]. Here, we generated a bipartite network that included the 85 bins of jumbo phages with a dataset of available Caudovirales complete genomes in RefSeq (3012 genomes; downloaded July 5th, 2020) and the full set of reference jumbo phages described above. To construct the bipartite network, we compared proteins encoded in all the phage genomes to the VOG database, and each genome was linked to VOG hits that were present (Fig. 1, Supplementary Dataset 2, see Methods for details). To identify groups of phage genomes with similar VOG profiles, we employed a spinglass community detection algorithm [42] to generate genome clusters. Similar methods have recently been used to analyze evolutionary relationships in other dsDNA viruses [41]. The marine jumbo phages of this study clustered into five groups that included both jumbo and non-jumbo phage genomes (Fig. 2a). We refer to these five clusters as Phage Genome Clusters (PGCs): PGC_A, PGC_B, PGC_C, PGC_D, and PGC_E. These PGCs included cultured phages and metagenome-derived jumbo phages found in various environments (i.e. aquatic, engineered) and isolated on a diversity of hosts (i.e. Firmicutes, Proteobacteria, Bacteroidetes) (Fig. 2b, c). Of the marine jumbo phages, 135 belonged to PGC_A, 11 to PGC_B, 90 to PGC_C, 7 to PGC_D, and 1 to PGC_E (Fig. 1b). In addition to this network-based analysis, we also examined phylogenies of the major capsid protein (MCP) and the terminase large subunit (TerL) encoded by the marine jumbo phages and the same reference phage set examined in the network (Fig. 1c, d). With the exception of PGC_A, the marine jumbo phages that belong to the same PGC appeared more closely related to each other than those belonging to different clusters. The polyphyletic placement of jumbo phage PGCs in these marker gene phylogenies is consistent with the view that genome gigantism evolved multiple times, independently within the Caudovirales [6].Fig. 1: Bipartite network and marker gene analyses of jumbo phages.a Network with marine jumbos and references as nodes and edges based on shared VOGs. Marine jumbo phage nodes are colored by PGC as detected with spinglass community detection analysis, other nodes are in gray. Edges and VOG nodes have been omitted to more clearly represent the pattern of phage clustering. Node size corresponds to the natural log of genome length in kilobases. b Barchart of the number of members in each PGC. PGCs with marine jumbo phages are denoted with a star and the number of marine jumbo phages in that PGC. Proportion of marine jumbo phages in that PGC is colored. Phylogenies of TerL (c) and MCP (d) proteins with references and bins. Inner ring and branches are colored by the 5 PGCs that marine jumbo phages belong to. Navy blue circles in the outer ring denote marine jumbo phages.Full size imageFig. 2: Statistics of the Phage Genomes Clusters (PGCs).a Boxplot of genome length in each network cluster (x-axis is PGC number). Star denotes PGC with a marine jumbo phage and the color matches the PGC letters of Fig. 1. b Stacked barplot of the metagenome environment from which each phage derives from in each PGC (x-axis). Reference (yellow) are cultured phages, in black are the bins of jumbo phages from this study. c Stacked barplot of the host phylum of the RefSeq cultured phages in each cluster; metagenomic phages are in gray.Full size imageWe then compared functional content encoded by the marine jumbo phages in the PGCs to identify functional differences that distinguish these groups. PGC_E was excluded from this analysis because this genome cluster contained only a single jumbo phage. Collectively, most genes of the marine jumbo phages could not be assigned a function (mean: 86.60%, std dev: 7.01%; Supplementary Dataset 3), which is common with environmental viruses [43, 44]. Genes with known functions primarily belonged to functional categories related to viral replication machinery, such as information processing and virion structure (Fig. 3a), and these genes drove the variation between the genome clusters of marine jumbo phages (Fig. 3b). A recent comparative genomic analysis of cultivated jumbo phages was able to identify three types of jumbo phages that are defined by different infection strategies and host interactions (referred to as Groups 1–3) [6]. We cross-referenced our PGCs and found that PGCs B, C, and D of this study corresponded to Groups 1, 2, and 3, respectively, suggesting that these genome clusters contain phages with distinct infection and replication strategies. PGC_A corresponded to multiple groups, indicating that this genome cluster contains a particularly broad diversity of phages.Fig. 3: Functional predictions of PGCs.a Functional categories for genes encoded by jumbo phages averaged by PGC. b Heatmap of proportion of genomes in each PGC that contain the listed genes. Listed genes were selected based on containing a known function and having a variance between the PGCs above 0.2. Dendrogram was generated based on hierarchical clustering in pheatmap.Full size imageThe second largest phage cluster with marine jumbo phages, PGC_B, consists of 238 phages (11 (4.6%) marine jumbo phages, including 10 bins generated here), and included cultured phages of Group 1, which is typified by Pseudomonas aeruginosa phage PhiKZ. Supporting this correspondence with Group 1, all marine jumbo phages of PGC_B encoded the same distinct replication and transcription machinery, including a divergent family B DNA polymerase and a multi-subunit RNA polymerase (Fig. 3b, Supplementary Dataset 3). These marine jumbo phages also encoded a PhiKZ internal head protein, and they uniquely encoded shell and tubulin homologs which has recently been found in PhiKZ phages to assist in the formation of a nucleus-like compartment during infection that protects the replicating phage from host defenses [18, 19]. Although we could not confidently predict hosts for the 11 metagenomic marine jumbo phages in this PGC_B (Supplementary Dataset 1), the cultured phages of this genome cluster infect pathogenic bacteria belonging to the phyla Proteobacteria (178 phages) and Firmicutes (6 phages) (Fig. 2c), implicating a potential host range for marine jumbo phages in PGC_B.The next largest phage genome cluster, PGC_C, comprised of 156 phages total (90 marine jumbo phages (57.7%); 4 bins generated from this study) and included reference jumbo phages in Group 2 (31, 19.9%) which are typified by Alphaproteobacteria and Cyanobacteria phages. Likewise, the host range of other cultured phages in PGC_C support the Group 2 correspondence, either infecting Cyanobacteria (139 phages) or Proteobacteria (4 phages) (Fig. 2c). Furthermore, all 3 marine metagenomic phages in PGC_C for which hosts could be predicted were matched to Cyanobacteria hosts (Supplementary Dataset 1). Functional annotations of PGC_C marine jumbo phages revealed nearly all encode a family B DNA polymerase (97.8% of phages) and the photosystem II D2 protein (PF00124, VOG04549) characteristic of cyanophages (90% of phages) (Fig. 3b). This PGC included the reference Prochlorococcus phage P-TIM68 (NC_028955.1), which encodes components of both photosystem I and II as a mechanism to enhance cyclic electron flow during infection [45]. This suggests that an enhanced complement of genes used to manipulate host physiology during infection may be a driver of large genome sizes in this group. Additionally, most of the PGC_C marine jumbo phages encoded lipopolysaccharide biosynthesis proteins (76%), which have been found in cyanophage genomes that may induce a “pseudolysogeny” state, when infected host cells are dormant, by changing the surface of the host cell and preventing additional phage infections [6] (Supplementary Dataset 3). Taken together, most marine jumbo phages of PGC_C likely follow host interactions of jumbo cyanophages, such as potentially manipulating host metabolism by encoding their own photosynthetic genes and potentially inducing a pseudolysogenic state.Finally, phages of PGC_D totaled at 47 phages, of which 7 were marine jumbo phages generated in this study (14.9%). This group included Group 3 jumbo phages (15, 31.9%), which is primarily distinguished by encoding a T7-type DNA polymerase but is not typified by a particular phage type or host range. Supporting this grouping, all marine jumbo phages in this study encoded a T7 DNA polymerase which belongs to family A DNA polymerases (Fig. 3b, Supplementary Dataset 3). Most of the other genes distinctively encoded by the marine jumbo phages in this group included structural genes related to T7 (T7 baseplate, T7 capsid proteins), a eukaryotic DNA topoisomerase I catalytic core (PF01028), and DNA structural modification genes (MmcB-like DNA repair protein, DNA gyrase B). Hosts of metagenomic marine jumbo phages in PGC_D could not be predicted (Supplementary Dataset 1); however, cultured Group 3 jumbo phages in PGC_D all infect Proteobacteria, primarily Enterobacteria and other pathogens.The largest of the phage genome clusters, PGC_A, contained 469 phages, including 135 marine jumbo phages (63 bins from this study). This genome cluster contained the largest jumbo phages, such as Bacillus phage G (498 kb) and the marine megaphage Mar_Mega_1 (656 kb) recently recovered from the English Channel [39]. Unlike other PGCs, PGC_A contained mostly metagenomic phages (401, 85%, Fig. 2b, c). Considering PGC_A contains the largest jumbo phages (Figs. 1b, 2a), the vast genetic diversity in this PGC might explain why few genes were found to distinguish this group. Of the genes unique to PGC_A, only one was present in at least half of the phages (51.9%), which was a Bacterial DNA polymerase III alpha NTPase domain (PF07733). The host ranges of cultured phages from this PGC further reflect the large diversity of this group and included a variety of phyla and genera that can perform complex metabolisms or lifestyles, such as the nitrogen-fixing Cyanobacteria of the Nodularia genus isolated from the Baltic Sea (accessions NC_048756.1 and NC_048757.1) and the Bacteroidetes bacteria Rhodothermus isolated from a hot spring in Iceland (NC_004735.1) [46]. Because this group contains an abundance of metagenome-derived genomes that encode mostly proteins with no VOG annotation (Supplementary Dataset 2), it is possible that it includes several distinct lineages that could not be distinguished using the community detection algorithm of the bipartite network analysis.Relative abundance of jumbo bacteriophages across size fractionsTo explore the distribution of the marine jumbo phages in the ocean, we first examined the size fractions in which the jumbo phages were most prevalent. To remove redundancy for the purposes of read mapping, we examined the 244 jumbo phages at the population-level ( >80% genes shared with >95% average nucleotide identity [24]), corresponding to 142 populations (11 unique to this study, corresponding to 47 bins). We then mapped Tara Oceans metagenomes onto the 142 jumbo phage populations, and 102 of these populations could be detected [min. 20% of genome covered], resulting in 74 populations in PGC_A, 2 in PGC_B, 22 in PGC_C, 3 in PGC_D, and 1 in PGC_E. Out of the 225 Tara Oceans metagenomes examined, 213 (94.6%) contained at least one jumbo phage population (median: 7, Supplementary Dataset 4). Jumbo phages were more frequently detected in samples below 0.22 µm ( More

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Following the work in36, we construct an epidemiological model which tracks the disease dynamics and population of two species of hosts following the introduction of a pathogen. The native host (hereafter simply referred to as “type 1”) is vulnerable to the disease, but due to being well adapted to the native habitat has high fecundity when uninfected. The invasive host (hereafter referred to as “type 2”), has coevolved defenses to the pathogen that increase both its tolerance of and resistance to the disease, but is not inherently as well-adapted to the habitat in the absence of infection (i.e., its intrinsic rate of growth in the new habitat is lower than that of the native).Our initial conditions correspond to a population of uninfected type 1 hosts with a small number of both uninfected and infected type 2 hosts, representing an invasion by a novel competitor carrying a novel pathogen into the type 1 population. We consider a vector-borne pathogen, and make the simplifying assumption that there is an already abundant competent vector species in the habitat. (For this initial formulation, we considered a scenario of mosquito-borne infections in birds, such as avian malaria37 or West Nile virus38, to motivate concrete choices.)The model couples two biological dynamics: the daily vector-borne spread of the disease among hosts, and a yearly host breeding cycle. We simulate in discrete time-steps that represent days using an SIR model taking into account the interactions between the disease, the two species of host, and the vectors. The model also includes a passive death rate for hosts of vectors, which increases for hosts while infected. While the vectors are assumed to breed daily, the hosts reproduce as part of an assumed annual breeding season, every (t_c) time-steps (typically equal to 365). These dynamics were informed by considering an annually breeding bird population in a tropical environment, however, they are not meant to reflect the realism of any one biological system. They are chosen here merely to allow a clean interpretation of modeled scenarios. Future models should explore the impact of greater variety in the dynamics of possible vector and host reproductive patterns.Epidemiological modelThe model tracks eight variables corresponding to combinations of host species and vectors with their infection status. Hosts may be of type 1 or 2, and are either susceptible to the disease ((S_1, S_2)), currently infected ((I_1, I_2)), or recovered ((R_1, R_2)). We assume that recovery is complete and recovered individuals suffer no residual effects from their infection aside from a lifelong immunity to becoming reinfected. (We later set the recovery rate for host type 1 to 0, so (R_1 = 0) at all times, but leave it defined for the sake of generality.) For simplicity, we model using only one stage of infection in which individuals are both infectious and symptomatic. The model also tracks the status of the vector population, which may either be susceptible ((S_v)) or infected ((I_v)). We assume that vectors do not recover from the disease, but also suffer no negative effects from being infected, acting only as carriers.For convenience of notation, we denote the total number of hosts$$begin{aligned} H = S_1 + I_1 + R_1 + S_2 + I_2 + R_2 end{aligned}$$and the relative frequencies of infection within their respective population$$begin{aligned} F_1 = frac{I_1}{H}, F_2 = frac{I_2}{H},F_v = frac{I_v}{S_v+I_v} end{aligned}$$which allows some equations to be written more compactly. Table 1 shows a summary of these variables.Table 1 Variables.Full size tableThe model also has several constant parameters that affect the dynamics. (beta _j) determines the probability that hosts of type j become infected when bitten by a single infected vector. We typically set (beta _1 > beta _2), making type 2 hosts less likely to become infected.Likewise, (delta _j) determines the probability that a vector becomes infected when biting an infected host of type j.(b_j) determines the bite rate for vectors on host type j. We assume that each vector bites the same number of hosts per day, so each vector’s probability of becoming infected depends only on the frequency of infection among hosts, while each host will be bitten more if there are more vectors.(gamma _j) determines the proportion of infected hosts of type j that recover from the disease each day. We typically set (gamma _1 = 0 < gamma _2), meaning infected hosts of type 1 do not recover, while infected type 2 recover after an average of (1/gamma _2) days.(mu _{j-}) determines the daily death rate for uninfected hosts of type j and (mu _{j+}) determines the death rate for infected host of type j. We typically set (mu _{1-} = mu _{2-}< mu _{2+} < mu _{1+}), meaning uninfected hosts have the same death rate regardless of type, infected type 2 have a higher death rate than uninfected hosts, and infected type 1 have the highest. (Both susceptible and recovered hosts are considered to be uninfected.) Table 2 shows a summary of parameters related to the SIR dynamics.Equation 1 shows continuous ordinary differential equations approximating the dynamics. Note that the actual model instantiates these in discrete time-steps using the forward Euler method with (h = 1).$$ begin{aligned}&frac{dS_1}{dt} = - S_1 beta _1 b_1 I_v /H - S_1 mu _{1-} \&frac{dI_1}{dt} = S_1 beta _1 b_1 I_v /H - gamma _1 I_1 - I_1 mu _{1+} \&frac{dR_1}{dt} = I_1 gamma _1 - R_1 mu _{1-} \&frac{dS_2}{dt} = -S_2 beta _2 b_2 I_v /H - S_2 mu _{2-} \&frac{dI_2}{dt} = S_2 beta _2 b_2 I_v /H - I_2 gamma _2 - I_2 mu _{2+} \&frac{dR_2}{dt} = I_2 gamma _2 - R_2 mu _{2-}\&frac{dS_v}{dt} = alpha _v H -S_v delta _1 b_1 F_1 -S_v delta _2 b_2 F_2 -S_v mu _v\&frac{dI_v}{dt} = S_v delta _1 b_1 F_1 + S_v delta _2 b_2 F_2 - I_v mu _v\ end{aligned} $$ (1) Table 2 Parameters for SIR dynamics.Full size tableFollowing a standard SIR model, susceptible hosts can become infected, and infected hosts become recovered, but each equation also contains a negative term corresponding to deaths. Thus, the total population of hosts is strictly decreasing in this time-frame. We assume that the vectors breed on a much shorter timescale than hosts, so we include a term for their births here, while host births are implemented by a yearly breeding event. We assume no vertical disease transmission, so all new vectors begin in the susceptible category. We assume that the daily birthrate for each vector increases with access to hosts, and decreases with competition among other vectors for hosts and breeding sites, so we set it equal to (frac{alpha _v H}{S_v + I_v}), where (alpha _v) is a constant scaling factor. Since the birthrate for each vector contains the total number of vectors in its denominator, the total number of vector births in the population will simply be (alpha _v H).A population with a larger number of hosts will be able to sustain a larger number of vectors. For a population with a constant number of hosts, the equilibrium vector population will be proportional to the number hosts: aH where (a = frac{alpha _v}{mu _v}) is the equilibrium vector density (number of vectors per host). For instance if (a = 2), then in equilibrium there will be twice as many vectors as hosts. Given a fixed number of hosts, the population of vectors will asymptotically approach the equilibrium value. In practice the total number of hosts is constantly changing, so the population of vectors will chase after this moving equilibrium, though for our standard parameters (alpha _v) and (mu _v) are sufficiently large such that this will occur on a short timescale, and the population of vectors remains close to the current equilibrium value.Breeding eventTable 3 shows a summary of parameters related to the breeding event. Every (t_c) days (typically 365), a breeding event occurs according to the following process.Table 3 Parameters for breeding event.Full size tableLet$$begin{aligned}&Delta S_1 = t_c alpha _{1-}(S_1+R_1)+t_calpha _{1+} I_1 \&Delta S_2 = t_c alpha _{2-}(S_2+R_2)+t_calpha _{2+} I_2 \ end{aligned}$$be the number of new host offspring of each type born this generation. In order to maintain consistency of temporal units among the parameters, each birthrate parameter is multiplied by (t_c). Let H be the current total number of hosts. Let$$begin{aligned} c = {left{ begin{array}{ll} 0 &{} hbox {if } H ge kappa \ 1 &{} hbox {if } H + Delta S_1 + Delta S_2 le kappa \ frac{kappa -H}{Delta S_1 + Delta S_2} &{} hbox {otherwise} \ end{array}right. } end{aligned}$$be the proportion of offspring that survive to adulthood. (None, if the population is already above carrying capacity. All, if the difference between the reproducing population size and the carrying capacity exceeds the new births. If the population is approaching carrying capacity, juvenile mortality scales proportionally so that the population will hit carrying capacity but not exceed it.)Then$$begin{aligned}&S_1 + c Delta S_1 rightarrow S_1 \&S_2 + c Delta S_2 rightarrow S_2 \ end{aligned}$$We assume there is no vertical disease transmission, so all new hosts begin in the susceptible category. We assume that the host population is iteroparous, such that the new offspring and the existing adult population both carry over to the next generation. If the new population would exceed the carrying capacity, we assume the limited space or supplies reduces the number of successful offspring so that the population exactly reaches the carry capacity by reduction in juvenile survival rather than population-wide competition that could also reduce the adult population.The carrying capacity is therefore what drives the interspecific host competition. Because births of both species are summed and then normalized by the total number of births, the higher the birthrate of one host, the larger a fraction of the available space it will capture during the breeding event. Similarly, the lower the death-rate of a host, the less space it frees up for the next breeding event. Even if one host species would be able to sustain a stable population on its own, the presence of a more fit competitor can lead to the extinction of the less fit type by driving its effective birth rate down.Immune-reproductive trade-offs and boundary conditionsWe assume that host type 1 is evolutionarily stable in the absence of the disease; an uninfected monoculture population below the carrying capacity will have at least as many births as deaths each cycle. In a continuous version of this model where births and deaths happened simultaneously, this might be defined by (alpha _{1-} ge mu _{1-}) . However in our model, the population spends many days decreasing due to deaths before the next breeding event occurs. The population exponentially decays throughout the cycle, and then jumps up during the breeding event. The number of new host births is proportional to the number of hosts at the start of the breeding event, which will be the lowest value of any other time during the cycle. Thus, the birth rate needs to be high enough that the surviving hosts can compensate despite their diminished numbers. Taking this into account, we get the condition$$begin{aligned}&alpha _{1-} ge frac{1-(1- mu _{1-})^{t_c}}{(1-mu _{1-})^{t_c}} \ end{aligned}$$Which is a higher bound on (alpha _{1-}) than the simpler one above, but will be close to it if (mu _{1-}) and (t_c) are small.To implement the scenario in which type 2 has increased resistance and tolerance to the disease at the expense of overall fecundity, we implement the following boundary conditions:$$begin{aligned}&beta _1 > beta _2 \&0 = gamma _1< gamma _2 \&mu _{1-} = mu _{2-}< mu _{2+} < mu _{1+} \&alpha _{1-} > alpha _{2-} > alpha _{2+} > alpha _{1+} end{aligned}$$Type 2 hosts are less likely to contract the disease, and are able to recover from it, while type 1 lack the immunological strength to eradicate it completely. Additionally, while both types of host are weakened by the disease, type 2 suffer fewer negative effects. However, this stronger immune response comes at the cost of reducing their birth rate when compared to healthy type 1 hosts.Due to the heterogeneous population, there is ambiguity in defining (R_0) for the disease. The two types of host have different transmission rates and durations of infection, and will therefore be responsible for different amounts of disease spread. To resolve this, we define several related values. Let (R_0^j) be the (R_0) of the disease in a homogeneous population of type j hosts: the average number of hosts infected (indirectly, through vectors) from a single infected host in a population consisting entirely of type j hosts.$$begin{aligned}&R_0^1 = frac{delta _1 beta _1 a b_1^2}{mu _v mu _{1+}} \&R_0^2 = frac{delta _2 beta _2 a b_2^2}{mu _v (mu _{2+}+gamma _2)} end{aligned}$$We simplify the equation for (R_0^1) since (gamma _1 = 0). We define w to be the frequency of host type 1: (w := (S_1 + I_1)/H). Then (R_0) for the vectors is$$begin{aligned} R_0^v = R_0^1 w + R_0^2 (1-w) end{aligned}$$which will also be the effective (R_0) of the disease for the hosts in the mixed population.For simplicity of results, we restrict to the case where type 1 is more infectious overall than type 2, in particular (R_0^1 > R_0^2). This allows us to avoid edge cases in simulation outcomes which are beyond the scope of this paper. We intend to lift this restriction and study these outcomes in future work.NoteAlthough usual epidemiological model formulations can rely on the value 1 as the boundary condition for (R_0) to determine the epidemic potential of an outbreak, in this case we are calculating effective (R_0) in a dynamic host population, such that the decrease in disease spread due to saturation from recovered hosts and already infected hosts increases the actual thresholds. More accurate criteria require a technical and somewhat cumbersome analysis, which we leave for a future paper. More