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Study areaChina is one of the countries with the poorest per capita water resources in the world while also having the largest water consumption in the world. In 2018, China’s total water consumption was 601.55 billion m3, with 369.31 billion m3 of water used in agriculture, accounting for 61.4% of the total water2. Agriculture is the most important industrial sector in water resource consumption. However, due to regional and climate differences, the distribution of agricultural water resources is uneven, and the shortage of water resources seriously affects agricultural development in water-deficient areas.Figure 1 shows the agricultural water consumption in China by province for 2007 and 2018. The agricultural water consumption includes farmland irrigation water consumption (classified as paddy field, irrigated land, vegetable field, groundwater exploitation), forest, animal husbandry, fishery, and livestock (classified as forest and fruit, grassland, fish pond, animal husbandry, groundwater exploitation), domestic water consumption of rural residents and rural ecological environment water consumption. Previous studies have mainly considered the irrigation water consumption of the planting industry as the research object at the provincial or regional levels (e.g., eastern, central, and western regions). Few were able to consider all 31 provinces in China and have comprehensively assessed water consumption and water use efficiency in the various types of agricultural production3,4,5,6,10,16,17,22,23,24,25,30. In this study, the agricultural water use efficiency and its influencing factors are assessed based on the agricultural water consumption of agriculture, forestry, animal husbandry, and fishery in China.Figure 1Agricultural water consumption in China by province for (a) 2007 and (b) 2018. Note: Map created using ArcGIS [10.2], (http://www.esri.com/software/arcgis).Full size imageResearch methodIn this study, the agricultural water use efficiency (under the common frontier and the group frontier) is calculated using the super-efficiency slacks-based measure (Super-SBM) model. The significant factors affecting water-use efficiency are then analyzed through the threshold regression model.Super-efficiency SBM modelData envelopment analysis (DEA) is an efficiency evaluation method proposed by Charnes31, a famous American operational research scientist. While traditional radial and angular DEA models do not require the specific form of the estimation function, they ignore the relaxation of variables and result in efficiency values in the range of 0 to 1. If there are multiple efficiency value of decision making units(DMUs) with an efficiency value of 1, these values cannot be compared. The efficiency of the super efficiency DEA model can be greater than 1, which means that the efficiency level of all decision-making units can be compared.To avoid the problem of slack variables, Tone (2001) proposed the SBM model, which is a non-radial and non-angular DEA analysis method based on the relaxation variable measure16,17,18,19,20,32. The SBM model of unexpected output solves the slack problem of input and output variables, minimizing deviations in the efficiency measurement. The super-efficiency SBM model combines the super-efficiency DEA model and the SBM model. It is also one of the methods based on data envelopment analysis, which can measure the efficiency of all decision-making units and the slack of input and output variables.Assume n to be the decision-making units, each of which has m inputs, expected output r1, and unexpected output r2. Let X (X ∈ Rm), Yd (Yd ∈ Rs1), and Yu (Yu ∈ Rs2) be matrices, such that (X=[{x}_{1},dots ,{x}_{n}]in {R}^{m*n}) and (Y=[{y}_{1}^{d}, dots ,{ y}_{n}^{d}in {R}^{{r}_{1}*n}). The form of the super-efficiency SBM model is as follows1,17,19,54:$$min=frac{frac{1}{m}sum_{i=1}^{m}(overline{x}/{x}_{ik})}{1/left({r}_{1}+{r}_{2}right)*(sum_{r=1}^{{r}_{1}}overline{{y}^{d}}/{y}_{rk}^{d}+sum_{q=1}^{{r}_{2}}overline{{y}^{u}}/{y}_{qk}^{u}}.$$
(1)
Among them,$$overline{x}ge sum_{j=1ne k}^{n}{x}_{ij}{lambda }_{j}, i=1,dots ,m;$$
(2)
$$overline{{y}^{d}}le sum_{j=1,ne k}^{n}{y}_{rj}^{d}{lambda }_{j}, r=1,dots ,{s}_{1};$$
(3)
$$overline{{y}^{d}}ge sum_{j=1,ne k}^{n}{y}_{qj}^{u}{lambda }_{j}, q=1,dots ,{s}_{2};$$
(4)
$${lambda }_{y}ge 0,j=1,dots ,n;jne 0;$$
(5)
$$overline{x}ge {x}_{k},k=1,dots ,m;$$
(6)
$$overline{{y}^{d}}le {y}_{k}^{d},d=1,dots ,{r}_{1};$$
(7)
$$overline{{y}^{u}}ge {y}_{k}^{u},b=1,dots ,{r}_{2}.$$
(8)
Based on the Super-SBM model (Eq. 1) and its constraint formula, the agricultural water use efficiency for the different provinces was calculated for the period 2007–2018 using Maxdea 8 ultra software.Threshold effectConsidering the differences in economic development and technical levels, the agricultural water use in different regions of China shows characteristics of time-series evolution, spatial heterogeneity, and unbalanced spatial distribution. There is a non-linear relationship between the influencing factors of agricultural water use efficiency, which suggests the existence of certain threshold characteristics33,34. This means that for a particular determinant, agricultural water use efficiency would be affected differently depending on whether the parameter has crossed the threshold. In this study, the threshold panel model proposed by Hansen is used. The threshold value of the threshold variable is taken as the critical point, and the regression equation is divided into different stage intervals to analyze the influence of threshold variables on the explained variables at different stages . Therefore, according to the relationship between agricultural water use efficiency and its influencing factors in different regions, the following single threshold regression model is set:$${Y}_{it}=alpha {X}_{it}+{beta }_{1}{T}_{it}Ileft({T}_{it}le {gamma }_{1}right)+{beta }_{2}{T}_{it}Ileft({T}_{it} >{gamma }_{1}right)+C+{varepsilon }_{it},$$
(9)
such that i is the province; t is the year; Yit and Tit are the explanatory variables and explained variables, respectively; Xit is the control variable that has a significant impact on the explained variables; Tit is threshold variable, which changes with the different explanatory variables; γ is a specific threshold value; α is the corresponding coefficient vector; β1 and β2 represent the influence coefficients of the threshold variable Tit on the explained variable Yit in the case of ({T}_{it}le {gamma }_{1}) and ({T}_{it} >{gamma }_{1}) , respectively; C is a constant; ε is random disturbance term, ({varepsilon }_{it}sim i.i.d.N(0,{sigma }^{2})); and, I (·) is an indicative function. After obtaining the estimated value of each parameter, two tests need to be carried out: (1) establish whether the threshold effect is significant; and (2) determine whether the estimated threshold value is equal to the true value. In addition, the above equation assumes that only one threshold exists. For two or more thresholds, the model would have to be adjusted according to the data.Based on the panel data of 31 provinces in China from 2007 to 201844,45,46, Stata15.0 software was used to perform threshold regression on seven variables: per capita water resources, rural labor force, disposable income, government’s attention, foreign trade dependence, industrial structure, and gross domestic product (GDP). The threshold effect of each factor can be analyzed, and the impact on agricultural water consumption can be assessed using the threshold value.Variable selection and data sourceThe super-efficiency SBM model was used in calculating the agricultural water use efficiency for the 31 provinces in China from 2007 to 2018. The input–output indicators were defined before the calculations, as shown in Extended Data Table 1.The selection of input–output factors to measure the utilization efficiency of agricultural water resources follows the principles of availability and operability. The input variables included: (1) agricultural water consumption, (2) the number of employees in agriculture, forestry, animal husbandry, and fishery, (3) the total power of agricultural machinery, and (4) the expenditure of local finance on agriculture, forestry, and water affairs. In terms of output, the added value in agriculture, forestry, animal husbandry, and fishery (based on 2007) was used as the expected output, while ammonia nitrogen emission, agricultural chemical oxygen demand emission, and agricultural carbon emission comprised the unexpected output.This study considered the scale of carbon emissions released by the agricultural system. According to existing research, agricultural carbon emissions are associated with rural environmental pollution35. The main consequence of agricultural pollutant emissions is soil pollution, which leads to rural groundwater pollution36,37,39,40,41,41. The deterioration of groundwater quality adversely affects the development of the agricultural economy and threatens the safety of the drinking water supply for rural residents.The threshold regression model was used to investigate the convergence of agricultural water use efficiency and observe the changes in agricultural water consumption under different influencing factors. The control variables include the following: water resource endowment, the number of agricultural labor, the income level of rural residents, industrial structure, the degree of government’s attention, the degree of dependence on foreign trade, and the level of economic development, as shown in Extended Data Table 2. For water resource endowment (WR), WR is expressed in per capita water resource (m3 / person). Zhang Lixiao45,46 and previous studies have shown a negative correlation between water resource endowment and water resource utilization. For agricultural labor (ah), the variable is expressed by the number of people engaged in agriculture, forestry, animal husbandry, and fishery (10,000 people). Past studies suggest rural population affects the consumption of agricultural water resources47,50,51,52,53,52. For income levels, rural residents’ income level is indicated by the per capita disposable income of rural households. Wang Xueyuan et al.3 and Han Qing et al.53 argue that the increase in the rural residents’ income would limit agricultural water consumption. For industrial structure (× 2), which is expressed by the proportion of industrial added value in GDP, research has shown water resource efficiency would vary under different industrial structures54,57,56. For the government’s attention degree (GA), the variable is expressed by the proportion of agriculture, water affairs, and forestry spending in the total financial expenditure. The government’s support for comprehensive agricultural development and infrastructure and technology upgrading for agricultural, forestry, and water conservation significantly affects water resource utilization efficiency16,56,59,58. For the degree of dependence on foreign trade (open), the parameter is indicated by the proportion of the total import and export of agricultural and sideline products in the GDP. Changes in import demand can reduce or increase the consumption and pollution of water resources. Likewise, export demand changes, especially in high water-consuming and high polluting products, can significantly improve or degrade water resource efficiency. And for the level of economic development, expressed in terms of GDP, the level of regional economic development plays a positive role in promoting the efficiency of water resource utilization59,62,61. More

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Isolation and characterisation of viruses infecting the picoeukaryote Bathycoccus Clade BIIBathycoccus BII isolates RCC716 and RCC715 used in our experiments were originally cultured from a nutrient-limited region in the Indian Ocean. Clade BII as a whole has been reported extensively in warm oligotrophic ocean gyres based on metagenome analyses [22,23,24]. Peak abundances occurr when well-developed deep chlorophyll maxima are present, or throughout the photic zone during mixing periods at Station ALOHA of the Hawaii Ocean Time-series [12]. We targeted BATS for viral isolation in springtime because Bathycoccus has been observed at relatively high abundance during this period using qPCR [74]. Here, three viruses were isolated against RCC716 [12] using seawater flown from BATS/Bermuda to the laboratory, obviating bringing this finicky strain into the field for use as a viral host. We then purified the viruses by serial dilutions and sequenced the partial PolB gene to determine whether they were evolutionarily different from other cultured viruses. BLASTn and preliminary phylogenetic analysis using GenBank nr sequences indicated they were distinct from described viruses with deposited sequences, with best BLASTn hits to Bathycoccus prasinos viruses (62–74% nucleotide identity). Transmission electron microscopy (TEM) revealed that all three viruses have similar morphology to other characterised prasinoviruses [75], with icosahedral capsids diameter ranging between 120 and 140 nm (Fig. 1A).Fig. 1: Morphology and evolutionary relationships of newly discovered Bathycoccus viruses.A Transmission electron micrographs of BII-V1, BII-V2 and BII-V3 (scale bar, 50 nm). The capsid diameters (n = 6 virions) measured 138 ± 2 nm (BII-V1), 150 ± 5 nm (BII-V2) and 152 ± 11 nm (BII-V3). B Maximum Likelihood (ML) phylogenetic reconstruction of green algal viruses inferred from a concatenated alignment of 22 core proteins shared among the viruses (7,001 positions) under the LG + G + F model. Node support was calculated from 1000 bootstrap (BS) replicates, with all branches acquired support values of 100% (white dots). Viruses infecting Chlorella were used as an outgroup and the branch connecting the prasinoviruses to the outgroup was truncated for display purpose. The new Bathycoccus viruses isolated against Bathycoccus Clade II (sensu [12]) isolate RCC716 (named as species Bathycoccus calidus herein, see below) are in bold. Colours reflect different host species within each genus. Letters alongside vertical lines (a and b) correspond to Bathycoccus viral clades. C Venn diagram of the shared and unique protein-encoding genes in the genome sequences of the new Bathycoccus viruses.Full size imageGenomic sequencing and multi-gene evolutionary analysesAssembly of DNA sequences from the viral isolates after deep sequencing by Illumina rendered one complete dsDNA genome sequence (BII-V3), and two others may still be partial (Table 1). The BII-V2 genome, which was in one contig, was similar in size (~208 kb) to that of BII-V3 (~212 kb). The BII-V1 genome assembly was ~174 kb and comprised of four linear dsDNA scaffolds. The viral concentrate was deeply sequenced ( >50x coverage) and minor fragmentation of the genome was partially related to repeats that were not resolved during assembly. The total number of putative open reading frames (ORFs) varied from 220 in BII-V1 to 235 in BII-V2 (Table 1). Gene synteny was globally well-conserved across the BII-Vs and the BpV1 and BpV2 viruses of B. prasinos (Fig. S1), with limited genomic rearrangements. Other genome characteristics such as the coding proportion (~90%) and G + C % (~36%) were similar to other described prasinoviruses infecting Mamiellophyceae [64, 75], for which the reported number of proteins range from 203 to 268 and G + C % from 37 to 45%. However, the full-length PolB gene from the genome assemblies differed for BII-V3 from the other two, in having a 329 amino acid intein (Supplementary information table S3). Likewise, inteins have been reported at the same PolB position in uncultivated prasinoviruses from the subtropical Pacific Ocean [76], where Bathycoccus BII is abundant [12].Table 1 Genomic characteristics of the three Bathycoccus viruses (BII-Vs) isolated against Clade BII isolate RCC716.Full size tableTo reconstruct a robust phylogeny for the new viruses, we employed 22 proteins previously identified as being shared across all available green algal virus genomes, including both prasinoviruses and chloroviruses [65]. We found all 22 in the predicted coding sequences of BII-V1; however, DNA helicase (SNF2) was not found in BII-V2 or -V3, FAD-dependent thymidylate synthase (thy1) and the topoisomerase IV were not found in BII-V2, nor was the prolyl 4-hydroxylase in the BII-V3 genome. Additional searches with tBLASTn did not recover these genes or fragments of them, suggesting they have been lost. Phylogenomic reconstruction grouped the three BII-Vs with the two BpVs [32], in a fully supported clade that branched adjacent to a large group of viruses that infect various species of Ostreococcus and Micromonas (Fig. 1B). The clade of Bathycoccus viruses was segregated in two subclades with BII-V2 and BII-V3 clustering together adjacent to BII-V1 and BpVs (Fig. 1B). While better resolution of the position of BII-V1 awaits greater taxonomic sampling, our results demonstrated that the three new viruses branch adjacent or basally to BpVs.Variation in prasinovirus gene content and functions encodedThe three Bathycoccus Clade BII viruses had 72–77% of their proteins held in common, and ~30 unique proteins as well as a few proteins shared by just two of the three viruses (Fig. 1C). The 170 shared proteins had higher amino acid identities between BII-V2 and BII-V3 (73% aa identity) than to BII-V1 (69% and 68%, respectively). Generally, only 19–21% of Bathycoccus viral genes could be assigned a functional category, based on EggNOG classification. Similar functional category distributions were observed across both prasinoviruses and chloroviruses, including lipid metabolism, RNA processing and modification, and nucleotide metabolism and transport (Fig. 2A). Other functional categories were more variable, such as cell wall/membrane/envelope biogenesis genes prevalent in chloroviruses (potentially related to their enveloped nature), as well as genes involved in modification of the capsid with compounds such as with chitin and hyaluronan [77, 78] that are absent from prasinoviruses sequenced to date (Fig. 2A). Within prasinoviruses, most of the unique proteins in the Bathycoccus viruses lack defined functional categories. Among those with functional assignments, all five Bathycoccus viruses encoded a P2X receptor in the intracellular trafficking and secretion category, and both BII-V2 and -V3 encode two proteins putatively involved in degrading the aromatic compound 4-hydroxy-2-oxopentanoate to acetyl-CoA (secondary metabolite category), that otherwise are only encoded by one other prasinovirus, MpV1 [32]. Similar to the phylogenetic relationships, the functional category distributions of BII-V1 were closer to those of BpVs than to BII-Vs. The primary difference was in carbohydrate metabolism, where BII-V2 and -V3 each encodes ribulose-phosphate 3-epimerase (involved in the pentose phosphate pathway and carbon fixation; not found in any other available virus genomes, but encoded by B. prasinos) and TDP-glucose 4,6-dehydratase (involved in biosynthesis of rhamnose and encoded by most other chloroviruses and prasinoviruses [79]). Notably, the putative high-affinity phosphate transporter (PHO4, also termed HAPT) was only present in BII-V1 and BpV1, as well as OtV2 (isolated against the Ostreococcus Clade OII ecotype), and most sequenced viruses of O. lucimarinus (Supplementary information table S3). This gene is hypothesised to enhance phosphate uptake during infection under phosphorus‐limited host growth [25], as observed for the PstS phosphate transport system expressed by cyanophages [80], mitigating limitation of this key component of viral genomes. However, most isolated prasinovirus genomes come from waters that are not considered phosphate-limited, hence presence of this gene may connect to poising the host for responding to sudden availability of other nutrients, such as nitrogen, which is often limiting in the ecosystems from which these viruses were isolated. Studies of virus-cell responses under various limiting nutrients are required to understand the retention of this host-derived HGT.Fig. 2: Distribution of functions and orthologous protein families across genome-sequenced prasinoviruses.A Functional category distributions across 21 genome-sequenced prasinoviruses and chloroviruses based on EggNOG categorisation. Viruses are clustered by similarity in their distribution of the functional categories on the y-axis and the frequency of each category across the viral genomes determines clustering along the x-axis ordering. Genes with homology to proteins in the EggNOG database but could not be assigned a function are in the “function unknown” category. B Orthogroups presence/absence patterns ordered along the x-axis by ranking according to the total number of genes in the orthogroup. For inclusion, the orthogroup was required to include protein sequences from at least two different viral genomes. Viruses are ordered along the vertical by their presence/absence pattern reconstructed by hierarchical clustering (topology on the left). Top histogram: frequency of each orthogroup in sequenced prasinoviruses. C Genes in each virus (number) not assigned to any orthogroup, with viruses in the same vertical order as B.Full size imageHierarchical clustering of orthologous proteins revealed patterns across prasinoviruses that generally corresponded with phylogenetic relationships. The BII- and Bp-viruses shared 130 orthologous proteins and hierarchical clustering (Fig. 2B) followed the clade structure of the phylogenomic reconstruction (Fig. 1B) with the exception of BII-V1 that grouped with BII-Vs, as well as OtV6, which grouped with Micromonas viruses. These orthologous proteins had on average 72% amino acid identity between BII-V2 and BII-V3, and 88% between the two B. prasinos viruses, but between 65 to 67% when comparing members of these two groups (Table 2). BII-V1 orthologs also had 67% and 66% amino acid identity to BII-V2 and BII-V3, respectively, while they had 83% and 80% identity to BpV1 and BpV2, respectively. Collectively, these results indicate that BII-V2 and -V3 diverged from BpVs prior to the divergence of BII-V1.Table 2 Average percent amino acid identity of the orthologous proteins between the five Bathycoccus viruses.Full size tableOf the 130 orthologous Bathycoccus virus proteins, 37% were assigned putative functions revealing core components of this viral group (Supplementary information table S3). These included genes involved in DNA replication and transcription, including PolB (type II), a DNA topoisomerase, a transcription factor S-II, mRNA capping enzymes, ribonucleases, a ribonucleotide reductase, and a dUTPase. Several others are necessary for viral particle synthesis, such as genes encoding structural elements for assembling the virion, including capsid proteins (5–6 copies per genome), as well as transcriptional regulators connected to the replication cycle. The BII viruses showed a number of differences among orthologous protein families. In addition to each having “unique” protein sets, there was a set of BII-V specific orthogroups, as well as some shared with BpVs, and/or other prasinoviruses (Fig. 1C and Supplementary information table S3). First, six predicted proteins showed orthologs across the three BII-Vs, but were not present in other prasinoviruses sequenced to date. Only one of these six was assigned putative function, belonging to the XRE family of transcriptional regulators. Additionally, all BII viruses harboured a tandem duplication of the FstH gene, while other sequenced prasinoviruses (including the two Clade BI viruses) have one copy (Supplementary information table S3). This ATP-dependent metalloprotease has been shown to be involved in photosystem II repair in cyanobacteria [81], and is present in genomes of photosynthetic eukaryotes, including all Mamiellophyceae [15, 16]. In Arabidopsis and Chlamydomonas it has been shown to be involved in protein quality control in the thylakoid membranes [82]. A gene of unknown function was also duplicated in the BII-virus genomes, that is a single copy in BpVs and absent from other sequenced prasinoviruses. Genes putatively encoding a glucose-1-phosphate adenylyltransferase, a glycosyltransferase and a thiamine pyrophosphate-requiring enzyme involved in amino acid biosynthesis were sporadically found in BII-viruses.Considering the two Bathycoccus virus subclades (Fig. 1B), there is one predicted protein of unknown function exclusive to BpV1, BpV2 and BII-V1 and six predicted proteins shared only by BII-V2 and BII-V3. Among the latter, one belonged to the Ribulose-5-Phosphate-3-Epimerase (RPE) family, which catalyses the interconversion of D-ribulose 5-phosphate (Ru5P) into d-xylulose 5-phosphate, as part of the Calvin cycle (although no transit peptide was detected using TargetP) and in the oxidative pentose phosphate pathway. The ortholog analyses further showed that among prasinoviruses, 9, 17 and 18 genes were unique to BII-V1, BII-V2 and BII-V3, respectively (Fig. 2B). Apart from one nucleotidyltransferase and one glycosyltransferase (group 1) in BII-V1, none of these unique genes had known functions.To study the evolutionary aspects of the shared prasinovirus proteins, we constructed and examined 130 phylogenies of orthogroups shared between Bathycoccus viruses. Nine showed a topology where all three BII-Vs grouped together with full support (100% bootstrap support), separate from the BpV orthologs, and in contrast to the multi-gene phylogeny where BII-V1 grouped with BpVs (Fig. 1B). The average amino acid similarities within each of these nine protein ortholog groups ranged from 85 to 88% between BII-Vs proteins, while they were 77 to 81% between BII-Vs and BpVs, different from overall amino acid similarity averages (Table 2). Interestingly, proteins from three of these nine ortholog groups, all lacking known functions, were adjacent to each other in the genome, or separated by only one gene. This synteny and co-location likely reflects the acquisition of these genes before co-infecting viruses diverged via viral recombination [83].Infection dynamics of Bathycoccus virusesGeneral host specificity of BII-viruses was assessed using two B. prasinos isolates (CCMP1898 and RCC4222, Clade BI), the two available Clade BII isolates (RCC715 and RCC716), four Ostreococcus species and one Micromonas species (Table 3). None were able to infect the B. prasinos, Ostreococcus or Micromonas isolates tested, suggesting BII-V specificity for Bathycoccus Clade BII. Similar host specificity has been observed in O. lucimarinus viruses, none of which infect O. tauri [64], and other viruses of eukaryotic and prokaryotic algae [84, 85]. Some other prasinoviruses appear to have broader host ranges [85,86,87], or their host species are less divergent than the two known Bathycoccus clades. For example, generalist viruses isolated against Micromonas commoda can infect M. bravo [85]. Further investigations are necessary to determine the extent to which the six shared proteins in BII-Vs (absent from BpVs), are responsible for the differences in host and virus specificity of interactions, versus variations in the shared Bathycoccus virus proteins (65–83% similarity). Importantly, host specificity tests for the new viruses described herein were limited by weak sampling of Bathycoccus diversity (in culture; all that we could acquire were tested).Table 3 Results of cross infectivity tests of BII-V1, BII-V2 and BII-V3 against isolates representing various picoprasinophyte species within the Class Mamiellophyceae.Full size tableAlthough specific for the BII clade, the three BII-Vs exhibited variations in infectivity of the two cultured BII strains available, despite their isolation from the same sample and having identical ITS1 and ITS2 sequences. BII-V1 lysed and cleared RCC715 and RCC716 cultures after four days (Table 3). The same was true for BII-V2 and BII-V3, when incubated with RCC716. Different from results for BII-V1, we found that while BII-V2 and -V3 initially lysed RCC715 cultures, resistant populations became evident at day 7 of infectivity tests, and measureable lysis of RCC715 could not be achieved thereafter. These results underscored the need to further examine host-virus interactions for the three new viruses.Infection dynamics over time course experiments further illuminated differences in BII-V impacts on hosts. In these experiments, growth rates of the uninfected (control) RCC715 and RCC716 cultures were 0.45 ± 0.04 day−1 and 0.49 ± 0.06 per day, respectively, similar to rates during the pre-experiment acclimation period (T-test, p  > 0.05). Host and virus dynamics were similar for RCC715 and RCC716 infected with BII-V1 (Fig. S2 and Fig. 3), with cell numbers starting to diverge from control abundances 10 h after inoculation (T-test, p  More

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Data setsRadioactivity measurement data for several species of wild game mammals and birds in Fukushima Prefecture from May 2011 to March 2018 were released to the public by the Fukushima Prefecture Government (https://emdb.jaea.go.jp/emdb/en/portals/1040501000/). We extracted the data for wild boar (Sus scrofa), 1404 samples, and Asian black bear (Ursus thibetanus), 422 samples. The resulting boar and bear data sets contained total radioactive cesium activity (134Cs + 137Cs isotopes) values (in Bq/kg) from animals captured at different times and locations within Fukushima Prefecture. The data were imported for analysis into R 4.0.3 software21.We ln-transformed the cesium activity values to bring their distribution closer to normal, creating the variable LnCsTot. To facilitate regression analyses (described below), we removed instances of missing data and cesium levels below detection: 20 samples (1.4%) for boar and 15 samples (3.3%) for bears. The time when each sample was taken (labeled “Day of collection” in the Fukushima Prefecture Government data set) was converted to years since the Fukushima accident (since March 11, 2011), assuming that 1 year = 365.25 days. This time of sample collection in years was called variable T.Since for each sample some time passed between sample collection and radioactivity measurement (labeled “Result found Date”, called Tr in our notation), we needed to correct the reported LnCsTot values for physical decay over this time, which was different for different samples. The procedure used to perform this correction is described in Supplementary methods. The data with corrected total cesium values (LnCsc) are provided in Supplementary data (Supplementary_Dataset_File_Full).Mathematical modelTo describe the data on ln-transformed total radioactive cesium levels (LnScc) in each species as function of time after the accident (T), we developed the following simple mathematical model (Eqs. 1A, 1B):$${LnCs}_{c}=X+Q-mu times {T}^{nu }+Atimes mathrm{sin}left[2times pi times left(T+Pright)right], $$
(1A)
$$X=mathrm{ln}left[mathrm{exp}left(LnCs{134}_{t{0}_{r}}right)times {2}^{-frac{T}{{Th}_{Cs134}}}+mathrm{exp}left(LnCs{137}_{t{0}_{r}}right)times {2}^{-frac{T}{{Th}_{Cs137}}}right]$$
(1B)
Here the term X represents the estimated average radioactive cesium level in the studied area, based on the intercepts (LnCs134t0r for 134Cs and LnCs137t0r for 137Cs, respectively) from robust regression discussed in Supplementary methods, and taking into account only physical decay for each isotope (with half-lives of ThCs134 for 134Cs and ThCs134 for 137Cs, respectively). The terms Q, µ, ν, A and P represent adjustable model parameters. Parameter Q represents the fitted relationship between radioactive cesium levels in the animal (Bq/kg), relative to the external environment (Bq/m2). Parameter µ represents the net rate of radioactive cesium reduction in animal tissues over time due to all processes except physical decay (e.g. decrease in bioavailability due to migration of cesium into deeper soil layers, human-mediated cleanup efforts, etc.). Parameter ν is a potential power dependence for these processes. By default, ν was set to ν = 1, but exploratory calculations using ν = 2 or treating ν as a freely adjustable parameter (≥ 0.1) were performed as well. Parameters A and P in the sine function represent a sinusoidal approximation for seasonal changes in radioactive cesium levels in animal tissues (e.g. due to seasonal variations in diet and life style), where A is the amplitude of the oscillations, P is the phase shift, and the period is set to 1 year. For simplicity, these parameters were assumed to be the same for both studied cesium isotopes. The descriptions of each parameter are also presented in Table 1.Table 1 The meanings of all parameters used in our mathematical model (Eq. 1A, 1B) for radioactive cesium levels in wild boar (Sus scrofa) and Asian black bear (Ursus thibetanus).Full size tableModel fitting approachesInitially, we used nonlinear ordinary least squares (OLS) regression (nls R function) to fit the model (Eq. 1A, 1B) to the data. To find the global optimum fit, we repeated the fitting procedure 2000 times with slightly different random initial parameter values and recorded the solution with the smallest root mean squared error (RMSE). Diagnostics on this regression included checking of convergence criteria and analyses of residuals (by scatter plot and histogram, regressing residuals as function of T, visualizing the QQ plot, autocorrelation and partial autocorrelation functions with 95% confidence intervals, performing the Shapiro–Wilk normality test, and calculating skewness and kurtosis). For boar data, diagnostics revealed problems with convergence (both X-convergence and relative convergence) and non-normality of residuals: e.g. Shapiro–Wilk p-value = 1.476 × 10–7, skewness = − 0.37, kurtosis = 3.50. For black bear data similar problems occurred with convergence, but residuals were closer to the normal distribution (perhaps due to smaller sample size): e.g. Shapiro–Wilk p-value = 0.0526, skewness = − 0.058, kurtosis = 2.45.Due to these issues, we used robust nonlinear regression (nlrob R package) to reduce the effects of “outlier” data points. To find the global optimum, we repeated the fitting procedure 2000 times with slightly different random initial parameter values and selected the solution with the smallest absolute value of median residuals. The best-fit parameters for OLS and robust regressions were somewhat different for both boar and bear data. For boar data, the minimum robustness weight was 0.339 and the median was 0.762, and the corresponding values for black bear data were 0.557 and 0.821, respectively.For each species, we compared the performances of model variants with different assumptions about parameter ν: (1) The default case with ν = 1, which represents an exponential rate of radioactive cesium decrease due to processes other than physical decay. (2) The case with ν = 2, which represents quadratic decay. (3) The case with ν being freely adjustable (≥ 0.1). The comparisons were based on Akaike information criterion (AIC)22,23. The purpose of these calculations was to better assess the shape of the time course for non-physical factors involved in radioactive cesium level decline in animal tissues over time after the accident.In addition to analyzing the full data set for each species, we also performed separate analyses on subsets of data from specific locations: from those districts of Fukushima Prefecture where the mean radioactive cesium levels in animal samples were the highest, and where a sufficiently large number of samples was present. For wild boar, the two selected districts for this subset analysis were Soso and Kenpoku (819 samples), and for black bear they were Kenpoku and Kenchu (163 samples).To further assess the sensitivity of model results to geographical and temporal factors, we also constructed a separate subset of data for each species. This subset excluded data from the Aizu and Minamiaizu districts, which are separated by mountains from the Fukushima Daiichi Nuclear Power Plant, and excluded data collected ≤ 6 months after the accident. These restrictions were intended to determine model performance on data collected in a more geographically contiguous area after the initial abrupt changes in contamination levels were completed and the system entered the phase of more stable kinetics. The purpose of all these analyses was to assess whether the time course of radioactive cesium levels in the bodies of each species differed between locations with high contamination vs. those with lower contamination, and as function of time after the accident.We were interested in quantifying not only the center of the distribution of radioactive cesium values in each species over time, but also in assessing the lower and upper tails of this distribution. For this purpose, we fitted the model (Eq. 1A, 1B) for each species using quantile regression (nlrq function in quantreg R package) for the median (50th percentile), and also for the 25th and 75th percentiles. Initial parameter estimates for the quantile regressions were taken from best-fit parameters from robust regression described above. The 25th and 75th percentiles were selected instead of more extreme values (e.g. 5th and 95th) because the latter resulted in poor quality fits due to limited amounts of data at the fringes of the distribution.To assess the variability of model parameters by location in more detail, we used mixed effects modeling (nlme R package) on the data from each species. Since original OLS fits suggested substantial deviations of residuals from the normality assumption, we performed mixed effects modeling on data with some outlier data points removed. The OutlierDetection package in R removed 43 boar samples and 5 bear samples. These outliers are listed in the Supplementary_outlier_data_points file. The remaining samples were used for mixed effects model fitting, but model performance metrics like coefficient of determination (R2) and RMSE were assessed on the full data set (with outliers included) for each species.Since the Fligner-Killeen test of homogeneity of variances by district generated low p-values for both species (4.6 × 10–14 for boar and 0.018 for black bear), we allowed modelled variances to differ by district (using the weights option in nlme). We investigated several random effects structures for some or all model parameters, with randomness by district only, or by district and municipality within district. Model diagnostics were the same as for fixed effects OLS modeling described above, and also included boxplots of model residuals by district. The mixed effects model variants with different random effects structures were compared using the anova function in R, and also by assessing convergence criteria, normality of residuals, skewness, and kurtosis. Consequently, preferred mixed effects model variants were selected for the full data as well as for the subset of two districts with high radioactive cesium levels, separately for each species.Model extrapolation from training to testing dataTo investigate how the robust and quantile regression fits of our model could extrapolate beyond the time range that was used for model fitting, we split the data for each species into “training” (early times) and “testing” (later times) parts. The split was done based on time since the accident (T variable), so that approximately ½ of the samples were assigned to the training and testing sets, respectively. For wild boar data, the training set included times between 0.20 and 3.45 years after the accident, and the testing set included times between 3.45 and 7.03 years. For black bear data, the training set included times between 0.42 and 3.46 years after the accident, and the testing set included times between 3.46 and 6.87 years.We also evaluated an alternative approach to splitting the data, where the split was done randomly instead of by time. In other words, any data point regardless of time had an equal probability of being assigned to either the training or the testing data set. Both the training and testing data subsets generated by this random split included the complete time range. This approach was implemented in context of the sensitivity analysis described above.For each species, robust and quantile regressions were fitted to training data, and their predictions were calculated for testing data. For robust regression, RMSE was calculated on testing data for two scenarios: (1) for the model fitted to training data only, and (2) for the model fitted over the entire data range (training + testing). These RMSE values for conditions 1 and 2 were compared to assess the quality of model extrapolation. Extrapolation performance for robust and quantile regressions was also assessed visually by plotting the model predictions and data.Application of the model to wild boar data from the Chernobyl accident areaTo compare the results of our analysis of wild boar contamination with radioactive cesium in the area affected by the Fukushima accident with data from another location, we also analyzed wild boar data from the Chernobyl accident area. These data were published by Gulakov14 and contain summaries of 137Cs contamination levels in the muscles of 188 boar collected between 1991 and 2008 (i.e. from 5 to 22 years after the 1986 accident). Sampling was carried out in three zones with different land contamination levels with 137Cs. This data set provides important information on radioactive cesium contamination in wild boar in the Chernobyl area. Unfortunately, 137Cs measurements in each sampled boar were not provided by Gulakov14, and only summary statistics are available for each zone and year after the accident (Tables 1–3 in reference14): number of animals, mean, minimum and maximum 137Cs levels.We could not apply the full model (Eq. 1A, 1B) to these summary data which lacked seasonality information and 134Cs data. However, we were able to perform a weighted linear regression to quantify the ecological half-life of 137Cs in Chernobyl boar and the relationship between 137Cs levels in the animals (Bq/kg), relative to the external environment (Bq/m2). The data used for this analysis, derived from Gulakov14, are provided in Supplementary data (Supplementary_Dataset_File_Full). They contain the following variables. Zone = location of sample collection (Alienation, Permanent control or Periodic control). Time = time in years after the Chernobyl accident. LnMeanCs = ln-transformed mean 137Cs level in boar muscle (Bq/kg). LnMeanCs_c = LnMeanCs − X, where X is ln-transformed 137Cs land contamination (Bq/m2) in the given zone, corrected for physical decay of 137Cs. Weight = weighting of each data point used for regression. Weight = number of animals/(ln[maximum 137Cs level] − ln[minimum 137Cs level])2. These approximately inverse-variance weights were normalized by the overall mean across all data points, so that the mean weight across all data points was set to 1.These data were analyzed by weighted linear regression in R, where LnMeanCs_c was allowed to depend on Time and Zone variables. Model variants containing all possible combinations and pairwise interactions between these predictor variables were fitted and their performances were compared using the Akaike information criterion with correction for small sample size (AICc). These calculations were performed using the glmulti R package. Multimodel inference (MMI) was performed on this collection of fitted model variants. It resulted in the calculation of model-averaged parameter estimates, 95% CIs and importance scores, corrected for model selection uncertainty. Of main interest here were the intercept parameter, which is analogous to parameter Q in the full model (Eq. 1A, 1B), and the Time parameter, which is analogous to parameter µ in the full model. The ecological half-life for 137Cs was calculated based on the Time parameter. More

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