Ecology

General characterization of seven newly isolated HMO-2011-type phagesIn this study, we used four Roseobacter strains (FZCC0040, FZCC0042, FZCC0012, and FZCC0089) and one SAR11 strain (HTCC1062) to isolate phages. FZCC0040 and FZCC0042 belong to the Roseobacter RCA lineage [22], FZCC0012 shares 99.8% 16S rRNA gene identity with Roseobacter strain HIMB11 [57], and FZCC0089 belongs to a newly identified Roseobacter lineage located close to HIMB11 and SAG-019 lineages (Supplementary Fig. 1).A total of seven phages were newly isolated and analyzed in this study (Table 1). The complete phage genomes range in size from 52.7 to 54.9 kb, harbor 62 to 84 open reading frames (ORFs), and feature a G + C content ranging from 33.8 to 48.6%. Compared to other HMO-2011-type phages, pelagiphage HTVC033P has a relatively lower G + C content of 33.8%, similar to the G + C content of its host HTCC1062 (29.0%) and of other described pelagiphages [21, 26,27,28]. The G + C content of other six roseophages ranges from 42.2 to 48.6%, which is also similar to the G + C content of the hosts they infect (44.8 to 54.1%).Despite their distinct host origins, these phage genomes show considerable similarity in terms of gene content and genome architecture (Fig. 1). They all display clear similarity with the previously reported SAR116 phage HMO-2011 [20] and HMO-2011-type RCA phages [22]. Overall, these phages share 19.2 to 79.1% of their genes with previously reported HMO-2011-type phages and all contain homologues of HMO-2011-type DNA replication and metabolism genes, structural genes, and DNA packaging genes. Moreover, their overall genome structure is conserved with that of HMO-2011-type phages. Considering these observations, we tentatively classified these seven phages into the HMO-2011-type group. Of the 11 currently known HMO-2011-type isolates, one infects the SAR116 strain IMCC1322, one infects the SAR11 strain HTCC1062, and the remaining nine all infect Roseobacter strains; this suggest that HMO-2011-type phages infect diverse bacterial hosts. HTVC033P is the first pelagiphage identified to belong to the HMO-2011-type viral group. Our study has also increased the number of known types of pelagiphages. To date, pelagiphages belonging to a total of nine distinct viral groups have been isolated and analyzed [21, 26,27,28].Fig. 1: Alignment and comparison of genomes of HMO-2011-type isolates and representative HMO-2011-type MVGs from major subgroups.HMO-2011-type phage isolates are shown in red. Phages isolated in this study are indicated with red asterisks. Predicted open reading frames (ORFs) are represented by arrows, with the left or right arrow points indicating the direction of their transcription. The numbers inside the arrows indicate ORF numbers. ORFs annotated with known functions are marked using distinct colors according to their functions. HMO-2011-type core genes are indicated with blue asterisks. The color of the shading connecting homologous genes indicates the level of amino acid identity between the genes. To clearly present the genomic comparison, several MVGs were rearranged to start from the same gene as in the HMO-2011-type phages. DNAP DNA polymerase, Endo endonuclease, RNR ribonucleoside-triphosphate reductase, PhoH phosphate starvation-inducible protein, MazG MazG nucleotide pyrophosphohydrolase domain protein, ThyX thymidylate synthase, GRX glutaredoxin, TerS terminase small subunit, TerL terminase large subunit.Full size imageIdentification and sequence analyses of HMO-2011-type MVGsTo identify HMO-2011-type MVGs, we performed a metagenomic mining and retrieved a total of 207 HMO-2011-type MVGs (≥50% genome completeness) from viromes in the worldwide ocean, from tropical to polar oceans (Supplementary Table 1). These MVGs range in size from 29.2 to 67.9 kb and their G + C content range from 31.3 to 52.4%. In addition, 45 HMO-2011-type MVGs were also identified from some non-marine habitats, suggesting that HMO-2011-type phages are widely distributed worldwide (Supplementary Table 1).Genomic analysis confirmed that all HMO-2011-type MVGs exhibit genomic synteny with HMO-2011-type phages (Fig. 1). Although some of these HMO-2011-type MVGs are highly similar to their cultivated relatives, most MVGs appear to have more genomic variations. To resolve the evolutionary relationship among the HMO-2011-type phages, a phylogenetic tree was constructed based on the concatenated sequences of five core genes. We found that HMO-2011-type phages are evolutionarily diverse and can be separated into at least 10 well-supported subgroups ( >2 members), with 140 MVGs clustering into previously identified HMO-2011-type groups (subgroups I and III in Fig. 2A) [22], and the remaining 67 MVGs forming new subgroups (Fig. 2A). Among these HMO-2011-type subgroups, three contain cultivated representatives (subgroups I, III, and IX). Subgroup I contains the greatest number of phages, including six cultivated representatives and 123 MVGs (Fig. 2A). The cultivated representatives in subgroup I include a phage that infect SAR116 strain and five phages that infect Roseobacter strains. Subgroup III contains four cultivated representatives that infect two Roseobacter strains, and 17 MVGs. Pelagiphage HTVC033P and nine MVGs form subgroup IX. Other subgroups have no cultivated representatives yet. The results of phylogenomic analysis showed that subgroups I to VI are closely related, whereas subgroups VII to X are located on a separate branch and are more distinct from the subgroups I to VI, which suggests that these subgroups are more evolutionarily distant. A phylogenomic-based approach with GL-UVAB workflow [53] was also performed to cluster these HMO-2011-type genomes, which showed similar grouping results (Supplementary Fig. 2).Fig. 2: Phylogenomic and shared-gene analyses of HMO-2011-type phages.A A maximum-likelihood tree was constructed using concatenated sequences of five hallmark genes. HMO-2011-type phages were grouped into 10 subgroups based on the phylogeny. Shading is used to indicate the subgroups. HMO-2011-type phage isolates are shown in red. Genomes containing an integrase gene are indicated by red triangles. The G + C content and completeness of the genomes are indicated. Scale bar indicates the number of amino acid substitutions per site. B Heatmap showing the percentage of shared genes between HMO-2011-type genomes. Phages in the same subgroup are boxed.Full size imageA previous study suggested the use of the percentage of shared proteins as a means of defining phage taxonomic ranks and proposed that phages with ≥20 and ≥40% orthologous proteins in common can be grouped at the taxonomic ranks of subfamily and genus, respectively [58]. Overall, most of the calculated percentages between HMO-2011-type genomes fall within the 20 to 100% range and most of the percentages between genomes within the same subgroup fall within the 40 to 100% range (Fig. 2B). Therefore, our results suggest that the HMO-2011-type is roughly a subfamily-level phage taxonomic group containing at least ten genus-level subgroups in the Podoviridae family.Conserved genomic structure and variation in HMO-2011-type phagesOf the 1235 orthologous protein groups (≥2 members) identified in HMO-2011-type genomes, only 254 proteins groups could be assigned putative biological functions (Supplementary Table 2). Comparative genomic analysis clearly revealed the conserved functional module structure of all HMO-2011-type genomes. All HMO-2011-type phage genomes can be roughly divided into the DNA metabolism and replication module, structural module and DNA packaging module (Fig. 1). Most of the homologous genes are scattered in similar loci of the HMO-2011-type genomes. Core genome analysis based on complete HMO-2011-type genomes revealed that HMO-2011-type genomes share a common set of ten core genes (Fig. 1). These core genes are mostly genes related to essential function in phage replication and development, including genes encoding DNA helicase, DNA primase, DNA polymerase (DNAP), portal protein, capsid protein, and terminase small and large subunits (TerL and TerS) as well as several genes with no known function, suggesting that phages in this group employ similar overall infection and propagation processes (Fig. 1).Most members in subgroups I and III and one member in subgroup II possess a tyrosine integrase gene (int) located upstream of the DNA replication and metabolism module, whereas all subgroup IV to X genomes contain no identifiable lysogeny-related genes. This result suggests that members of subgroups IV to X might be obligate lytic phages. Integrase genes typically occur in the genomes of temperate phages and are responsible for site-specific recombination between phage and host bacterial genomes [59, 60]. In subgroup III, RCA phage CRP-3 has been experimentally demonstrated to be capable of integrating into the host genome [22]. Thus, certain int-containing HMO-2011-type phages are also likely to be temperate phages.In the DNA metabolism and replication modules, genes encoding DNA primase, DNA helicase, DNAP, ribonucleotide reductase (RNR), and endonuclease can be identified; and DNA helicase, DNA primase, and DNAP are core to all HMO-2011-type phages. All reported HMO-2011-type phages contain an atypical DNAP, in which a partial DnaJ central domain is located between the exonuclease domain and the DNA polymerase domain [20, 22]. The Escherichia coli DnaJ protein, a co-chaperone [61], has been shown to be involved in diverse functions [62] and to be critical for the replication of phage Lambda [63,64,65]. The sequence analysis revealed that DNAP sequences of these seven new HMO-2011-type phages and 207 MVGs also present this unusual domain structure and contain two repeats of the CXXCXGXG motifs involved in zinc binding [66] in the partial DnaJ domain (Supplementary Fig. 3). RNR gene is frequently detected in subgroups I, II, III, IV, V, and X genomes but not in the other subgroup genomes. RNRs, which are widely distributed in diverse phage genomes, are involved in catalyzing the reduction of ribonucleotides to deoxyribonucleotides, and thus play a crucial role in providing deoxyribonucleoside triphosphates for phage DNA biosynthesis and repair [67,68,69]. RNR genes clustered with the RNR gene in phage HMO-2011 were previously reported to dominate the class II viral RNRs in examined marine viromes [69]. In the remaining two modules, genes involved in phage structure (e.g., genes encoding capsid and portal proteins), packaging of DNA (TerL and TerS genes), and cell lysis were detected. The proteins encoded by these genes play key roles in phage morphogenesis and virion release.Examination of the distribution of the orthologous groups among the subgroups revealed clear pan-genome differences in various subgroups (Fig. 3). Most subgroups harbor subgroup-specific genes not identified in other subgroups, although  no function has yet been assigned to most of these genes. Notably, the phages in subgroups VII, VIII, and IX possess genomic features that differentiate them from phages in other subgroups, specifically with regard to the G + C content and gene content. The members of these three subgroups are closely related to each other in the phylogenetic tree and harbor several subgroup-specific genes. The G + C content of the phage genomes in these subgroups ranges from 31.9 to 35.4%, significantly smaller than other subgroups but similar to the G + C content of SAR11 bacteria and other known pelagiphages. HTVC033P is the only cultivated representative of subgroup IX. The aforementioned results suggest that the phages in subgroup VII, VIII, and IX might have related bacterial hosts and are highly likely to be pelagiphages. The host prediction using RaFAH tool also assigned Pelagibacter as their potential hosts (Supplementary Table 1). Subgroup X is located near these three subgroups in the phylogenetic tree, and the G + C content of the phages in this subgroup ranges from 34.4 to 39.0%. The host prediction assigned Roseobacter as their potential hosts. The hosts of this subgroup still remain to be experimentally investigated.Fig. 3: Distribution and functional classification of orthologous protein groups across HMO-2011-type genomes.Only orthogroups containing >10 members or showing subgroup-specific features are shown. Subgroup-specific genes are boxed in red. Genes that are absent in a specific subgroup are boxed in orange.Full size imageMetabolic capabilities of HMO-2011-type phagesAll HMO-2011-type phage genomes harbor several host-derived auxiliary metabolic genes (AMGs) potentially involved in diverse metabolic processes. Some AMGs in HMO-2011-type phages have been discussed previously [20, 22].Subgroups VII, VIII, IX, and X possess distinct AMGs as compared with the other subgroups. For example, the genes encoding FAD-dependent thymidylate synthase (ThyX, PF02511) and MazG pyrophosphohydrolase domains are absent in all subgroups VII, VIII, IX, and X genomes but frequently detected in other subgroup genomes. ThyX protein is essential for the conversion of dUMP to dTMP mediated by an FAD coenzyme and is therefore a key enzyme involved in DNA synthesis [70, 71]. The thyX gene is commonly found in microbial genomes and phage genomes. Phage-encoded ThyX has been suggested to compensate for the loss of host-encoded ThyA and thus play crucial roles in phage nucleic acid synthesis and metabolism during infection [72]. Except in the case of subgroups VII, VIII, IX, and X genomes, the mazG gene, which encodes a nucleoside triphosphate pyrophosphohydrolase is sporadically distributed in HMO-2011-type genomes. MazG protein is predicted to be a regulator of nutrient stress and programmed cell death [73] and has been hypothesized to promote phage survival by keeping the host alive during phage propagation [74]. The Escherichia coli MazG can interfere with the function of the MazEF toxin–antitoxin system by decreasing the cellular level of (p)ppGpp [73]. However, a recent study showed that a cyanophage MazG has no binding or hydrolysis activity against alarmone (p)ppGpp but has high hydrolytic activity toward dGTP and dCTP, and it was speculated to play a role in hydrolyzing high G + C host genome for phage replication [75]. Whether the MazG proteins encoded by HMO-2011-type phages play a similar role in phage propagation remained to be investigated.Five MVGs in subgroup I contain a gene encoding a DraG-like family ADP-ribosyl hydrolase (ARH). In cellular ADP-ribosylation systems, ARH catalyzes the cleavage of the ADP-ribose moiety, and thereby counteract the effects of ADP-ribosyl transferases [76]. It has been reported that ARH in Rhodospirillum rubrum regulates the nitrogen fixation [77]. However, the function of this phage-encoded ARH in the phage propagation process remains unclear.We also observed that several MVGs possess genes involved in iron–sulfur (Fe–S) cluster biosynthesis, including an Fe–S cluster assembly scaffold gene (iscU) that involved in Fe–S cluster assembly and transfer [78] and an Fe–S cluster insertion protein gene (erpA). Fe–S cluster participates in a wide variety of cellular biological processes [79]. The discovery of these genes suggests that these phages may play important roles in Fe–S cluster biogenesis and function.The gene encoding sodium-dependent phosphate transport protein (PF02690) has been identified in eight subgroup I genomes. The Na/Pi cotransporter family protein is responsible for high-affinity, sodium-dependent Pi uptake, and thus the protein plays a critical role in maintaining phosphate homeostasis [80]. This gene might function in the transport of phosphate into cells during phage infection. The presence of Na/Pi cotransporter genes suggests that some HMO-2011-type phages may have the potential to regulate host phosphate uptake in phosphate-limited ocean environments in order to benefit phage replication and propagation.Identification and phylogenetic analysis of HMO-2011-type DNAPsThe genetic diversity and geographically distribution of HMO-2011-type phages in marine environments was further inferred from DNAP gene analyses. A total of 2433 HMO-2011-type DNAP sequences with sequence sizes ranging from 540 to 779 amino acids were identified and subjected to phylogenetic analysis (Supplementary Table 3).Among the identified HMO-2011-type DNAPs, 2030 sequences were retrieved from the GOV 2.0 Tara expedition upper-ocean viral populations (0–1000 m), from tropical to polar regions. HMO-2011-type DNAP genes were identified from all analyzed upper-ocean viromes, suggesting the global prevalence of HMO-2011-type phages in upper oceans.A previous study revealed that marine viromes contain various types of tailed phage genomes that encode a family A DNAP gene [81]. To estimate the importance of HMO-2011-type phages, we calculated the proportion of HMO-2011-type DNAPs based on the number of HMO-2011-type DNAP sequences and the total number of family A DNAP sequences ( >470 aa) in each GOV 2.0 viral population dataset. This analysis revealed that HMO-2011-type DNAPs accounted for up to 19.7% of all family A DNAPs in each GOV 2.0 dataset (Supplementary Table 4). We found that the HMO-2011-type DNAP sequences appear to be more dominant in epipelagic viromes than in mesopelagic viromes (p  More

The prevalence of S. aureus isolation from the different examined samplesStaphylococcal infections represent a public health issue in hospitals and health care settings as well as a major economical and welfare problem in dairy animal farming25. The prevalence of S. aureus isolation from the farm under the study (Table 2) showed that 63 (33.1%) out of 190 different samples were bacteriologically positive. Moreover, the isolation was mainly obtained from manager swabs followed by milk machine swabs, nasal swabs and hand swabs (60.0, 53.3, 40.0 and 28.0%, respectively), and to a lesser extent in milk samples (24.0%). Meanwhile it was not isolated at any percent from water trough swabs, at X2 = 48.8, P  More

Generation timeDuring the infectious period, an infected individual may produce a secondary infection. However, the individual’s infectiousness is not constant during the infectious period, but it can be approximated by the probability distribution of the generation time (GT), which accounts for the time between the infection of a primary case and the infection of a secondary case. Unfortunately, such distribution is not as easy to estimate as that of the serial interval, which accounts for the time between the onset of symptoms in a primary case to the onset of symptoms of a secondary case. This is because the time of infection is more difficult to detect than the time of symptoms onset. Ganyani et al.27 developed a methodology to estimate the distribution of the GT from the distributions of the incubation period and the serial interval. Assuming an incubation period following a gamma distribution with a mean of 5.2 days and a standard deviation (SD) of 2.8 days, they estimated the serial interval from 91 and 135 pairs of documented infector-infectee in Singapore and Tianjin (China). Then, they found that the GT followed a gamma distribution with mean = 5.20 (95% CI = [3.78, 6.78]) days and SD = 1.72 (95% CI = [0.91, 3.93]) for Singapore (hereafter GT1), and with mean = 3.95 (95% CI = [3.01, 4.91]) days and SD = 1.51 (95% CI = [0.74, 2.97]) for Tianjin (hereafter GT2). Ng et al.28 applied the same methodology to 209 pairs of infector-infectee in Singapore and determined a gamma distribution with mean = 3.44 (95% CI = [2.79, 4.11]) days and SD 2.39 (95% CI = [1.27, 3.45]; hereafter GT3). Figure 3 shows the probability density functions (PDF) of such distributions, fGT. The differences between them are remarkable. For example, the 54.5%, 81.0%, and 80.7% of the contagions are produced in a pre-symptomatic stage (in the first 5.2 days after primary infection) assuming GT1, GT2, and GT3, respectively.Figure 3Probability density function of the generation time distribution, fGT(t), of GT1 (blue line; Singapore27), GT2 (yellow line; Tianjin27), GT3 (red line; Singapore28), and GTth (black line; theoretical distribution). Bars are the discretized version, (widetilde{{f_{GT} }}left( n right)), of the PDF of GTth.Full size imageTheoretically, assuming that the incubation periods of two individuals are independent and identically distributed, which is quite plausible, the expected/mean values of the GT and the serial interval should be equal29,30. The mean of the serial interval is easier to estimate than that of the GT. For that reason, we assume a mean serial interval as estimated from a meta-analysis of 13 studies involving a total of 964 pairs of infector-infectee, which is 4.99 days (95% CI = [4.17, 5.82])31, is more reliable than the aforementioned means of the GT. This value is within the error estimates of the means of GT1 and GT2, but not for GT3. Then, we construct a theoretical distribution for the GT that follows a gamma distribution (hereafter GTth) with mean = 4.99 days and SD = 1.88 days. This theoretical distribution can be seen in Fig. 3 and approximates the average PDF of three gamma distributions with mean = 4.99 and the SD of GT1, GT2, and GT3. We assume a conservative CI = [1.51, 2.39] for the theoretical SD, defined with the minimum and maximum SD values of GT1, GT2, and GT3. GTth shows 63.1% of pre-symptomatic contagions.
R

0

from r
In theory, the basic reproduction number R0 can be estimated as far as the intrinsic growth rate r, and the distributions of both the latent and infectious periods are known26,32,33,34. The latent period accounts for the period during which an infected individual cannot infect other individuals. It is observed in diseases for which the infectious period starts around the end of the incubation period, as happened with influenza35 and SARS36. However, from Fig. 3 it is inferred that COVID-19 is transmissible from the moment of infection, and we will assume a null latent period. Then, if the GT follows a gamma distribution, R0 can be estimated from the formulation of Anderson and Watson32, which was adapted to null latent periods by Yan26 as$$ R_{0} = frac{{mean_{GT} }}{{1 – left( {1 + mean_{GT} cdot r cdot frac{1}{{shape_{GT} }}} right)^{{ – shape_{GT} }} }} cdot r, $$
(4)
where meanGT is the mean GT and shapeGT is one of the two parameters defining the gamma distribution, which can be estimated as$$ shape_{GT} = frac{{left( {mean_{GT} } right)^{2} }}{{left( {SD_{GT} } right)^{2} }}. $$
(5)
For GTth, we get R0 = 1.50 (CI = [1.41, 1.61]) for REMEDID I(n) and R0 = 1.76 (CI = [1.60, 1.94]) for official I(n). For the other three GT distributions, R0 ranges from 1.39 (CI = [1.27, 1.58]) to 1.51 (CI = [1.34, 1.80]) for REMEDID I(n) and from 1.59 (CI = [1.40, 1.88]) to 1.78 (CI = [1.51, 2.23]) for official I(n) (Table 1). In all cases, R0 from GTth are within those from the three known GT distributions and indistinguishable from them within the error estimates. The lower (upper) bound of the CI is estimated as the minimum (maximum) R0 obtained from all the possible combinations of 100 evenly spaced values covering the CI of r, meanGT and SDGT. Then, following the Bonferroni correction, the reported CI present at least a 85% of confidence level for GT1, GT2, and GT3, but it cannot be assured for GTth since the CI of its SD is unknown. In general, all these R0 estimates are lower than those summarised by Park et al.20.Table 1 R0 and HIT values of the ancestral SARS-CoV-2 variant estimated from GT1, GT2, GT3, and GTth, and REMEDID and official infections. For date0, “Dec.” means December 2019, and “Jan.” means January 2020.Full size tableAlternatively, R0 can be estimated by applying the Euler–Lotka equation29,33,$$ R_{0} = frac{1}{{mathop smallint nolimits_{0}^{ + infty } e^{ – rt} cdot f_{GT} left( t right)dt}}. $$
(6)
In this case, we get values closer to previous estimates20. In particular, for GTth, we get R0 = 2.12 (CI = [1.81, 2.48]) for REMEDID I(n) and R0 = 2.92 (CI = [2.28, 3.75]) for official I(n). For the other three GT distributions, R0 ranges from 1.63 (CI = [1.43, 1.90]) to 2.21 (CI = [1.59, 2.95]) for REMEDID I(n) and from 1.97 (CI = [1.59, 2.54]) to 3.11 (CI = [1.84, 4.90]) for official I(n) (Table 1). The CI are estimated as in Eq. (4).R0 from a dynamical modelWe designed a dynamic model with Susceptible-Infected-Recovered (SIR) as stocks that accounts for the infectiousness of the infectors. Such a model is a generalisation of the Susceptible-Exposed-Infected-Recovered (SEIR) model37. Births, deaths, immigration and emigration are ignored, which seems reasonable since the timescale of the outbreak is too short to produce significant demographic changes. For the sake of simplicity, the recovered stock includes recoveries and fatalities, and it is denoted as R(t). A random mixing population is assumed, that is a population where contacts between any two people are equally probable. Time is discretized in days, so the real time variable t is replaced by the integer variable n. As a consequence, the derivatives in the differential equations defining the dynamic model explained below are discrete derivatives.The size of the population is fixed at N = 100,000, and then, for any day n we get$$ tilde{S}left( n right) + left( {mathop sum limits_{k = 0}^{20} tilde{I}left( n-k right)} right) + tilde{R}left( n right) = N, $$
(7)
where (tilde{S}left( n right)), (tilde{I}left( n right)), and (tilde{R}left( n right)) are the discretized versions of S(t), I(t), and R(t) and (tilde{I}) is assumed to be null for negative integers. The summation is a consequence of the infectiousness, which is approximated according to the GT, whose PDF is discretized as$$ widetilde{{f_{GT} }}left( n right) = mathop smallint limits_{n – 1}^{n} f_{GT} left( t right) dt, $$
(8)
from n = 1 to 20. Figure 3 shows (widetilde{{f_{GT} }}left( n right)) for GTth. Truncating at n = 20 accounts for 99.99% of the area below the PDF of all the GT. Then, an infected individual at day n0 is expected to produce on average$$ widetilde{{R_{e} }}left( {n_{0} + n} right) cdot widetilde{{f_{GT} }}left( n right) $$
(9)
infections n days later, where (widetilde{{R_{e} }}left( n right)) is the discretized version of Re(t). From this expression, it is obvious that values of (widetilde{{R_{e} }}left( n right) < 1) will produce a decline of infections. Conversely, infections at day n0 are produced by all individuals infected during the previous 20 days as$$ tilde{I}(n_{0} ) = tilde{R}_{e} left( {n_{0} } right) cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{f_{GT} }}left( n right)} right), $$ (10) whose continuous version has been reported in previous studies29,38. The expression in brackets is called total infectiousness of infected individuals at day n039. According to Eq. (1), Eq. (10) can be expressed in terms of R0 as$$ tilde{I}(n_{0} ) = R_{0} cdot frac{{tilde{S}left( {n_{0} } right)}}{N} cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{f_{GT} }}left( n right)} right). $$ (11) As we want a dynamic model capable of providing (tilde{I}left( {n_{0} } right)) from the stocks at time step n0 − 1, we replaced (tilde{S}left( {n_{0} } right)) by (tilde{S}left( {n_{0} - 1} right)) in Eq. (11). This assumption makes sense in a discrete domain since the infections at time n0 take place in the susceptible population at time n0 − 1. Then, assuming that all stocks are set to zero for negative integers, our dynamic model can be expressed in terms of Eq. (7) and the following differential equations:$$ delta tilde{I}(n_{0} ) = R_{0} cdot frac{{tilde{S}left( {n_{0} - 1} right)}}{N} cdot left( {mathop sum limits_{n = 1}^{20} tilde{I}left( {n_{0} - n} right) cdot widetilde{{{text{f}}_{GT} }}left( n right)} right) - tilde{I}(n_{0} - 1), $$ (12) $$ delta tilde{S}left( {n_{0} } right) = {-}tilde{I}left( {n_{0} } right), $$ (13) $$ delta tilde{R}left( {n_{0} } right) = tilde{I}left( {n_{0} - 21} right), $$ (14) where (delta tilde{I}), (delta tilde{S}), and (delta tilde{R}) are the (discrete) derivatives of (tilde{I}), (tilde{S}), and (tilde{R}), respectively. Applying the initial conditions (tilde{S}left( 0 right) = N - 1), (tilde{I}left( 0 right) = 1), and (tilde{R}left( 0 right) = 0), it is assumed that the outbreak was produced by only one infector. The latter is not true in Spain, since several independent introductions of SARS-CoV-2 were detected40. However, for modelling purposes it is equivalent to introducing a single infection at day 0 or M infections produced by the single infection n days later. Then, the date of the initial time n = 0 is accounted as a parameter date0, which is optimised, as well as R0, to minimise the root-mean square of the residual between the model simulated (tilde{I}left( n right)) and the REMEDID and official I(n) for the period from date0 to n0.The model was implemented in Stella Architect software v2.1.1 (www.iseesystems.com) and exported to R software v4.1.1 with the help of deSolve (v1.28) and stats (v4.1.1) packages, and the Brent optimisation algorithm was implemented. For REMEDID I(n) and GTth, we obtained date0 = 13 December 2019 and R0 = 2.71 (CI = [2.33, 3.15]). Optimal solutions combine lower/higher R0 and earlier/later date0 (Fig. 4), which highlights the importance of providing an accurate first infection date to estimate R0. When the other three GT distributions were considered, we obtained similar date0, ranging from 12 to 17 December 2019, and R0 values ranging from 2.08 (CI = [1.86, 2.42]) to 2.85 (CI = [2.05, 3.25]; see Table 1). For official infections, date0 was set to 1 January 2020 for all cases, and R0 ranged from 1.81 (CI = [1.64, 2.07]) to 2.41 (CI = [1.80, 2.91]). The CI are estimated as in Eq. (4).Figure 4Root-mean square (RMS) of the residuals between infections from the model, which depends on date0 (x-axis) and R0 (y-axis), and REMEDID (from MoMo ED) and official infections. Parameters optimizing the model are highlighted in purple. RMS larger than 1275 (left panel) and 103 (right panel) are saturated in white.Full size image More

1.Federal Office for the Environment (FOEN). Action Plan for the Swiss Biodiversity Strategy (FOEN, Bern, 2017).2.Geldmann, J. & González-Varo, J. P. Conserving honey bees does not help wildlife. Science 359, 392–393 (2018).Article 

Google Scholar 
3.Egerer, M. & Kowarik, I. Confronting the modern gordian knot of urban beekeeping. Trends Ecol. Evol. 35, 956–959 (2020).Article 

Google Scholar 
4.Herrera, C. M. Gradual replacement of wild bees by honeybees in flowers of the Mediterranean Basin over the last 50 years. Proc. R. Soc. B Biol. Sci. 287, 16–20 (2020).
Google Scholar 
5.Torné-Noguera, A., Rodrigo, A., Osorio, S. & Bosch, J. Collateral effects of beekeeping: impacts on pollen-nectar resources and wild bee communities. Basic Appl. Ecol. 17, 199–209 (2016).Article 

Google Scholar 
6.Magrach, A., González-Varo, J. P., Boiffier, M., Vilà, M. & Bartomeus, I. Honeybee spillover reshuffles pollinator diets and affects plant reproductive success. Nat. Ecol. Evol. 1, 1299–1307 (2017).Article 

Google Scholar 
7.Prendergast, K. S., DIxon, K. W. & Bateman, P. W. Interactions between the introduced European honey bee and native bees in urban areas varies by year, habitat type and native bee guild. Biol. J. Linn. Soc. 133, 725–743 (2021).Article 

Google Scholar 
8.Herbertsson, L., Lindström, S. A. M., Rundlöf, M., Bommarco, R. & Smith, H. G. Competition between managed honeybees and wild bumblebees depends on landscape context. Basic Appl. Ecol. 17, 609–616 (2016).Article 

Google Scholar 
9.Stevenson, P. C. et al. The state of the world’s urban ecosystems: what can we learn from trees, fungi, and bees? Plants People Planet 2, 482–498 (2020).Article 

Google Scholar 
10.Ropars, L., Dajoz, I., Fontaine, C., Muratet, A. & Geslin, B. Wild pollinator activity negatively related to honey bee colony densities in urban context. PLoS ONE 14, e0222316 (2019).CAS 
Article 

Google Scholar 
11.Venter, Z. S. & Sydenham, M. A. K. Continental-scale land cover mapping at 10 m resolution over Europe (ELC10). Remote Sens. 13, 2301 (2021).Article 

Google Scholar 
12.Hardin, G. The tragedy of the commons. Science 162, 1243–1248 (1968).CAS 
Article 

Google Scholar 
13.Tew, N. E. et al. Quantifying nectar production by flowering plants in urban and rural landscapes. J. Ecol. 109, 1747–1757 (2021).Article 

Google Scholar 
14.Baldock, K. C. R. et al. A systems approach reveals urban pollinator hotspots and conservation opportunities. Nat. Ecol. Evol. 3, 363–373 (2019).Article 

Google Scholar 
15.Casanelles-Abella, J. et al. Applying predictive models to study the ecological properties of urban ecosystems: A case study in Zürich, Switzerland. Landsc. Urban Plan. 214, 104137 (2021).Article 

Google Scholar 
16.IPBES. Summary for policymakers of the global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES, 2019).17.IUCN. IUCN’s Key Messages. First Draft of the Post-2020 Global Biodiversity Framework. In Convention on Biological Diversity Third meeting of the Open-Ended Working Group on the Post-2020 Global Biodiversity Framework (OEWG3) 15 (IUCN, 2021).18.Baldock, K. C. R. Opportunities and threats for pollinator conservation in global towns and cities. Curr. Opin. Insect Sci. 38, 63–71 (2020).Article 

Google Scholar 
19.Henry, M. & Rodet, G. The apiary influence range: a new paradigm for managing the cohabitation of honey bees and wild bee communities. Acta Oecologica 105, 103555 (2020).Article 

Google Scholar 
20.Ignatieva, M. & Hedblom, M. An alternative urban green carpet. Science 362, 148–149 (2018).CAS 
Article 

Google Scholar 
21.Vega, K. A. & Küffer, C. Promoting wildflower biodiversity in dense and green cities: The important role of small vegetation patches. Urban For. Urban Green. 62, 127165 (2021).Article 

Google Scholar 
22.Fabián, D., González, E., Sánchez Domínguez, M. V., Salvo, A. & Fenoglio, M. S. Towards the design of biodiverse green roofs in Argentina: assessing key elements for different functional groups of arthropods. Urban For. Urban Green. 61 (2021).23.Vega, K. A., Schläpfer-Miller, J. & Kueffer, C. Discovering the wild side of urban plants through public engagement. Plants People Planet 3, 389–401 (2021).Article 

Google Scholar 
24.Von Büren, R. S., Oehen, B., Kuhn, N. J. & Erler, S. High-resolution maps of Swiss apiaries and their applicability to study spatial distribution of bacterial honey bee brood diseases. PeerJ 2019, 1–21 (2019).
Google Scholar 
25.QGIS Development Team. QGIS Geographic Information System (Open Source Geospatial Foundation Project, 2020).26.R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2019).27.R Studio Team. R studio: Integrated Development for R (RStudio, Boston, 2020).28.Casanelles-Abella, J. & Moretti M. Challenging the sustainability of urban beekeeping: evidence from Swiss cities. Envidat. https://doi.org/10.16904/envidat.239 (2021).29.Casanelles-Abella, J. Code for the paper: Challenging the sustainability of urban beekeeping: evidence from Swiss cities (v. 1.0). Zenodo https://doi.org/10.5281/zenodo.5618254 (2021).30.Swiss Fedearl Office of Topography Swisstopo. SWISSIMAGE 25. https://www.swisstopo.admin.ch/en/geodata/images/ortho/swissimage25.html#links (Swisstopo, 2021). More

1.Guisan, A. et al. Predicting species distributions for conservation decisions. Ecol. Lett. 16, 1424–1435 (2013).PubMed 
PubMed Central 

Google Scholar 
2.Robinson, L. M. et al. Pushing the limits in marine species distribution modelling: Lessons from the land present challenges and opportunities. Glob. Ecol. Biogeogr. 20, 789–802 (2011).
Google Scholar 
3.Yates, K. L. et al. Outstanding challenges in the transferability of ecological models. Trends Ecol. Evol. 33, 790–802 (2018).PubMed 

Google Scholar 
4.Mayor, S. J., Schneider, D. C., Schaefer, J. A. & Mahoney, S. P. Habitat selection at multiple scales. Ecoscience 16, 238–247 (2009).
Google Scholar 
5.Mannocci, L. et al. Temporal resolutions in species distribution models of highly mobile marine animals: Recommendations for ecologists and managers. Divers. Distrib. 23, 1098–1109 (2017).
Google Scholar 
6.Sequeira, A. M. M., Bouchet, P. J., Yates, K. L., Mengersen, K. & Caley, M. J. Transferring biodiversity models for conservation: Opportunities and challenges. Methods Ecol. Evol. 9, 1250–1264 (2018).
Google Scholar 
7.Cleguer, C., Grech, A., Garrigue, C. & Marsh, H. Spatial mismatch between marine protected areas and dugongs in New Caledonia. Biol. Conserv. 184, 154–162 (2015).
Google Scholar 
8.Hays, G. C. et al. Translating marine animal tracking data into conservation policy and management. Trends Ecol. Evol. 34, 459–473 (2019).PubMed 

Google Scholar 
9.Hays, G. C. et al. Key questions in marine megafauna movement ecology. Trends Ecol. Evol. 31, 463–475 (2016).PubMed 

Google Scholar 
10.Hazen, E. L. et al. WhaleWatch: A dynamic management tool for predicting blue whale density in the California Current. J. Appl. Ecol. 54, 1415–1428 (2017).
Google Scholar 
11.Sequeira, A. M. M. et al. Overhauling ocean spatial planning to improve marine megafauna conservation. Front. Mar. Sci. 6, 639 (2019).
Google Scholar 
12.Marsh, H. & Sobtzick, S. Dugong dugon. In The IUCN RedList of Threatened Species (2019:e.T6909A160756767). https://dx.doi.org/https://doi.org/10.2305/IUCN.UK.2015-4.RLTS.T6909A160756767.en. Accessed November 2020 (2019).13.Marsh, H., O’Shea, T. J. & Reynolds, J. E. I. Ecology and Conservation of the Sirenia: Dugongs and Manatees Vol. 18 (Cambridge University Press, 2011).
Google Scholar 
14.Pimiento, C. et al. Functional diversity of marine megafauna in the Anthropocene. Sci. Adv. 6, eaay7650 (2020).CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar 
15.Nowicki, R. J., Thomson, J. A., Fourqurean, J. W., Wirsing, A. J. & Heithaus, M. R. Loss of predation risk from apex predators can exacerbate marine tropicalization caused by extreme climatic events. J. Anim. Ecol. https://doi.org/10.1111/1365-2656.13424 (2021).Article 
PubMed 

Google Scholar 
16.Wirsing, A. J., Heithaus, M. R. & Dill, L. M. Living on the edge: Dugongs prefer to forage in microhabitats that allow escape from rather than avoidance of predators. Anim. Behav. 74, 93–101 (2007).
Google Scholar 
17.Aragones, L. V., Lawler, I. R., Foley, W. J. & Marsh, H. Dugong grazing and turtle cropping: Grazing optimization in tropical seagrass systems?. Oecologia 149, 635–647 (2006).PubMed 
ADS 

Google Scholar 
18.Preen, A. Impacts of dugong foraging on seagrass habitats: Observational and experimental evidence for cultivation grazing. Mar. Ecol. Prog. Ser. 124, 201–213 (1995).ADS 

Google Scholar 
19.Unsworth, R. K. F., Collier, C. J., Waycott, M., Mckenzie, L. J. & Cullen-Unsworth, L. C. A framework for the resilience of seagrass ecosystems. Mar. Pollut. Bull. 100, 34–46 (2015).CAS 
PubMed 

Google Scholar 
20.Tol, S. J. et al. Long distance biotic dispersal of tropical seagrass seeds by marine mega-herbivores. Sci. Rep. 7, 1–8 (2017).CAS 
ADS 

Google Scholar 
21.Ponnampalam, L. S., Fairul Izmal, J. H., Adulyanukosol, K., Ooi, J. L. S. & Reynolds, J. E. Aligning conservation and research priorities for proactive species and habitat management: The case of dugongs Dugong dugon in Johor, Malaysia. Oryx 49, 743–749 (2015).
Google Scholar 
22.Preen, A. The Status and Conservation of Dugongs in the Arabian Region. Saudi Arabia, Meteorological and Environmental Protection Administration (MEPA), Coastal and Marine Management Series. Report, No 10, (1989).23.Preen, A. Distribution, abundance and conservation status of dugongs and dolphins in the southern and western Arabian Gulf. Biol. Conserv. 118, 205–218 (2004).
Google Scholar 
24.Findlay, K. P., Cockcroft, V. G. & Guissamulo, A. T. Dugong abundance and distribution in the Bazaruto Archipelago, Mozambique. Afr. J. Mar. Sci. 33, 441–452 (2011).
Google Scholar 
25.Pilcher, N. J. et al. A low-cost solution for documenting distribution and abundance of endangered marine fauna and impacts from fisheries. PLoS ONE 12, e0190021 (2017).PubMed 
PubMed Central 

Google Scholar 
26.Hashim, M. et al. Using fisher knowledge, mapping population, habitat suitability and risk for the conservation of dugongs in Johor Straits of Malaysia. Mar. Policy 78, 18–25 (2017).
Google Scholar 
27.Bayliss, P. & Hutton, M. Integrating Indigenous Knowledge and Survey Techniques to Develop a Baseline for Dugong (Dugong dugon) Management in the Kimberley. Final Report of project 1.2.5 of the Kimberley Marine Research Program Node of the Western Australian Marine Science Institution, WAMSI (2017).28.Campbell, R., Holley, D. & Bardi-Jawi Ranger Group. Movement Behaviours and Habitat Usage of West Kimberley Dugongs : A Community Based Approach Final Report to the National Marine Mammal Centre November 2010. Final Report to the National Marine Mammal Centre (2010).29.Cleguer, C. et al. Working with the Community to Understand Use of Space by Dugongs and Green Turtles in Torres Strait. Final Report to the Mura Badulgal Representative NativeTitle Body Corporate and the Department of the Environment, National Environment Science Program TropicalWater Quality Hub (James Cook University, Townsville, 2016).30.Gredzens, C. et al. Satellite tracking of sympatric marine megafauna can inform the biological basis for species co-management. PLoS ONE 9, e98944 (2014).PubMed 
PubMed Central 
ADS 

Google Scholar 
31.Holley, D. Movement Patterns and Habitat Usage of Shark Bay Dugongs. MSc thesis, Edith Cowan University, Perth. https://ro.ecu.edu.au/cgi/viewcontent.cgi?article=1070&context=theses (2006).32.Sheppard, J. et al. Movement heterogeneity of dugongs, Dugong dugon (Müller), over large spatial scales. J. Exp. Mar. Bio. Ecol. 334, 64–83 (2006).
Google Scholar 
33.Hagihara, R. et al. Improving the Estimates of Abundance of Dugongs and Large Immature and Adult-Sized Green Turtles in Western and Central Torres Strait. Report to the National Environmental Science Programme (Reef and Rainforest Research Centre Limited, Cairns 2016).34.De Iongh, H. H., Langeveld, P. & Van Der Wal, M. Movement and home ranges of dugongs around the Lease Islands, East Indonesia. Mar. Ecol. 19, 179–193 (1998).ADS 

Google Scholar 
35.Cleguer, C., Garrigue, C. & Marsh, H. Dugong (Dugong dugon) movements and habitat use in a coral reef lagoonal ecosystem. Endanger. Species Res. 43, 167–181 (2020).
Google Scholar 
36.Sheppard, J., Jones, R. E., Marsh, H. & Lawler, I. R. Effects of tidal and diel cycles on dugong habitat use. J. Wildl. Manag. 73, 45–59 (2009).
Google Scholar 
37.Sheppard, J., Marsh, H., Jones, R. E. & Lawler, I. R. Dugong habitat use in relation to seagrass nutrients, tides, and diel cycles. Mar. Mammal Sci. 26, 855–879 (2010).
Google Scholar 
38.Zeh, D. R. et al. Evidence of behavioural thermoregulation by dugongs at the high latitude limit to their range in eastern Australia. J. Exp. Mar. Bio. Ecol. 508, 27–34 (2018).
Google Scholar 
39.UNESCO. Lagoons of New Caledonia: Reef Diversity and Associated Ecosystems (U.W.H. Centre, 2009).40.Payri, C. New Caledonia: World of Corals (IRD Editions/Solaris, Marseille/Nouméa, 2018).41.Oremus, M., Garrigue, C. & Cleguer, C. Isolement et diversité génétique des dugongs de Nouvelle-Calédonie (Unpublished Report, 2011).42.Oremus, M., Garrigue, C. & Cleguer, C. Etude génétique complémentaire sur le statut de la population de dugong de Nouvelle-Calédonie (Unpublished Report, 2015).43.Garrigue, C., Patenaude, N. & Marsh, H. Distribution and abundance of the dugong in New Caledonia, southwest Pacific. Mar. Mammal Sci. 24, 81–90 (2008).
Google Scholar 
44.Cleguer, C. et al. Drivers of change in the relative abundance of dugongs in New Caledonia. Wildl. Res. 44, 365–376 (2017).
Google Scholar 
45.Gonson, C. et al. Decadal increase in the number of recreational users is concentrated in no-take marine reserves. Mar. Pollut. Bull. 107, 144–154 (2016).CAS 
PubMed 

Google Scholar 
46.Fraser, K. C. et al. Tracking the conservation promise of movement ecology. Front. Ecol. Evol. 6, 150 (2018).
Google Scholar 
47.Hussey, N. E. et al. Aquatic animal telemetry: A panoramic window into the underwater world. Science (80-.) 348, 1255642 (2015).
Google Scholar 
48.Hagihara, R. et al. Compensating for geographic variation in detection probability with water depth improves abundance estimates of coastal marine megafauna. PLoS ONE 13, e0191476 (2018).PubMed 
PubMed Central 

Google Scholar 
49.Sequeira, A. M. M. et al. The importance of sample size in marine megafauna tagging studies. Ecol. Appl. 29, e01947 (2019).CAS 
PubMed 

Google Scholar 
50.Derville, S., Constantine, R., Baker, C. S., Oremus, M. & Torres, L. G. Environmental correlates of nearshore habitat distribution by the Critically Endangered Maui dolphin. Mar. Ecol. Prog. Ser. 551, 261–275 (2016).CAS 
ADS 

Google Scholar 
51.Derville, S., Torres, L. G., Iovan, C. & Garrigue, C. Finding the right fit: Comparative cetacean distribution models using multiple data sources and statistical approaches. Divers. Distrib. 24, 1657–1673 (2018).
Google Scholar 
52.Pinto, C. et al. Using individual tracking data to validate the predictions of species distribution models. Divers. Distrib. 22, 682–693 (2016).
Google Scholar 
53.Tingley, M. W., Wilkerson, R. L., Howell, C. A. & Siegel, R. B. An integrated occupancy and space-use model to predict abundance of imperfectly detected, territorial vertebrates. Methods Ecol. Evol. 7, 508–517 (2016).
Google Scholar 
54.Roberts, J. J. et al. Habitat-based cetacean density models for the U.S. Atlantic and Gulf of Mexico. Sci. Rep. 6, 22615 (2016).CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar 
55.Mannocci, L., Roberts, J. J., Pedersen, E. J. & Halpin, P. N. Geographical differences in habitat relationships of cetaceans across an ocean basin. Ecography (Cop.) 43, 1250–1259 (2020).
Google Scholar 
56.Wirsing, A. J., Heithaus, M. R. & Dill, L. M. Fear factor: Do dugongs (Dugong dugon) trade food for safety from tiger sharks (Galeocerdo cuvier)?. Oecologia 153, 1031–1040 (2007).PubMed 
ADS 

Google Scholar 
57.Jollit, I. Spatialisation des activités humaines et aide à la décision pour une gestion durable des écosystèmes coralliens: la pêche plaisancière dans le lagon sud-ouest de la Nouvelle-Calédonie. PhD dissertation, Université de la Nouvelle-Calédonie (2010).58.Maitland, R. N., Lawler, I. R. & Sheppard, J. K. Assessing the risk of boat strike on Dugongs Dugong dugon at Burrum Heads, Queensland, Australia. Pac. Conserv. Biol. 12, 321–326 (2006).
Google Scholar 
59.Preen, A. Interactions Between Dugongs and Seagrasses in a Subtropical Environment. PhD dissertation, James Cook University, Townsville, Australia (1992).60.Hodgson, A. Dugong Behaviour and Responses to Human Influences. PhD dissertation, James Cook University (2004).61.Edwards, H. H. et al. Influence of manatees’ diving on their risk of collision with watercraft. PLoS ONE 11, e0151450 (2016).PubMed 
PubMed Central 

Google Scholar 
62.Rycyk, A. M. et al. Manatee behavioral response to boats. Mar. Mamm. Sci. 34, 924–962 (2018).
Google Scholar 
63.Garrigue, C. Macrophyte associations on the soft bottoms of the South-West Lagoon of New Caledonia: Description, structure and biomass. Bot. Mar. 38, 481–492 (1995).
Google Scholar 
64.Andréfouët, S. et al. Nation-wide hierarchical and spatially-explicit framework to characterize seagrass meadows in the Indo-Pacific: Example application to New Caledonia. Mar. Pollut. Bull. 173, 113036 (2021).PubMed 

Google Scholar 
65.Cleguer, C. Informing Dugong Conservation at Several Spatial and Temporal Scales in New Caledonia. PhD dissertation, James Cook University (2015).66.Anderson, P. K. Dugongs of Shark Bay, Australia–Seasonal migration, water temperature and forage. Natl. Geogr. Res. 2, 473–490 (1986).
Google Scholar 
67.Heithaus, M. R. & Dill, L. M. Food availability and tiger shark predation risk influence bottlenose dolphin habitat use. Ecology 83, 480–491 (2002).
Google Scholar 
68.Roger, J. Données bathymétriques et topographiques de Nouvelle-Calédonie : Réalisation d’un MNT terre-mer pour l’étude de l’aléa tsunami (projet TSUCAL). (Institut de Recherche pour le Développement, 2020).69.Andréfouët, S. et al. Global assessment of modern coral reef extent and diversity for regional science and management applications: A view from space. In Opening Talk, 10th International Coral Reef Symposium (eds Suzuki, Y. et al.) 1732–1745 (Japanese Coral Reef Society, 2006).
Google Scholar 
70.Andréfouët, S., Cabioch, G., Flamand, B. & Pelletier, B. A reappraisal of the diversity of geomorphological and genetic processes of New Caledonian coral reefs: A synthesis from optical remote sensing, coring and acoustic multibeam observations. Coral Reefs 28, 691–707 (2009).ADS 

Google Scholar 
71.Rousseeuw, P. J. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987).MATH 

Google Scholar 
72.Marsh, H. & Rathbun, G. B. Development and application of conventional and satellite radio tracking techniques for studying dugong movements and habitat use. Aust. Wildl. Res. 17, 83–100 (1990).
Google Scholar 
73.Lanyon, J. M. et al. A method for capturing dugongs (Dugong dugong) in open water. Aquat. Mamm. 32, 196–201 (2006).
Google Scholar 
74.Cleguer, C., Derville, S., Kelly, N., Lambourne, R. & Garrigue, C. Programme SIREN : Suivi à fine échelle de la fréquentation et du déplacement des dugongs dans la zone Voh-Koné- Pouembout , pour une gestion améliorée de l’espèce Rapport final (Technical report prepared for Koniambo Nickel SAS, 2020).75.Johnson, D., London, J., Lea, M. A. & Durban, J. Continuous-time correlated random walk model for animal telemetry data. Ecology 89, 1208–1215 (2008).PubMed 
PubMed Central 

Google Scholar 
76.Barraquand, F. & Benhamou, S. Animal movements in heterogeneous landscapes: Identifying profitable places and homogeneous movements bouts. Ecology 89, 3336–3348 (2008).PubMed 

Google Scholar 
77.Hyndman, R. et al. Forecast: Forecasting Functions for Time Series and Linear Models. https://pkg.robjhyndman.com/forecast/ (R package version 8.15, 2021).78.Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. & Team, R. C. nlme: Linear and Nonlinear Mixed Effects Models. https://CRAN.R-project.org/package=nlme (R package version 3.1–152, 2021).79.Hastie, T. J. & Tibshirani, R. J. Generalized Additive Models, volume 43 of Monographs on Statistics and Applied Probability (Chapman and Hall/CRC, 1990).
Google Scholar 
80.Wood, S. N. Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. R. Stat. Soc. 73, 3–36 (2011).MathSciNet 
MATH 

Google Scholar 
81.Wood, S. N. Generalized Additive Models: An Introduction with R (CRC Press, 2017).MATH 

Google Scholar 
82.Friedman, J. H. Greedy function approximation: A gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001).MathSciNet 
MATH 

Google Scholar 
83.Cox, T. & Schepers, L. Tides: Quasi-periodic Time Series Characteristics. https://CRAN.R-project.org/package=Tides (R package version 2.1., 2018).84.Boldina, I. & Beninger, P. G. Strengthening statistical usage in marine ecology: Linear regression. J. Exp. Mar. Bio. Ecol. 474, 81–91 (2016).
Google Scholar 
85.Russell, L. emmeans: Estimated Marginal Means, aka Least-Squares Means. https://CRAN.R-project.org/package=emmeans (R package version 1.4.7., 2020).86.R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2020).
Google Scholar  More

1.Burgess, S. C., Baskett, M. L., Grosberg, R. K., Morgan, S. G. & Strathmann, R. R. When is dispersal for dispersal? Unifying marine and terrestrial perspectives. Biol. Rev. 91, 867–882 (2016).PubMed 

Google Scholar 
2.Cowman, P. F. & Bellwood, D. R. Vicariance across major marine biogeographic barriers: Temporal concordance and the relative intensity of hard versus soft barriers. Proc. R. Soc. B Biol. Sci. 280, 20131541 (2013).
Google Scholar 
3.Floeter, S. R. et al. Atlantic reef fish biogeography and evolution. J. Biogeogr. 35, 22–47 (2008).
Google Scholar 
4.Luiz, O. J. et al. Ecological traits influencing range expansion across large oceanic dispersal barriers: Insights from tropical Atlantic reef fishes. Proc. R. Soc. B Biol. Sci. 279, 1033–1040 (2012).
Google Scholar 
5.Rocha, L. A. et al. Recent invasion of the tropical Atlantic by an Indo-Pacific coral reef fish. Mol. Ecol. 14, 3921–3928 (2005).PubMed 

Google Scholar 
6.Thornhill, D. J., Mahon, A. R., Norenburg, J. L. & Halanych, K. M. Open-ocean barriers to dispersal: A test case with the Antarctic Polar Front and the ribbon worm Parborlasia corrugatus (Nemertea: Lineidae). Mol. Ecol. 17, 5104–5117 (2008).CAS 
PubMed 

Google Scholar 
7.Fraser, C. I., Kay, G. M., du Plessis, M. & Ryan, P. G. Breaking down the barrier: Dispersal across the Antarctic Polar Front. Ecography 40, 235–237 (2017).
Google Scholar 
8.Thorrold, S. R. & McKinnon, A. D. Response of larval fish assemblages to a riverine plume in coastal waters of the central Great Barrier Reef lagoon. Limnol. Oceanogr. 40, 177–181 (1995).ADS 

Google Scholar 
9.Rocha, L. A. Patterns of distribution and processes of speciation in Brazilian reef fishes. J. Biogeogr. 30, 1161–1171 (2003).
Google Scholar 
10.Lentz, S. J. The Amazon River plume during AmasSeds: Subtidal current variability and the importance of wind forcing. J. Geophys. Res. 100, 2377–2390 (1995).ADS 

Google Scholar 
11.Figueiredo, A. G., Allison, M. & Nittrouer, C. A. Amazon Discharge: Internal Report for AMASSEDS Researches. (1991).12.Nittrouer, C. A. & DeMaster, D. J. The Amazon shelf setting: Tropical, energetic, and influenced by a large river. Cont. Shelf Res. 16, 553–573 (1996).ADS 

Google Scholar 
13.Jo, Y.-H., Yan, X. H., Dzwonkowski, B. & Liu, W. T. A study of the freshwater discharge from the Amazon River into the tropical Atlantic using multi-sensor data. Geophys. Res. Lett. 32, 1–4 (2005).
Google Scholar 
14.Moura, R. L. et al. An extensive reef system at the Amazon River mouth. Sci. Adv. 2, 1–11 (2016).
Google Scholar 
15.Francini-Filho, R. B. et al. Perspectives on the Great Amazon Reef: Extension, biodiversity, and threats. Front. Mar. Sci. 5, 142 (2018).
Google Scholar 
16.Neumann-Leitão, S. et al. Zooplankton from a reef system under the influence of the Amazon River plume. Front. Microbiol. 9, 1–15 (2018).
Google Scholar 
17.Targino, A. K. G. & Gomes, P. B. Distribution of sea anemones in the Southwest Atlantic: Biogeographical patterns and environmental drivers. Mar. Biodivers. 50, 80 (2020).
Google Scholar 
18.Barroso, C. X., Lotufo, T. M. C. & Matthews-Cascon, H. Biogeography of Brazilian prosobranch gastropods and their Atlantic relationships. J. Biogeogr. 43, 2477–2488 (2016).
Google Scholar 
19.Brandini, F. P., Lopes, R. M., Gutseit, K. S. & Sassi, R. Planctonologia na Plataforma Continental do Brasil: Diagnose e Revisão Bibliográfica. (CEMAR/MMA/CIRM/FEMAR, 1997).20.Loder, J. W., Boicourt, W. C. & Simpson, J. H. Western ocean boundary shelves coastal segment (W). Sea 11, 3–27 (1998).
Google Scholar 
21.Chollett, I., Mumby, P. J., Müller-Karger, F. E. & Hu, C. Physical environments of the Caribbean Sea. Limnol. Oceanogr. 57, 1233–1244 (2012).ADS 

Google Scholar 
22.Costello, M. J. et al. Marine biogeographic realms and species endemicity. Nat. Commun. 8, 1057 (2017).PubMed 
PubMed Central 
ADS 

Google Scholar 
23.Saeedi, H., Simões, M. & Brandt, A. Endemicity and community composition of marine species along the NW Pacific and the adjacent Arctic Ocean. Prog. Oceanogr. 178, 102199 (2019).
Google Scholar 
24.OBIS. Ocean Biogeographic Information System. http://www.iobis.org (2021).25.Spalding, M. D. et al. Marine ecoregions of the world: A bioregionalization of coastal and shelf areas. Bioscience 57, 573–583 (2007).
Google Scholar 
26.Hortal, J. et al. Seven shortfalls that beset large-scale knowledge of biodiversity. Annu. Rev. Ecol. Evol. Syst. 46, 523–549 (2015).
Google Scholar 
27.Baselga, A. Partitioning the turnover and nestedness components of beta diversity. Glob. Ecol. Biogeogr. 19, 134–143 (2010).
Google Scholar 
28.Fu, H. et al. Local and regional drivers of turnover and nestedness components of species and functional beta diversity in lake macrophyte communities in China. Sci. Total Environ. 687, 206–217 (2019).CAS 
PubMed 
ADS 

Google Scholar 
29.Costello, M. J., Stocks, K., Zhang, Y., Grassle, J. F. & Fautin, D. G. About the Ocean Biogeographic Information System. Vol. 29. (2007).30Miloslavich, P. et al. Marine biodiversity in the Caribbean: Regional estimates and distribution patterns. PLoS ONE 5, e11916 (2010).PubMed 
PubMed Central 
ADS 

Google Scholar 
31.Boltovskoy, D. & Valentin, J. L. Overview of the history of biological oceanography in the southwestern Atlantic, with emphasis on plankton. in Plankton Ecology of the Southwestern Atlantic (eds. Hoffmeyer, M. S., Sabatini, M. E., Brandini, F. P., Calliari, D. L. & Santinelli, N. H.). 3–34. https://doi.org/10.1007/978-3-319-77869-3_1 (Springer, 2018).32Costello, M. J. et al. A census of marine biodiversity knowledge, resources, and future challenges. PLoS ONE 5, e12110 (2010).PubMed 
PubMed Central 
ADS 

Google Scholar 
33.Lopes, R. M. Marine zooplankton studies in Brazil: A brief evaluation and perspectives. An. Acad. Bras. Ciênc. 79, 369–379 (2007).PubMed 

Google Scholar 
34.Alves-Júnior, F. D. A. et al. Taxonomy of deep-sea shrimps of the superfamily Oplophoroidea Dana 1852 (Decapoda: Caridea) from Southwestern Atlantic. Zootaxa 4613, 401–442 (2019).
Google Scholar 
35.Eduardo, L. N. et al. Biodiversity, ecology, fisheries, and use and trade of Tetraodontiformes fishes reveal their socio-ecological significance along the tropical Brazilian continental shelf. Aquat. Conserv. Mar. Freshw. Ecosyst. 30, 761–774 (2020).
Google Scholar 
36.Tosetto, E. G., Bertrand, A., Neumann-Leitão, S., Costa da Silva, A. & Nogueira Júnior, M. Spatial patterns in planktonic cnidarian distribution in the western boundary current system of the tropical South Atlantic Ocean. J. Plankton Res. 43, 270–287 (2021).
Google Scholar 
37.Tosetto, E. G., Neumann-Leitão, S. & Nogueira Júnior, M. New species of Eirenidae (Hydrozoa: Leptothecata) from the Amazonian coast (northern Brazil). Sci. Mar. 84, 421–430 (2020).
Google Scholar 
38.Santana, C. S. et al. Amazon river plume influence on planktonic decapods in the tropical Atlantic. J. Mar. Syst. 212, 103428 (2020).
Google Scholar 
39.Tosetto, E. G., Neumann-Leitão, S., Bertrand, A. & Júnior, M. N. First record of Cirrholovenia polynema (Hydrozoa: Leptothecata) in the Western Atlantic Ocean. Ocean Coast. Res. 69, e21006 (2021).
Google Scholar 
40.Roberts, C. M. et al. Marine biodiversity hotspots and conservation priorities for tropical reefs. Science 295, 1280–1284 (2002).CAS 
PubMed 
ADS 

Google Scholar 
41.Bowen, B. W., Muss, A., Rocha, L. A. & Grant, W. S. Shallow mtDNA coalescence in Atlantic Pygmy angelfishes (genus Centropyge) indicates a recent invasion from the Indian Ocean. J. Hered. 97, 1–12 (2005).
Google Scholar 
42.Rocha, L. A., Robertson, D. R., Roman, J. & Bowen, B. W. Ecological speciation in tropical reef fishes. Proc. R. Soc. B Biol. Sci. 272, 573–579 (2005).
Google Scholar 
43.Rocha, L. A., Rocha, C. R., Robertson, D. R. & Bowen, B. W. Comparative phylogeography of Atlantic reef fishes indicates both origin and accumulation of diversity in the Caribbean. BMC Evol. Biol. 8, 157 (2008).PubMed 
PubMed Central 

Google Scholar 
44.Agard, J. B. R., Hubbard, R. H. & Griffith, J. K. The relation between productivity, disturbance and the biodiversity of Caribbean phytoplankton: Applicability of Huston’s dynamic equilibrium model. J. Exp. Mar. Biol. Ecol. 202, 1–17 (1996).
Google Scholar 
45.Toonen, R. J., Bowen, B. W., Iacchei, M. & Briggs, J. C. Biogeography, marine. in Encyclopedia of Evolutionary Biology (ed. Kliman, R. M.). 166–178. https://doi.org/10.1016/B978-0-12-800049-6.00120-7 (Academic Press, 2016).46.Briggs, J. C. & Bowen, B. W. Marine shelf habitat: Biogeography and evolution. J. Biogeogr. 40, 1023–1035 (2013).
Google Scholar 
47.Bradbury, I. R., Laurel, B., Snelgrove, P. V. R., Bentzen, P. & Campana, S. E. Global patterns in marine dispersal estimates: The influence of geography, taxonomic category and life history. Proc. R. Soc. B Biol. Sci. 275, 1803–1809 (2008).
Google Scholar 
48.Bartlow, A. W. & Agosta, S. J. Phoresy in animals: Review and synthesis of a common but understudied mode of dispersal. Biol. Rev. 96, 223–246 (2021).PubMed 

Google Scholar 
49.South Atlantic Zooplankton. (Backhuys Publishers, 1999).50.Mapstone, G. M. Global diversity and review of Siphonophorae (Cnidaria: Hydrozoa). PLoS ONE 9, 1–37 (2014).
Google Scholar 
51.Young, C. M., Sewell, M. A. & Rice, M. E. Atlas of Marine Invertebrate Larvae. Vol. 6. (Academic Press, 2002).52.Strathmann, R. Length of pelagic period in echinoderms with feeding larvae from the Northeast Pacific. J. Exp. Mar. Biol. Ecol. 34, 23–27 (1978).
Google Scholar 
53.Haddoock, S. H. D. A golden age of gelata Past and future research on planktonic ctenophores and cnidarians. Hydrobiologia 530–531, 549–556 (2004).
Google Scholar 
54Dossa, A. N. et al. Near-surface western boundary circulation off Northeast Brazil. Prog. Oceanogr. 190, 102475 (2021).
Google Scholar 
55.Luiz, O., Floeter, S., Rocha, L. & Ferreira, C. Perspectives for the lionfish invasion in the South Atlantic: Are Brazilian reefs protected by the currents?. Mar. Ecol. Prog. Ser. 485, 1–7 (2013).ADS 

Google Scholar 
56.Maldonado, M. The ecology of the sponge larva. Can. J. Zool. 84, 175–194 (2006).
Google Scholar 
57.Giangrande, A. Polychaete reproductive patterns, life cycles and life histories: An overview. in Oceanography and Marine Biology. Vol. 35. (eds. Ansell, A., Gibson, R. N. & Barnes, M.) (CRC Press, 1997).58.Nogueira Júnior, M. & Oliveira, V. M. Strategies of plankton occupation by polychaete assemblages in a subtropical estuary (south Brazil). J. Mar. Biol. Assoc. U. K. 97, 1651–1661 (2017).
Google Scholar 
59Assunção, R. V. et al. 3D characterisation of the thermohaline structure in the southwestern tropical Atlantic derived from functional data analysis of in situ profiles. Prog. Oceanogr. 187, 102399 (2020).
Google Scholar 
60.Molleri, G. S. F., Novo, E. M. L. M. & Kampel, M. Space-time variability of the Amazon River plume based on satellite ocean color. Cont. Shelf Res. 30, 342–352 (2010).ADS 

Google Scholar 
61.López, R., López, J. M., Morell, J., Corredor, J. E. & Del Castillo, C. E. Influence of the Orinoco River on the primary production of eastern Caribbean surface waters: Primary Production of Caribbean waters. J. Geophys. Res. Oceans 118, 4617–4632 (2013).ADS 

Google Scholar 
62.Hsieh, T. C., Ma, K. H. & Chao, A. iNEXT: iNterpolation and EXTrapolation for Species Diversity. (2014).63.Clarke, K. R. & Gorley, R. N. PRIMER 6 + PERMANOVA. (2006).64.Larsson, J. et al. Package ‘eulerr’. (2018).65.Baselga, A. & Orme, C. D. L. betapart: An R package for the study of beta diversity. Methods Ecol. Evol. 3, 808–812 (2012).
Google Scholar  More

1.Hawes, T. C., Worland, M. R., Convey, P. & Bale, J. S. Aerial dispersal of springtails on the Antarctic Peninsula: Implications for local distribution and demography. Antarct. Sci. 19, 3–10 (2007).ADS 

Google Scholar 
2.Benton, T. G. & Bowler, D. E. Linking dispersal to spatial dynamics in Dispersal Ecology and Evolution 251–265 (Oxford University Press, 2013). https://doi.org/10.1093/acprof:oso/9780199608898.003.0020.3.Rochat, E., Manel, S., Deschamps-Cottin, M., Widmer, I. & Joost, S. Persistence of butterfly populations in fragmented habitats along urban density gradients: Motility helps. Heredity (Edinb). 119, 328–338 (2017).CAS 
PubMed 
PubMed Central 

Google Scholar 
4.Machado, F. P., Roldán-Correa, A. & Schinazi, R. B. Colonization and collapse. ALEA, Lat. Am. J. Probab. Math. Stat. 14, 719–731 (2017)5.Junior, V. V., Machado, F. P. & Roldán-Correa, A. Dispersion as a survival strategy. J. Stat. Phys. 164, 937–951 (2016).MathSciNet 
MATH 
ADS 

Google Scholar 
6.Saastamoinen, M. et al. Genetics of dispersal. Biol. Rev. 93, 574–599 (2018).PubMed 

Google Scholar 
7.Nichols, R. A. & Hewitt, G. M. The genetic consequences of long distance dispersal during colonization. Heredity (Edinb). 72, 312–317 (1994).
Google Scholar 
8.Bonte, D. et al. Costs of dispersal. Biol. Rev. 87, 290–312 (2012).PubMed 

Google Scholar 
9.Clobert, J., Le Galliard, J.-F., Cote, J., Meylan, S. & Massot, M. Informed dispersal, heterogeneity in animal dispersal syndromes and the dynamics of spatially structured populations. Ecol. Lett. 12, 197–209 (2009).PubMed 

Google Scholar 
10.Skelsey, P., With, K. A. & Garrett, K. A. Why dispersal should be maximized at intermediate scales of heterogeneity. Theor. Ecol. 6, 203–211 (2013).PubMed 

Google Scholar 
11.Payo-Payo, A. et al. Colonisation in social species: The importance of breeding experience for dispersal in overcoming information barriers. Sci. Rep. 7, 1–7 (2017).ADS 

Google Scholar 
12.Newman, D. & Pilson, D. Increased probability of extinction due to decreased genetic effective population size: Experimental populations of Clarkia pulchella. Evolution (N. Y.) 51, 354–362 (1997).
Google Scholar 
13.Bijlsma, R., Bundgaard, J. & Boerema, A. C. Does inbreeding affect the extinction risk of small populations? Predictions from Drosophila. J. Evol. Biol. 13, 502–514 (2000).
Google Scholar 
14.Reed, D. H., Briscoe, D. A. & Frankham, R. Inbreeding and extinction: The effect of environmental stress and lineage. Conserv. Genet. 3, 301–307 (2002).CAS 

Google Scholar 
15.Reed, D. H., Lowe, E. H., Briscoe, D. A. & Frankham, R. Fitness and adaptation in a novel environment: Effect of inbreeding, prior environment, and lineage. Evolution (N. Y.) 57, 1822–1828 (2003).
Google Scholar 
16.Crawford, K. M. & Whitney, K. D. Population genetic diversity influences colonization success. Mol. Ecol. 19, 1253–1263 (2010).CAS 
PubMed 

Google Scholar 
17.Szücs, M. et al. Rapid adaptive evolution in novel environments acts as an architect of population range expansion. Proc. Natl. Acad. Sci. USA 114, 13501–13506 (2017).PubMed 
PubMed Central 

Google Scholar 
18.Charlesworth, D. & Willis, J. H. The genetics of inbreeding depression. Nat. Rev. Genet. 10, 783–796 (2009).CAS 
PubMed 

Google Scholar 
19.Tien, N. S. H., Sabelis, M. W. & Egas, M. Inbreeding depression and purging in a haplodiploid: Gender-related effects. Heredity (Edinb). 114, 327–332 (2015).CAS 
PubMed 

Google Scholar 
20.Smith, A. L. et al. Dispersal responses override density effects on genetic diversity during post-disturbance succession. Proc. R. Soc. B Biol. Sci. 283, 20152934 (2016).21.Clotuche, G. et al. The formation of collective silk balls in the spider mite Tetranychus urticae Koch. PLoS ONE 6, e18854 (2011).CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar 
22.Clotuche, G., Navajas, M., Mailleux, A.-C. & Hance, T. Reaching the ball or missing the flight? Collective dispersal in the two-spotted spider mite Tetranychus urticae. PLoS ONE 8, e77573 (2013).CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar 
23.Carew, M., Schiffer, M., Umina, P., Weeks, A. & Hoffmann, A. Molecular markers indicate that the wheat curl mite, Aceria tosichella Keifer, may represent a species complex in Australia. Bull. Entomol. Res. 99, 479–486 (2009).CAS 
PubMed 

Google Scholar 
24.Hein, G. L., French, R., Siriwetwiwat, B. & Amrine, J. W. Genetic characterization of North American populations of the wheat curl mite and dry bulb mite. J. Econ. Entomol. 105, 1801–1808 (2012).CAS 
PubMed 

Google Scholar 
25.Kuczyński, L. et al. A comprehensive and cost-effective approach for investigating passive dispersal in minute invertebrates with case studies of phytophagous eriophyid mites. Exp. Appl. Acarol. 82, 17–31 (2020).PubMed 
PubMed Central 

Google Scholar 
26.Helle, W. & Wysoki, M. 1.3.2 Arrhenotokous parthenogenesis. In World Crop Pests (eds Lindquist, E. E., Sabelis, M. W., Bruin, J.) vol. 6, 169–172 (Elsevier, 1996).27.Miller, A. D., Umina, P. A., Weeks, A. R. & Hoffmann, A. A. Population genetics of the wheat curl mite (Aceria tosichella Keifer) in Australia: Implications for the management of wheat pathogens. Bull. Entomol. Res. 102, 199–212 (2012).28.Sabelis, M. W. & Bruin, J. 1.5.3 Evolutionary ecology: Life history patterns, food plant choice and dispersal. World Crop Pests 6, 329–366 (1996).
Google Scholar 
29.Laska, A., Rector, B. G., Skoracka, A. & Kuczyński, L. Can your behaviour blow you away? Contextual and phenotypic precursors to passive aerial dispersal in phytophagous mites. Anim. Behav. 155, 141–151 (2019).
Google Scholar 
30.Lacy, R. C. Loss of genetic diversity from managed populations: Interacting effects of drift, mutation, immigration, selection, and population subdivision. Conserv. Biol. 1, 143–158 (1987).
Google Scholar 
31.Powell, J. R. The effects of founder-flush cycles on ethological isolation in laboratory populations of Drosophila in Genetics. In Speciation and the Founder Principle (eds Giddings, L. V. et al.) 239–251 (Oxford University Press, 1989).
Google Scholar 
32.Jamieson, I. G. Efecto fundador, endogamia y pérdida de diversidad genética en cuatro programas de reintroducción de Aves. Conserv. Biol. 25, 115–123 (2011).PubMed 

Google Scholar 
33.Montero-Pau, J., Gómez, A. & Serra, M. Founder effects drive the genetic structure of passively dispersed aquatic invertebrates. PeerJ 6, e6094 (2018).PubMed 
PubMed Central 

Google Scholar 
34.Perrin, N. & Mazalov, V. Dispersal and inbreeding avoidance. Am. Nat. 154, 282–292 (1999).PubMed 

Google Scholar 
35.Aguilera-Olivares, D., Flores-Prado, L., Véliz, D. & Niemeyer, H. M. Mechanisms of inbreeding avoidance in the one-piece drywood termite Neotermes chilensis. Insectes Soc. 62, 237–245 (2015).
Google Scholar 
36.Tabadkani, S. M., Nozari, J. & Lihoreau, M. Inbreeding and the evolution of sociality in arthropods. Naturwissenschaften 99, 779–788 (2012).CAS 
PubMed 
ADS 

Google Scholar 
37.Yearsley, J. M., Viard, F. & Broquet, T. The effect of collective dispersal on the genetic structure of a subdivided population. Evolution (N. Y.) 67, 1649–1659 (2013).
Google Scholar 
38.van der Kooi, C. J., Matthey-Doret, C. & Schwander, T. Evolution and comparative ecology of parthenogenesis in haplodiploid arthropods. Evol. Lett. 1, 304–316 (2017).PubMed 
PubMed Central 

Google Scholar 
39.Li, X.-Y. & Kokko, H. Sex-biased dispersal: A review of the theory. Biol. Rev. 94, 721–736 (2019).PubMed 

Google Scholar 
40.Nault, L. R. & Styer, W. E. The dispersal of Aceria tulipae and three other grass-infesting Eriophyid mites in Ohio. Ann. Entomol. Soc. Am. 62, 1446–1455 (1969).
Google Scholar 
41.Southwood, T. R. E., May, R. M., Hassell, M. P. & Conway, G. R. Ecological strategies and population parameters. Am. Nat. 108, 791–804 (1974).
Google Scholar 
42.Frost, W. E. Polyphenic wax production in Abacarus hystrix (Acari: Eriophyidae), and implications for migratory fitness. Physiol. Entomol. 22, 37–46 (1997).
Google Scholar 
43.Ronce, O. & Clobert, J. Dispersal syndromes in Dispersal Ecology and Evolution (eds Baguette, M., Benton, T. G., Bullock, J. M.) vol. 1, 119–138 (Oxford University Press, 2012).44.Laska A. et al. A sink host allows a specialist herbivore to persist in a seasonal source. Proc. Roy. Soc. B, accepted for publication (2021).45.Skoracka, A. et al. Cryptic species within the wheat curl mite Aceria tosichella (Keifer) (Acari: Eriophyoidea), revealed by mitochondrial, nuclear and morphometric data. Invertebr. Syst. 26, 417 (2012).
Google Scholar 
46.Miller, A. D., Umina, P. A., Weeks, A. R. & Hoffmann, A. A. Population genetics of the wheat curl mite (Aceria tosichella Keifer) in Australia: Implications for the management of wheat pathogens. Bull. Entomol. Res. 102, 199–212 (2012).CAS 
PubMed 

Google Scholar 
47.Karpicka-Ignatowska, K. et al. A novel experimental approach for studying life-history traits of phytophagous arthropods utilizing an artificial culture medium. Sci. Rep. 9, (2019).48.Karpicka-Ignatowska, K., Laska, A., Rector, B. G., Skoracka, A. & Kuczyński, L. Temperature-dependent development and survival of an invasive genotype of wheat curl mite, Aceria tosichella. Exp. Appl. Acarol. 83, 513–525 (2021).PubMed 
PubMed Central 

Google Scholar 
49.Amrine, J. W. & Manson, D. C. M. Preparation, mounting and descriptive study of eriophyoid mites. In Eriophyoid Mites—Their Biology, Natural Enemies and Control Vol. 6 (eds Lindquist, E. E. & Bruin, M. W.) 383–396 (Elsevier, 1996).
Google Scholar 
50.de Lillo, E., Craemer, C., Amrine, J. W. & Nuzzaci, G. Recommended procedures and techniques for morphological studies of Eriophyoidea (Acari: Prostigmata). Exp. Appl. Acarol. 51, 283–307 (2010).PubMed 

Google Scholar 
51.R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. (2020). https://www.R-project.org/. Accessed 24 Apr 2020.52.Rousset, F. GENEPOP’007: A complete re-implementation of the GENEPOP software for Windows and Linux. Mol. Ecol. Resour. 8, 103–106 (2008).PubMed 

Google Scholar 
53.Fox, J. & Weisberg, S. An R Companion to Applied Regression 3rd edn. (Sage, 2019).
Google Scholar 
54.Brooks, M. E. et al. glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. R J. 9, 378–400 (2017).
Google Scholar 
55.Wood, S. N. Generalized Additive Models (Chapman and Hall/CRC, 2017). https://doi.org/10.1201/9781315370279.Book 
MATH 

Google Scholar 
56.Lenth R. emmeans: Estimated Marginal Means, aka Least-Squares Means. R package version 1.4.8. https://CRAN.R-project.org/package=emmeans More

Effects of water and nitrogen treatments on the yield of Isatis indigotica
As shown in Table 3, in the two-year experiment, both the water input and the nitrogen application rate had significant effects on the yield of Isatis indigotica.Table 3 Variance analysis of traits on the yield of Isatis indigotica.Full size tableAs shown in Fig. 4, with increasing water and nitrogen, the yield first increased and then decreased. The interaction between the water input and the nitrogen application rate reached a significant level (P  N1. At the levels of W1, W2, and W3, the yield of the N2 treatment increased by 5.3–7.9%, 6.5–6.9%, and 5.0–9.0% compared with those of the N3 treatment, respectively, and the yield of the N3 treatment increased by 1.4–1.9%, 1.5%-4.5%, and 1.7–3.5% compared with those of the N1 treatment, respectively. At the same nitrogen application level, the yield performance was W2  > W1  > W3. At the levels of N1, N2, and N3, the yield of the W2 treatment increased by 6.9–12.4%, 8.3–11.3%, and 6.8–13.5% compared with those of the W3 treatment, respectively, and the yield of the W3 treatment decreased by 1.6–3.9%, 1.5–1.6%, and 1.3–2.4% compared with those of the W1 treatment, respectively.Effects of the water and nitrogen treatments on the quality of Isatis indigotica
As shown in Table 4, in the two-year experiment, the water input and nitrogen application rate had significant impacts on the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharide in Isatis indigotica.Table 4 Variance analysis of traits the quality of Isatis indigotica.Full size tableAs shown in Fig. 5, The impacts decreased with increasing irrigation amount and nitrogen application rate. Compared with those in the W3N3 treatment, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharide in the W2N2 treatment increased by 4.5–5.9%, 2.7–3.1%, 5.2–6.0% and 1.8–2.1%, respectively. At the same irrigation level, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharides all decreased in the order N1  > N2  > N3. At the W2 level, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharide in the N1 treatment increased by 0.5–1.7%, 0.8–0.9%, 0.8–1.1% and 0.1–0.4%, respectively, compared with those in the N2 treatment. Compared with those in the N3 treatment, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharide in the N2 treatment increased by 1.9–2.1%, 1.5–2.2%, 2.1–2.2% and 0.6–1.1%, respectively.Figure 5The effects of the different treatments on the quality index of Isatis indigotica. The values shown are the mean ± SD, n = 3. Asterisks indicate a significant difference at the P ≤ 0.05 level.Full size imageAt the same nitrogen level, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharides all decreased in the order W1  > W2  > W3. At the N2 level, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharides in the W1 treatment increased by 1.5–2.0%, 1.8–2.1%, 3.0–3.1% and 0.4–0.9% compared with those in the W2 treatment, respectively. Compared with those in the W3 treatment, the contents of indigo, indirubin, (R,S)-epigoitrin and polysaccharides of the W2 treatment increased by 2.3–3.5%, 1.8–2.3%, 2.0–4.0% and 1.0–1.4%, respectively.Effects of the water and nitrogen treatments on the WUE of Isatis indigotica
As shown in Table 5, in the two-year experiment, the water input and nitrogen application rate had significant impacts on the WUE of Isatis indigotica (P  N3  > N1. At the W1, W2, and W3 levels, the WUE of the N2 treatment increased by 6.5–8.6%, 7.8–8.1%, and 7.4–10.4% compared with that of the N3 treatment, respectively, and the WUE of the N3 treatment increased by 2.9–3.1%, 3.9–6.0%, and 4.5–5.3% compared with that of the N1 treatment, respectively. Under the same nitrogen application rate level, the WUE performance was W1  > W2  > W3. At the N1, N2, and N3 levels, the WUE of the W1 treatment increased by 5.0–11.7%, 2.8–9.2%, and 2.0–10.9% compared with that of the W2 treatment, respectively, and the WUE of the W2 treatment increased by 24.2–29.5%, 24.3 -27.2%, and 23.5–30.3% compared with that of the W3 treatment, respectively.Effects of water and nitrogen treatments on NUE of Isatis indigotica
As shown in Table 6, in the two-year experiment, the water input and nitrogen application rate had significant impacts on the nitrogen fertilizer use efficiency (NUE) of Isatis indigotica (P  N2  > N3. At the levels of W1, W2, and W3, the NUE of the N1 treatment increased by 9.9–11.8%, 9.6–13.0%, and 6.3–11.6% compared with that of the N2 treatment, respectively, and the NUE of the N2 treatment increased by 31.0–37.6%, 28.8–29.2%, and 28.3–28.6% compared with that of the N3 treatment, respectively. At the same nitrogen application level, the NUE performance was W2  > W3  > W1. At the N1, N2, and N3 levels, the NUE of the W2 treatment increased by 5.7–6.1%, 2.5–4.8%, and 2.3–4.1% compared with that of the W3 treatment, respectively, and the NUE of the W3 treatment decreased by 3.4–8.0%, 6.9–8.2%, and 10.5–14.5% compared with that of the W1 treatment, respectively.Ethical guidelineThe authors confirm that relevant ethical guidelines were followed for plant usage.Land permit statementThe experimental land belongs to the Yimin Irrigation Experimental Station, in Minle County, Gansu Province, China. More