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As part of the streamflow data release, NEON released four relevant data products: Gauge Height26, Elevation of Surface Water29, Stage-discharge Rating Curves30, and Continuous Discharge15. Data users are able to download this full suite of information and protocols to inform decisions on data usage and applicability. We evaluated the quality of the Continuous Discharge product using all four relevant NEON data products, considering the validity of model inputs as well as the goodness-of-fit of final streamflow estimates. We analyzed 1) the fit of the regression between manual stage height readings and continuous pressure transducer data used to estimate continuous stream surface elevation, 2) the fit of rating curves transforming stream surface elevation to streamflow, and 3) the proportion of streamflow estimates over the maximum manually-measured streamflow.Stage classificationThe rating curve models predicting streamflow required continuous stream stage estimates as model inputs. NEON predicted continuous gauge height with a two step approach. First, continuous in-stream transducer readings were converted to water height by applying an offset between the transducer elevation and the staff gauge (Eq. 1). This offset is derived from the NEON geolocation database as the difference between the location of the pressure transducer and the staff gauge27. The offset changes only when the location of either the staff gauge or transducer moves.$${h}_{wc}=frac{{P}_{sw}}{p,ast ,g},ast ,1000+{h}_{stage}$$
(1)
Conversion of pressure data to water height used by NEON27 where hwc is the estimated water column height (m), Psw is calibrated surface water pressure (kPa), p is the density of water (999 kg/m3), g is the acceleration due to gravity (9.81 m/s2), and hstage is the offset between the pressure transducer and the staff gauge (m).Then, NEON uses a linear regression between manually-measured reference stage height and the calculated gauge height from Eq. 1, yielding final predictions of continuous stream gauge height27. In an ideal setting, stage and gauge height should correlate perfectly28. In the field, sensor uncertainty, manual reference measurement error, and shifting conditions in the stream can convolute the relationship. We tested the goodness of fit between continuously estimated stream gauge height values and manual stage measurements using the Nash-Sutcliffe model efficiency coefficient (Eq. 2). Nash-Sutcliffe coefficient is a commonly used metric in hydrology used to evaluate how well a model performed relative to observed values (manually measured stage and calculated gauge height). For the purposes of this discussion, manual reference measurements will be referred to as ‘stage’ and automated, sensed readings as ‘gauge height’.$$NSE=1-frac{Sigma {left({Q}_{o}-{Q}_{m}right)}^{2}}{Sigma {left({Q}_{o}-{bar{Q}}_{o}right)}^{2}}$$
(2)
Equation 2 presents Nash-Sutcliffe model efficiency coefficient, where Qo is an observed value (streamflow or stage height), Qm is a modeled value, and ({bar{Q}}_{o}) is the mean of observed values.Stage, gauge height, and regression data were sourced from the NEON Continuous Discharge product, representing what was directly applied to streamflow estimation. Up to 26 stage measurements were available per year. We examined every regression between stage and gauge height (one per site year in which data was available) and classified each as either ‘good’, ‘fair’, or ‘poor’ quality based on their goodness of fit. Regressions with a NSE (Eq. 2) of 0.90 or greater were considered good, those with a NSE of less than 0.90 but greater than or equal to 0.75 were considered fair, and those with an NSE of less than 0.75 were considered poor (Fig. 2).Drift detectionBecause electronic instruments, such as pressure transducers, can have systematic directional drift, referred to as ‘drift’, during deployment, we developed an approach to detect periods of time when NEON’s Elevation of Surface Water product drifted. We used two methods to assess and flag the potential for instrument drift at monthly time steps. First, we flagged any period the manually measured stage fell outside NEON’s uncertainty bound for gauge height made at the same time. From this, we calculated the proportion of stage measurements outside of the gauge height uncertainty bounds per month. This proved to be a relatively lenient filter that missed periods of manually identified drift. We found adding a second filter that flagged any month where the difference between the manually measured stage and gauge height exceeded 6 cm, was effective in catching the majority of periods where drift was identified. Second, we calculated the average differences between stage and gauge height for each month (Fig. 3). To determine appropriate cut-off values to classify areas of potential drift, we manually audited and flagged periods of observable directional drift. Our goal was to set a maximum cut-off difference which retained as much usable data as possible while still capturing 70% of the manually flagged directional drift periods. Applying this method, we determined a cut-off value of 6 cm average monthly deviation between observed and predicted stage values.Using these two filters in combination, we again classified data into three groups: ‘likely no drift’, ‘potential drift’, and ‘not assessed’. Site-months with no more than 50% of stage measurements outside of the gauge height time series uncertainty and an average difference between stage and gauge height less than 6 cm were considered to have ‘likely no drift’. Site-months with either more than 50% of stage readings outside of the gauge height time series uncertainty or an average difference between stage and gauge height more than 6 cm were deemed to have ‘potential drift’. Site-months with no stage measurements could not be evaluated and were considered ‘not assessed’. Although this approach to identify drift is imperfect, in that slight drift could be missed and times without manual measurements are not possible to assess, we believe this is a helpful method given the data available from NEON and the fact drift has been observed when visually inspecting data (Fig. 3).Rating curve classificationTo evaluate how well rating curves predicted streamflow, we assessed each rating curve used to convert stage to discharge. NEON prepares a new rating curve for each site’s water year (beginning on October 1st)27. In cases where NEON reported multiple rating curves for a site’s water year each curve was assessed separately across the time series which it was used. We classified rating curves into three tiers based on two metrics: the Nash-Sutcliffe coefficient (Eq. 2) between observed and predicted streamflow, and the percentage of continuous discharge values above the maximum manually measured gauging used to construct the rating curve.First, we calculated the Nash-Sutcliffe coefficient for each rating curve to estimate how well rating curves captured the variation in the stage-streamflow relationship. We used the reported values for modeled and manually measured streamflow from the ‘Y1simulated’ and ‘Y1observed’ columns in the ‘sdrc_resultsResiduals’ table of the Stage-discharge rating curves product. NEON generally conducts between 12 and 24 manual gaugings per year to build and maintain the stage-discharge relationship.Second, we calculated the percentage of continuous streamflow values outside the range of manually measured estimates of streamflow. This was useful to assess if the stage-discharge relationship is representative of observed flow conditions. The relationship between discharge and stage is often nonlinear, with inflection points around changes in channel morphology making gauging the stream at high and low flow conditions critical to building a reliable rating curve16. A rating curve based on a large number of direct field measurements all taken during a narrow range of baseflows, for example, could generate a rating curve with a high Nash-Sutcliffe coefficient that is unreliable when extrapolated to high or low flow events. Using these two metrics, we were able to classify rating curves into categories of relative quality. To calculate the percentage of values in the continuous streamflow product that fall outside the range of manually gauged streamflow values, we extracted the maximum and minimum gauging values from the ‘sdrc_resultsResiduals’ table in the Stage-discharge Rating Curve product. We then compared the predicted values derived from each rating curve (as reported in the ‘csd_continuousDischarge’ table) to the extracted range and calculated the proportion of values which fell outside of it.We used the Nash-Sutcliffe coefficient and percentage of streamflow values over the maximum observed field measurements to classify rating curves into three categories outlined in Table 1.To integrate stage-gauge regressions, drift detections, and rating curve classification, we produced a summary table with classifications for all three tests and the corresponding metrics used in each classification (Fig. 5). The table is grouped by month and site so users can query sites and determine which months have the appropriate data for their needs. More

Myxococcota and Bdellovibrionota were active constituents of activated sludge microbiotaTo explore the predating activity and diversity of predatory bacteria in activated sludge, 13C-labeled Escherichia coli and Pseudomonas putida cells (determined as 97.09 and 97.30 atom% 13C, respectively) were added to the sludge microcosms for maximumly eight days of incubation, and 13C incorporation was examined using rRNA-SIP to identify prokaryotic and eukaryotic microorganisms involved in actively consuming the 13C-labeled prey cells. Bacterial 16S rRNA gene amplicon sequencing-based analysis indicated the relative contribution of 47.9% and 42.7% of the obtained sequences by the added biomass upon amendment in the 13C-E. coli (Fig. 1A) and 13C-P. putida (Fig. 1B) microcosms, which dropped below 1.0% after 16 h and eight days of incubation, respectively. The overall bacterial community structure at the steady state was highly comparable to that of the control microcosms (Fig. 1C), indicating that the prey cell amendments did not induce too strong fluctuation in the microbiota structure during the SIP experiment that prevented disentangling the indigenous community dynamics.Fig. 1: The dynamics of the prokaryotic communities and mineralization of the added 13C-biomass during the microcosm experiment.The overall prokaryotic communities were obtained by 16S rRNA gene amplicon sequencing of the total DNA from the activated sludge microcosms amended with 13C-E. coli (A) and 13C-P. putida (B) cells, and the control group (C) without amendment. The structure of the active prokaryotic communities was inferred based on amplicon sequencing of the light rRNA fractions from the microcosms amended with 13C-E. coli (D) and 13C-P. putida (E) cells. The temporal change in the proportion of produced 13CO2 in total CO2 indicated the mineralization of the 13C-labeled cells of E. coli and P. putida in duplicate microcosms (F). Relative sequence abundance of the ten most abundant prokaryotic phyla, together with the genera Escherichia-Shigella and Pseudomonas, was shown.Full size imageThe metabolically active bacterial communities, as inferred by 16S rRNA gene transcripts of the light rRNA fractions from the microcosms, were rather consistent throughout the experiment (Fig. 1D, E), but they showed clear compositional differences compared to the overall prokaryotic communities inferred by 16S rRNA gene amplicon sequences (Fig. 1A, B). Myxococcota and Bdellovibrionota species showed an average relative abundance of 17.5 (±0.7) % and 2.7 (±0.2) % in the 16S rRNA gene transcripts, respectively, which were significantly higher than 5.4 (±0.6) % and 1.3 (±0.1) % in the 16S rRNA genes of bacterial communities (p 1% in the 13C-heavy fractions, strong 13C-labeling was found for the as-yet-uncultivated myxobacterial mle1-27 clade (average EF 2.66 across time and treatments), which contributed to 10.3% to 38.9% of the 16S rRNA gene transcripts in the 13C-heavy fractions, indicating its high metabolic activity in consuming the 13C-labeled biomass of both E. coli and P. putida. Comparatively, Haliangium spp. and uncultured Polyangiaceae belonging to Myxococcota, as well as the as-yet-uncultivated OM27 clade belonging to Bdellovibrionota, also exhibited strong 13C-labeling (maximum EF across time: 2.4–39.5), but almost exclusively in the microcosms amended with 13C-E. coli cells (Fig. 2A). The as-yet-uncultivated myxobacterial VHS-B3-70 clade exhibited the strongest enrichment (average EF 16.67 across time and treatments) but made up only 0.2% to 2.3% of 16S rRNA gene transcripts of the 13C-heavy fraction (Fig. 2A). Overall, our microcosm experiment tracking added 13C-labeled prey bacterial cells with rRNA-SIP suggested prominent predatory activity of Myxococcota and Bdellovibrionota lineages including largely as-yet-uncultivated ones (e.g., the mle1-27, VHS-B3-70, and OM27 clades) in activated sludge.Fig. 2: The enrichment of incorporators of added 13C-biomass in heavy rRNA fractions and the temporal labeling patterns.13C-labeled prokaryotic (A) and micro-eukaryotic (B) genus-level taxa were identified by SIP in the microcosms added with E. coli and P. putida after one, two, and four days of incubation. Enrichment factor (EF) was calculated for microorganisms using heavy and light rRNA gradient fractions of the 13C- and 12C-microcosms to infer 13C-labeling. Taxa with an EF  > 0.1 in at least one of the treatment groups at one sampling time point was considered labeled. The area of circles indicates the relative sequence abundance of the labeled taxa in heavy 13C-rRNA. The negative EFs and positive EFs 1% in the heavy rRNA fractions of at least one of the 13C-E. coli and 13C-P. putida microcosms at a sampling point.Full size imageMyxococcota and Bdellovibrionota predated more selectively than protistsFor the micro-eukaryotes, several taxa belonging to Ciliophora, especially Cyrtophoria spp. and Telotrochidium spp., and also Peritrichia spp., Vaginicola spp., Aspidisca spp., and Epistylis spp., were highly enriched (maximum EF across time and treatments: 0.9–6.7) in the 13C-heavy rRNA fractions (Fig. 3B), in agreement with the dominance of Ciliophora in the micro-eukaryotic rRNA gene transcripts (Fig. 2B). The Candida-Lodderomyces clade and Cyberlindnera-Candida clade within Ascomycota, Magnoliophyta spp. within Phragmoplastophyta, and Poteriospumella spp. and unclassified Chromulinales within Ochrophyta were also strongly labeled (maximum EF: 13.5–242.5, Fig. 2B). Moreover, the 13C-biomass incorporation by micro-eukaryotes was independent of whichever prey bacteria (Fig. 2B, D), revealing no detectable prey preference in the metabolically active micro-eukaryotic predators. On the contrary, differential labeling by 13C-E. coli and 13C-P. putida cells was frequently observed for the predatory bacteria (Fig. 2A, C). The most obvious example was the OM27 clade ASVs belonging to Bdellovibrionota, which were found to incorporate 13C-labeled biomass exclusively of E. coli (Fig. 2C). Comparatively, Haliangium-affiliated ASV27 and ASV63 were labeled only by 13C-E. coli, ASV57 labeled by both 13C-E. coli and 13C-P. putida, while ASV72 and ASV76 were also labeled by 13C-P. putida, but only at a later sampling point (Fig. 2C). These results on the divergent labeling patterns with the tested prey bacteria together strongly implied population-specific predating behaviors of predatory bacteria in activated sludge.Fig. 3: In situ relative abundance of Myxococcota and Bdellovibrionota in aerobic and anaerobic sludge at a local WWTP (WWTP01) based on sampling over two years.The abundance of the abundant genera belonging to Myxococcota and Bdellovibrionota in aerobic and anaerobic sludge were compared according to amplicon sequencing-based analysis of bacterial 16S rRNA gene V3-V4 region. The top 10 abundant genus-level taxa across samples collected from eight samplings are shown, with the putative predators identified by SIP in the microcosm experiment highlighted. The asterisk denotes significant difference in relative abundance between aerobic and anaerobic sludges (p 0.1% in the activated sludge of WWTP01, including the putative predators identified in the microcosm experiment, i.e., Haliangium spp. (2.8 ± 0.7%) which represented the most abundant myxobacterial lineage in the activated sludge, uncultured Polyangiaceae (0.4 ± 0.1%), and the mle1-27 clade (0.2 ± 0.0%; Fig. 3). Moreover, Pajaroellobacter (1.2 ± 0.2%), Nannocystis (0.4 ± 0.1%), Phaselicystis (0.3 ± 0.1%), and several other myxobacterial clades, although not identified as putative predators in the microcosm experiment, were among the abundant myxobacteria in situ in the activated sludge. Although the myxobacterial genera showed comparable relative abundance in the anaerobic tanks, fed by returned activated sludge, to their counterparts in the aerobic tanks, the obligately aerobic myxobacteria were presumably metabolically inactive in the anerobic sludge. Unlike Myxococcota, members of Bdellovibrionota altogether showed significantly higher relative abundance in the aerobic sludge (1.0 ± 0.2%) than in the anaerobic sludge (0.6 ± 0.1%, paired samples Wilcoxon test p  More

Orchard site selectionThe survey was conducted from 2018 to 2019 in the Circum-Bohai Bay region, which included Shandong, Hebei, and Liaoning provinces and Beijing, and the Loess Plateau region, which included Shanxi and Shaanxi provinces. Five typical production counties were selected in each province or city. Representative orchards were selected according to the production of the main varieties in each county (orchard area was greater than 1.0 ha; the pear trees were 15 to 25 years old; and the yield of orchards ranged from 40 to 60 t ha−1). A total of 225 orchards were investigated (Fig. 1), including 150 in the Circum-Bohai Bay region and 75 in the Loess Plateau region (Table 1).Fig. 1The locations of the 225 pear orchards.Full size imageTable 1 Numbers of pear orchard and main cultivated varieties investigated in Circum-Bohai Bay and Loess Plateau.Full size tableSample collection and pretreatmentSoil and leaf samples were collected at the stage in which the growth of new shoots ceased, from July 1 to July 1510. Eleven sampling sites were determined in each orchard according to an “S” shape sampling method (Fig. 2), and soil samples from the 0–20 cm, 20–40 cm and 40–60 cm layers were collected. The soil samples of the same soil layer at each sampling site were mixed into one sample. Then, the soil samples were air-dried, ground and sifted with a nylon sieve for determination of nutrient concentrations.Fig. 2The “S” shape sampling method. The red dots are the sampling locations.Full size imageTen to fifteen pear trees in each orchard of the same size and vigour and 5 to 10 mature leaves from the middle of a long shoot from the periphery of each tree were selected for leaf sampling11. Then, all the leaves from the same orchard were mixed into one leaf sample. The leaves were washed with tap water containing a detergent, with deionized water, with 0.01 M hydrochloric acid and then with deionized water again and then dried at 100 °C for 30 min and at 70 °C to a constant weight. Then, the leaf samples were crushed into a powder and sifted with a nylon sieve for nutrient determination.Fruit samples were collected at the ripening stage. Pear trees from which leaf samples were collected from each orchard were selected for fruit sample collection. Three to five peripheral fruits of the same size were collected from each tree, and fruit samples from the same orchard were mixed into one sample. The fruits were washed with tap water containing a detergent, with deionized water, with 0.01 M hydrochloric acid and then with deionized water again, cut into slices and then dried at 100 °C for 30 min and at 70 °C to a constant weight. Then, the fruit samples were crushed into a powder and sifted with a nylon sieve for nutrient determination.Sample determinationVarious indicators of soil and plant samples were determined according to the method of Cui et al.12 and Bao13.Soil pH determinationA potentiometric method was used to measure soil pH. Carbon dioxide-free water was added to soil that had been passed through a 2 mm sieve at a water-soil ratio of 2.5:1. The soil solution was stirred for 1 min and left undisturbed for 30 min. Each soil sample was measured more than three times with a pH meter (FE20K PLUS PH, Mettler-Toledo, Switzerland), and the difference in the parallel determination results was less than 0.2 pH units. The electrode was washed with deionized water and dried with filter paper after each sample measurement. A calibration solution was used to calibrate the electrode between measurements after every 10 soil samples.Soil organic matter determinationSoil organic matter was measured according to the Schollenberger method using chromic acid redox titration. Five millilitres of a 0.8 M 1/6 K2Cr2O7 solution was added to a test tube with approximately 0.5000 g of soil that had been passed through a 0.25 mm sieve. The mixture was then added to 5 mL concentrated sulfuric acid and shaken gently to disperse the soil. The tube was placed in a phosphoric acid bath, heated to 170 °C and boiled for 5 min. To condense the water vapour that escaped during the heating process, a small funnel was placed on the top of the test tube. The substances in the test tube and funnel were transferred to a conical flask after cooling. Then, the solution was added to 1,10-phenanthroline hydrate and titrated with 0.2 M FeSO4 until it turned maroon. A blank experiment was performed when each batch of samples was measured. The soil organic matter content was calculated according to the following formula:$${rm{omega }}left({rm{OM}}right)=frac{left({rm{V}}-{rm{V}}0right)times {rm{c}}times 3times 1.724times {rm{f}}}{{rm{m}}}$$
(1)
ω(OM): soil organic matter content; c: standard FeSO4 solution concentration; V: volume of the standard FeSO4 used in titration; V0: volume of standard FeSO4 used in titrating control sample; 3: molar mass of a quarter of carbon; 1.724: the conversion factor from organic carbon to organic matter; f: oxidation correction coefficient (the value was 1.1); m: mass of oven-dried soil sample.Soil total N determinationTotal N was determined by the semitrace Kjeldahl method. Approximately 1.0000 g of air-dried soil that had been passed through a 0.25 mm sieve was added to a digestion tube. Meanwhile, the soil moisture content was measured to calculate the mass of the oven-dried soil. Two grams of accelerator and 5 mL of concentrated sulfuric acid were added to the tube. The tube was then covered with a small funnel, and the sample was digested at 360 °C for 15–20 min. The mixture was digested for 1 h until the colour changed from brown to greyish green or greyish white. Two digested soilless samples were used as controls. After the digestion tube cooled, it was placed in a distiller, and a small amount of deionized water was added. Five millilitres of a 2% boric acid indicator was added to a 150 mL conical flask, and the flask was placed at the end of the condenser tube. Then, the digestion solution was distilled until the distillate volume was approximately 75 mL. The distillate was titrated with 0.01 M standard hydrochloric acid to a purplish red colour endpoint. The soil total N concentration was calculated according to the following formula:$${rm{omega }}({rm{N}})=frac{({rm{V}}-{rm{V}}0)times {rm{c}}times 14}{{rm{m}}}$$
(2)
ω(N): soil total N concentration; c: standard acid concentration; V: volume of the standard acid used in titration; V0: volume of standard acid used in titrating control sample; 14: molar mass of N; m: mass of oven-dried soil sample.Soil alkaline hydrolysable N determinationApproximately 2.00 g of air-dried soil that have been passed through a 2 mm sieve was placed in the outer chamber of a diffuser. The diffuser was gently rotated to evenly distribute the soil in the outer chamber. Two millilitres of H3BO3 indicator was placed in the inner chamber of the diffusion dish. The edge of the frosted glass surface of the diffuser was coated with alkaline glycerin and covered with frosted glass. The diffuser was covered tightly and secured with rubber bands after 10.00 mL of 1 M NaOH was injected into the diffuser through a hole in the frosted glass. The diffuser was placed in a 40 °C incubator for alkaline hydrolysis diffusion for 24 h. Then, the mixture was titrated with 0.01 M standard hydrochloric acid until it turned purplish red. A blank test was performed at the same time as the samples. The soil alkaline hydrolysable N concentration was calculated according to the following formula:$${rm{omega }}({rm{N}})=frac{({rm{V}}-{rm{V}}0)times {rm{c}}times 14}{{rm{m}}}$$
(3)
ω(N): soil alkaline hydrolysable N concentration; c: standard acid solution concentration; V: volume of the standard acid used in titration; V0: volume of standard acid used in titrating control sample; 14: molar mass of N; m: mass of air-dried soil sample.Soil available P determinationApproximately 2.50 g of air-dried soil that had been passed through a 2 mm sieve was placed in a plastic bottle and 50 mL of 0.5 M NaHCO3 was added. After the bottle was shaken for 30 min, the mixture was immediately filtered with phosphorus-free filter paper. Ten millilitres of the filtrate was accurately measured into a conical flask, and 5.00 mL of Mo-Sb-Vc colour developer and 10 mL of deionized water were added. The absorbance of the mixture was measured at approximately 700 nm after 30 min using a UV-Vis spectrophotometer (UV1900PC, AuCy Instrument, Shanghai, China). Finally, the P concentration was calculated according to a standard curve prepared with solutions of different P concentrations. A blank test was performed at the same time that the samples were determined.Soil available K determinationApproximately 5.00 g of air-dried soil that had been passed through a 2 mm sieve was placed in a plastic bottle, and 50 mL of 1.0 M NH4OAc was added. After the sample was shaken for 30 min, the mixture was immediately filtered with dry filter paper. The concentration of K in the filtrate was determined directly by a flame photometer (LM12-FP6430, Haifuda, China) according to a standard curve prepared with solutions of different K concentrations. A blank test was performed at the same time that the samples were determined.Leaf and fruit N determinationApproximately 0.3000 g of plant powder that had been passed through a 0.5 mm sieve was placed into a digestion tube and 5 mL concentrated sulfuric acid was added. Then, the digestion tube was placed onto a digestion stove at 360 °C after two doses of 2 mL H2O2, and the sample was digested until the mixture turned brown. After the tube cooled, 2 mL H2O2 was added, and the digestion was continued for 5 min. This process was repeated until the mixture turned clear. The mixture was diluted to 100 mL in a volumetric flask for testing after it cooled. Then, 5 to 10 mL of the liquid to be tested was accurately measured into a distiller for distillation. The distillation and titration processes were the same as those used for ammonium in the Soil total N determination section. A blank test was performed at the same time as sample measurement. The leaf or fruit N concentration was calculated according to the following formula:$${rm{omega }}({rm{N}})=frac{({rm{V}}-{rm{V}}0)times {rm{c}}times 14times {rm{V}}1}{{rm{m}}times {rm{V}}2}$$
(4)
ω(N): total N concentration; c: standard acid concentration; V: volume of the standard acid used in titration; V0: volume of standard acid used in titrating control sample; 14: molar mass of N; m: mass of oven-dried sample; V1: volume of the digestion solution after constant volume; V2: measured volume of digestion solution after constant volume.Leaf and fruit P, K, Ca, Fe, Mn, Cu, Zn, B determinationApproximately 0.5000 g of plant powder that had been passed through a 0.5 mm sieve was placed in a digestion tube and a 10 mL mixture of concentrated nitric acid and hypochlorous acid (4:1) was added. After the sample was left undisturbed for more than 4 h, it was placed onto a digestion stove and heated to 150 °C so that NO2 could volatilize slowly. Then, the temperature was appropriately increased to a temperature not higher than 250 °C until the digestive solution was transparent and approximately 2 mL remained. The solution was transferred into a volumetric flask after cooling and adjusted to a constant volume of 50 mL. The solution was then filtered, and the concentration of each element in the solution was determined by a plasma emission spectrometer (ICP-OES, OPTIMA 3300 DV, 75 Perkin-Elmer, USA). A blank test was performed at the same time as sample measurement. The leaf or fruit P, K, Ca, Fe, Mn, Cu, Zn, and B concentrations were calculated according to the following formula:$${rm{omega }}({rm{P}},{rm{K}},{rm{Ca}},{rm{Fe}},{rm{Mn}},{rm{Cu}},{rm{Zn}},{rm{B}})=frac{rho ({rm{P}},{rm{K}},{rm{Ca}},{rm{Fe}},{rm{Mn}},{rm{Cu}},{rm{Zn}},{rm{B}})times {rm{V}}times {rm{f}}}{{rm{m}}}$$
(5)
ω(P, K, Ca, Fe, Mn, Cu, Zn, B): P, K, Ca, Fe, Mn, Cu, Zn, B concentration in leaf or fruit; ρ(P, K, Ca, Fe, Mn, Cu, Zn, B): the concentration of P, K, Ca, Fe, Mn, Cu, Zn or B in the liquid to be measured; V: volume of the liquid to be measured after constant volume; f: dilution ratio of the liquid to be measured; m: mass of oven-dried sample. More

Flash recordingAll field recording and experiments were performed at the paddy field in the Northern Chita Peninsula, Aichi Prefecture, central Japan, in June and July between 2003 and 2016. The ambient temperature at the firefly’s active period was measured using a thermometer. The flashes were recorded with a digital video camera (NV-GS-400, Panasonic, Japan) mounted on a tripod at a height of 30–50 cm from ground and a distance of 1.0–1.5 m away from the specimen. Isolated specimens were selected for recording to exclude the background light from other nontarget specimens. When another specimen appeared near the target specimen, the video recording was cancelled. When a female copulated during video recording in the field, her flashes until 1 min before copulation were regarded as those of a ‘receptive female’. To record the flashes of a ‘mated female’, the female specimens already mated were prepared in aquariums (because virgin and mated females cannot be distinguished in the field): the eggs were obtained from wild female specimens collected one year before at the same field and reared to adults; immediately after emergence the virgin female was confined in a small container with two cultured males for two nights to facilitate copulation. As the parents of the reared specimens were collected from the observation field (same genetic background), the rearing temperature was almost the same as that of the natural field, the emergence period of the cultured specimens overlapped with that of the natural population, the adult body sizes of the reared and natural specimens were indistinguishable, and the flash pattern of the cultured mated females was indistinguishable from that of the wild (potentially) mated females. Thus, we believe that there was no influence of different rearing environments, i.e., the flash behavior of the cultured mated female specimens is expected to be substantially the same as that of wild mated female specimens. To distinguish them from wild (potentially) mated females, the elytra of cultured mated females were marked with colored ink before placing them in the field, and after three days, the flashes of ink-marked specimens were recorded. Of note, we never observed male attraction and copulation in any of the mated females used for field observation; thus, the mated females were unreceptive.Waveform analysisSequential still images were captured from video files at 30 frames per second using VirtualDub (GPL), and then the light intensities in the images were qualified (8-bit linear gray scaling from black to white at 0–255) using ImageJ software. In this study, we defined ‘flash’ as a luminescent waveform from baseline to baseline and ‘flickering’ as fluctuation above baseline in a single flash. The waveforms containing a saturated signal (255, white) were omitted. The waveforms of the maximum signal value lower than 50 were also omitted because of the difficulty in separating signal and noise. Approximately 10–90 waveforms per individual were analyzed; thus, the effect of the occasional interruption of the flash recording by the specimen’s movement and/or vegetation swinging between the specimen and the video camera is statistically ignorable. FD is defined as the time interval between the beginning and the end of a flash (Fig. S1). Flicker intensity (FI) was defined as$${text{FI}} = left{ {begin{array}{*{20}l} {mathop {max }limits_{1 le i le n} left( {frac{{{text{min}}left( {p_{i} ,p_{i + 1} } right) – t_{i} }}{{min left( {p_{i} , p_{i + 1} } right) + t_{i} }}} right)} hfill & {{text{if}} , n ge 1} hfill \ 0 hfill & {{text{if}} , n = 0} hfill \ end{array} } right.$$where p, t, and n denote the peak and the trough (local extrema) in the waveform of a flash and the number of toughs in the flash, respectively (Fig. S1). In total, we measured the FD and FI values of 347, 94, and 355 waveforms from 13 sedentary males, 7 receptive females, and 8 mated females, respectively. We did not consider the flash brightness as a factor because the measured value of the light intensity depends largely on the distance between the light source and the detector; thus, the actual brightness of the lantern cannot be practically measured in the field.e-FireflyFor male attraction experiments, we built an electronic LED device, the e-firefly, to generate patterned flashes with various FDs and FIs using a chip LED (green type, λmax = 568 nm, Everlight Electronics, Taiwan; Figs. S2 and S3) with a microcontroller PIC16F628A (Microchip Technology, USA) (see Figs. S4-S5). An example of the program for the microcontroller is shown in Supplementary Data S1. The brightness was constant in all programs. Flickering frequency ranged between 5–12 Hz, which corresponds to that of sedentary male flashes (approximately 10 Hz)15. To prevent direct access of the attracted specimen to the light source, the chip LED was covered by a steel net painted green (see Fig. S2). For flying male attraction experiments, when the male landed within a 100-mm distance from the e-firefly, we judged the attraction to be a success; otherwise, it was a failure. For sedentary male attraction experiments, the e-firefly was placed 200–300 mm away from the sedentary male. When the approaching male touched the steel net covering the e-firefly, to warrant a positive approach, we measured the time the male remained on the net. If the male did not move away from the net for more than 2 min, we judged the attraction to be a success (strict criterion for judgment); otherwise, it was a failure.Spectral measurementThe luminescence spectra of e-firefly and A. lateralis were measured using a Flame-S spectrophotometer (Ocean Insight, USA). The living A. lateralis specimens were anesthetized on ice and frozen at − 20 °C until use. The lantern started luminescence by thawing at room temperature, and the spectrum was measured during luminescence (within 5 min).Statistical analysisFirst, we considered a discriminant analysis using a logistic regression model that discriminates between receptive females and others in the observational data. We fitted several models with combinations of FD and FI, quadratic terms of FD and FI (FD2, FI2), interaction of FD and FI (FD (times) FI), and temperature (T) as explanatory variables. Based on Akaike’s information criteria (AIC) values and model simplicity, we chose the logistic regression model with FD, FI, FD2 and T as explanatory variables. Let (p)(({varvec{x}})) denote the conditional probability that a flash is from a receptive female given ({varvec{x}}=left(mathrm{FD},mathrm{ FI},mathrm{ T}right)) and (widehat{p})(({varvec{x}})) denote its estimate. The coefficients of the logistic regression model are estimated as follows.
[Model for the observational data with temperature (T)]
$$begin{gathered} {text{log}}frac{{hat{p}}}{{1 – hat{p}}} = begin{array}{*{20}l} { – 32.26 + 69.69 times FD – 43.47 times FI – 76.63 times FD^{2} + 0.87 times T} hfill \ {~quad left( {6.50} right)quad quad left( {15.37} right)quad quad quad left( {8.56} right)quad quad quad quad left( {17.44} right)quad quad quad left( {0.19} right)~~} hfill \ end{array} hfill \ quad {text{AIC: 84}}{text{.75}} hfill \ end{gathered}$$[Model for the observational data without temperature (T)]$$begin{gathered} {text{log}}frac{{hat{p}}}{{1 – hat{p}}} = begin{array}{*{20}l} { – 7.69~ + 47.57 times FD~ – 38.29 times FI~ – 52.86 times FD^{2} ~} hfill \ {~;left( {1.86} right)quad quad left( {9.68} right)quad quad quad left( {7.08} right)quad quad quad quad left( {11.38} right)~~} hfill \ end{array} hfill \ quad {text{AIC: 114}}{text{.89}} hfill \ end{gathered}$$where values in parentheses indicate standard deviations. The same applies hereafter. Temperature (T) is included in the model not because it affects the occurrence of receptive females but because it affects the FD and/or FI of receptive females. The AIC value increased by 30, which is substantial, when temperature was excluded from the model.Figure 2 shows the FD and FI of each flash from receptive females, mated females and males with the discriminant boundaries of receptive females from others for (p=0.5).We next considered a discriminant analysis for the experimental data. Let ({q}^{f}({varvec{x}})) denote the conditional probability that a flying male is attracted to a flash of ({varvec{x}}=left(mathrm{FD},mathrm{ FI},mathrm{ T}right)) and lands, and ({widehat{q}}^{f}({varvec{x}})) denote its estimate. Among several models we fit, the smallest AIC value is attained by the logistic regression model with FD, FI and T as explanatory variables, but the AIC is not much different from the model with FD and FI only.
[Model for flying males with temperature (T)]
$$begin{gathered} {text{log}}frac{{hat{q}^{f} }}{{1 – hat{q}^{f} }} = begin{array}{*{20}l} { – 0.74~~ – 2.42 times FD – 16.82 times FI + 0.31 times T} hfill \ {~;left( {4.01} right)quad quad left( {0.83} right)quad quad quad left( {4.88} right)quad quad quad quad left( {0.20} right)~} hfill \ end{array} hfill \ quad {text{AIC}}:66.96 hfill \ end{gathered}$$

[Model for flying males without temperature (T)]
$$begin{gathered} {text{log}}frac{{hat{q}^{f} }}{{1 – hat{q}^{f} }} = begin{array}{*{20}l} { – 5.36~ – 1.72 times FD – 13.69 times FI} hfill \ {~;left( {1.49} right)quad quad left( {0.63} right)~quad quad left( {4.09} right)~~} hfill \ end{array} hfill \ quad {text{AIC}}:67.61 hfill \ end{gathered}$$
For sedentary males, the model with the smallest AIC value includes all the quadratic terms of FI and FD but not temperature. Let ({q}^{s}({varvec{x}})) denote the conditional probability that a sedentary male is attracted to a flash of ({varvec{x}}=left(mathrm{FD},mathrm{ FI},mathrm{ T}right)) and ({widehat{q}}^{s}left({varvec{x}}right)) denote its estimate. The logistic regression model for ({q}^{s}({varvec{x}})) with the best AIC value is given as follows.
[Model for sedentary males]
$${text{log}}frac{{hat{q}~^{s} }}{{1 – hat{q}~^{s} }} = begin{array}{*{20}l} { – 0.68~ + 7.84 times FD~ + 48.17 times FI – 5.35 times FD^{2} – 166.70 times FI^{2} – 65.67 times FD times FI} hfill \ {;left( {0.97} right)quad quad quad left( {2.99} right)quad quad quad left( {17.74} right)quad quad quad left( {1.74} right)quad quad quad quad left( {72.34} right)quad quad quad quad left( {17.67} right)~} hfill \ end{array}$$
Figure 3 shows successes and failures of attraction of flying males on the left and sedentary males on the right with estimated discriminant boundaries.Let us now estimate probabilities that a flying male is attracted and lands or a sedentary male is attracted to a flash when a flash is from a receptive female or when a flash is either from a sedentary male or mated female. The probability that a flying male is attracted and lands when a flash is from a receptive female is a conditional probability and is expressed as follows.$$begin{aligned} Pleft(left.begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} right|begin{array}{*{20}c} {text{Receptive }} \ {{text{female}}} \ end{array} right) & = frac{{Pleft( {begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} {text{ and }}begin{array}{*{20}c} {text{Receptive }} \ {{text{female}}} \ end{array} } right) }}{{Pleft( {begin{array}{*{20}c} {{text{Receptive}}} \ {{text{female}}} \ end{array} } right)}}, \ Pleft( {begin{array}{*{20}c} {{text{Receptive}}} \ {{text{female}}} \ end{array} } right) & = mathop int_{Omega } Pleft(left. begin{array}{*{20}c} {{text{Receptive}}} \ {{text{female}}} \ end{array} right|{varvec{x}} right)fleft( {varvec{x}} right)d{varvec{x}} = mathop int_{Omega }pleft( {varvec{x}} right) fleft( {varvec{x}} right)d{varvec{x}} hspace{5mm}{text{and}} \ Pleft( {begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} {text{ and }}begin{array}{*{20}c} {text{Receptive }} \ {{text{female}}} \ end{array} } right) & = mathop int_{Omega } Pleft(left. begin{array}{*{20}c} {{text{Receptive}}} \ {{text{female}}} \ end{array} right|varvec{x} right)Pleft(left. begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} right|{varvec{x}} right)fleft( {varvec{x}} right)d{varvec{x}} \ & = mathop int_{Omega } pleft( varvec{x} right)q^{f} left( {varvec{x}} right)fleft( {varvec{x}} right)d{varvec{x}}mathbf{.} \ end{aligned}$$Integrals are taken over the domain (Omega) of ({varvec{x}}=(FD, FI, T)) of all females and males, and (f({varvec{x}})) is the joint density function of ({varvec{x}}.) Because (f({varvec{x}})) is unknown, we use the empirical distribution of the observational data, and conditional probabilities given ({varvec{x}}) are replaced with their estimates by logistic regression models. Let ({{varvec{x}}}_{i}=left(F{D}_{i}, F{I}_{i}, {T}_{i}right), i=mathrm{1,2},dots N) denote the (i) th observation in the observational data. The estimates of probabilities are given as follows:$$begin{aligned} hat{P}left( {begin{array}{*{20}c} {{text{Receptive}}} \ {{text{female}}} \ end{array} }right) & = frac{1}{N}mathop sum limits_{i = 1}^{n} hat{p}left( {{varvec{x}}_{i} } right) hspace{15mm} {text{and}} \ hat{P}left( {begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} {text{ and }}begin{array}{*{20}c} {text{Receptive }} \ {{text{female}}} \ end{array} } right) & = frac{1}{N}mathop sum limits_{i = 1}^{n} hat{p}left( {{varvec{x}}_{i} } right) hat{q}^{f} left( {{varvec{x}}_{i} } right). \ end{aligned}$$Thus,$$hat{P}left( left. begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array} right| begin{array}{*{20}c} {text{Receptive }} \ {text{female}} \ end{array} right) = frac{{mathop sum nolimits_{i = 1}^{n} hat{p}left( {{varvec{x}}_{i} } right) hat{q}^{f} left( {{varvec{x}}_{i} } right)}}{{mathop sum nolimits_{i = 1}^{n}hat{p}left(varvec{x}_i right)}}.$$Similarly, we have$$begin{aligned} hat{P}left( left.begin{array}{*{20}c} {text{Flying male}} \ {text{is attracted}} \ end{array}right| {text{Others}} right) & = frac{{mathop sum nolimits_{i = 1}^{n} (1 – hat{p}left( {{varvec{x}}_{i} } right)) hat{q}^{f} left( {{varvec{x}}_{i} } right)}}{{mathop sum nolimits_{i = 1}^{n} (1 – hat{p}left( {{varvec{x}}_{i} } right))}} \ hat{P}left( left. begin{array}{*{20}c} {text{Sedentary male}} \ {text{is attracted}} \ end{array} right| begin{array}{*{20}c} {text{Receptive }} \ {text{female}} \ end{array} right)& = frac{{mathop sum nolimits_{i = 1}^{n} hat{p}left( {{varvec{x}}_{i} } right) hat{q}^{s} left( {{varvec{x}}_{i} } right)}}{{mathop sum nolimits_{i = 1}^{n} hat{p}left( varvec{x}_{i} right)}}hspace{15mm} {text{ and}} \hat{P}left(left. begin{array}{*{20}c} {text{Sedentary male}} \ {text{is attracted}} \ end{array}right| {text{Others}} right) & = frac{{mathop sum nolimits_{i = 1}^{n} left( {1 – hat{p}left( varvec{x}_{i} right)} right) hat{q}^{s} left( {varvec{x}_{i} } right)}}{mathop sum nolimits_{i = 1}^{n} left( {1 – hat{p}left( varvec{x}_{i} right)} right)} . \ end{aligned}$$The estimated probabilities are shown in Table 1.Table 1 Estimated probabilities of a flying male and a sedentary male being attracted to flashes from a receptive female and from others.Full size table More

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