Philippa Kaur

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Acoustic measurementsA set of acoustic echo sounder data was used to analyze fish density. This was collected within the Mycto-3D-MAP program using split-beam echo sounders at 38 and 120 kHz. The Mycto-3D-MAP program included multiple large-scale oceanographic surveys during 2 years and a dedicated cruise in the Kerguelen area. The dataset was collected during 4 large-scale surveys in 2013 and 2014, both in summer (including both northward and southward transects) and in winter, corresponding to 6 acoustic transects of 2860 linear kilometers (see Table 1 for more details). Note that all legs except summer 2014 (MYCTO-3D-Map cruise) were logistic operations, during which environmental in situ data (such as temperature or salinity profiles) could not be collected. The data were then treated with a bi-frequency algorithm, applied to the 38 and 120 kHz frequencies (details of data collection and processing are provided in37). This provides a quantitative estimation of the concentration of gas-bearing organisms, mostly attributed to fish containing a gas-filled swimbladder in the water column38. Most mesopelagic fish present swimbladders and several works pointed out that myctophids are the dominant mesopelagic fish in the region39. Therefore, we considered the acoustic signal as mainly representative of myctophids concentration. Data were organized in acoustic units, averaging acoustic data over 1.1 km along the ship trajectory on average. Myctophid school length is in the order of tens of meters40. For this reason, acoustic units were considered as not autocorrelated. Every acoustic unit is composed of 30 layers, ranging from 10 to 300 meters (30 layers in total).The dataset was used to infer the Acoustic Fish Concentration (AFC) in the water column. We considered as AFC of the point ((x_i), (y_i)) of the ship trajectory the average of the bifrequency acoustic backscattering of 29 out of 30 layers (the first layer, 0-10 m, was excluded due to surface noise) AFC quantity is dimensionless.As the previous measurements were performed through acoustic measurements, a non-invasive technique, fishes were not handled for this study.Table 1 Details of the acoustic transects analyzed.Full size tableRegional data selectionThe geographic area of interest of the present study is the Southern Ocean. To select the ship transects belonging to this region, we used the ecopartition of41. Only points falling in the Antarctic Southern Ocean region were considered. We highlight that this choice is consistent with the ecopartition of42 (group 5), which is specifically designed for myctophids, the reference fish family (Myctophidae) of this study. Furthermore, this choice allowed us to exclude large scale fronts (i.e., fronts that are visible on monthly or yearly averaged maps) which have been the subject of past research works43,44. In this way our analysis is focused specifically on fine-scale fronts.Day-night data separationSeveral species of myctophids present a diel vertical migration. They live at great depths during the day (between 500 and 1000 m), ascending at dusk in the upper euphotic layer, where they spend the night. Since the maximal depth reached by the echo sounder we used is 300 m, in the analysis reported in Figs. 2 and 3 we excluded data collected during the day. However, their analysis is reported in SI.1. A restriction of our acoustic analyses to the ocean upper layer is also consistent with the fact that the fine-scale features we computed are derived in this work by satellite altimetry, thus representative of the upper part of the water column ((sim 50) m). Finally, we note that the choice of considering the echo sounder data in the first 300 m of the water columns is coherent with the fact that LCS may extend almost vertically in depth even at 600 m depth45,46 and with the fact that altimetry-derived velocity fields are consistent with subsurface currents in our region of interest down to 500 m20.Satellite dataVelocity current data and Finite-Size Lyapunov Exponent (FSLE) processing. Velocity currents are obtained from Sea Surface Height (SSH), which is measured by satellite altimetry, through geostrophic approximation. Data, which were downloaded from E.U. Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu/), were obtained from DUACS (Data Unification and Altimeter Combination System) delayed-time multi-mission altimeter, and displaced over a regular grid with spatial resolution of (frac{1}{4}times frac{1}{4}^circ) and a temporal resolution of 1 day.Trajectories were computed with a Runge-Kutta scheme of the 4th order with an integration time of 6 hours. Finite-size Lyapunov Exponents (FSLE) were computed following the methods in14, with initial and final separation of (0.04^circ) and (0.4^circ) respectively. This Lagrangian diagnostic is commonly used to identify Lagrangian Coherent Structures. This method determines the location of barriers to transport, and it is usually associated with oceanic fronts9. Details on the Lagrangian techniques applied to altimetry data, including a discussion of its limitation, can be found in10.Temperature field and gradient computation The Sea Surface Temperature (SST) field was produced from the OSTIA global foundation Sea Surface Temperature (product id: SST_GLO_ SST_L4_NRT_OBSERVATIONS_010_001) from both infrared and microwave radiometers, and downloaded from CMEMS website. The data are represented over a regular grid with spatial resolution of (0.05times 0.05^circ) and daily-mean maps. The SST gradient was obtained from:$$begin{aligned} Grad SST=sqrt{g_x^2+g_y^2} end{aligned}$$where (g_x) and (g_y) are the gradients along the west-east and the north-south direction, respectively. To compute (g_x), the following expression was used:$$begin{aligned} g_x=frac{1}{2 dx}cdot (SST_{i+1}-SST_{i-1}) end{aligned}$$where the SST values of the adjacent grid cells (along the west-east direction: cells (i+1) and (i-1)) were employed. dx identifies the kilometric distance between two grid points along the longitude (which varies with latitude). The definition is analog for (g_y), considering this time the north-south direction and (dysimeq 5) km (0.05(^circ)).Chlorophyll field Chlorophyll estimations were obtained from the Global Ocean Color product (OCEANCOLOUR_ GLO_CHL_L4_REP_OBSERVATIONS_009_082-TDS) produced by ACRI-ST. This was downloaded from CMEMS website. Daily observations were used, in order to match the temporal resolution of the acoustic and satellite observations. The spatial resolution of the product is 1/24(^{circ }).Estimation of satellite data along ship trajectory For each point ((x_i), (y_i)) of the ship trajectory, we extracted a local value of FSLE, SST gradient, and chlorophyll concentration. These were obtained by considering the respective average value in a circular around of radius (sigma) of each point ((x_i), (y_i)) . Different (sigma) were tested (ranging from 0.1(^circ) to 0.6(^circ)), and the best results were obtained with (sigma =0.2^circ), reference value reported in the present work. This value is consistent with the resolution of the altimetry data.Statistical processingFront identification FSLE and SST gradient were used as diagnostics to detect frontal features, since they are typically associated with front intensity and Lagrangian Coherent Structures10. Note that the two diagnostics provide similar but not identical information. FSLEs are used to analyze the horizontal transport and to identify material lines along which a confluence of waters with different origins occur. These lines typically display an enhanced SST gradient because water masses of different origin have often contrasted SST signature. However, this is not a necessary condition. FSLE ridges may be invisible in SST maps if transport occurs in a region of homogeneous SST. Conversely, SST gradient unveils structures separating waters of different temperatures, whose contrast is often – but not always – associated with horizontal transport. Therefore, even if they usually detect the same structures, these two metrics are complementary. Frontal features were identified by considering a local FSLE (or SST gradient, respectively) value larger than a given threshold. The threshold values have been chosen heuristically but consistently with the ones found in previous works. For the FSLEs, we used 0.08 days(^{-1}), a threshold value in the range of the ones chosen in18 and47. For the SST gradient, we considered representative of thermal front values greater than 0.009({^circ })C/km, which is about half the value chosen in47. However, in that work, the SST gradient was obtained from the advection of the SST field with satellite-derived currents for the previous 3 days, a procedure which is known to enhance tracer gradients.Bootstrap method The threshold value splits the AFC into two groups: AFC co-located with FSLE or SST gradient values over the threshold are considered as measured in proximity of a front (i.e., statistically associated with a front), while AFC values below the threshold are considered as not associated with a frontal structure. The statistical independence of the two groups was tested using a Mann-Whitney or U test. Finally, bootstrap analysis is applied following the methodologies used in47. This allows estimating the probability that the difference in the mean AFC values, over and under the threshold, is significant, and not the result of statistical fluctuations. Other diagnostics tested are reported in SI.1.Linear quantile regression Linear quantile regression method48 was employed as no significant correlation was found between the explanatory and the response variables. This can be due to the fact that multiple factors (such as prey or predator distributions) influence the fish distribution other than the frontal activity considered. The presence of these other factors can shadow the relationship of the explanatory variables (in this case, the FSLE and the SST gradient) with the mean value of the response variable (the AFC). A common method to address this problem is the use of the quantile regression48,49, that explores the influence of the explanatory variables on other parts of the response variable distribution. Previous studies, adopting this methodology, revealed the limiting role played by the explanatory variables in the processes considered50. The percentiles values used are 75th, 90th, 95th, and 99th. The analysis is performed using the statistical package QUANTREG in R (https://CRAN.R-project.org/package=quantreg, v.5.3848,51), using the default settings.Chlorophyll-rich waters selection The AFC observations were considered in chlorophyll-rich waters if the corresponding chlorophyll concentration was higher than a given threshold. All the other AFC measurements were excluded, and a linear regression performed between the remaining AFC and FSLE (or SST gradient) values. The corresponding thresholds (one for FSLE and one for SST gradient case) were selected though a sensitivity test reported in SI.1. These resulted in 0.22 and 0.17 mg/m(^3) for FSLE and for SST gradient, respectively. These values are consistent among them and, in addition, they are in coherence with previous estimates of chlorophyll concentration used to characterise productive waters in the Southern Ocean (0.26mg/m(^3)52).Gradient climbing modelAn individual-based mechanistic model is built to describe how fish could move along frontal features. We assume that the direction of fish movement along a frontal gradient is influenced by the noise of the prey field (SI. 2). Specifically, we consider a Markovian process along the (one dimensional) cross-front direction. Time is discretized in timesteps of length (varDelta tau). We presuppose that, at each timestep, the fish chooses between swimming in one of the two opposite cross-front directions (“left” and “right”). This decision depends on the comparison between the quantity of a tracer (a cue) present at its actual position and the one perceived at a distance (p_R) from it, where (p_R) is the perceptual range of the fish. We consider the fish immersed in a tracer whose concentration is described by the function T(x).An expression for the average velocity of the fish, (U_F(x)), can now be derived. We assume that the fish is able to observe simultaneously the tracer to its right and its left. Fish sensorial capacities are discussed in SI.2. The tracer observed is affected by noise. Noise distribution is considered uniform, with (-xi _{MAX}{tilde{T}}(x_0-varDelta x)), the fish will move to the right, and, vice versa, to the left. We hypothesize that the observational range is small enough to consider the tracer variation as linear, as illustrated in Fig. S7 (SI. 3). In this way:$$begin{aligned}&{tilde{T}}(x_0+varDelta x)=T(x_0)+ p_R,frac{partial T}{partial x}+xi _1 \&{tilde{T}}(x_0-varDelta x)=T(x_0)- p_R,frac{partial T}{partial x}+xi _2 ;. end{aligned}$$In case of absence of noise, or with (xi _{MAX}p_R,frac{partial T}{partial x}). If (T(x_0+varDelta x) >T(x_0-varDelta x)) (as in Fig. S7), and the fish will swim leftward if$$begin{aligned} xi _1-xi _2 >2p_R,frac{partial T}{partial x}; . end{aligned}$$Since (xi _1) and (xi _2) range both between (-xi _{MAX}) and (xi _{MAX}), we can obtain the probability of leftward moving P(L). This will be the probability that the difference between (xi _1) and (xi _2) is greater than (2p_R,frac{partial T}{partial x})$$begin{aligned} P(L)&=frac{1}{8xi _{MAX}^2} bigg (2 xi _{MAX} – 2 p_R,frac{partial T}{partial x}bigg )^2\&=frac{1}{2} bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2 end{aligned}$$.The probability of moving right will be$$begin{aligned} P(R)&=1-P(L) end{aligned}$$and their difference gives the frequency of rightward moving$$begin{aligned} P(R)-P(L)&=1-2P(L)=1-bigg (1-frac{p_R}{xi _{MAX}},frac{partial T}{partial x}bigg )^2\&=frac{p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg ); , end{aligned}$$where the absolute value of (frac{partial T}{partial x}) has been added to preserve the correct climbing direction in case of negative gradient. The above expression leads to:$$begin{aligned} U_F(x)=frac{V p_R}{xi _{MAX}}frac{partial T}{partial x}bigg (2-frac{p_R}{xi _{MAX}}bigg |frac{partial T}{partial x}bigg |bigg );. end{aligned}$$
(1)
We then assume that, over a certain value of tracer gradient (frac{partial T}{partial x}_{MAX}), the fish are able to climb the gradient without being affected by the noise. This assumption, from a biological perspective, means that the fish does not live in a completely noisy environment, but that under favorable circumstances it is able to correctly identify the swimming direction that leads to higher prey availability. This means that$$begin{aligned} p_R*frac{partial T}{partial x}_{MAX}=xi _{MAX},. end{aligned}$$
(2)
Substituting then (2) into (1) gives:$$begin{aligned} U_F(x)=V frac{frac{partial T}{partial x}}{frac{partial T}{partial x}_{MAX}}bigg (2-frac{big |frac{partial T}{partial x}big |}{frac{partial T}{partial x}_{MAX}}bigg );. end{aligned}$$
(3)
Finally, we can include an eventual effect of transport by the ocean currents, considering that the tracer is advected passively by them, simply adding the current speed (U_C) to Expr. (3).The representations provided are individual based, with each individual representing a single fish. However, we note that all the considerations done are also valid if we consider an individual representing a fish school. (U_F) will then simply represent the average velocity of the fish schools. This aspect should be stressed since many fish species live and feed in groups, especially myctophids (see SI.2 for further details).Continuity equation in one dimension The solution of this model will now be discussed. The continuity equation is first considered in one dimension. The starting scenario is simply an initially homogeneous distribution of fish, that are moving in a one dimensional space with a velocity given by (U_{F}(x)).We assume that in the time scales considered (few days to some weeks), the fish biomass is conserved, so for instance fishing mortality or growing rates are neglected. In that case, we can express the evolution of the concentration of the fish (rho) by the continuity equation$$begin{aligned} frac{partial rho }{partial t}+nabla cdot mathbf{j },=,0 end{aligned}$$
(4)
in which (mathbf{j }=rho ;U_{F}(x)), so that Eq. (4) becomes$$begin{aligned} frac{partial rho }{partial t}+nabla cdot big (rho ;U_{F}(x)big ),=,0;. end{aligned}$$
(5)
In one dimension, the divergence is simply the partial derivate along the x-axis. Eq. (5) becomes$$begin{aligned} frac{partial rho }{partial t}=-frac{partial }{partial x} bigg (rho ;U_{F}bigg ) end{aligned}$$
(6)
Now, we decompose the fish concentration (rho) in two parts, a constant one and a variable one (rho ,=,rho _0+{tilde{rho }}). Eq. (6) will then become$$begin{aligned} frac{partial rho }{partial t}=-U_Ffrac{partial {tilde{rho }}}{partial x}-rho frac{partial U_F}{partial x};. end{aligned}$$
(7)
Using Expr. (3), Eq. (7) is numerically simulated with the Lax method. In Expr. (3) we impose that (U_F(x)=V) when (U_F(x) >V). This biological assumption means that fish maximal velocity is limited by a physiological constraint rather than by gradient steepness. Details of the physical and biological parameters are provided in SI.6. More

Test surfacesWe used smooth and hairy, homogeneous and striped (with different widths of black and white stripes) test surfaces. In order to mimic the curved zebra back, all test surfaces had a convex cylindrical shape (length: 15 cm, radius: 7 cm). In the schlieren measurements (see subsection “Schlieren imaging”), the cylinder’s horizontal long axis was perpendicular (Supplementary Fig. S1A,B) or parallel (Supplementary Fig. S1C) to the collimated horizontal light beam illuminating the target area, while the stripes were perpendicular (Supplementary Fig. S1A) or parallel (Supplementary Fig. S1B) to the cylinder’s long axis. Supplementary Tables S1 and S2 list the patterns, colours and names of the 8 smooth and 10 hairy test surfaces. The smooth surfaces were composed of cardboard squares (15 cm × 15 cm) (Supplementary Fig. S2). The hairy surfaces were composed of cattle, horse and zebra hides glued by dextrin to a cylindrical (length: 15 cm, radius: 7 cm) gypsum base (Supplementary Fig. S3). Surfaces hsc1(7b7w)perp, hsc1(8b7w)par, hsc3(3b2w)perp and hsgc3(3s2L)perp were used to model that the black stripes of zebras could be separately erected, while the white remained flat7. No animals were killed, the horse and cattle hides were provided by Hungarian horse and cattle keepers, while the zebra hide was obtained from a Hungarian zoological garden.Thermography of lamplit test surfacesUsing a thermocamera (VarioCAM, Jenoptik Laser Optik Systeme GmbH, Jena, Germany, nominal precision of ± 1.5 K, with relative pixel-to-pixel precision  1 s. Since in the upper rectangular window of the filtered schlieren images the lifespan t of local minima of I(x) was very short, we performed statistics only for the lower rectangular window.For the statistical analysis of the characteristics of I(x) (Nmin, ΔI, dave) and air stream behaviour (t, dcovered, v, dmax, dse), we applied Principal Component Analysis (PCA) and fitted ellipses to component scores with 95% confidence interval. We applied Wilcoxon rank sum test with Bonferroni correction for the datasets. Because of the large sample size of the dataset Nmin, ΔI, dave—for smooth test surfaces 4475 observations per surface and for hairy test surfaces 5369 observations per surface—, the Wilcoxon rank sum test would result in highly significant differences for almost all comparisons15. Therefore, we used a Monte Carlo approach, where we randomly selected 250 (≈ 5% of the full dataset) samples, ran the Wilcoxon rank sum test with Bonferroni correction, recorded the results, repeated this 499 times (to have 500 runs) and finally the average of the results of the 500 runs was calculated. The data evaluation was made by our custom-written scripts in Python programming language. For statistical analyses we used the R statistical package 3.6.316.Disturbance caused by an artificial wind and a butterflyTo demonstrate the influence of very weak winds on the air streams above lamplit test surfaces, we blew air by a compressor with a press of 1.6 bar from 1.5 m above the following test surfaces: ss1(8b7w), hsz(8b7w)perp, hsh1(8b8w)perp and hhbc. The compressor tube ended in an air-blow gun. Before the measurements, the air pressure was 4 bar in the 3-litre compressor tank, and the regulator was set to 1.6 bar. The compressor was turned off prior to recording a given sequence and during the measurement the air-blow gun was used to generate horizontal “wind” until the pressure decreased to 1 bar (atmospheric pressure). The artificial wind speed created by the compressor was measured (with accuracy  More

The CV represents the discrete degree of trait values, that is, the size of the trait space (Fig. 6b; Supplementary Note S1); S and K are generally used to describe the shape of trait distribution (Fig. 6c,d, Supplementary Note S1). Environment filtering can force a trait to deviate from the original distribution, with characteristics of smaller CV and larger S and K values16,17. Partly consistent with our hypothesis, MAT significantly exerted positive effects on the total concentration of CV, S, and K, but weaker negative effects on the three values of Chl a/b (Fig. 6a). That is, the distributions of Chl concentration and composition shifted in opposite directions under global warming: Chl concentration was distributed in a broader but more differential way (Fig. 7a), while Chl a/b was distributed in a narrower but more uniform way (Fig. 7b).Figure 7Theoretical sketches of distribution shifts for (a) chlorophyll concentration and (b) composition (Chl a/b) under global warming. Purple curves denote the current distributions, and pink ones represent the scenario under global warming. Dashed lines denote the normal distribution in the respective scenarios. It is supposed that the distribution of chlorophyll concentration will shift toward higher mean, CV, S and K values, while Chl a/b shifts toward higher mean but lower CV, S and K values under warming. Chl chlorophyll, CV coefficient of variation, S skewness, K kurtosis.Full size imageThe trait distributional shift under warming is possibly caused by the relative role of species turnover and intraspecific variation (due to plasticity and/or heritable differentiation)25. For Chl concentration and composition, very weak phylogenetic signals were found in three plateaus (Supplementary Table S2), indicating the phenotypic plasticity of Chl, which environments have influenced during the long-term evolution. However, plasticity and intraspecific variation are not the focus of the discussion. Because the species compositions were significantly different among the three plateaus: with only a few species overlapping (Supplementary Fig. S3), and the dominant species and co-existing species gradually varied along the 30 sites (Supplementary Table S3). Shifts in Chl distributions under warming may be interpreted mainly by the alternation of species composition.For Chl concentration, a broader trait space (higher CV) and a more skewed distribution (higher S and K) under warming conditions indicate several new species that differ in functions (here refer to rare species with higher Chl concentration) appeared or increased. This contributed to the long tail of the curve and raised the average Chl concentration. At the same time, most of the other species converged at lower Chl concentrations; that is, Chl concentration undergoes more substantial differentiation and functional contrasting species co-exist under warming. The concentration of Chl is representative of plant growth rate and production ability. Its distribution shift may imply a possible trend of polarisation in functions: both acquisitive and conservative species occur simultaneously. This alteration in species composition indicates changing biotic interactions26. The co-existence of functional contrasting species allows individuals to avoid competition and enhance the exploitation of resources and niche27,28, which is of great importance in optimising community functions28,29. In desert and alpine regions, functional contrasting species with large inter-specific trait variations improve community multi-functionality and enable better resistance to climate change17,30.However, despite the shift in species composition, the distribution of Chl a/b only changed slightly compared to the Chl concentration under warming. The ratio of Chl a to Chl b represents the plant allocation to RC and LHC in PS and the efficiency trade-offs between light capture and light conversion6,7. This ratio is characteristic of conservatism which is mainly manifested in the following aspects: (1) Chl a/b is independent of Chl concentration (orthogonal relationship of the two; Supplementary Fig. S2); (2) Chl a/b distributed more converged with higher K and lower CV (Supplementary Table S1); (3) relative fixed allometric relationships were found between Chl a and Chl b (beside TP; Fig. 8). Plants may adjust their RC and LHC allocation to a common ratio of 3:1 despite large variations in light availability or Chl concentration, which has also been confirmed by a study from forests14. Considering that RC is costlier than LHC, plants tend to sustain the Chl a/b as low as possible unless there is a functional imbalance caused by environmental stress such as warming9,31.Figure 8Standardised major axis regression of chlorophyll a to chlorophyll b in three plateaus. Slopes were given and compared among regions; different lowercase words denote significant (p  More

This study uses SincNet according to the instructions provided by the authors for its application in a different dataset32. This section provides an introduction to SincNet and NIPS4Bplus before detailing the experimental procedure.SincNetThe first convolutional layer of a standard CNN trained on the raw waveform learns filters from the data, where each filter has a number of parameters that matches the filter length (Eq. 1).$$yleft[ n right] = xleft[ n right] times fleft[ n right] = mathop sum limits_{i = 0}^{I – 1} xleft[ i right] cdot fleft[ {n – i} right],$$
(1)

where (xleft[ n right]) is the chunk of the sound, (fleft[ n right]) is the filter of length (I), and (yleft[ n right]) is the filtered output. All the elements of the filter ((i)) are learnable parameters. SincNet replaces (fleft[ n right]) with another function (g) that only depends on two parameters per filter: the lower and upper frequencies of a rectangular bandpass filter (Eq. 2).$$gleft[ {n,f_{l} ,f_{h} } right] = 2f_{h} sincleft( {2pi f_{h} n} right) – 2f_{l} sincleft( {2pi f_{l} n} right),$$
(2)

where (f_{l} text{ and } f_{h}) are the learnable parameters corresponding to the low and high frequencies of the filter and (sincleft( x right) = frac{sinleft( x right)}{x}). The function (g) is smoothed with a Hamming window and the learnable parameters are initialised with given cut-off frequencies in the interval (left[ {0,frac{{f_{s} }}{2}} right]), where (f_{s}) is the sampling frequency.This first layer of SincNet performs the sinc-based convolutions for a set number and length of filters, over chunks of the raw waveform of given window size and overlap. A conventional CNN architecture follows the first layer, that in this study maintains the architecture and uses both standard and enhanced settings. The standard settings used are those of the TIMIT speaker recognition experiment27,32. They include two convolutional layers after the first layer with 60 filters of length 5. All three convolutions use layer normalisation. Next, three fully-connected (leaky ReLU) layers with 2048 neurons each follow, normalised with batch normalisation. To obtain frame-level classification, a final softmax output layer, using LogSoftmax, provides a set of posterior probabilities over the target classes. The classification for each file derives from averaging the frame predictions and voting for the class that maximises the average posterior. Training uses the RMSprop optimiser with the learning rate set to 0.001 and minibatches of size 128. A sample of sinc-based filters generated during this study shows their response both in the time and the frequency domains (Fig. 4).Figure 4Examples of learned SincNet filters. The top row (a–c) shows the filters in the time domain, the bottom row (d–f) shows their respective frequency response.Full size imageThe SincNet repository32 provides an alternative set of settings used in the Librispeech speaker recognition experiment27. Tests of the alternative settings, which include changes in the hidden CNN layers, provided similar results to those of the TIMIT settings and are included as Supplementary Information 1.NIPS4BplusNIPS4Bplus includes two parts: sound files and rich labels. The sound files are the training files of the 2013 NIPS4B challenge for bird song classification23. They are a single channel with a 44.1 kHz sampling rate and 32 bit depth. They comprise field recordings collected from central and southern France and southern Spain15. There are 687 individual files with lengths from 1 to 5 s for a total length of 48 min. The tags in NIPS4Bplus are based on the labels released with the 2013 Bird Challenge but annotated in detail by an experienced bird watcher using dedicated software15. The rich labels include the name of the species, the class of sound, the starting time and the duration of each sound event for each file. The species include 51 birds, 1 amphibian and 9 insects. For birds there can be two types of vocalisations: call and song; and there is also the drumming of a woodpecker. Calls are generally short sounds with simple patterns, while songs are usually longer with greater complexity and can have modular structures or produced by one of the sexes8,13. In the dataset, only bird species have more than one type of sound, with a maximum of two types. The labels in NIPS4Bplus use the same 87 tags present in the 2013 Bird Challenge training dataset with the addition of two other tags: “human” and “unknown” (for human sounds and calls which could not be identified). Tagged sound events in the labels typically correspond to individual syllables although in some occasions the reviewer included multiple syllables into single larger events15. The tags cover only 569 files of the original training set of 687 files. Files without tags include 100 that, for the purpose of the challenge, had no bird sounds but only background noise. Other files were excluded for different reasons such as vocalisations hard to identify or containing no bird or only insect sounds15. The 2013 Bird Challenge also includes a testing dataset with no labels that we did not use15.The total number of individual animal sounds tagged in the NIPS4Bplus labels is 5478. These correspond to 61 species and 87 classes (Fig. 5). The mean length of each tagged sound ranges from ~ 30 ms for Sylcan_call (the call of Sylvia cantillans, subalpine warbler) to more than 4.5 s for Plasab_song (the song of Platycleis sabulosa, sand bush-cricket). The total recording length for a species ranges from 0.7 s for Turphi_call (the call of Turdus philomelos, song thrush) to 51.4 s for Plasab_song. The number of individual files for each call type varies greatly from 9 for Cicatr_song (the call of Cicadatra atra, black cicada) to 282 for Sylcan_call.Figure 5Distribution of sound types by number of calls (number of files) and total length in seconds. Sound types are sorted first by taxonomic group and then by alphabetical order.Full size imageProcessing NIPS4BplusThe recommended pre-processing of human speech files for speaker recognition using SincNet includes the elimination of silent leading and trailing sections and the normalisation of the amplitude27. This study attempts to replicate this by extracting each individual sound as a new file according to the tags provided in the NIPS4Bplus labels. A Python script42 uses the content of the labels to read each wavefile, apply normalisation, select the time of origin and length specified in each individual tag and save it as a new wavefile. The name of the new file includes the original file name and a sequential number suffix according to the order in which tags are listed in the label files (the start time of the sound) to match the corresponding call tags at the time of processing. Each wavefile in the new set fully contains a sound according to the NIPS4Bplus labels. A cropped file may contain sounds from more than one species15, with over 20% of the files in the new set overlapping, at least in part, with sound from another species. The machine learning task does not use files containing background noise or the other parts of the files that are not tagged in the NIPS4Bplus labels. A separate Python script42 generates the lists of files and tags that SincNet requires for processing. The script randomly generates a 75:25 split into lists of train and test files and a Python dictionary key that assigns each file to the corresponding tag according to the file name. The script selects only files confirmed as animal sounds (excluding the tags “unknown” and “human”) and generates three different combinations of tags, as follows: (1) “All classes”: includes all the 87 types of tags originally included in the 2013 Bird Challenge training dataset; (2) “Bird classes”: excludes tags for insects and one amphibian species for a total of 77 classes; and (3) “Bird species”: one class for each bird species independently of the sounds type (call, songs and drumming are merged for each species) for a total of 51 classes. The script also excludes three very short files (length shorter than 10 ms) which could not be processed without code modifications.To facilitate the repeatability of the results, this study attempts to maintain the default parameters of SincNet used in the TIMIT speaker identification task27,32. The number and length of filters in the first sinc-based convolutional layer was set to the same values as the TIMIT experiment (80 filters of length 251 samples) as was the architecture of the CNN. The filters were initialised following the Mel scale cut-off frequencies. We did change the following parameters: (1) reduced the window frame size (cw_len) from 200 to 10 ms to accommodate for the short duration of some of the sounds in the NIPS4Bplus tags (such as some bird vocalisations); (2) reduced the window shift (cw_shift) from 10 to 1 ms in proportion to the reduction in window size (a value a 0.5 could not be given without code modifications); (3) updated the sampling frequency setting (fs) from the TIMIT 16,000 to the 44,100 Hz of the present dataset; and (4) updated the number of output classes (class_lay) to match the number of classes in each training run.To evaluate performance, the training sequence was repeated with the same settings and different random train and test file splits. Five training runs took place for each of the selection of tags: “All classes”, “Bird classes” and “Bird species”.Enhancements and comparisonsChanges in the parameters of SincNet result in different levels of performance. To assess possible improvements and provide baselines to compare against other models we attempted to improve the performance by adjusting a series of parameters, but did not modify the number of layers or make functional changes to the code other than the two outlined below. The parameters tested include: the length of the window frame size, the number and length of the filters in the first layer, number of filters and lengths of the other convolutional and fully connected layers, the length and types of normalisation in the normalisation layers, alternative activation and classification functions, and the inclusion of dropouts (Supplementary Information 1). In addition the SincNet code includes a hard-coded random amplification of each sound sequence; we also tested changing the level and excluding this random amplification through changes in the code. In order to process window frames larger than some of the labelled calls in the NIPS4Bplus dataset, the procedure outlined earlier in which files are cut according to the labels was replaced by a purpose-built process. The original files were not cut, instead a custom python script42 generated train and test file lists that contain the start and length of each labelled call. A modification of the SincNet code42 uses these lists to read the original files and select the labelled call. When the call is shorter than the window frame the code randomly includes the surrounding part of the file to complete the length of the window frame. Grid searches for individual parameters or combinations of similar parameters, over a set number of epochs, selected the best performing values. We also tested the use of the Additive Margin Softmax (AM-softmax) as a cost function37. The best performing models reported in the results use combinations of the best parameter values (Supplementary Information 1). All enhancements and model comparisons use the same dataset selection, that is the same train and test dataset split, of the normalised files for each set of tagged classes.The comparison using waveform + CNN models trained directly on the raw waveform, replaces the initial sinc-based convolution of SincNet with a standard 1d convolutional layer27, thus retaining the same network architecture as SincNet. As with SincNet enhancements, a series of parameter searches provided the best parameter combinations to obtain the best performing models.The pre-trained models used for comparison are DenseNet121, ResNet50 and VGG16 with architectures and weights sourced from the Torchvision library of PyTorch33. We tested three types of spectrograms: Fast Fourier Transform (FFT), Mel spectrum (Mel) and Mel-frequency cepstral coefficient (MFCC) to fine-tune the pre-trained models. FFT calculations used a frame length of 1024 samples, 896 samples overlap and a Hamming window. Mel spectrogram calculations used 128 Mel bands. Once normalised and scaled to 255 pixel intensity three repeats of the same spectrogram represented each of the three input channels of the pre-trained models. The length of sound used to generate the spectrograms was 3 s, and similarly with routines above, for labelled calls shorter than 3 s the spectrogram would randomly include the surrounding sounds. That is, the extract would randomly start in the interval between the end of the labelled call minus 3 s and the start of the call plus 3 s. This wholly includes the labelled call but its position is random within the 3 s sample. A fully connected layer replaced the final classifying layer of the pre-trained models to output the number of labelled classes. In the fine-tuning process the number of trainable layers of the model was not limited to the final fully connected layer, but also included an adjustable number of final layers to improve the results. The learning rate set initially to 0.0001 was halved if the validation loss stopped decreasing for 10 epochs.MetricsMeasures of performance include accuracy, ROC AUC, precision, recall, F1 score, top 3 accuracy and top 5 accuracy. Accuracy, calculated as part of the testing routine, is the ratio between the number of correctly predicted files of the test set and the total number of test files. The calculation of the other metrics uses the Scikit-learn module43 relying on the predicted values provided by the model and performing weighted averages. The ROC AUC calculation uses the mean of the posterior probabilities provided by SincNet for each tagged call. In the pre-trained models the ROC AUC calculations used the probabilities obtained after normalising the output with a softmax function. More

Sample collection and filtrationWe used 40 water samples for eDNA metabarcoding from 27 sites in 9 rivers and 13 lakes in Japan from 2016 to 2018 (Fig. 4). Sampling ID and detailed information for each site are listed in Supplementary Table S1. In the river water sampling, 1-L water samples were collected from the surface of at the shore of each river using bleached plastic bottles. In the field, a 1-ml Benzalkonium chloride solution (BAC, Osvan S, Nihon Pharmaceutical, Tokyo, Japan)33 was added to each water sample to suppress eDNA degeneration before filtering the water samples. We did not include field negative control samples in the HTS library, considering the aim of the presents study. The lake samples were provided by Doi et al. (2020)34 as DNA extracted samples. In the lake samples, 1-L water samples were collected from the surface at shore sites at each lake. The samples were then transported to the laboratory in a cooler at 4 °C. Each of the 1-L water samples was filtered through GF/F glass fiber filter (normal pore size = 0.7 μm; diameter = 47 mm; GE Healthcare Japan Corporation, Tokyo, Japan) and divided into two parts (maximum 500-ml water per 1 GF/F filter). To prevent cross-contamination among the water samples, the filter funnels, and the measuring cups were bleached after filtration. All filtered samples were stored at -20 ℃ in the freezer until the DNA extraction step.Figure 4Sampling sites used in the present study. Blue circles and orange triangles show the locations of the river and lake samples, respectively. Detailed information on each site is listed in Supplementary Table S1. This map has been illustrated using QGIS ver.3.10 (http://www.qgis.org/en/site/) based on the Administrative Zones Data (http://nlftp.mlit.go.jp/ksj/gml/datalist/KsjTmplt-N03-v2_3.html) which were obtained from free download service of the National Land Numerical Information (http://nlftp.mlit.go.jp/ksj/index.html, edited by RN). There was no need of obtaining permissions for editing and publishing of map data.Full size imageDNA extraction and library preparationThe total eDNA was extracted from each filtered sample using the DNeasy Blood and Tissue Kit (QIAGEN, Hilden, Germany). Extraction methods were according to Uchii et al.35, with a few modifications. A filtered sample was placed in the upper part of a Salivette tube and 440 μL of a solution containing 400 μL Buffer AL and 40 μL Proteinase K added. The tube with the filtered sample was incubated at 56 °C for 30 min. Afterward, the tube was centrifuged at 5000 × g for 3 min, and the solution at the bottom part of the tube was collected. To increase eDNA yield, 220-μL Tris–EDTA (TE) buffer was added to the filtered sample and the sample re-centrifuged at 5000 × g for 1 min. Subsequently, 400 μL of ethanol was added to the collected solution, and the mixture was transferred to a spin column. Afterward, the total eDNA was eluted in 100-μL buffer AE according to the manufacturer’s instructions. All eDNA samples were stored at -20 °C until the library preparation step.In the present study, we used a universal primer set “MiFish” for eDNA metabarcoding9. The amplicon library was prepared according to the following protocols. In the first PCR, the total reaction volume was 12 μL, containing 6.0μL 2 × KOD buffer, 2.4 μL dNTPs, 0.2 μL KOD FX Neo (TOYOBO, Osaka, Japan), 0.35 μL MiFish-U-F (5ʹ-ACACTCTTTCCCTACACGACGCTCTTCCGATCTNNNNNNGTCGGTAAAACTCGTGCCAGC-3ʹ), MiFish-U-R (5ʹ-GTGACTGGAGTTCAGACGTGTGCTCTTCCGATCTNNNNNNCATAGTGGGGTATCTAATCCCAGTTTG-3ʹ), MiFish-E-F (5ʹ-ACACTCTTTCCCTACACGACGCTCTTCCGATCTNNNNNNRGTTGGTAAATCTCGTGCCAGC-3ʹ) and MiFish-E-R (5ʹ-GTGACTGGAGTTCAGACGTGTGCTCTTCCGATCTNNNNNNGCATAGTGGGGTATCTAATCCTAGTTTG -3ʹ) primers with Illumina sequencing primer region and 6-mer Ns, and 2 μL template DNA. The thermocycling conditions were 94 ℃ for 2 min, 35 cycles of 98 ℃ for 10 s, 65 ℃ for 30 s, 68 ℃ for 30 s, and 68 ℃ for 5 min. The first PCR was repeated four times for each sample, and the replicated samples were pooled as a single first PCR product for use in the subsequent step. The pooled first PCR products were purified using the Solid Phase Reversible Immobilization select Kit (AMPure XP; BECKMAN COULTER Life Sciences, Indianapolis, IN, USA) according to the manufacturer’s instructions. The DNA concentrations of purified first PCR products were measured using a Qubit dsDNA HS assay kit and a Qubit 3.0 fluorometer (Thermo Fisher Scientific, Waltham, MA, USA). All purified first PCR products were diluted to 0.1 ng/μL with H2O, and the diluted samples were used as templates for the second PCR. In the first PCR step, the PCR negative controls (four replicates) were included in each experiment. A total of three PCR negative controls were included in the library (PCR Blank 1–3 samples in Supplementary Table S1, S2, S4, and S5).The second PCR was performed to add HTS adapter sequences with 8-bp dual indices. The total reaction volume was 12 μL, containing 6.0 μL 2 × KAPA HiFi HotStart ReadyMix, 1.4 μL forward and reverse primer (2.5 μM), 1 μL purified first PCR product, and 2.2 μL H2O. The thermocycling conditions were 95 ℃ for 3 min, 12 cycles of 98 ℃ for 20 s, 72 ℃ for 15 s, and 72 ℃ for 5 min.Each Indexed second PCR product was pooled in the equivalent volume, and 25 μL of the pooled libraries were loaded on a 2% E-Gel SizeSelect agarose gels (Thermo Fisher Scientific), and a target library size (ca. 370 bp) was collected. The quality of the amplicon library was checked using an Agilent 2100 Bioanalyzer and Agilent 2100 Expert (Agilent Technologies Inc., Santa Clara, CA, USA), and the DNA concentrations of the amplicon library were measured using Qubit dsDNA HS assay Kit using a Qubit 3.0 fluorometer.High-throughput sequencingAmplicon library was sequenced using iSeq and MiSeq platforms (Illumina, San Diego, CA, USA). To normalize the percentage of pass-filtered read numbers, the sequencing runs using the same libraries were performed using iSeq i1 Reagent and MiSeq Reagent Kit v2 Micro. Both sequencing was performed with 8 million pair-end reads and 2 × 150 bp read lengths. Each library was spiked with approximately 20% PhiX control (PhiX Control Kit v3, Illumina, San Diego, CA, USA) before sequencing runs according to the recommendation of Illumina. The wells of cartridges in the iSeq run were loaded with 20 μL of 50 pM library pool, and sequencing performed at Yamaguchi University, Yamaguchi, Japan. The wells of cartridges for MiSeq runs were loaded with 600 μL of 16 pM library pool, and sequencing performed at Illumina laboratories (Minato-ku, Tokyo, Japan). Subsequently, the sequencing dataset outputs from iSeq and MiSeq were subjected to pre-processing and taxonomic assignments. All sequence data are registered in the DNA Data Bank of Japan (DDBJ) Sequence Read Archive (DRA, Accession number: DRA10593).Pre-processing and taxonomic assignmentsWe used the USEARCH v11.066736 for all data pre-processing activities and taxonomic assignment of the HTS datasets obtained from the iSeq and MiSeq platforms16,37. First, pair-end reads (R1 and R2 reads) generated from iSeq and MiSeq platforms were assembled using the “fastq_mergepairs” command with a minimum overlap of 10 bp. In the process, the low-quality tail reads with a cut-off threshold at a Phred score of 2, and the paired reads with too many mismatches ( > 5 positions) in the aligned regions were discarded38. Secondly, the primer sequences were removed from the merged reads using the “fastx_truncate” command. Afterward, read quality filtering was performed using the “fastq_filter” command with thresholds of max expected error  > 1.0 and  > 50 bp read length. The pre-processed reads were dereplicated using the “fastx_uniques” command, and the chimeric reads and less than 10 reads were removed from all samples as the potential sequence errors. Finally, an error-correction of amplicon reads, which checks and discards the PCR errors and chimeric reads, was performed using the “unoise3” command in the unoise3 algorithm39. Before the taxonomic assignment, the processed reads from the above steps were subjected to sequence similarity search using the “usearch_global” command against reference databases of fish species that had been established previously (MiFish local database v34). The sequence similarity and cut off E-value were 99% and 10–5, respectively. If there was only one species with ≧ 99% similarity, the sequence was assigned to the top-hit species. Conversely, sequences assigned to two or more species in the ≧ 99% similarity were merged as species complex and listed in the synonym group. Generally, the species complexes were assigned to the genus level (e.g., Asian crucian carp Carassius spp.). Species that were unlikely to inhabit Japan were excluded from the candidate list of species complexes. For example, the sequence of one of bitterling Acheilignathus macropterus included other different two species, A. barbatus and A. chankaensis, as the species of the 2nd hit candidate; however, the two species are not currently found in Japan. Therefore, the sequence was assigned to A. macropterus in the present study. Because we used only freshwater fish species, we removed the operational taxonomic units (OTUs) assigned to marine and brackish fishes from each sample. Finally, sequence reads of each fish species were arranged into the matrix, with the rows and columns representing the number of sites and fish species (or genus), respectively.We evaluated sequence quality based on (1) the percentage of clustering passing filter (% PF) and (2) sequencing quality score ≧ % Q30 (Read1 and Read2) between iSeq and MiSeq platforms. The % PF value is an indicator of signal purity for each cluster40. The condition leads to poor template generation, which decreases the % PF value40. In the present study, a  > 80% PF value was set as the threshold of sequence quality in iSeq and MiSeq runs. Sequence quality scores (Q score) measure the probability that a base is called incorrectly. Higher Q scores indicate lower probability of sequencing error, and lower Q scores indicate probability of false-positive variant calls resulting in inaccurate conclusions41. In the present study, the % Q30 values (error rate = 0.001%) were used for the comparison of sequence quality between iSeq and MiSeq. The parameters were collected directly using Illumina BaseSpace Sequence Hub. We also evaluated changes in sequence reads in pre-processing steps between iSeq and MiSeq platforms. Sequence reads were assessed based (1) merge pairs, (2) quality filtering, and (3) denoising. In each step, the change in the number of reads before and after processing was calculated. The calculated numbers of sequence reads are listed in Supplementary Table S2 and S3 in series.Comparing sequence quality and fish fauna between iSeq and MiSeqTo test a relationship of remained sequence reads between iSeq and MiSeq in each pre-processing part, we performed spearman’s rank correlation test in each step. In the present study, however, the sequencing run by iSeq and MiSeq was performed only once each for the same sample. Therefore, we could not assess the variabilities of the sequence read in quality checks and taxonomic assignment in the same samples between iSeq and MiSeq.Before the comparison of fish fauna, rarefaction curves were illustrated for each sample in both iSeq and MiSeq to confirm that the sequencing depth adequately covered the species composition using the “rarecurve” function of the “vegan” package ver. 2.5–6 (https://github.com/vegandevs/vegan) in R ver. 3.6.242. In the present study, the differences in the numbers of sequence reads among samples were confirmed in the two sequencers, but rarefaction curves were saturated in all iSeq and MiSeq samples (Supplementary Fig. S6 and S7). We performed a rarefaction using the “rrarefy” function in “vegan” package to match up the iSeq sequence depths of each sample with that of MiSeq. However, the number of species in each sample on the iSeq have not changed before or after the rarefaction. Therefore, we have used the raw data set before the rarefaction for the subsequent analyses.We compared the species detection capacities of iSeq and MiSeq based on environmental DNA metabarcoding. Using fish faunal data obtained from iSeq and MiSeq, non-metric multidimensional scaling (NMDS) was performed in 1000 separate runs using the “metaMDS” functions in the “vegan” package ver. 2.5–6. For NMDS, the dissimilarity of the fish fauna was calculated based on the incidence-based Jaccard indices. To evaluate the differences in species composition and variance across sites between the two HTS, we performed a permutational multivariate analysis of variance (PERMANOVA) and the permutational analyses of multivariate dispersions (PERMDISP) with 10,000 permutations, respectively. For the PERMANOVA and PERMDISP, we used the “adonis”, and “betadisper” functions in the “vegan” package ver. 2.5-6.Comparison of fish species detectability between eDNA metabarcoding and conventional methodsWe evaluated species detectability between the two HTS by comparing the fish species lists of the two HTS with lists from conventional methods. Five sampling sites were selected from Kyushu and Chugoku districts (R23–27 in Fig. 4). The fish fauna data obtained by conventional methods were based on the results of a previous study43. The conventional surveys were conducted through hand-net sampling and visual observation by snorkeling (see a previous study43 for the detailed methods). The count data of each species were replaced with the incidence-based datasets (presence or absence) for comparing with the eDNA metabarcoding datasets. Fish sequence reads of each sampling site obtained by eDNA metabarcoding were also replaced with the incidence-based data.To test the detectability of species observed by conventional methods, the fish species compositions in five rivers were compared between the eDNA metabarcoding (iSeq and MiSeq) and the conventional methods. To visualize the differences in the species composition between HTSs and conventional methods, heat maps were illustrated for each sampling site. To assess differences in the number of species among methods at each river, the repeated measures analysis of variance (ANOVA) was performed among iSeq, MiSeq, and conventional methods. If a significant difference was found in repeated measures ANOVA, the Tukey–Kramer multiple comparison test was performed to analyze differences among methods.Using fish faunal data obtained from iSeq, MiSeq, and conventional methods, the NMDS was performed in 1000 separate runs with Jaccard indices. The PERMANOVA was performed with 1000 permutations to assess the differences in fish fauna among the methods and sites. Furthermore, to evaluate variance across sites among methods, the PERMDISP was also performed with 1000 permutations. To visualize the number of species in each method and the number of common species between methods, Venn diagrams were illustrated for each river using the “VennDiagram” package ver. 1.6.2 in R44. More

Site descriptionField experiments were conducted at the Changwu Experimental Station (35° 12′ N, 107° 40′ E, altitude 1200 m) located in Shaanxi Province, China. The experimental site was in the typical dryland farming area on the Loess Plateau. Annual precipitation in the area averaged 582 mm between 1957 and 2013, with a mean annual temperature of 9.7 °C over that period. Rainfall and temperature during the two study years are shown in Fig. S1. Soils were generally of the Calcaric Regosol group, according to the FAO/UNESCO soil classification system52, and were composed of 4% sand, 59% silt, and 37% clay53. The 0–20 cm soil properties were the following: pH, 8.4; organic matter content, 11.8 g kg−1; total N content, 0.87 g kg−1; and Olsen-P, 14.4 mg kg−1.Experimental design and field managementTwo-year experiment was arranged in a randomized complete block design with three replicate plots during 2012 and 2013 growing seasons25,54_ENREF_53. The study was conducted using the soybean cultivar (Glycine max L.) cv. Zhonghuang 24 and the maize cultivar (Zea mays L.) cv. Zhengdan 958 grown in cereal–legume agricultural systems. Zhonghuang 24 was bred from Jilin 21 and fendou 31 × Zhongdou 19 (deposition number 2008003); Zhengdan 958 was the offspring of inbred Zheng 58 and Chang 7-2 (deposition number 20000009), which are approved in China. The cropping system treatments were as follows:

1.

Sole-cropped soybean (S).

2.

Sole-cropped maize (M).

3.

Two rows of maize intercropped with two rows of soybean (M2S2).

4.

Two rows of maize intercropped with four rows of soybean (M2S4).

Each plot measured 6 m × 4 m, with row spacing of 50 cm for maize and soybean both in sole crops and intercrops. Individual plants were spaced at 22 cm and 19 cm for maize and soybean, respectively, with one plant per stand for maize and two plants per stand for soybean to attain densities of 90,000 and 210,000 plants ha−1, respectively. In 2012, seeds of maize and soybean were sown on 25 April and harvested on 28 September, and in 2013, seeds were sown on 20 April and harvested on 25 September. Before sowing, basal fertilizer was applied at a rate of 90 kg N ha−1 as urea (46% N) and 150 kg P2O5 ha−1 as superphosphate (12%, P2O5), and then additional fertilizers were uniformly spread in each plot, which were then ploughed into the 0–30 cm soil layer using a rotary tiller. All of the plots received 67.5 kg N ha−1 as urea at the bell and silking stages using a hole-seeding machine. No irrigation was applied, and weeds were removed by hand when sighted. The research on plants complied with relevant institutional, national, and international guidelines and legislation.Above- and below-ground measurementsThe Pn was measured with a LI-6400 portable photosynthesis system (LI-COR Inc., Lincoln, NE, USA) from 9:00 to 11:00 h at 120 days after sowing, which corresponds to the milk stage in maize and full seed stage in soybean7,13. We measured photosynthesis of ear leaves of maize, the first spreading leaves at the top of soybean in both the sole crops and intercrops. The Pn values were calculated as the sum of the mean readings for five leaves in each plot. The LAI values, DIFN were recorded using a Plant Canopy Analyzer (Li-2200, LiCor Inc., Lincoln, NE, USA) without direct sunlight at milk stage of maize. One above-canopy measurement and three below-canopy measurements at the soil surface were taken for four replicates in each plot. SPAD were collected using a hand-held dual wavelength meter (SPAD 502, Chlorophyll meter, Minolta Camera Co., Ltd., Japan) at milk stage of maize. Measurements were taken midway along the ear leaves of maize and the first spreading leaves at the top of soybean from five adjacent plants at the center of row in each plot.The SWS was measured gravimetrically using a soil auger at 10 cm intervals over a depth of 100 cm and at 20 cm intervals over a depth of 200 cm at milk stage of maize for three replicates in each plot. The SWS was calculated for each plot in the 0–200 cm soil profile for the soil moisture using the following formula: SWS = SWC × SD × SBD, where SWC represents soil water content, SD represents soil depth, and SBD represents soil bulk density. Apparent water use during crop growth season was expressed as evapotranspiration (ET), which was determined according to the following formula: ET = ΔSWS + P, where ΔSWS is the change in soil water storage in the top 200 cm and P is the rainfall (mm) between planting and at milk stage in maize. The six adjacent plant samples were collected at milk stage of maize in the middle two rows of each plots (Fig. S2). The sampling included shoots and roots of maize and soybean. At the cotyledonary node, above-ground parts were separated from below-ground parts. Soil core samples (9 cm diameter × 15 cm) at the intra-row of crop were collected to a depth of 100 cm using an auger and separated in 10-cm sections to determine the root growth in sole-cropping and intercropping systems. The samples were exposed to 105 °C for 30 min and then dried to a constant weight at 75 °C. The oven-dried samples were put in small plastic bags after grinding. The study of N and P uptake are the most common among mineral elements55,56. Concentrations of N and P in the plant dry matter were determined after digestion with H2SO4 and H2O2; N concentration was measured according to the Kjeldahl method20, whereas P concentration was measured by the molybdenum-antimony anti-spectrophotometric method16. Crop N and P uptake were calculated by the actual above-ground biomass multiplied by plant tissue N and P concentrations. Grain yield was estimated at harvest from 6 m2 for maize and soybean based on the average of three plot replicates.Data analysisThe LER for assessment of land use advantage. LER is sum of ratio of intercrop to sole crop for maize and soybean yield57:$$ LER = LER_{m} + LER_{s} ,;LER_{m} = frac{{Y_{im} }}{{Y_{sm} }}, ;LER_{s} = frac{{Y_{is} }}{{Y_{ss} }} $$where LERm and LERs are patial LER for maize and soybean, respectively. Yim and Yis are yields of maize and soybean under intercrops, respectively. Ysm and Yss are the yield of maize and soybean under sole crop, respectively.The water equivalent ratio (WER) was calculated to measure water use advantage of intercropping58:$$ WER = WER_{m} + WER_{s} ,;WER_{m} = frac{{Y_{im} /ET_{im} }}{{Y_{sm} /ET_{sm} }},;WER_{s} = frac{{Y_{is} /ET_{is} }}{{Y_{ss} /ET_{ss} }} $$where WERm and WERs are patial WER for maize and soybean, respectively. ETim and ETis are ET of maize and soybean under intercrops, respectively. ETsm and ETss are the ET of maize and soybean under sole crop, respectively.All analyses were conducted in SPSS Statistics 17.0 (SPSS Inc., Chicago, IL, USA). Treatment means showing significant differences among different cropping systems were separated using one-way ANOVA or least significant difference (LSD) at a threshold of 5% to compare the effect of yield, above- and below-ground related parameters (Pn, LAI, SPAD, DIFN, SWS, N and P uptake) in different maize–soybean intercropping. The variation in Pn, LAI, SPAD, DIFN, SWS, N, and P uptake of crop, and the effects of cropping system × year were made using Univariate General Linear Models. Pearson’s correlation test was used to analyze between LER and above-and below-ground biomass of maize and soybean. The effects of above- and below-ground factors on biological yield were quantified, by calculating the contribution value of some key factors to yield. The effects of between above- (LAI, SPAD, DIFN) and below-ground (SWS, N and P uptake) competition on the biological yield and contribution rate were conducted by the linear regression model59:$$ Y = beta_{0} LAI + beta_{1} SPAD + beta_{2} DIFN + beta_{3} SWS + beta_{4} {text{N}} + beta_{5} {text{P}} + beta_{6} X + beta_{7} $$
(1)
where Y represents biological yield, LAI represents leaf area index, SPAD represents chlorophyll, DIFN represents diffuse non interceptance, SWS represents soil water storage, N represents crop nitrogen uptake, P represents crop phosphorus uptake, X represents interaction for LAI, SPAD, DIFN, SWS, N, and P, and β0, β1, β2, β3, β4, β5, β6 and β7 represent the fitted parameters. The standard regression coefficients (Beta) of LAI, SPAD, DIFN, SWS, N, and P were determined on the basis of Eq. (1) to split their influence on the biological yield by the following equations:$$ beta_{0}^{prime } = beta_{0} times left( {LAI^{prime } /Y^{prime } } right) $$
(2)
$$ beta_{1}^{prime } = beta_{1} times left( {SPAD^{prime } /Y^{prime } } right) $$
(3)
$$ beta_{2}^{prime } = beta_{2} times left( {DIFN^{prime } /Y^{prime } } right) $$
(4)
$$ beta_{3}^{prime } = beta_{3} times left( {SWS^{prime } /Y^{prime } } right) $$
(5)
$$ beta_{4}^{prime } = beta_{4} times left( {{text{N}}^{prime } /Y^{prime } } right) $$
(6)
$$ beta_{5}^{prime } = beta_{5} times left( {{text{P}}^{prime } /Y^{prime } } right) $$
(7)
where β0′, β1′, β2′, β3′, β4′, and β5′ represent the standard regression coefficients for LAI, SPAD, DIFN, SWS, N, and P. LAI′, SPAD′, DIFN′, SWS′, N′, and P′ represent the standard deviations for LAI, SPAD, DIFN, SWS, N, and P. Y′ is the standard deviation for the modeled biological yield. More

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