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Photosynthetic pigments in rice leaf bladesThe contents of chlorophylls a, and b and carotenoids showed an upward trend with increasing nitrogen application rate. Pigments in the N4 treatment were significantly higher than those in the N1 treatment at the heading and maturity stages (Fig. 1).Figure 1Effects of different nitrogen application rates on photosynthetic pigments in rice leaves. Note N0:0 kg ha-1; N1:75 kg ha-1; N2:150 kg ha-1; N3: 225 kg ha-1; N4:300 kg ha-1; Chla, chlorophyll (a); Chlb, chlorophyll (b); significant differences between rice varieties and nitrogen treatments (P  0.05) (Table 2).Table 2 Relationship between photosynthetic pigments and fluorescence parameters in rice leaves.Full size tableRelationships among rice yield and its components, photosynthetic pigments, and fluorescence parametersAt the booting stage, carotenoids had a significant positive correlation with EPN. At the heading stage, carotenoids had a significant negative correlation with SPP. At the maturity stage, chlorophylls a and b and carotenoids had significant positive correlations with EPN. However, chlorophyll a and carotenoids had a significant negative correlation with SF (Table 3).Table 3 Relationship between rice yield and its components, photosynthetic pigments, and fluorescence parameters.Full size tableAt the booting stage, qP was negatively correlated with EPN at the 5% significance level, and the correlation coefficient was − 0.892. At the heading stage, Fv/Fm and Y(NO) were negatively correlated with EPN and SPP (P  More

Collection of parental coloniesWildtype colonies of H. echinata were collected by staff of the Alfred Wegener Institute within the German Bight around Sylt (55°02′ N; 08°28′ E) with the research vessel MYA II in a depth of 1–3.5 m. Here, the mean annual SST ranges between 1 and 20 °C47, and the salinity between 25 and 33 PSU48. The sampling took place in April 2016 (scenario 1) and June 2016 (scenario 2). The hydroid colonies were transported to the Carl von Ossietzky University of Oldenburg, and cultured in artificial sea water (Aqua Medic, Germany) at 12 °C and 34 PSU. Before the transport, the hermit crabs were removed from the shells colonized by hydroids. At the University of Oldenburg, the colonies were fed daily with two-day-old living Artemia salina nauplii.Reproduction and larval settlementJuvenile hydroids were cultured as described in the Helgoland Manual of Animal Development27 Eder et al.31. Overall, 10 male and 10 female adult H. echinate colonies were placed together into one big holding tank to release eggs and sperm for fertilization. The fertilized eggs then transformed into larvae. The transformation of the larvae was induced by caesium chloride49 following the protocol of as described by Eder et al.31, which randomly settled onto black glass tiles (dimensions 10 mm × 10 mm × 2 mm, Mosaikstein, Germany), at least 2–3 larvae on each tile. The colonized glass tiles were then randomly dispersed into the different treatment tanks. As these recruits result from sexual reproduction of overall 20 parental colonies, we can assume high genetic variability of individuals. For individual identification of juvenile colonies, prior to the experiment the glass tiles were engraved underneath with consecutive numbers. After three weeks, the juvenile colonies growing closer to the edges were removed to avoid edge effects, leaving one colony per tile. Prior to the start of the experiments, the colonies were kept in artificial seawater at 18 °C and 34 PSU for 24 h post settlement. From day five of post-settlement onwards, juveniles were fed with two-day-old living Artemia salina nauplii.Experimental setupThe influence of temperature and food availability on the growth of H. echinata colonies was tested in two different experiments (= scenarios) to evaluate the effect of ambient and future environmental conditions on H. echinata in the subtidal (scenario 1, Fig. 7, left panel) and in the intertidal, a habitat characterized by high temperature fluctuations (scenario 2, Fig. 7, right panel). In both scenarios, colonies were exposed to two different temperatures (control and high) cross-factored with two different food conditions (low and high; Fig. 7).Figure 7Experimental design for analysing growth performance and mortality of juvenile H. echinata in two experiments, scenario 1 (left) and 2 (right). The larvae (b) of wild type colonies (a) were settled on glass tiles (c) and transferred to holding tanks for experimental exposure to variable temperature and food conditions (d): HF = high food (dark blue and red tanks); LF = low food (light blue and red tanks); 18 °C = control temperature (blue tanks); 21 °C = high temperature (red tanks). All treatments in scenario 2 contained an extra temperature step of + 1.5 °C for six hours daily. Throughout the experimental timeline and in each treatment, the growth performance of H. echinata was monitored (e). Additionally, a numerical growth model was developed (f dark grey arrows) based on daily analysis of morphological parameters (colony area, polyp number) in hydroids in treatments HF/18 °C and LF/18 °C of scenario 2 and validated (g light grey arrows) by comparing simulated and experimental growth data in all treatments of both scenarios.Full size imageThe control temperature of ~ 18 °C simulated the actual sea surface temperature (SST) during summer in the German Bight (data from Helgoland Roads, 2010–2014, http://www.st.nmfs.noaa.gov). The high temperature of ~ 21 °C was chosen according to predicted increasing SST by the end of the century in the North Sea 8.To evaluate the influence of food availability on the growth potential in hydroids as a response to increasing SST, colonies were fed with two-day-old living A. salina nauplii ( > 1000 nauplii/ml per tank per feeding event) following either a high food (HF) or a low food (LF) scheme (Fig. 7) according to Eder et al.31. Colonies with HF were fed five times a week and with LF three times a week. The LF treatments simulated ´food stress` and were patterned on the predicted decrease in primary and secondary production during the next decades6,50.All experimental conditions, including temperature and food, but also salinity, pH, as well as water quality (ammonium, nitrite and nitrate) were constantly monitored. The temperature was measured every ten minutes using HOBO Tidbit v2 Temp Loggers (Onset, USA). The salinity was checked prior to every water exchange (five times a week) with a hand-held refractometer (Arcarda, Germany). Twice a week, the pH was measured with a pH controller (Aqua Medic, Germany), and concentrations of ammonium, nitrite and nitrate were determined with test kits (JBL, Germany). The water quality was checked once a week before the water exchange. If the limit values for ammonium, nitrite and phosphate (0.25 mg/l, 0.2 mg/l and 0.1 mg/l) were exceeded, an additional water change was performed to ensure a consistently good water quality. Juvenile colonies were exposed to a 14 h-light and 10 h-dark cycle according to in-situ conditions in the German Bight in summer (July/August)31. Each replicate tank, covered by a lid to reduce evaporation and cooling, was provided with air through an air stone, which was placed in the middle of each tank and connected to a pump (HP-40, Hiblow, Japan). To minimize bacterial and algal growth on the glass tiles they were cleaned once a week, without touching the colonies.Scenario 1In the first experiment (Fig. 7, left panel) conducted in June–August 2016, the growth of 80 H. echinata colonies was analysed. The juvenile colonies growing on glass tiles were randomly dispersed into 24 holding tanks containing 100 ml artificial sea water (3–4 glass tiles per tank, 6 replicate tanks per treatment) and exposed for six weeks to, overall, four experimental treatments: HF/18 °C, HF/21 °C, LF/18 °C, LF/21 °C (Fig. 7, left panel). The temperature treatments in this scenario were chosen according to more stable conditions in the subtidal (Fig. 8, grey solid lines), with a control temperature of 18.5 °C ± 0.41 (mean ± SD; Fig. 8, lower grey line) and a high temperature of 20.8 °C ± 0.23 (mean ± SD; Fig. 8, upper grey line). The 24 holding tanks containing the juvenile hydroids were placed in two temperature-constant water baths as described in Eder et al.31. A thermostatic heater (Thermo control 300, Eheim, Germany) and two circulation pumps (Voyager Nano, Sicce, Italy) in each water bath kept temperatures constant at 18 °C and 21 °C, respectively.Figure 8Daily temperature profiles of the control (18 °C; bottom) and high-temperature (21 °C; top) treatments in scenario 1(solid grey lines) and 2 (dotted black lines). In both scenarios, light was provided to experimental animals daily between 8 am and 10 pm (yellow box). All treatments in scenario 2 contained an extra temperature step of + 1.5 °C for six hours daily (between 15:00 and 21:00 h; red box).Full size imageScenario 2The second scenario (Fig. 7, right panel) was conducted in October-December 2016, testing 71 juvenile H. echinata colonies under fluctuating temperature stress. The tiles were dispersed randomly into 32 holding tanks (2–3 glass tiles per tank, 8 replicate tanks per treatment) filled with 300 ml artificial sea water and exposed to four different treatments for five weeks, respectively: HF/18 °C + 1.5 °C, HF/21 °C + 1.5 °C, LF/18 °C + 1.5 °C, LF/21 °C + 1.5 °C (Fig. 7, right panel). This scenario contained an additional temperature step (+ 1.5 °C) for all treatments, to implement daily temperature fluctuations and mimic natural variations in the intertidal during high and low tide51; Fig. 8, black dotted lines). Therefore, the control temperature treatments of 18.2 °C ± 0.60 was increased daily for six hours to 19.5 °C ± 0.17 (mean ± SD; Fig. 8, lower black line), and the high temperature treatments of 20.7 °C ± 0.55 to 22.3 °C ± 0.06 (mean ± SD; Fig. 8, upper black line). The holding tanks were placed into temperature-controlled incubators (MIR-554, Panasonic Healthcare Co., Japan & MIR-553, Sanyo Electric Co., Japan) for each temperature regime.Growth rates and mortalityThroughout the experiment, the colonies developed normally without any signs of polyp or tentacle deformation. Each colony was morphometrically analyzed on a weekly basis in terms of colony area and number of polyps, as indicators for individual growth performance. These parameters were determined throughout both experiments by analyzing weekly photographs of colonies (Fig. 1), taken through a binocular microscope (Leica M205 C, Leica Microsystems, Germany) between the ages of 5–46 days post-settlement (scenario 1) and 8–36 days post-settlement (scenario 2). In scenario 1, the photographs of animals in the HF and LF treatments were taken three days apart for logistical reasons. The area of each colony was determined graphically by an automated script developed using Matlab (Version R2015b, The MathWorks, Inc., USA). The script identifies the shape of the largest patch on each glass tile and excludes the spaces between the stolonal channels. Geometric patterns were not taken into consideration to counteract potential morphological differences based on genetic variations or similarities (e.g. sheet or runner like colonies). For the determination of polyp number, only completely developed polyps equipped with tentacles were counted, whereas buddies were ignored. The juveniles did not reach sexual maturity during the experiment, therefore the colonies consisted exclusively of feeding polyps.Additionally, we analyzed mortality rates by day 35 post-settlement for both scenarios, which were characterized by visible colony-wide signs of cell necrosis and tissue detachment from the surface.In the treatments HF/18 °C and LF/18 °C of the second scenario, daily pictures of eight colonies (four colonies of each treatment) were taken between day 8 and 27 post-settlement to develop and validate a numerical growth model.Model development and validationTo identify physiological response mechanisms of juvenile hydroids exposed to nutrient and temperature stress, we developed a numerical growth model based on morphological data. The effect of environmental stress was simulated by phenomenological relationships, such as temperature-driven metabolism and the negative effects of resource limitation on growth rates. To identify unexpected trends and features in the experimental growth data, the results of the model simulations were compared to the experimental data.The model simulated the day-to-day growth of the colonies through building up feeding polyps and the stolon system. The polyps were described by nodes of a growing network connected by stolon branches. The energy was treated as an artificial, dimensionless quantity that was distributed over the nodes of the network. Food uptake resulted in an increase of the energy amount of every feeding polyp. Energy loss was accounted for by temperature-dependent rest and activity respiration according to van’t Hoff’s rule and the costs for stolon and polyp growth. The energy of a node was equally distributed to adjacent stolons and polyps at a fixed distribution rate, whereby pressure inequalities in stolon branches were not considered due to an assumed constant stolon diameter.The model was initialized by one feeding polyp. Depending on the available energy, the colony developed feeding polyps first to increase its energy intake. Then, if enough energy was left, the colony built up stolon branches of a certain length in an arbitrary direction. The energy needed for stolon growth was proportional to the length and had to exceed the parameterized amount for the growth of a stolon of reference length. The minimum distance between two polyps was also parameterized, as well as the energy needed for this process.Parameter values were partly taken from the experiments and partly estimated by automatic parameter optimization (Supplementary Table 1). For this, the parameters of the model were trained to the lab data of the LF/18 °C treatment (scenario 2) in respect to the number of feeding polyps and area of the colony. The trained parameter set was then used for all other simulations. The simulation was repeated 100 times per treatment, with the respective temperature and food scheme and randomized stolon growth. The model was programmed in C and ran for 43 days (scenario 1) and 37 days (scenario 2) with a time step of 6 h to simulate the periods of frequent temperature stress in scenario 2 (= additional temperature step). The model was calibrated using the treatment LF/18 °C (scenario 2).StatisticsWe compared the growth performance over time between experimental data and simulated data, for both scenarios separately. Area and polyp growth rates were compared by a pairwise Wilcoxon test with multiple-testing adjustment (Bonferroni-Holmes) in R (R version 3.5.1, R Core Team 2018). The 18 °C high-food condition (HF/18 °C) was set as the reference group. The respective parameters ((alpha ,b)) were calculated as follows:

1.

Area growth (colony area as a function of time) of the individual colonies was square root transformed and fitted with a linear model of the form, (sqrt[4]{{varvec{A}}}left( {varvec{t}} right) = {varvec{a}} + {varvec{bt}} + {varvec{varepsilon}}left( {varvec{t}} right),user2{ })([4])({{varvec{A}}}left( {varvec{t}} right) = {varvec{a}} + {varvec{bt}} + {varvec{varepsilon}}left( {varvec{t}} right),user2{ }) where ({varvec{A}}) is the colony area, ({varvec{a}},{varvec{b}}) represent intercept and slope of the fitted area growth curve, respectively, and ({varvec{varepsilon}}) is the model error.

2.

The polyp growth (number of polyps as a function of time) was fitted using the parametric Gompertz function without transformation, usually used to describe tumour growth kinetics (Laird, 1964) as follows: ({varvec{N}}left( {{varvec{t}};{varvec{alpha}},{varvec{beta}}} right) = {varvec{e}}^{{{varvec{alpha}}/{varvec{beta}}left( {1 – {varvec{e}}^{{ – user2{beta t}}} } right)}} ,user2{ }) where ({varvec{alpha}} > 0) is the initial growth constant, (mathop {lim }limits_{{{varvec{t}} to 0}} frac{{varvec{d}}}{{{varvec{dt}}}}{varvec{N}}left( {varvec{t}} right) = user2{alpha N}left( {varvec{t}} right),user2{ }) i.e. initial exponential growth, (mathop {lim }limits_{{{varvec{t}} to 0}} {varvec{N}}left( {varvec{t}} right) = exp left( {user2{alpha t}} right)), and ({varvec{beta}} > 0) is the growth constant at the maximum growth rate, i.e., (frac{{varvec{d}}}{{{varvec{dt}}}}{varvec{N}}left( {{varvec{t}} = {varvec{t}}_{{mathbf{i}}} } right) = user2{beta N}left( {{varvec{t}} = {varvec{t}}_{{mathbf{i}}} } right) = frac{{varvec{beta}}}{{varvec{e}}}{varvec{e}}^{{{varvec{alpha}}/{varvec{beta}}}}), with ({varvec{t}}_{{mathbf{i}}} = left( {ln frac{{varvec{alpha}}}{{varvec{beta}}}} right)/{varvec{beta}}) defining the inflexion point of the (sigmoidal) growth curve. The function follows the trend of a logistic growth curve, but is characterized by asymmetric growth through saturation. In both experiments, saturation was probably not reached, but in scenario 2, growth declined towards the end of the experiment. This decline was set as an indicator for the end of the optimal growth phase and, therefore, the end of the experiment. The ({varvec{beta}}) parameter determined for the experimental polyp growth curve of each colony was always significantly lower than the respective ({varvec{alpha}}) parameter and did not differ significantly across the conditions. This allowed us to compare the conditions in terms of the ({varvec{alpha}}) parameter only.

The analysis of numerical growth model data followed the same procedure. Then, the growth curves over time (polyp number, colony area) for the experimental data and the simulation were qualitatively compared based on the shape and the discrepancies between the curves. Parametric functions to experimental growth curves were fitted using NonlinearModelFit in Wolfram Mathematica (Version 11, Wolfram Research, UK). R was used for statistical analysis and for producing graphical output. The effect sizes (Cohen’s effect size, Odds Ratio) are presented in the supplements (Supplementary Table 4, 5).In addition, we analyzed the experimental data in terms of mortality, which was defined as the proportion of colonies that died 35 days after settlement, using the proportion test in R.Animal rightsAll applicable international, national, and/or institutional guidelines of the University Oldenburg and the federal state Lower Saxony (Germany) for the care and use of animals were followed. More

We consider a response variable measured at n different sites denoted Yi (i stands for a site), L local variables which can be continuous or discrete and are denoted as xil (l stands for a local variable and i for a site) and K landscape variables denoted as zrk (k stands for a landscape variable and r for a polygon in the landscape). In the Bsiland method, the effect of landscape variables is modelled using buffers with (p_{{i},delta_{k}}^{k}), the percentage of the landscape variable k in a buffer of radius δk and centered on site i. Since the Bsiland model is based on the generalized linear models framework, the expected value of the response variable Yi is modelled as follows:$$ mu_{i} = mu + sumlimits_{l in L} {alpha_{l} x_{i}^{l} } + sumlimits_{k in K} {beta_{k} p_{{i},delta_{k}}^{k} } $$
(1)
where µ is the intercept, αl and βk are the effects of local and landscape variables, respectively.The Fsiland method is based on Spatial Influence Functions (SIFs) in a similar framework to Chandler & Hepinstall-Cymerman 9. To simplify computations, the entire study area is not considered as continuous but rasterized, i.e. pixelated on a regular grid, named R. The value of each landscape variable k at a pixel r is described in zrk. For instance, if the landscape variable k is a presence/absence variable, zrk is equal to one or zero. The expected value of the response variable Yi is then modelled as follows:$$ mu_{i} = mu + sumlimits_{l in L} {alpha_{l} x_{i}^{l} } + sumlimits_{k in K} {beta_{k} } sumlimits_{r in R} {f_{{delta}_{k}} (d_{i,r} )z_{r}^{k} } $$
(2)
where fδk(.) is the SIF associated with the landscape variable k and di,r is the distance between the center of pixel r and the observation at site i. The SIF is a density function decreasing with the distance. The scale of effect of a landscape variable k is calibrated through the parameter δk, the mean distance of fδk. Two families of SIF are currently implemented in the siland package, exponential and Gaussian families defined as fδ(d) = 2/(πδ2)exp(-2d/δ) and fδ(d) = 1/(2δ)2exp(-π(d/2δ)2), respectively19. The effect of a landscape variable k is modelled by two parameters: an intensity parameter, βk describing its strength and its direction and a scale parameter, δk, describing how this effect declines with distance. Each pixel potentially has an effect on the response variable at any observation site. No set of scales of effects is initially determined. In Eq. 2, the sum on the regular grid R is an approximation of the integration on the continuous study area. The choice of the grid definition is a tradeoff between computing precision and computing time. The smallest the mesh size of the grid is, the better are the precision but the longer the computing time is (and the larger the required memory size is). The parameters estimation may be very sensitive to this mesh size. To obtain a reliable estimation, we recommend to ensure, after the estimation procedure, that mesh size is at least three times smaller than the smallest estimated SIF (see Supplementary Fig. S2 online for details). If not, it is recommended to proceed with a new estimation with a smaller mesh (by using the wd argument of the Fsiland function, set at 30 by default).All parameters, µ, {α1,…, αK}, {β1,…, βK} but also {δ1,…, δK} are simultaneously estimated by likelihood maximization for both Bsiland and Fsiland methods. We have developed a sequential algorithm. At the initialization stage, values are arbitrarily defined for the {δ1,..,δK} scales parameters. In step A, the µ, {α1,.., αK}, {β1,.., βK} parameters are estimated using the classical maximization procedures implemented in the lm and glm functions knowing the fixed values of the scale parameters. In step B, the scale parameters are estimated by likelihood maximization knowing the parameters estimated in step A. The values of the scale parameters are then fixed at the new estimated values. Steps A and B are thus repeated until the relative increase in likelihood decreased below a threshold or the maximum number of repetitions is reached. Tests performed (obtained using the summary function) are similar to those given by summary.lm or summary.glm function (see R Core Team16 for details, this implies that tests are given conditionally to the estimated scale parameters.). More

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S. LaDeau, S. Earl, S. Barrott, E. Borer and S. Pennings aided in identifying errors in Crossley et al.’s online data. K. Roeder provided comments on an early draft of this manuscript. J. Taylor aided in identifying changes in Konza watershed names. We thank all LTER information managers and principal investigators who help keep online metadata updated. We thank P. Montz, J. Haarstad, A. Kuhl, M. Ayres, R. Holmes and the numerous others who did the hard work to generate these long-term datasets. NSF DEB-1556280 to M.K. and Konza Prairie LTER NSF DEB-1440484 supported this work. More