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Our findings highlight the critical role of polyP in Sodalinema stali-formed cyanobacterial mats, as it was dynamically accumulated and recycled during acclimation to P fluctuations.Cellular response to progressive P starvationAnalogous to planktonic cyanobacteria, growth under low P availability could be sustained by recycling polyP, which acted as a primary P source (Fig. 2a) [16, 23, 24]. We further attribute the rapid reduction of easily dispensable cellular P-containing compounds to the substitution of cellular phospholipids with S- or N-containing membrane lipids to maintain growth at the onset of P stress (Fig. 2a) [15, 23]. However, the exhaustion of this easily dispensable P pool limited proliferation in Phase 2, and the metabolic strategy switched from a focus on growth towards maintenance (Fig. 5). The interpretation of prevailing cellular processes based on our results is graphically summarized and explained in detail below (Fig. 5).Fig. 5: Schematic interpretation of cellular phosphorus (P) cycling in a cyanobacterial mat, based on significant changes of the monitored parameters (arbitrary units).a At low P availability, initially contained polyphosphate (polyP) was recycled simultaneously with phosphate uptake to sustain growth at constant C:N:P ratios. Further proliferation at the onset of P stress in Phase 1 was sustained by mobilization of cellular P, e.g. phospholipids, which led to rapidly increasing C:N:P ratios. Severe P stress in Phase 2, indicated by increasing APase activity, prevented proliferation and photosynthesis, indicated by a loss of green chlorophyll pigments. PolyP accumulation by deficiency response occurs with severely increasing P stress, whereby globular DNA accumulation indicates the allocation of P contained in DNA into polyP. P re-addition to the P-stressed cells in Phase 3 triggered overplus uptake and narrow C:N:P ratios, transitioning to luxury uptake at higher C:N:P ratios following polyP recycling. b At high P availability, polyP in Phase 1 was accumulated by overplus uptake at narrow C:N:P ratios, transitioning to luxury uptake at higher C:N:P ratios during polyP recycling in Phase 2. P-deprivation in Phase 3 did not affect the cells, which we attributed to a sufficient amount of phosphate in the residual medium or within the biofilm matrix. Arrows indicate phosphorus transformation processes, whereby arrows pointing towards DNA represent cell growth. Yellow granules = polyP, blue granules = globular DNA spheres, P = phospholipids, S = substitute lipids.Full size imageSevere P stress in Phase 2 was indicated by the colour change from green towards yellow-green (Fig. S1) and increasing APase activity (Fig. 2a). The colour change suggested the loss of photosynthetic pigments [40], but we could not clarify whether this occurred through active cellular pigment reduction or degradation of available chlorophyll e.g., by oxidation. The increasing APase activity (Fig. 2a) suggested that Sodalinema stali is capable of hydrolysing organic P [14]. Even though APase expression did not trigger proliferation, it likely hydrolysed a potentially available organic P pool, as increasing DIC, NH4 and decreasing pH indicated progressive decay and remineralisation of organic matter (Fig. 1a). This suggests that in analogous oligotrophic environments with often fluctuating conditions, the strategy has to be maximizing the utilization of external P sources contained in organic and inorganic sediment particles that get trapped in the EPS [41]. The sediment can contain large amounts of organic P [42] and the fluctuating physico-chemical gradients in the EPS matrix due to high daytime pH and low oxygen conditions at night, facilitate P desorption from metal oxides, leading to higher dissolved phosphate concentrations within the mat, compared to the overlying water body [3]. However, alternating redox conditions at the SWI could also trigger polyP release from benthic microorganisms to the sediments, where it could act as a P source for the benthic food-chain, or ultimately trigger the formation of mineral P phases [32], to sustainably remove P from the aquatic cycle. Either way, we suggest that polyP-containing cyanobacterial mats critically impact P fluxes at the SWI.With persisting severe P stress and increasing APase activity in Phase 2, polyP accumulation as a deficiency response was observed (Fig. 2a), which has been reported from planktonic cyanobacteria of different habitats [24, 29, 23], as well as stream periphyton [28]. However, the reasons causing this deficiency response remain unresolved. In marine phytoplankton of the oligotrophic Sargasso Sea, Martin et al. [23] excluded that polyP-rich cells were in a perpetual overplus state with ‘undetectable’ pulses driving this state and suggested that polyP accumulation occurred as a cellular stress response. In other studies, reduced biosynthesis of P-rich rRNA coincided with deficiency responses [26, 28] and led to the suggestion that polyP accumulation at P concentrations below a certain threshold required for growth occurs because of P allocation changes away from growth and towards storage. Further, APase can hydrolytically cleave phosphate groups from nucleic acids and convert DNA-lipid-P to DNA-lipids, which were shown to self-assemble into globular lipid-based DNA micelles [43]. These preferentially anchor on cell membranes [44], and indeed, such DNA spheres were found to accumulate at the cell’s polar membranes in our experiments adjacent to polyP during deficiency response (Fig. 4a: Phase 2,c). Therefore, we suggest that intracellular P recovery by cleavage from P-rich DNA and reallocation to polyP, and potentially reduced rRNA synthesis [31], is also a strategy in benthic mats of Sodalinema stali as a response to severe P stress when P availability is too low to sustain growth. This supports the theory of a reallocation of resources away from growth towards flexibly available P and energy storage. Such direct intracellular P cycling could be beneficial to help retain P within the cyanobacterial population; while external P moieties such as dissolved organic P within the matrix can act as an additional P source, they are also likely to be subject to nutrient competition between cyanobacteria and other organisms inhabiting the matrix.Such effects of potential interactions in terms of nutrient competition or provision between cyanobacteria and mutualistic microorganisms contained within the same EPS matrix are difficult to assess and we cannot exclude some potential effects on our results. However, mutualistic microorganisms that are naturally contained in many cyanobacterial or algal cultures are often critical for metacommunity functioning and hence, working with axenic mat-forming strains may even further falsify any obtained results. Furthermore, microscopic analyses revealed that Sodalinema always dominated the biomass and hence, it is here considered reasonable to work with a non-axenic culture.Cellular response to a simulated P pulseIn P-deficient cells, the affinity of the P uptake system is typically increased to maximize P uptake for future pulses [13, 45]. The simulated P pulse to the P-stressed cells in Phase 3 led to a rapid increase of the cellular P content by 1260% relative to C within 3 days (Fig. 2a), whereby P was accumulated to a significant part as polyP, which is characteristic for overplus uptake [25]. Many different types of oligotrophic aquatic habitats experience only temporal P pulses, e.g., from redox changes at the benthic interface leading to P release from the sediment [32], storm run-off [28], upwelling [46], or excretions of aquatic animals [47]. The capability of microorganisms to immediately take up, store, and efficiently re-use this P by overplus uptake is hence of critical importance for a population to sustain a potential subsequent period of low P availability. Overplus uptake is typically accompanied by the overall slow growth of the population and cellular recovery from P starvation, including ultrastructural organization and recovery of the photosynthetic apparatus [48]. This took one week after re-feeding of P-starved Nostoc sp. PCC 7118 cells [48]—a timeframe very similar to the delayed onset of photosynthesis observed in our study, indicated by the elevated pH at day 9 (Fig. 1a). Regarding overplus-triggering mechanisms following P pulses, Solovochenko et al. [48] suggested that overplus uptake occurs due to a delayed down-regulation of high-affinity Pi transporters, which are active during P starvation, and emphasized the simultaneous advantage of osmotically inert polyP accumulation as a response to dramatically high phosphate concentrations in the cells. Even though APase levels declined following our experimental P re-addition, they were significantly elevated for at least 9 days (Fig. 2a). As our experimental design involved replacing the medium with APase-free, BG11 + medium after Phase 2, we assume that the APase detected in Phase 3 was actively produced, and we conclude that previously relevant, low-P response mechanisms are slowly disengaged with some sort of lag, even when ambient P is repleted. Following cellular recovery, Sodalinema now recycled stored polyP instead of further accumulating it during the transition from overplus-to luxury uptake, which was reflected in the increasing C:N:P molar ratios and decreasing polyP levels without significant additional phosphate uptake (Figs. 1a, 2a, 5).Qualitative observations on polyP distributionMost methods applied to analyse polyP in microorganisms are quantitative and do not contain information on its spatial distribution within a population. The here observed variable distribution of polyP between the cells during luxury uptake and deficiency response, as well as the retention of polyP in few individual filaments during polyP recycling in Phase 1 of the low P experiment (Fig. 4) suggests strategies of either slow growth with a retention of polyP, or of high growth with polyP recycling. This was also suggested for cells of a unicellular Synechocystis sp. PCC 6803 population during overplus uptake [47]. In contrast, polyP in our experiment was distributed homogeneously between all cyanobacterial cells during overplus uptake (Fig. 4a: Phase 3, Fig. 4b: Phase 1). Yet, we are unaware of any polyP distribution study in multicellular or mat-forming cyanobacteria and hence, further mechanisms of interactions, e.g., cell-to-cell communication [49, 50], might also contribute to purposeful differentiation of cells or filaments within a common matrix.In summary, our study shows that the mat-forming Sodalinema stali (1) is capable of luxury uptake, overplus uptake and deficiency response with a heterogenous polyP distribution during polyP recycling, luxury uptake and deficiency response, while (2) dynamically adjusting cellular P content to changing phosphate concentrations. (3) Proliferation is sustained under the expense of polyP, followed by P acquisition from other easily dispensable cellular P-containing compounds under the onset of P stress. (4) Further, biosynthetic allocation changes away from growth towards maintenance with relative polyP accumulation at the expense of P-rich DNA are conducted under severe P stress. Our findings demonstrate the extraordinary capabilities of mat-forming cyanobacteria to adapt their P acquisition strategies to strong P fluctuations. While lasting proliferation under P limitation requires the mobilization of additional P sources through regeneration of P from particulate matter, the transition to net P accumulation under excess ambient P is rapid and effective. Since current projections of climate and land use change include intensified pulses of P load to aquatic ecosystems [50], e.g., through external input from surplus of agriculture fertilizer, inefficient wastewater treatment plants, and internal loads via the mobilization of legacy P, these P ‘bioaccumulators’ could form an important component in P remediation by temporarily accumulating P within the mat, and synthesizing polyP that could ultimately stimulate the formation of mineral P phases to sustainably remove P from the aquatic cycle. More

DatasetsImage acquisitionFor this study, we assembled three datasets: one for training of the RootDetector Convolutional Neural Network (Training-Set), one for a performance comparison between humans and RootDetector in segmenting roots in minirhizotron images (Comparison-Set), and one for the validation of the algorithm (Validation-Set). The Training-Set contained 129 images comprised of 17 randomly selected minirhizotron images sampled in a mesocosm experiment (see “Mesocosm sampling” Section), 47 randomly selected minirhizotron images sampled in a field study (see “Field sampling” Section) as well as the 65 minirhizotron images of soy roots published by Wang et al.15. The Comparison-Set contained 25 randomly selected minirhizotron images from the field-study which all were not part of the images included in the Training- and Validation-Sets. The Validation-Set contained 10 randomly selected minirhizotron images from the same field study, which had not been used in the Training-Set. All images were recorded with 2550 ✕ 2273 pixels at 300 dpi with a CI-600 In-Situ Root Imager (CID Bio-Science Inc., Camas, WA, USA) and stored as .tiff files to reduce compression loss. For all training and evaluation purposes we used raw, unprocessed output images from the CI-600.Mesocosm samplingThe mesocosm experiment was established in 2018 on the premises of the Institute for Botany and Landscape Ecology of the University of Greifswald (Fig. S1). It features 108 heavy duty plastic buckets of 100 l each, filled to two thirds of their height with moderately decomposed sedge fen peat. Each mesocosm contained one minirhizotron (inner diameter: 64 mm, outer diameter: 70 mm, length: 650 mm) installed at a 45°angle and capped in order to avoid penetration by light. The mesocosms were planted with varying compositions of plant species that typically occur in north-east German sedge fens (Carex rostrata, Carex acutiformis, Glyceria maxima, Equisetum fluviatile, Juncus inflexus, Mentha aquatica, Acorus calamus and Lycopus europaeus). The mesocosms were subjected to three different water table regimes: stable at soil surface level, stable at 20 cm below soil surface and fluctuating between the two levels every two weeks. The minirhizotrons were scanned weekly at two levels of soil depth (0–20 cm and 15–35 cm) between April 2019 and December 2021, resulting in roughly 9500 minirhizotron images of 216 × 196 mm. Manual quantification of root length would, based on own experience, take approximately three hours per image, resulting in approximately 28,500 h of manual processing for the complete dataset. Specimens planted were identified by author Dr. Blume-Werry, however no voucher specimen were deposited. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation.Field samplingThe field study was established as part of the Wetscapes project in 201716. The study sites were located in Mecklenburg-Vorpommern, Germany, in three of the most common wetland types of the region: alder forest, percolation fen and coastal fen (Fig. S2). For each wetland type, a pair of drained versus rewetted study sites was established. A detailed description of the study sites and the experimental setup can be found in Jurasinski et al.16. At each site, 15 minirhizotrons (same diameter as above, length: 1500 mm) were installed at 45° angle along a central boardwalk. The minirhizotrons have been scanned biweekly since April 2018, then monthly since January 2019 at two to four levels of soil depth (0–20 cm, 20–40 cm, 40–60 cm and 60–80 cm), resulting in roughly 12,000 minirhizotron images of 216 × 196 cm, i.e. an estimated 36,000 h of manual processing for the complete dataset. Permission for the study was obtained from the all field owners. Figure 1Overview of the RootDetector system. The main component is a semantic segmentation network based on the U-Net architecture. The root length is estimated by skeletonizing the segmentation output and applying the formula introduced by Kimura et al.17. During training only, a weight map puts more emphasis on fine roots.Full size imageThe CNN RootDetectorImage annotationFor the generation of training data for the CNN, human analysts manually masked all root pixels in the 74 images of the Training-Set using GIMP 2.10.12. The resulting ground truth data are binary, black-and-white images in Portable Network Graphics (.png) format, where white pixels represent root structures and black pixels represent non-root objects and soil (Fig. 2b). All training data were checked and, if required, corrected by an expert (see “Selection of participants” for definition). The Validation-Set was created in the same way but exclusively by experts.Figure 2Example of segmentation and result of skeletonization. A 1000 by 1000 pixel input image (a), the manually annotated ground truth image (b), the RootDetector estimation image (c), the combined representation image (error map, d with green indicating true positives, red indicating false positive, blue indicating false negatives), the skeletonized RootDetector estimation image (e), and the skeletonized ground truth image (f).Full size imageArchitectureRootDetector’s core consists of a Deep Neural Network (DNN) based on the U-Net image segmentation architecture[27]nd is implemented in TensorFlow and Keras frameworks18. Although U-Net was originally developed for biomedical applications, it has since been successfully applied to other domains due to its generic design.RootDetector is built up of four down-sampling blocks, four up-sampling blocks and a final output block (Fig. 1). Every block contains two 3 × 3 convolutional layers, each followed by rectified linear units (ReLU). The last output layer instead utilizes Sigmoid activation. Starting from initial 64 feature channels, this number is doubled in every down-block and the resolution is halved via 2 × 2 max-pooling. Every up-block again doubles the resolution via bilinear interpolation and a 1 × 1 convolution which halves the number of channels. Importantly, after each up-sampling step, the feature map is concatenated with the corresponding feature map from the down-sampling path. This is crucial to preserve fine spatial details.Our modifications from the original architecture include BatchNormalization19 after each convolutional layer which significantly helps to speed up the training process and zero-padding instead of cropping as suggested by Ronneberger, Fischer, & Brox20 to preserve the original image size.In addition to the root segmentation network, we trained a second network to detect foreign objects, specifically the adhesive tape that is used as a light barrier on the aboveground part of the minirhizotrons. We used the same network architecture as above and trained in a supervised fashion with the binary cross-entropy loss. During inference, the result is thresholded (predefined threshold value: 0.5) and used without post-processing.TrainingWe pre-trained RootDetector on the COCO dataset21 to generate a starting point. Although the COCO dataset contains a wide variety of image types and classes not specifically related to minirhizotron images, Majurski et al.22 showed, that for small annotation counts, transfer-learning even from unrelated datasets may improve a CNNs performance by up to 20%. We fine-tuned for our dataset with the Adam optimizer23 for 15 epochs and trained on a total of 129 images from the Training-Set (17 mesocosm images, 47 field-experiment images, 65 soy root images). To enhance the dataset size and reduce over-fitting effects, we performed a series of augmentation operations as described by Shorten & Khoshgoftaar24. In many images, relatively coarse roots ( > 3 mm) occupied a major part of the positive (white) pixel space, which might have caused RootDetector to underestimate fine root details overall. Similarly, negative space (black pixels) between tightly packed, parallel roots was often very small and might have impacted the training process to a lesser extent when compared to large areas with few or no roots (Fig. 2). To mitigate both effects, we multiplied the result of the cross-entropy loss map with a weight map which emphasizes positive–negative transitions. This weight map is generated by applying the following formula to the annotated ground truth images:$$omega left( x right) = 1 – left( {tanh left( {2tilde{x} – 1} right)} right)^{2}$$
(1)
where ω(x) is the average pixel value of the annotated weight map in a 5 × 5 neighborhood around pixel x. Ronneberger, Fischer, & Brox20 implemented a similar weight map, however with stronger emphasis on space between objects. As this requires computation of distances between two comparatively large sets of points, we adapted and simplified their formula to be computable in a single 5 × 5 convolution.For the loss function we applied a combination of cross-entropy and Dice loss 25:$${mathcal{L}} = {mathcal{L}}_{CE} + lambda {mathcal{L}}_{Dice} = – frac{1}{N}sumnolimits_{i} {wleft( {x_{i} } right)y_{i} log left( {x_{i} } right) + lambda frac{{2sumnolimits_{i} {x_{i} y_{i} } }}{{sumnolimits_{i} {x_{i}^{2} sumnolimits_{i} {y_{i}^{2} } } }}}$$
(2)

where x are the predicted pixels, y the corresponding ground truth labels, N the number of pixels in an image and λ a balancing factor which we set to 0.01. This value was derived empirically. The Dice loss is applied per-image to counteract the usually high positive-to-negative pixel imbalance. Since this may produce overly confident outputs and restrict the application of weight maps, we used a relatively low value for λ.Output and post-processingRootDetector generates two types of output. The first type of output are greyscale .png files in which white pixels represent pixels associated with root structures and black pixels represent non-root structures and soil (Fig. 2c). The advantage of .png images is their lossless ad artifact-free compression at relatively small file sizes. RootDetector further skeletonizes the output images and reduces root-structures to single-pixel representations using the skeletonize function of scikit-image v. 0.17.1 (26; Fig. 2e,f). This helps to reduce the impact of large diameter roots or root-like structures such as rhizomes in subsequent analyses and is directly comparable to estimations of root length. The second type of output is a Comma-separated values (.csv) file, with numerical values indicating the number of identified root pixels, the number of root pixels after skeletonization, the number of orthogonal and diagonal connections between pixels after skeletonization and an estimation of the physical combined length of all roots for each processed image. The latter is a metric commonly used in root research as in many species, fine roots provide most vital functions such as nutrient and water transport3. Therefore, the combined length of all roots in a given space puts an emphasis on fine roots as they typically occupy a relatively smaller fraction of the area in a 2D image compared to often much thicker coarse roots. To derive physical length estimates from skeletonized images, RootDetector counts orthogonal- and diagonal connections between pixels of skeletonized images and employs the formula proposed by Kimura et al.17 (Eq. 3).$$L = left[ {N_{d}^{2} + left( {N_{d} + N_{o} /2} right)^{2} } right]^{{1/2}} + N_{o} /2$$
(3)
where Nd is the number of diagonally connected and No the number of orthogonally connected skeleton pixels. To compute Nd we convolve the skeletonized image with two 2 × 2 binary kernels, one for top-left-to-bottom-right connections and another for bottom-left-to-top-right connections and count the number of pixels with maximum response in the convolution result. Similarly, No is computed with a 1 × 2 and a 2 × 1 convolutional kernels.Performance comparisonSelection of participantsFor the performance comparison, we selected 10 human analysts and divided them into three groups of different expertise levels in plant physiology and with the usage of digital root measuring tools. The novice group consisted of 3 ecology students (2 bachelor’s, 1 master’s) who had taken or were taking courses in plant physiology but had no prior experience with minirhizotron images or digital root measuring tools. This group represents undergraduate students producing data for a Bachelor thesis or student assistants employed to process data. The advanced group consisted of 3 ecology students (1 bachelor’s, 2 master’s) who had already taken courses in plant physiology and had at least 100 h of experience with minirhizotron images and digital root measuring tools. The expert group consisted of 4 scientists (2 PhD, 2 PhD candidates) who had extensive experience in root science and at least 250 h of experience with digital root measuring tools. All methods were carried out in accordance with relevant institutional, national, and international guidelines and legislation and informed consent was obtained from all participants.Instruction and root tracingAll three groups were instructed by showing them a 60 min live demo of an expert tracing roots in minirhizotron images, during which commonly encountered challenges and pitfalls were thoroughly discussed. Additionally, all participants were provided with a previously generated, in-depth manual containing guidelines on the identification of root structures, the correct operation of the root tracing program and examples of often encountered challenges and suggested solutions. Before working on the Comparison-Set, all participants traced roots in one smaller-size sample image and received feedback from one expert.Image preparation and root tracingBecause the minirhizotron images acquired in the field covered a variety of different substrates, roots of different plant species, variance in image quality, and because tracing roots is very time consuming, we decided to maximize the number of images by tracing roots only in small sections, in order to cover the largest number of cases possible. To do this, we placed a box of 1000 × 1000 pixels (8.47 × 8.47 cm) at a random location in each of the images in the Comparison-Set and instructed participants to trace only roots within that box. Similarly, we provided RootDetector images where the parts of the image outside the rectangle were occluded. All groups used RootSnap! 1.3.2.25 (CID Bio-Science Inc., Camas, WA, USA;27), a vector based tool to manually trace roots in each of the 25 images in the comparison set. We decided on RootSnap! due to our previous good experience with the software and its’ relative ease of use. The combined length of all roots was then exported as a csv file for each person and image and compared to RootDetector’s output of the Kimura root length.ValidationWe tested the accuracy of RootDetector on a set of 10 image segments of 1000 by 1000 pixels cropped from random locations of the 10 images of the Validation-Set. These images were annotated by a human expert without knowledge of the estimations by the algorithm and were exempted from the training process. As commonly applied in binary classification, we use the F1 score as a metric to evaluate the performance RootDetector. F1 is calculated from precision (Eq. 4) and recall (Eq. 5) and represents their harmonic mean (Eq. 6). Ranging from 0 to 1, higher values indicate high classification (segmentation) performance. As one of the 10 image sections contained no roots and thus no F1 Score was calculable, it was excluded from the validation. We calculated the F1 score for each of the nine remaining image sections and averaged the values as a metric for overall segmentation performance.$$Precision;(P) = frac{{tp}}{{tp + fp}}$$
(4)
$$Recall;(R) = frac{{tp}}{{tp + fn}}$$
(5)
$$F1 = 2*frac{{P*R}}{{P + R}}$$
(6)
where P = precision, R = recall, tp = true positives; fp = false positives, fn = false negatives.Statistical analysisWe used R Version 4.1.2 (R Core Team, 2021) for all statistical analyses and R package ggplot2 Version 3.2.128 for visualizations. Pixel identification-performance comparisons were based on least-squares fit and the Pearson method. Root length estimation-performance comparisons between groups of human analysts (novice, advanced, expert) and RootDetector were based on the respective estimates of total root length plotted over the minirhizotron images in increasing order of total root length. Linear models were calculated using the lm function for each group of analysts. To determine significant differences between the groups and the algorithm, 95% CIs as well as 83% CIs were displayed and RootDetector root length outside the 95% CI were considered significantly different from the group estimate at α = 0.0529. The groups of human analysts were considered significantly different if their 83% CIs did not overlap, as the comparison of two 83% CIs approximates an alpha level of 5%30,31.This study is approved by Ethikkommission der Universitätsmedizin Greifswald, University of Greifswald, Germany. More

Real-world dataThe dataset consisted of 2986 observations from 902 freshwater shallow lakes in Denmark and North America (data extracted from the LAGOSNE database on 22 February 2022 via R LAGOSNE package version 2.0.2)56 (Supplementary Fig. 9). The Danish lakes were sampled for one or several years from 1984 to 2020 (data extracted in October 2021 from https://odaforalle.au.dk/main.aspx) (Supplementary Fig. 10). Prerequisites for inclusion in the analysis were that lakes had been sampled for physical and chemical variables at least four times or at least three times over the growing season (May to September) for the Danish or North American lakes, respectively, had a mean depth of less than 3 m and were freshwater. Water chemistry samples were analysed using standard methods and data for total phosphorus (TP), total nitrogen (TN) and chlorophyll-a are included here57. The mean and range of TP, TN and chlorophyll-a for the combined sites is given in Table 1, along with the values for each region separately.To gain a longer-term perspective on the relationship between nutrients and chlorophyll-a, we calculated the across-year averages of the summer means of TP, TN and chlorophyll-a, sequentially increasing numbers of years included in the mean up to a total of a five-year mean, at which point there were only 99 lakes left in the dataset. In calculating the multi-year means we allowed a maximum gap of 2 years between observations (i.e. two observations could cover 3 years) to avoid including time series with too many missing years in between. Hence, only lakes with sufficient numbers of sequential data were included, resulting in a large drop in lake numbers as the length of the multi-year mean increased (Table 2).Numerical methodsDiagnostic tests or proxies of alternative equilibriaWe modelled the response of chlorophyll-a to TP and TN using generalised-linear models58 with Gamma distribution and an identity link on untransformed data for single-year and multiple-year means up to 5-year means. We used the Gamma distribution, as chlorophyll fit this significantly better than a normal or log-normal distribution. We used psuedo R2 of the model along with the patterns of residuals, and finally, we plotted the kernel density of the chlorophyll-a values as diagnostics of the presence, absence or prevalence of alternative equilibria in the simulated and real work data.To test how appropriate these diagnostics or proxies of alternative stable states in terms of how well they identify the existence of alternative stable states in randomly sampled multi-year data, we

1.

Simulated two scenarios for the main manuscript, with and without alternative stable states in the data, which were as close to the real-life data as possible. The results of these scenarios appear in the main text (please see details below in the “Data Simulation” section).

2.

We provide multiple scenarios with different degrees, or prevalence, of alternative stable states in the data, see simulations of alternative stable state scenarios. The results of these scenarios appear in Supplementary note 2.

Hierarchical bootstrap approachThere are a large number of permutations of data, both real-world and simulated, that can provide a mean of the two to five sequential years from each lake in the time series data. It was vital to have a method that selects the data for analysis that provides a valid and comparable representation of both real work and simulated data and the models’ errors. In order to provide this we used a non-parametric hierarchical bootstrap procedure38. The flowchart shows the data preparation and data analysis steps of the hierarchical bootstrap procedure (Fig. 4). In the first step (step 1 in Fig. 4), all possible longer-term means are calculated for each lake. To keep as much data as possible, we decided to allow for up to 2 years of gap in the data between years. Taking the 5-year mean data as an example, if data from a lake existed for the years 1991 and 1994−1997, a 5-year mean would be calculated for the years 1991, 1994, 1995, 1996 and 1997. However, if the time series would contain a larger gap, e.g. data would only exist for the years 1991 and 1995–1998, no 5-year mean could be calculated. After the selection procedure, all the 2-year, 3-year and 5-year means are transferred into a new table (step 2 in Fig. 4).Fig. 4Data preparation and analysis steps of the hierarchical bootstrap procedure.Full size imageThe procedure is the same for each temporal scale from 2-year means to 5-year means. For the example of 5 mean years, lakes are randomly sampled from the full 5-year mean dataset in step 2 (Fig. 4) with replacement up to the number of lakes as in the original dataset, for the 5-year means 99 (step 3a). Here, the same lake can appear multiple times or not at all. This step is common for every bootstrap procedure59. However, since we have nested data (5-year means within lakes), we need a second step, in which for every resampled lake in step 3a, one 5-year mean is chosen (step 3b in Fig. 4). Then the three GLM models are produced from the randomly selected data in step 3c (Fig. 4). These steps are then repeated 1000 times to get a good representation of the uncertainties of the model. To ensure a fair comparison between single-year data and their equivalent multi-year mean data, we repeated the bootstrap procedure with single years only using only the lakes for which we also calculated multi-year means. To take the five-year mean as an example, there were 99 lakes where we could calculate at least one 5-year mean observation. First, we ran the bootstrap procedure to calculate 5-year mean values of TP, TN and chlorophyll-a (1000 times) and then took single years’ values of TP, TN and chlorophyll-a (1000 times) from exactly the same 99 lakes. With this approach, exactly the same datasets with the same lakes and observations within lakes are used for the calculation of the multi-year means and their single-year counterparts, making for a robust analysis. The GLM models did not always converge. If either the TP, TN or TP*TN model with interaction did not converge, the iteration was not used in further analysis. The number of converging models equal for each iteration of random samples is given in the results.The described hierarchical approach is the best way to reflect the structure of the original data. A simple, non-hierarchical bootstrap would favour lakes with more five-year means over lakes with fewer five-year means, simply because these make up a larger part of the data. Furthermore, sampling without replacement at the lake level would result in five-year means from lakes with few data dominating the produced random dataset, as every lake would be sampled every time, which then would result in high model leverage of 5-year means from lakes with less data. In contrast, the hierarchical procedure ensures that every lake has the same chance to end up in the randomly sampled bootstrap, in the second step, it ensures that of each sampled lake, every 5-year mean has the same chance to end up in the random dataset. These notions are in agreement with the findings of an assessment on how to properly resample hierarchical data by non-parametric bootstrap38.Data simulationGeneral approach of simulation assumptions and proceduresWe generated random scatter for the generalised-linear model based on Gamma distributions for two different “populations” of lakes with two different intercepts and slopes. At first, we calculated the linear equations for the two populations:For each population i and j, 99 samples (equalling the number of lakes in real-life data with 5-year means, nlake) were generated with a specific number of data points depending on the scenario (nyear) each, hence nlake = 1−99 for each population of lakes, e.g. with 20 years (nyear = 20) each.We found the real nutrient data to be normally distributed, with total nitrogen (TN) having a range between 0.33 and 4.93 mg/L and a constant coefficient of variation (CV, with a mean CV of 0.35) across this range (the same is true for total phosphorus (TP) at a shorter range). Hence, for each nlake, the x for the nyear = 20 were generated based on the mean range (mean per lake of the real-life data) and CV (0.35) from the real-life TN concentration data, hence with a range of 0.33 to 4.33 mg/L. Therefore the values and random variability of x in the simulations are close to the true values of the TN concentrations. The x is then fed into the linear equations above.To the resulting yi and yj we added random noise based on the Gamma distribution (using the rgamma function in R). We used a Gamma distribution because the Chlorophyll-a concentration also follows a Gamma distribution. The variability of a Gamma distribution is expressed by the shape variable. The variability of chlorophyll-a, its shape value, equals 2.63. This shape value was used in the Gamma distribution of yi and yj. The final calculated yi and yj had therefore a random rate calculated as shape/yi or shape/yj. Hence, their variability in the y dimension was close to the true chlorophyll-a variability.The data from both lake populations were then pooled and randomly sampled using the same hierarchical bootstrap procedure with 500 iterations for the scenarios in the supplementary materials and with 1000 iterations for main text simulation scenarios, which is identical to what was done for the real-world data.Simulation scenarios based on characteristics of real-world dataThe real-world 5-year mean data consisted of 99 lakes with 5–20 years of data for each lake. For the simulation scenario in the main text, we therefore randomly sampled between 5 and 20 data points for each of the 99 simulated lakes based on the x distribution described above. Intercepts and slopes of the simulation, resembled the range of the true data (see scatter plots in Fig. 2 of the main manuscript).In the alternative stable state scenario, we chose two slopes and intercepts for different populations of lakes:

Population i: ai = 0, bi = 40

Population j: aj = 50, bj = 120

We based the slopes and intercepts of the ASS scenarios on the diagnostic combination defined by Scheffer and Carpenter7 which propose an abrupt shift in (a) the time series, (b) the multimodal distribution of states and (c) the dual relationship to a controlling factor. Here, the idea is that an ecosystem will jump from one state to the next at the same (nutrient) conditions (different intercept and/or slope, condition a within ref. 7), where any change in the nutrient will have different effects on algae or macrophytes (best represented by different slope, condition c), resulting in a multimodal distribution of the response (condition b). Hence, simulations are in line with what is predicted for ASS, but we took great lengths to also show other possibilities with the simulations in the Supplementary information to ensure we did not overlook any occasional occurrence of alternative equilibria.Here, the appearance of alternative stable states in the data could happen at any point in the time series of a single lake, or the entire time series could include only one of the two alternative stable states. To accommodate these alternative stable state constellations (for each of which we made a separate simulation scenario, (see Supplementary Note 2, “Simulations of alternative stable state constellations”), we forced the alternative stable state scenario to be constructed of 1/3 of data with one state, 1/3 of data with the second state and 1/3 of data where both alternative states could occur. In the latter case, the alternative stable state appeared after the first 20% but before the last 20% of the time series. Since the variability and range of x (nutrient) and y (chlorophyll -a response) is simulated as close as possible to the real-world data in all scenarios, the measures taken here (variable time series and combination of different alternative stable state scenario constellations) produce a simulation as close to the real-world data as possible. Specifically, we found the real-world nutrient data to be normally distributed, with total nitrogen (TN) having a range between 0.33 and 4.93 mg/L and a constant coefficient of variation (CV, with a mean CV of 0.35) across this range (the same is true for total phosphorus (TP) at a shorter range). Hence, for each simulated lake, the x were generated based on this mean range and CV. Furthermore, the resulting yi and yj were randomised by using a Gamma distribution (using the rgamma function in R). We used a Gamma distribution because the chlorophyll-a concentration also follows a Gamma distribution. The variability of a Gamma distribution is expressed by the shape variable. The variability of chlorophyll-a, its shape value, equals 2.63. This shape value was used in the Gamma distribution of yi and y. The final calculated yi and yj had, therefore a random rate calculated as shape/yi or shape/y. Hence, their variability in the y dimension was close to the true chlorophyll-a variability.For the scenario without alternative stable states, both populations of data had the same intercept and slope:

Population i: ai = 0, bi = 40

Population j: aj = 0, bj = 40.

Please see Supplementary Note 2 for further simulations of different potential constellations of alternative states. There we show that our approach finds alternative stable states in response to nutrient concentration, even if they appear in time series from different lakes.Assessment of diagnostic tests or proxies of alternative equilibriaWe modelled the response of chlorophyll-a to TP and TN using generalised-linear models3 with Gamma distribution and an identity link on untransformed data for single-year and multiple-year means up to 5-year means. We used the Gamma distribution, as chlorophyll fit this significantly better than a normal or log-normal distribution. We used R2 of the model along with the patterns of residuals, and finally, we plotted the kernel density of the chlorophyll-a values as diagnostics of the presence, absence or prevalence of alternative equilibria in the simulated and real work data.The comparison of how the diagnostics/proxies of alternative stable states respond to the variation in the prevalence of alternative equilibria in the simulated datasets provides a robust assessment of their ability to identify both the presence and absence of alternative equilibria. It is the response of these diagnostic tests over time, with the increase in the temporal perspective as more years are added to the mean values of TP, TN and chlorophyll-a, that are key to the identification of the presence and or absence of alternative equilibria in a given dataset. The simulations show that a dataset which contains alternative equilibria will show (1) no improvement in R2 as the temporal perspective of the data increases (more years in the multi-year mean); (2) an increased bimodality in the residuals of the models of nutrients predicting chlorophyll-a will increase as more years are added to the multi-year mean and (3) the kernel density function of chlorophyll-a will display increasingly bimodality as more years are added to the mean. In the absence of alternative equilibria, the patterns differ with an R2, and increase in unimodality of residuals and a consistent unimodal pattern in the kernel density function. Thus, the diagnostic tests provide a robust test of both the presence and absence of alternative equilibria in a given dataset.Alternative stable state assessment for real data with limited data rangeIt could be the case that alternative stable states do not appear in the full dataset but only in a limited TN and TP concentration range. We filtered and re-analyzed the data, only keeping data points within the following two ranges: – TN concentration = 0.5−2 mg/L–TP concentration = 0.05−0.4 mg/L. In the filtered data, 1329 out of the original 2876 single-year data points, 289 out of 1028 3-year mean data points and 212 out of the 864 five-mean year data points remained. The filtered data consisted of data points from 550, 48 and 27 lakes for the single-year data, 3-year means and 5-year means, respectively. The smaller range resulted in lower R² of the models, yet the pattern that multi-year means result in higher R² compared to single-year data was largely consistent, apart from the 5-year mean TN models for which both, the single-year and mean data resulted in very low R² (Supplementary Fig. 6). Furthermore, due to the lower number of samples, the errors of all proxies are higher, making conclusions more difficult than for the full data. Still, we do not see any clear indication of alternative stable states in the scatter plots (two groups of dots are not appearing (Supplementary Fig. 5), the Kernel density plots (or model residuals (Supplementary Fig. 6)). i.e. no signs of bimodality in residuals or Kernel density plots. Please see details on this analysis in the supplementary material.Details and the R code for the steps for the random multi-year sampling can be found in the supplementary materials.Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More

There is a growing impetus to leverage our fundamental understanding of microbial community assembly towards applied problems. With microbes contributing to diverse physiological, biogeochemical, and agricultural processes, the potential to control and optimise microbial communities holds promise for interventions ranging from industrial and environmental remediation to human medicine and biofuel production [1, 2]. Realising this goal is contingent on high fidelity between theory, experiments, and the natural dynamics of target systems.Theoretical and experimental research in microbial community optimisation has largely proceeded along two parallel paths. Theoretical approaches leverage mathematical models and metabolic networks to predict which species combinations are stable and how they can optimise a given function (e.g., maximum biomass, waste degradation or host health) [3,4,5,6,7]. Experimental studies often take a combinatorial approach, iteratively assembling different species combinations in vitro and evaluating their stability and functional attributes [8,9,10,11]. Both theory and experiments are valuable but they are also susceptible to their own modus operandi that may limit their correspondence and their translation to real-world systems. On the one hand, theoretical approaches typically adopt the analytical tractability of steady state dynamics, where microbial consumers and the resources on which they depend are assumed to establish a stable equilibrium. On the other hand, experimental approaches almost exclusively embrace the high-throughput efficiency of serial-batch culture, where consumers and resources are made to fluctuate over several orders of magnitude with each serial passage. This raises an important question: should we expect unity in the composition of optimised communities emerging under continuous resource supply (e.g., chemostat) versus the discrete pulsed resource supply of, for example, serial-batch culture?To explore how microbial community composition varies under contrasting resource supply dynamics, we performed simulations of a classical resource-competition model:$$frac{{dN_i}}{{dt}} = N_ileft( {mathop {sum}limits_{j = 1}^n {mu _{ij}left( {R_j} right) – m} } right)$$
(1)
$$frac{{dR_j}}{{dt}} = {Psi}_jleft( {R_j} right) – mathop {sum }limits_{i = 1}^n Q_{ij}mu _{ij}left( {R_j} right)N_i,$$
(2)
where Ni is the population density of consumer i, Rj is the concentration of resource j, μij(Rj) is the per capita functional response of consumer i, m is the per capita mortality rate due to dilution, Ψj(Rj) is the resource supply function, and Qij is the resource quota of consumer i on resource j (amount of resource per unit consumer). The consumer functional response is given by the Monod function, (mu _{ij}(R_j) = mu _{max_{ij}}frac{{R_j}}{{K_{s_{ij}} + R_j}}) , where (mu _{max_{ij}}) is the maximum growth rate and (K_{s_{ij}}) is the half saturation constant for consumer i on resource j.To set up the simulations, we randomly sampled the parameters of the Monod growth functions, (μmax and Ks) for five species competing for five substitutable resources (essential resources are treated separately in the supplementary information, with similar findings). In one set of parametrisations (n = 100 unique competitor combinations) we used both random μmax and Ks, and in another set (n = 100) we imposed a trade-off in maximum growth rate and substrate affinity (( {frac{{mu _{max}}}{{K_s}}} )) (Fig. 1a). The rationale for imposing a trade-off is that metabolic theory predicts that organisms that invest energy into a high maximum growth rate will have lower substrate affinities and vice versa [12, 13]. To ensure reasonable growth rates relative to the time-scale of resource pulsing, we sampled μmax such that minimum doubling times spanned from 21 to 52 min (when all resources are non-limiting). For each of the random competitor combinations, we simulated resources under continuous or pulsed resource supply with resource replenishment every 1/2, 1, 2, 4, 12, or 24 h. Under pulsed resource supply, Ψj(Rj) and m are removed from Eq. (1) and (2) and replaced by discontinuous resource pulsing and cell transfer at fixed intervals. The total resource flux (and mortality) was held constant under all frequencies of resource supply i.e., less frequent replenishment corresponds to larger resource pulses (see Supplementary Information for full model/simulation specifications).Fig. 1: Quantifying compositional overlap between communities assembled under continuous vs. pulsed resource supply.a Per capita growth responses (Monod functions) from a single iteration of the model assuming a trade-off between maximum growth rate and resource affinity (colours correspond to individual consumers). b Time series of consumers in a under different resource supply regimes. Numbers above individual panels reflect pulsing intervals in hours. The amplitude of population fluctuations increases with longer intervals between pulses, with distinct phases of growth, saturation, and instantaneous mortality visible at a finer temporal resolution (Fig. S10). c Example measure of compositional overlap (Jaccard similarity index) between communities assembled under continuous resource supply (far left panel in b) vs. pulsing every two hours (centre panel in b).Full size imageAfter allowing the competitors to reach a steady state (time-averaged over 24 h under pulsed treatments), we quantified the correspondence between the continuous supply treatment and the pulsed treatments using the Jaccard similarity index, (Jleft( {A,B} right) = frac{{left| {A cap B} right|}}{{left| {A cup B} right|}}) (0 ≤ J(A,B) ≤ 1), where the numerator gives the number of species (max = 5) that persist under continuous (A) and pulsed (B) resource supply, and the denominator gives the number of species (max = 5) that persist under continuous or pulsed resource supply (Fig. 1b, c).Under both sets of simulations (with and without enforcing a trade-off between maximal growth rate and resource affinity), we observe that the similarity in final community composition between continuous and pulsed resource supply decays with increasingly large intervals between resource replenishment (Fig. 2a). When no trade-off is imposed between maximum growth rate and resource affinity (orange line in Fig. 2a) the mean compositional similarity is only 0.68 when resources are pulsed every 2 h and down to 0.41 when resources are pulsed every 24 h (typical of serial-batch culture). The rate of decay in the Jaccard index is more severe when a trade-off is imposed between maximum growth rate and substrate affinity, to the extent that once pulsing intervals reach four hours there is almost zero overlap in community composition (blue line in Fig. 2a).Fig. 2: Impact of resource supply regime on community composition and abundance weighted mean trait values.a Compositional overlap (Jaccard similarity) between communities under continuous versus pulsed resource supply. Orange lines, points and circles denote model parametrisations with random sampling of both μmax and Ks; blue lines, points and circles denote model parametrisations with a trade-off imposed between μmax and resource affinity (( {frac{{mu _{max}}}{{K_s}}} )). Simulation parameters provided in the Supplementary Information. b Mean trait values for affinity and μmax averaged for each consumer across the five resources and weighted by their final abundance at the end of a simulation (cont. = continuous). In both a and b, small points (jittered for clarity) give the result of an individual simulation; large circles indicate the corresponding mean.Full size imageEcological theory provides an intuitive explanation for these observations. When resources are more continuously supplied, the better competitor is the one that can sustain a positive growth rate at the lowest concentrations of a limiting resource (i.e., has a higher resource affinity or lower R* in the language of resource competition theory [14]). In contrast, under increasingly pulsed resource supply, the better competitor is the one that can grow rapidly at higher resource concentrations. Having a high resource affinity (low R*) is of little benefit if resource concentrations fluctuate over large amplitudes because it only confers an ephemeral competitive advantage in the brief period before the resource is completely depleted (ahead of the next resource pulse). Instead, a high maximum growth rate is optimal because it allows the consumer to grow rapidly and quickly deplete a shared limiting resource. This high maximum growth strategy is, however, sub-optimal under continuous resource supply because a low R* strategist can draw the resource down and hold it at a concentration at which the maximum growth strategist is unable to maintain a positive growth rate.Looking at the mean trait values for resource affinity and μmax weighted by each consumer’s final abundance, it is indeed apparent that consumers with a higher affinity (averaged across the five resources) are favoured under continuous resource supply, while consumers with high maximum growth rates are favoured under pulsing intervals of increasing length (Fig. 2b). Enforcing this trade-off, therefore, leads to the rapid decline in compositional similarity we observe under resource pulsing. Notably, it also leads to a richness peak at intermediate pulsing intervals, where these alternative strategies have a higher probability of coexisting [15] (Fig. S1). At the same time, we still observe a decline in compositional similarity when μmax and Ks are randomly sampled independently of each other simply because the trade-off between maximum growth and resource affinity will emerge occasionally by chance. Two experimental tests of microbial community composition under continuous versus pulsed resource supply are consistent with these observations [16, 17].To evaluate the sensitivity of these observations to different assumptions, we ran additional simulations under various alternative model parameterisations and formulations. In brief, comparable trends to those described above are observed when: i) maximum growth rates are faster or slower than those presented in the main text (Figs. S2, S3); ii) all resources are assumed to be essential to growth (following Liebig’s law of the minimum) (Fig. S4); iii) a weaker trade-off is imposed between maximum growth and affinity (Figs. S5, S6); or iv) mortality is continuous rather than intermittent (Figs. S7, S8). We also investigated the relationship between observed compositional overlap and the dynamical stability under continuous resource supply, anticipating that more stable communities would tend to be more resistant to compositional shifts under resource pulsing. The reality appears more nuanced, namely that weaker dynamical stability at the limit of constant resource supply is associated with higher variance in compositional overlap under continuous vs. pulsed conditions (Fig. S9). In other words, systems with weaker stability are less predictable. A wide range of other microbial traits and trade-offs may interact unpredictably with the relationship between resource supply and community composition. The potential modulating role of system instabilities generated by cross-feeding interactions, non-convex trade-off functions, and the evolution of specialist versus generalist strategies present several especially valuable lines of enquiry [18,19,20].Although these observations are germane to any consumer-resource system, our emphasis here is on the emerging field of microbial community optimisation, where the practical implications are especially timely and important; namely, the resource supply regime must be tailored to the community being optimised. For example, wastewater treatment might be more appropriately modelled under continuous resource supply [21], whereas fermented food and beverage production may be more closely allied to the pulsed resource dynamics observed in batch culture [22]. Resource supply might also be manipulated to favourably modify the competitive hierarchy in an existing community (e.g., by regulating the rate of nutrient supply to the gut through meal timing). Indeed, there is emerging evidence that feeding frequency can drive significant changes in gut microbiota composition [23, 24]. Thus, resource supply dynamics should be considered both a constraint in the design of novel microbial communities and as a tuning mechanism for the optimisation of preexisting communities like those found in the human gut. More

At December’s United Nations Convention on Biological Diversity summit (COP15), an insidious threat emerged to national parks — even as scientists argued for expanding protected areas. The World Travel & Tourism Council wants commercial tourism to be allowed to build developments in national parks globally, without obligation to help finance park conservation (see go.nature.com/3x2fsi9). This would undermine existing private tourism developments that do support conservation.
Competing Interests
The authors declare no competing interests. More

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