Ecology

In recent years there has been an increasing concern regarding the global decline of pollinators and pollination services1,2,3. Recent studies estimate that over 87% of the flowering plant species rely on biotic pollination4. Pollination is a mutualistic interaction, and plants provide pollinators with various rewards, including nectar, oil, or excess pollen to feed upon5,6. Although bees are the most well-known pollinator group, pollination can be performed by a wide variety of species, including mammals, birds, reptiles, and other insects.Plant-pollinator interactions are among the key processes that generate and maintain biodiversity7,8. The coevolutionary processes involved in animal pollination have helped maintain the structure and function of entire communities and species’ networks. Wild plant species and natural ecosystems provide several products and services, including nutrient cycling, medicine, food, a source of pollinators for domesticated crops, and alternative food and shelter sources for agricultural pollinators9. However, the complex web of interactions and the large number of species involved (ca. 400,000 species globally) makes it challenging to estimate pollinators’ value in natural ecosystems, particularly when the life history of so many pollinator species remains little studied and understood10.Pollinators also provide highly valuable ecosystem services to crops11,12. More than 70% of the world’s crops depend directly on insect pollination, making pollination key to food security11,13. The European honeybee (Apis mellifera) is likely the most economically important pollinator of crops worldwide13,14. Honeybees are adaptable, easy to manage, and cost-efficient. However, in recent years, ‘colony collapse’ caused by several factors, including parasitic mites and the excessive use of pesticides and herbicides, have led to a decline in managed honeybee colonies in many parts of the world15,16,17. Similarly, habitat loss and fragmentation have detrimental effects on both native and commercial pollinators. In degraded habitats, pollinators struggle to find resources and nesting sites18,19,20.In Chile, pollination represents a multimillion-dollar business. Between January and October 2020, the export of Chilean fruit reached USD 4.149 million, while fresh vegetables generated USD 347 million during the same period21. Although agricultural pollinators have been well studied, native pollinators remain largely unknown. With over 460 species of native bees in Chile, approximately 70% are endemic; researchers have only begun to understand the relationships between native plants and their pollinators22,23,24. Also, managed honeybees and bumblebees introduced to Chile for crop pollination are highly invasive and easily leave croplands to forage in neighbouring native ecosystems25,26, competing directly with native pollinators for the ever-diminishing resources in native grasslands and forests posing a threat to Chile’s unique ecoregions25,27.Because of the importance of pollination in the maintenance of biodiversity and the economic benefits of agricultural crop production, there is an urgent need to understand the causes behind the current decline in pollinator species. In this sense, collating and reviewing existing information on pollinators and making this information easily accessible in the form of a user-friendly database is of immeasurable value. In this study, we compiled the information available about pollination and pollinators (sensu lato) for Chile, aiming to understand plant-pollinator interactions, identify knowledge and geographic gaps, and provide a baseline from which to carry out further studies. We aimed to make a datasheet with a format that was adaptable to different regions and other countries by allowing it to be easily understood, easy to access and find and aiming to avoid duplicity of data. This study represents the first systematic effort to compile the available information on pollination and pollinators for Chile. This pollination catalogue for Chile adds to other international efforts of systematising this information as, for example, the Catalogue of Afrotropical Bees28 and the CPC Plant Pollinators Database29. More

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Plant materialRice (Oryza sativa L.) plants used for the experiment were from the collection of Taiwan Agricultural Research Institute. The rice variety (Tainan No. 11) used in this study has enhanced resistance to rice blast. The use of plant materials complies with international, national, and/or institutional guidelines and legislation.Field areaThis study was carried out in experimental rice fields under low-external-input and conventional farming in central Taiwan (23.5859 N, 120.4083 E; 8.0 ha). The annual average temperature ranged from 23 to 25 °C, the annual average relative humidity ranged from 75 to 92%, and the annual rainfall ranged from 1020 to 2873 mm year−1 (average data between 2006 and 2016 measured at a nearby weather station; Fig. 1). The experimental paddy plots were defined by considering the typical dimensions of the agricultural fields in Taiwan (0.5 to 1.0 ha). A long-term experiment was conducted from 2006 to 2016 to study the effects of different agronomic management on biodiversity, productivity, and environment, including traceability system, soil fertility, nitrogen leaching, production costs, disease incidence and severity, the abundance of pest and beneficial insects, and weed dynamics.The treatments consisted of conventional farming with high chemical fertilizer input (CF) and low-external-input farming with low fertilizer input (LF). In the CF farming, we followed the fertilizer recommendations that are constructed to meet the nutrient requirements of the crop. In the LF farming, the chemical fertilizers were largely reduced compared to the recommendation (see next paragraph for the details). The experiment was conducted as a randomized complete block design (RCBD) with four replicates. In agricultural experiments, the RCBD is a standard procedure by grouping experimental units into blocks. For example, the design can control variation in the experiments by considering spatial influences and adjusting the effects of target factors in fields. Each experimental unit consisted of a 0.58 ± 0.16 ha of the area of the field. Additional nutrient management in the LF system includes (1) nitrogen-fixing and cover crops, (2) manure and compost applications, (3) plant and soil nutrient analyses for adjusting fertilization, and (4) reduced tillage. Soil-available potassium gradually decreased during the 10-year study period in the area of the LF system. Over the study period, the LF system achieved the similar level of crop production as that of the CF system (Fig. S1).In our study area, there were two growing seasons within a year: one in the first half of the year (from February to June) and one in the second half (from August to December). The ground fertilizers were applied before rice seedlings were transplanted, followed by additional fertilizations during the tillering and boosting stages. The total amount of fertilizers used for the CF system included 140–180 and 120–140 kg N ha−1, 70–72 and 60 kg P2O5 ha−1, and 85 and 60 kg K2O ha−1 for the first and second seasons, respectively. For the LF system, 100 and 80 kg N ha−1, 30 and 30 kg P2O5 ha−1, and 30 and 30 kg K2O ha−1 were applied in the first and second seasons, respectively. The larger amount of fertilizers for the first season was due to its longer duration. For each rice growing season, fungicides were applied to both farming systems once during the boosting stage. During the fungicide application, a 10% mixture of Cartap plus Probenazole or 6% probenazole for rice blast (both 30 kg ha−1) and 1.5% Furametpyr for sheath blight (20 kg ha−1) were used.Rice disease monitoringThe major rice disease (rice blast; Fig. S2) was monitored biweekly in the CF and LF systems over the two growing seasons per year, with each growing season including (in chronological order) the tillering, flowering, and maturing stages. There was a total of 123 occasions during our study. The plants were disease free when planted out. When the lesion of the rice blast began to appear in the fields from the tillering stage to the maturing stage, the effects of the two treatments (CF and LF systems) in the paddy fields on the disease incidence of rice blast (caused by Pyricularia oryzae) were investigated. For each plot (or experimental unit), the incidence of rice disease was randomly examined at 5 points and for 25 plexuses (i.e., each derived from one primary tiller) per point. The disease incidence was quantified as the percentage of infected plexuses that were determined based on the presence of infected leaves.The area under the disease progress curve (AUDPC) was used to quantify disease incidences over time, and the relative AUDPC ((RAUDPC)) was used because of unequal sampling duration in the growing seasons during our study period. For each plot (or experimental unit), we used the (RAUDPC) to summarize the incidences of disease during each growing season as follows:$$RAUDPC=frac{sum_{i=1}^{n-1}frac{{y}_{i}+{y}_{i+1}}{2}times left({t}_{i+1}-{t}_{i}right)}{100 times left({t}_{n}-{t}_{1}right)},$$
(1)
where ({y}_{i}) and ({t}_{i}) are the disease incidence (%) and time (day) at the (i)th observation, respectively, and (n) is the total number of observations.Bayesian modelingWe built a mechanistic model that was applied to assess the interplay within a network of relationships among weather fluctuation, farming system, and disease incidence in the paddy fields. The model describes how (1) temperature and relative humidity together influence the development of primary inoculum, (2) rainfall detaches the fungal spores on the host tissues, and (3) rainfall and wind catch the airborne spores onto the leaf area. These environmental processes determine the disease incidence in the model. In addition, this model considers that farming systems can suppress or accelerate disease incidence. By fitting our model to the observed incidence, Bayesian inference was used as the parameter estimation technique for the models. In addition, we tested the alternative mechanistic hypotheses based on a model-selection criterion and cross vaidation (see subsequent paragraphs).With a linearity assumption, the incidences of disease (RAUDPC) were modeled as an inverse-logit function of the progress rate of the development of primary inoculum ((IP) with values between 0 and 1) and the net catchment of the airborne spores by rainfall and wind ((CT) with values between 0 and 1; when subtracting the detachment of spores by rainfall from the host tissue) as follows:$$RAUDPC=invLogitleft({a}_{f}+{b}_{1}bullet logitleft(avg_IPright)+{b}_{2}bullet logitleft(avg_IPbullet avg_CTright)right),$$
(2)
where ({a}_{f}), ({b}_{1}), and ({b}_{2}) describe the constant baseline for different farming systems ((f) = the CF or LF system), the direct effect size of (avg_IP), and the mediating effect size of (avg_CT) through (IP), respectively. The two parameters ((avg_IP) and (avg_CT)) are averaged (IP) and (CT) during the growing season, respectively (see below for details). The effect sizes ({b}_{1}) and ({b}_{2}) have values more than zero. The constant baseline allows the management-specific acting in the model when they can influence the disease incidence.The process rate (IP) was simulated as a function of the temperature response ((fleft(Tright)) with values between 0 and 1) and hourly air relative humidity ((RH,) %) as follows20:$$IP= left{begin{array}{ll}0& mathrm{if}, RH 0) are the steepness and midpoint parameters to control the portion of spores caught by the wind, respectively.The Bayesian framework ‘Stan’49 and its R interface ‘RStan’50 were used to construct and fit the models. There were two competing models: either considering the difference between the CF and LF systems by not fixed to the same values of the constant baseline ({a}_{f}) in Formula (2) or not. For each model, four Markov Chain Monte Carlo (MCMC) chains (for numerical approximations of Bayesian inference) ran, each with 5,000 iterations, and the first half of the iterations of each chain were discarded as burn-in. The R-hat statistic of each parameter approaches a value of 1, indicating model convergence. With a total of 2,000 samples, collected as one sample for every 5 iterations for each chain, the model parameters and their posterior distribution were estimated. To compare the two competing models, we calculated the widely applicable information criterion (WAIC) using the R package ‘loo’51. The best model was determined based on the lowest WAIC. By using the same R package, we also performed the approximate leave-one-out cross-validation (LOO-CV) to estimate the predictive ability of the two Bayesian models. Here, we used the expected log predictive density (ELPD) to be the predictive performance.Compliance with ethical standardsThe authors declare that they have no conflict of interest. This article does not contain any studies involving animals performed by any of the authors. This article does not contain any studies involving human participants performed by any of the authors. More

Sentinel-1 data selectionThe Copernicus Sentinel-1 mission was launched by the European Space Agency (ESA) in 2014 with the Sentinel-1A satellite, complemented with the second Sentinel-1B satellite in 2016. Each satellite has a 12-days repeat cycle. Continuity of the Sentinel-1 mission has been approved by ESA until 2030 and replacement satellites will be launched. The satellites operate in different acquisition modes over different parts of the globe. Land masses are covered primarily by the Interferometric Wide-Swath Mode (IW) with a 250 km swath width across-track. Single-look-complex (SLC) Level 1.1 data are required for interferometric processing. Along-track, Sentinel-1 data are sliced into consecutive frames (slices) of about 250 km length. Data are distributed via ESA’s Scientific Sentinel-1 Hub, which is mirrored at NASA’s Alaska Satellite Facility DAAC (ASF-DAAC). During production, Sentinel-1 SLC data were accessed on the ASF-DAAC data repository which resides on Amazon’s AWS S3 bucket in region us-west-2.Sentinel-1 satellites cover various parts of Earth in ascending and descending flight direction in a total of 175 relative orbits. ESA’s flight plan has some areas covered every six days and in both flight directions, predominantly over Europe. For the production of this data set, Sentinel-1 SLC frames were selected from all available scenes acquired between December 1st 2019 and November 30th 2020. Over the one-year timeframe, a maximum of 30 to 31 acquisitions at 12-days repeat, and 60 to 61 acquisitions at 6-days repeat intervals can be expected. The following selection criteria were applied consecutively to achieve global coverage with uniform distribution of acquisitions across seasons (Fig. 1):

Global descending data (Fig. 1a) were selected where the one-year stack size had at least 25 acquisitions.

Spatial gaps were filled with ascending data (Fig. 1a) where the one-year stack size had at least 25 acquisitions.

For spatial consistency, over conterminous North America north of Panama, preference was given to ascending data where both ascending and descending data existed with stack sizes over 25 acquisitions.

For stack sizes less than 25 acquisitions, preference was given to the flight direction with the larger number of acquisitions.

Remaining gaps were filled with data from the flight direction available.

Fig. 1Flight direction, polarization mode, and InSAR stack sizes of 6- and 12-days repeat coverage of Sentinel-1 data acquired between December 1st 2019 and November 30th 2020 selected for processing.Full size imageArctic and Antarctic regions are typically covered with polarization modes of horizontal transmit (HH single- or HH/HV dual-polarization). Figure 1b shows the global distribution of the processed data in horizontal and vertical polarization transmit modes, respectively. Table 1 summarizes the number of selected scenes in the two flight directions and various polarization modes. The total number of processed Sentinel-1 SLC frames came to ~205,000 scenes with a total raw input data volume of about 850 Terabytes. Figure 1c,d show the spatial distribution of the final scene selection with the number of 6- and 12-days repeat-pass image pairs. Consistent 6-days repeat coverage with about sixty image pairs from either ascending or descending orbits could be processed over Europe, the coastal areas of Greenland and Antarctica, and some smaller areas around the world; note that in some regions (e.g., India, interior Greenland, Northern Canada, Eastern China) 6-days repeat coverage was available in certain seasons only (Fig. 1c). A consistent coverage with 12-days repeat-pass imagery, instead, could be processed almost globally with the nominal maximum of about thirty repeat-pass pairs in areas where only one satellite, Sentinel-1A or Sentinel-1B, acquired data in all but few areas above 60° N in Canada, Greenland, or Russia (Fig. 1d). In some small areas in the Midwestern United States, the Khabarovsk region in Far-Eastern Russia, or in the Northern Sahara, neither Sentinel-1A nor Sentinel-1B acquire data in IW mode, leading to small gaps in the final data set.Table 1 Number of Sentinel-1 Single Look Complex scenes processed.Full size tableProcessing approachThe overall processing workflow was developed based on the interferometric processing software developed by GAMMA Remote Sensing and geared towards efficient processing in the Amazon Web Services (AWS) cloud environment utilizing Earth Big Data LLC’s cloud scaling solutions. The workflow is divided into three main blocks as illustrated in Fig. 2. Sentinel-1A and -1B acquire data along 175 relative orbits/orbital tracks. Blocks 1 and 2 were processed on a per relative orbit basis; block 3 was initiated after blocks 1 and 2 had been completed for all relative orbits.Fig. 2Implementation of the Sentinel-1 interferometric processor in the AWS cloud environment.Full size imageProcessing Block 1For each SLC of a given relative orbit, processing block 1 entailed:

1.

Conversion of SLC image files to a GAMMA specific format. Each Sentinel-1 SLC, covering an area of ~250 × 250 km, consists of six SLC image files (one SLC image file for each of the three sub-swaths in co- (VV or HH) and cross-polarizations (VH or HV).

2.

Compensation of the SLC amplitudes for the noise equivalent sigma zero (NESZ).

3.

The orbit state vectors provided with the original Sentinel-1 SLCs were updated with the precision state vectors (AUX_POEORB) distributed by the Sentinel-1 payload data ground segment 20 days after data take with a precision (3σ) generally of the order of 1 cm (target requirement  More

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Our general strategy was to compare the performance of four approaches for inferring microbial associations from abundance data with overlying time-series signals. The approaches were (1) pairwise spearman correlation analysis (SCC) [1, 29], (2) Graphical lasso analysis (Glasso) [30, 31], (3) pairwise SCC analysis with a pre-processing step where seasonal and long-term splines were fit to and subtracted from each variable using a GAM (GAM-SCC), and (4) Glasso with the same GAM subtraction approach (GAM-Glasso). Our validation strategy for the GAM transformation consisted of generating mock datasets with underlying associations, masking those associations by adding seasonal and long-term signals to the abundance data, and comparing the predicted associations obtained from each network inference method to the true species-species associations.Data simulation: generating mock abundance data with time-series propertiesWe generated mock abundance datasets that had a predetermined, underlying network structure and contained long-term and seasonal species abundance patterns. First, a covariance matrix was generated to describe the relationships between species in a mock dataset (Fig. S1, Panel 1). The covariance matrices were constructed with underlying network structures that followed either a scale-free Barabási-Albert model, a random Erdős-Rényi model, or a model of network topology based on a real microbial dataset (American Gut dataset; Fig. S1) [32, 33]. The Erdős-Rényi and Barabási-Albert model datasets were generated so that each dataset contained 400 species and 200 samples, and the American Gut datasets were created so that each dataset contained 127 species and 200 samples. A random Bernoulli distribution was used to simulate the covariance matrix for the Erdős-Rényi networks. We set the probability of interactions occurring between species in a given Erdős-Rényi network to 1%. The Barabási-Albert networks were generated using the “sample_pa” function in the igraph package [34]. The “graph2prec” function in the SpiecEasi package was used to predict the covariance matrix of the American Gut dataset [33]. The covariance between species in a dataset was considered “high” or “low” when the true associations in the covariance matrix were set to 100 or 10 respectively (Fig. S1, Panel 1). These covariance matrices describe the “real”, underlying species interactions in our mock datasets.After generating a covariance matrix, the mean abundance for each species was generated from a normal distribution with a mean of 10 and a variance of 1. These mean abundance values and the covariance matrix were used to parameterize a multivariate normal distribution from which species abundance values for all 200 samples in a dataset were drawn (Fig. S1, Panel 2). The values generated from this multivariate normal distribution were the species abundance values without time-series features confounding the relationship between two associated species (Fig. S1, Panel 2).“Gradual” or “abrupt” seasonal trends were added to 0%, 25%, 50% or 100% of the species in each mock dataset. The gradual seasonal trend increased over 5 months, peaked at a specific month, and decreased over 5 months. Conversely, the abrupt seasonal signal increased over 2 months, peaked at a specific month, and decreased over 2 months (Fig. S1, Panel 3). These seasonal signals were generated by plugging a vector of consecutive integers of length 200 (Nt) into the gradual (Eq. (1)) or abrupt (Eq. (2)) seasonal equations (Fig. S1, Panel 3)…$$Gradual:S_t = left( {frac{{cos left( {N_t ast 2 ast frac{pi }{{12}}} right)}}{2}} right) + 0.5$$
(1)
$$Abrupt:,S_t = left( {left( {frac{{cos left( {N_t ast 2 ast frac{pi }{{12}}} right)}}{2}} right) + 0.5} right)^{10}$$
(2)
where N is the random vector of consecutive integers, S is the output seasonal vector, and t is the index of vectors N and S. The starting value of vector Nt was drawn at random for each species to allow the seasonal peaks to be centered at different months. Each element in the seasonal vector (St) was then multiplied by the corresponding element in the abundance vector (Xt) of a specific species to obtain mock species abundance values with a gradual or abrupt seasonal trend (Fig. S1, Panel 3).A long-term time-series trend was added to the abundance values of 0% or 50% of the species in the mock datasets (Fig. S1, Panel 4). When a long-term signal was applied to 50% of the species in a dataset, half of the species were randomly selected to have this long-term trend. Then, a vector of linear values was generated following Eq. (3) such that…$$Long – term,trend:,L_t = pm mleft( {L_{t – 1}} right) + 0.01$$
(3)
where Lt is the point in the line at the next time point and m is the slope of the line. The slope parameter (m) was generated from a random normal distribution with a mean of 0.01 and a variance of 0.01. The slope parameter (m) was also multiplied by −1 half of the time to ensure that half of the long-term trends increased over time and half decreased over time (Fig. S1, Panel 4). After generating the vector of linear values (Lt), each element of this vector was added to each element of the abundance vector (Xt) of a specific species to simulate long-term time-series trends (Fig. S1, Panel 4).Time-series predictor columns were added to each dataset after applying monthly and long-term abundance trends to a portion of the species in the mock datasets. The predictors that were used in the downstream GAM-based data transformation were the month of the year (i.e., 1–12) and the day of the time-series (i.e., 1–200). In total, we generated 100 mock datasets for every combination of conditions (84 combinations total; Table S1), resulting in 8400 mock time-series datasets that were used in the downstream count data transformation, GAM subtraction, and network analysis procedures.Data simulation: Simulating count data from abundance valuesThe 8400 time-series datasets that were generated using the methods described above were transformed to make the abundance values resemble high-throughput sequencing data because microbial time-series sampling efforts are often processed using such molecular methods (e.g., tag-sequencing, meta-omics). Analysis of high-throughput sequencing data is complicated by the compositional (i.e., relative) nature of the data and by the high number of zeros that may be prevalent in a dataset (i.e., zero-inflation; see Supplementary Information) [35, 36]. Relative abundances of different species in natural communities are also highly skewed, so that relatively few species constitute most of the organisms in a sample although many rare species are also present [37, 38]. Therefore, species abundances were first exponentiated to increase the prevalence of abundant species and to decrease the prevalence of rare species (Fig. S1, Panel 5). The exponentiated species abundance values were then converted to relative abundance values by dividing each species count by the sum of all species counts in a sample (Fig. S1, Panel 6). The resulting relative abundance values and time-series predictor variables were used in data normalization and GAM-transformation steps prior to carrying out the network analyses.Network inference: Count data normalization and GAM transformationSeveral steps were taken to back out the species-species relationships in the mock datasets. We advocate these steps to infer network structure from a real time-series dataset. A centered log-ratio (CLR) transformation was first applied to the species relative abundance values to normalize the mock species abundance data across samples using the “clr” function in the compositions package in R (Fig. 1) [39]. This transformation step is important to avoid spurious inferences induced by the inherent compositionality of relative abundance data [31, 33, 36]. In addition to the CLR transformation used in our main network iterations, we carried out additional network iterations using the modified CLR [40], cumulative sum scaling [41], and total sum scaling [42] transformations (see Supplementary Information). In all cases, the normalized dataset was copied, with one copy subjected to a subsequent GAM transformation, and the other one not GAM-transformed.Fig. 1: Steps used to carry out the GAM-based transformation of time-series species abundance data prior to carrying out pairwise spearman correlation (SCC) and graphical lasso (Glasso) ecological network analyses.The raw, species abundance data were first CLR-transformed (1). Generalized additive models (GAMs) were then fit to each species in the dataset (2) and the residuals of each GAM were checked for significant autocorrelation (3). The residuals of each GAM were extracted (4) and were used as input in the SCC and Glasso network analysis methods (5). Finally, the GAM-transformed network outputs were obtained (6; see text for additional details).Full size imageThe GAM transformation was carried out by fitting GAMs to each individual species in the dataset to remove monthly signals, long-term trends, and autocorrelation from the species abundance data. These GAMs were fit using the “gamm” function in the mgcv package in R [43, 44]. The GAMs that were used included the “month of year” parameter as a cyclical spline predictor and the “day of time-series” parameter as a penalized thin-plate spline predictor (“ts” in the mgcv package; Fig. 1), which given our one-dimensional data is analogous to a natural cubic spline. In addition, the first GAM included a continuous AR1 (“corCAR1” in the mgcv package) correlation structure term in the model. This corCAR1 model was revised for specific species when the GAM could not be resolved or when significant autocorrelation was detected in the GAM residuals (Fig. 1). The GAM revision step fit 4 new GAMs with different correlation structure terms (i.e., “AR1”, “CompSymm”, “Exp”, and “Gaus”) to the species that could not be fit using the corCAR1 model or that contained significant autocorrelation in the corCAR1 GAM residuals. Then, the correlation structure term that addressed these issues for the largest number of individuals was used as the GAM model for this group of species. After fitting a GAM to all of the species in the input dataset, the residuals of each GAM were extracted and were used as the new, GAM-transformed abundance values (Fig. 1). These GAM residuals represent species abundance values with a reduced influence of time (Fig. 2) and were used as input in the downstream GAM-SCC and GAM-Glasso network analyses.Fig. 2: A conceptual figure that demonstrates how the GAM transformation can remove seasonal signals while preserving ecologically relevant species co-occurrence patterns.In this example, the co-occurrence pattern between Species A and Species B persists even after the seasonal signals are removed by the GAM transformation.Full size imageNetwork inference: Network runs and statistical analysesThe pre-processed species abundance data with and without the GAM-removal of time-series signals were used in SCC and Glasso networks in order to compare the outputs of the SCC, GAM-SCC, Glasso, and GAM-Glasso network inference approaches (Fig. 1). Additional network iterations were also carried out using the CCLasso [45] and SPRING [40] network inference approaches (see Supplementary Information). For the SCC and Glasso network iterations, a nonparanormal transformation was applied to the species abundance datasets with and without the GAM transformation using the “huge.npn” function in the huge package in R [46]. Spearman correlation networks were then constructed by calculating the correlation between every pair of species in the mock abundance datasets. A Bonferroni-corrected p value of 0.01 was used as a cutoff to identify edges in these SCC networks. The Glasso networks were constructed by testing 30 regularization parameter values (i.e., lambdas) in each network using the “batch.pulsar” (criterion = “stars”; rep.num = 50) function in the pulsar package in R [47]. The lambda that resulted in the most stable network output was selected using the StARS method [48]. Finally, the graph that resulted from the StARS output was used to obtain a species adjacency matrix for the Glasso networks.The species-species associations predicted by the SCC, GAM-SCC, Glasso, and GAM-Glasso networks were compared to the true species-species associations and the F1 scores of the network predictions were calculated. The F1 score is a measure of classification performance (presence or absence of an edge) that accounts for uneven classes, which is essential when dealing with sparse networks. The F1 scores of the GAM-transformed networks were compared to the networks that did not undergo GAM transformation using paired Wilcoxon tests with Bonferroni correction. An adjusted p value of 0.01 was used as a cutoff to identify under what circumstances the GAM significantly improved the F1 score of a Glasso or SCC network.Network inference: Comparison of predicted network structuresAdditional networks were generated using the methods described above to compare the predicted network structures obtained from the GAM-Glasso, Glasso, GAM-SCC, and SCC approaches to the real network structures. These additional networks were constructed using smaller mock datasets to allow for better visualization of the network outputs and contained species with a gradual seasonal signal and high species-species covariance (see Supplementary Information). The average clustering coefficient and the degree distribution of these additional network outputs were calculated and used for the network structure comparisons. The average clustering coefficient of a network describes the likelihood that two species that are both associated with a third species are also associated with each other [49], and in a sense describes the “clumpiness” of a network. The network degree distributions describe the probability distribution of the number of interactions per node in a network [50]. More

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