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Bayesian data fusion for spatial prediction of categorical variables in environmental sciences

First developed to predict continuous variables, Bayesian Maximum Entropy (BME) has become a complete framework in the context of space-time prediction since it has been extended to predict categorical variables and mixed random fields. This method proposes solutions to combine several sources of data whatever the nature of the information. However, the various attempts that were made for adapting the BME methodology to categorical variables and mixed random fields faced some limitations, as a high computational burden. The main objective of this paper is to overcome this limitation by generalizing the Bayesian Data Fusion (BDF) theoretical framework to categorical variables, which is somehow a simplification of the BME method through the convenient conditional independence hypothesis. The BDF methodology for categorical variables is first described and then applied to a practical case study: the estimation of soil drainage classes using a soil map and point observations in the sandy area of Flanders around the city of Mechelen (Belgium). The BDF approach is compared to BME along with more classical approaches, as Indicator CoKringing (ICK) and logistic regression. Estimators are compared using various indicators, namely the Percentage of Correctly Classified locations (PCC) and the Average Highest Probability (AHP). Although BDF methodology for categorical variables is somehow a simplification of BME approach, both methods lead to similar results and have strong advantages compared to ICK and logistic regression.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Uncertain or indirect “soft” data, such as geologic interpretation, driller’s logs, geophysical logs or imaging, offer potential constraints or “soft conditioning” to stochastic models of discrete categorical subsurface variables in hydrogeology such as hydrofacies. Previous bivariate geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co) kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data “hardness” parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both 1) the data declustering and spatial correlation functions in cokriging and 2) the acceptance probability for change of category in simulated quenching. The degree or sensitivity to which soft data conditions a realization as a function of hardness can be quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g., as derived from a depth-dependency function, probability map, or “prior realization”) can be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorical variables. A practical example shows how tsim-s is capable of generating a large-scale three-dimensional simulation including curvilinear features.

54 ENVIRONMENTAL SCIENCES↗

New Capabilities for Sampling Tools

This report will discuss new capabilities that have been added to the sample.py and uniform_sampler.py codes. The codes have been updated to allow for both log-uniform sampling and categorical variables. The categorical variables do not have to be numeric. The different values for a categorical variable are specified in a limits file by having spaces between them. The difference between sample.py and uniform_sampler.py is that sample.py is for generating random samples and uniform_sampler.py is for generating samples or points on a fixed grid. After sourcing a file to set the environment, execute the codes with the commands: sample.py and uniform sampler.py .

97 MATHEMATICS AND COMPUTING↗

Advanced Method Optimization with Categorical and Constrained Continuous Parameters

Traditional approaches to analytical method optimization (e.g., univariate and “guess-and-check”) can be time-consuming, costly, and often fail to identify true optima within the parameter space. Previous work defined and implemented a generalized technique for method optimization for continuous method parameters, but a knowledge gap remains for the incorporation of categorical variables into these advanced method optimization schemes. This work presents and validates a generalized optimization approach that incorporates both continuous and categorical variables while also utilizing a multivariate, multiobjective optimization scheme with Karush–Kuhn–Tucker conditions to bound the optimization space to solutions within the physical limitations of the parameter space. Method optimization from a case study using GC–MS for the analysis of 11 analytical standards with objectives to minimize peak width and maximize peak height resulted in a 3 orders of magnitude improvement in the average peak height and a 2 orders of magnitude improvement in the average peak width compared to the least optimal (but reasonable) instrumental parameters utilized in this study. This approach to optimization allows for a customizable method optimization in which users can include both continuous and categorical variables to achieve objectives specific to their analytical goals. This approach significantly reduces the labor and cost associated with traditional method development approaches and can be applied in a variety of scientific fields across a range of laboratory techniques (e.g., instrument method development, sample preparation, and extraction techniques).

Amorphous materials↗

Development of Late Toxicity and International Prostate Symptom Score Resolution After External-Beam Radiotherapy Combined With Pulsed Dose Rate Brachytherapy for Prostate Cancer

Purpose: To investigate the development of gastrointestinal (GI) toxicity, genitourinary (GU) toxicity, erectile dysfunction, and International Prostate Symptom Score (IPSS) resolution in a cohort of patients treated with external-beam radiotherapy (EBRT) followed by a brachytherapy pulsed dose rate (PDR) boost. Methods and Materials: Between 2002 and 2008, 110 patients were treated with 46-Gy EBRT followed by PDR brachytherapy (24.96-28.80 Gy). The investigated outcome variables, GI toxicity, GU toxicity, erectile dysfunction, and IPSS were prospectively scored at several time points during follow-up. Association between time (as continuous and categorical variable) and the outcome variables was assessed using generalized linear models. Results: No statistically significant association was found between time (continuous) and GI toxicity (odds ratio [OR], 0.97; 95% confidence interval [CI], 0.89-1.06), GU toxicity (OR, 0.97; 95% CI, 0.91-1.03), erectile dysfunction (OR, 1.06; 95% CI, 0.99-1.11), and IPSS (-0.11; 95% CI, -0.41-0.20). Also, no statistically significant association was found between these variables and time as a categorical variable. GU toxicity was associated with IPSS resolution (OR, 1.16; 95% CI, 1.09-1.24). Posttreatment IPSS was associated with pretreatment IPSS (0.52; 95% CI, 0.25-0.79). Conclusions: No accumulation of high-grade toxicity over time could be established for a group of patients treated with EBRT and PDR brachytherapy for prostate cancer, probably because high-grade late toxicity resolves with time. Also, differences in IPSS values among patients are smaller after treatment than before treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Feature selection and causal analysis for microbiome studies in the presence of confounding using standardization

Abstract Background Microbiome studies have uncovered associations between microbes and human, animal, and plant health outcomes. This has led to an interest in developing microbial interventions for treatment of disease and optimization of crop yields which requires identification of microbiome features that impact the outcome in the population of interest. That task is challenging because of the high dimensionality of microbiome data and the confounding that results from the complex and dynamic interactions among host, environment, and microbiome. In the presence of such confounding, variable selection and estimation procedures may have unsatisfactory performance in identifying microbial features with an effect on the outcome. Results In this manuscript, we aim to estimate population-level effects of individual microbiome features while controlling for confounding by a categorical variable. Due to the high dimensionality and confounding-induced correlation between features, we propose feature screening, selection, and estimation conditional on each stratum of the confounder followed by a standardization approach to estimation of population-level effects of individual features. Comprehensive simulation studies demonstrate the advantages of our approach in recovering relevant features. Utilizing a potential-outcomes framework, we outline assumptions required to ascribe causal, rather than associational, interpretations to the identified microbiome effects. We conducted an agricultural study of the rhizosphere microbiome of sorghum in which nitrogen fertilizer application is a confounding variable. In this study, the proposed approach identified microbial taxa that are consistent with biological understanding of potential plant-microbe interactions. Conclusions Standardization enables more accurate identification of individual microbiome features with an effect on the outcome of interest compared to other variable selection and estimation procedures when there is confounding by a categorical variable.

59 BASIC BIOLOGICAL SCIENCES↗

Multinomial logistic regression modelling of obesity and overweight among primary school students in a rural area of Negeri Sembilan

Multinomial logistic regression is widely used to model the outcomes of a polytomous response variable, a categorical dependent variable with more than two categories. The model assumes that the conditional mean of the dependent categorical variables is the logistic function of an affine combination of predictor variables. Its procedure gives a number of logistic regression models that make specific comparisons of the response categories. When there are q categories of the response variable, the model consists of q-1 logit equations which are fitted simultaneously. The model is validated by variable selection procedures, tests of regression coefficients, a significant test of the overall model, goodness-of-fit measures, and validation of predicted probabilities using odds ratio. This study used the multinomial logistic regression model to investigate obesity and overweight among primary school students in a rural area on the basis of their demographic profiles, lifestyles and on the diet and food intake. The results indicated that obesity and overweight of students are related to gender, religion, sleep duration, time spent on electronic games, breakfast intake in a week, with whom meals are taken, protein intake, and also, the interaction between breakfast intake in a week with sleep duration, and the interaction between gender and protein intake.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization

Herein this article presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture’s integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.

97 MATHEMATICS AND COMPUTING↗

Spontaneous Intramuscular Hematomas of the Abdomen and Pelvis: A New Multilevel Algorithm to Direct Transarterial Embolization and Patient Management

PurposeTo report our experience using a multilevel patient management algorithm to direct transarterial embolization (TAE) in managing spontaneous intramuscular hematoma (SIMH).Materials and MethodsFrom May 2006 to January 2014, twenty-seven patients with SIMH had been referred for TAE to our Radiology department. Clinical status and coagulation characteristics of the patients are analyzed. An algorithm integrating CT findings is suggested to manage SIMH. Patients were classified into three groups: Type I, SIMH with no active bleeding (AB); Type II, SIMH with AB and no muscular fascia rupture (MFR); and Type III, SIMH with MFR and AB. Type II is furthermore subcategorized as IIa, IIb and IIc. Types IIb, IIc and III were considered for TAE. The method of embolization as well as the material been used are described. Continuous variables are presented as mean ± SD. Categorical variables are reported as percentages. Technical success, clinical success, complications and 30-day mortality (d30 M) were analyzed.ResultsTwo patients (7.5%) had Type IIb, four (15%) Type IIc and 21 (77.5%) presented Type III. The detailed CT and CTA findings, embolization procedure and materials used are described. Technical success was 96% with a complication rate of 4%. Clinical success was 88%. The bleeding-related thirty-day mortality was 15% (all with Type III).ConclusionTAE is a safe and efficient technique to control bleeding that should be considered in selected SIMH as soon as possible. The proposed algorithm integrating CT features provides a comprehensive chart to select patients for TAE.Level of Evidence4.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Positron Emission Tomography for Assessing Local Failure After Stereotactic Body Radiotherapy for Non-Small-Cell Lung Cancer

Purpose: We analyzed whether positron emission tomography (PET)/computed tomography standardized uptake values (SUVs) after stereotactic body radiotherapy (SBRT) could predict local recurrence (LR) in non-small-cell lung cancer (NSCLC). Methods and Materials: This study comprised 128 patients with Stage I (n = 68) or isolated recurrent/secondary parenchymal (n = 60) NSCLC treated with image-guided SBRT to 50 Gy over 4 consecutive days; prior radiotherapy was allowed. PET/computed tomography scans were obtained before therapy and at 1 to 6 months after therapy, as well as subsequently as clinically indicated. Continuous variables were analyzed with Kruskal-Wallis tests and categorical variables with Pearson chi-square or Fisher exact tests. Actuarial local failure rates were calculated with the Kaplan-Meier method. Results: At a median follow-up of 31 months (range, 6-71 months), the actuarial 1-, 2-, and 3-year local control rates were 100%, 98.5%, and 98.5%, respectively, in the Stage I group and 95.8%, 87.6%, and 85.8%, respectively, in the recurrent group. The cumulative rates of regional nodal recurrence and distant metastasis were 8.8% (6 of 68) and 14.7% (10 of 68), respectively, for the Stage I group and 11.7% (7 of 60) and 16.7% (10 of 60), respectively, for the recurrent group. Univariate analysis showed that SUVs obtained 12.1 to 24 months after treatment for the Stage I group (p = 0.007) and 6.1 to 12 months and 12.1 to 24 months after treatment for the recurrent group were associated with LR (p < 0.001 for both). Of the 128 patients, 17 (13.3%) had ipsilateral consolidation after SBRT but no elevated metabolic activity on PET; none had LR. The cutoff maximum SUV of 5 was found to have 100% sensitivity, 91% specificity, a 50% positive predictive value, and a 100% negative predictive value for predicting LR. Conclusions: PET was helpful for distinguishing SBRT-induced consolidation from LR. SUVs obtained more than 6 months after SBRT for NSCLC were associated with local failure. A maximum SUV greater than 5, especially at more than 6 months after SBRT, should prompt biopsy to rule out LR.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Data-driven high-fidelity 2D microstructure reconstruction via non-local patch-based image inpainting

Microstructure reconstruction problems are usually limited to the representation with finitely many number of phases, e.g. binary and ternary. However, images of microstructure obtained through experimental, for example, using microscope, are often represented as a RGB or grayscale image. Because the phase-based representation is discrete, more rigid, and provides less flexibility in modeling the microstructure, as compared to RGB or grayscale image, there is a loss of information in the conversion. In this paper, a microstructure reconstruction method, which produces images at the fidelity of experimental microscopy, i.e. RGB or grayscale image, is proposed without introducing any physics-based microstructure descriptor. Furthermore, the image texture is preserved and the microstructure image is represented with continuous variables (as in RGB or grayscale images), instead of binary or categorical variables, which results in a high-fidelity image of microstructure reconstruction. The advantage of the proposed method is its quality of reconstruction, which can be applied to any other binary or multiphase 2D microstructure. The proposed method can be thought of as a subsampling approach to expand the microstructure dataset, while preserving its image texture. Moreover, the size of the reconstructed image is more flexible, compared to other machine learning microstructure reconstruction method, where the size must be fixed beforehand. In addition, the proposed method is capable of joining the microstructure images taken at different locations to reconstruct a larger microstructure image. A significant advantage of the proposed method is to remedy the data scarcity problem in materials science, where experimental data is scare and hard to obtain. The proposed method can also be applied to generate statistically equivalent microstructures, which has a strong implication in microstructure-related uncertainty quantification applications. The proposed microstructure reconstruction method is demonstrated with the UltraHigh Carbon Steel micrograph DataBase (UHCSDB).

97 MATHEMATICS AND COMPUTING↗

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

59 BASIC BIOLOGICAL SCIENCES↗

CTGAN-TVAE

SAND2026-18914O CTGAN-TVAE (Conditional Tabular Generative Adversarial Networks-Tabular Variational Autoencoders) generates extensive sets of variable generation data through a hybrid framework. It enhances latent space representation by combining TVAE's robust feature-embedding with CTGAN's ability to condition categorical variables such as time. CTGAN-TVAE employs a fully connected neural network within a conditional generative adversarial network framework to manage continuous and categorical data effectively, capturing complex feature interactions without needing sequential modeling. This was developed as part of NNSA-MSIPP: Minority Serving Institution Partnership Program, Grant Number DE-NA0004016. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Newlun, Cody [Sandia National Lab. (SNL-CA), Liver↗

Uncertainty-aware mixed-variable machine learning for materials design

Abstract Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models’ predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.

36 MATERIALS SCIENCE↗

Associations of blood lead, cadmium, and mercury with estimated glomerular filtration rate in the Korean general population: Analysis of 2008-2010 Korean National Health and Nutrition Examination Survey data

Introduction: The objective of this study was to evaluate associations between blood lead, cadmium, and mercury levels with estimated glomerular filtration rate in a general population of South Korean adults. Methods: This was a cross-sectional study based on data obtained in the Korean National Health and Nutrition Examination Survey (KNHANES) (2008-2010). The final analytical sample consisted of 5924 participants. Estimated glomerular filtration rate (eGFR) was calculated using the MDRD Study equation as an indicator of glomerular function. Results: In multiple linear regression analysis of log2-transformed blood lead as a continuous variable on eGFR, after adjusting for covariates including cadmium and mercury, the difference in eGFR levels associated with doubling of blood lead were -2.624 mL/min per 1.73 m Superscript-Two (95% CI: -3.803 to -1.445). In multiple linear regression analysis using quartiles of blood lead as the independent variable, the difference in eGFR levels comparing participants in the highest versus the lowest quartiles of blood lead was -3.835 mL/min per 1.73 m Superscript-Two (95% CI: -5.730 to -1.939). In a multiple linear regression analysis using blood cadmium and mercury, as continuous or categorical variables, as independent variables, neither metal was a significant predictor of eGFR. Odds ratios (ORs) and 95% CI values for reduced eGFR calculated for log2-transformed blood metals and quartiles of the three metals showed similar trends after adjustment for covariates. Discussion: In this large, representative sample of South Korean adults, elevated blood lead level was consistently associated with lower eGFR levels and with the prevalence of reduced eGFR even in blood lead levels below 10 {mu}g/dL. In conclusion, elevated blood lead level was associated with lower eGFR in a Korean general population, supporting the role of lead as a risk factor for chronic kidney disease.

60 APPLIED LIFE SCIENCES↗

Classifier-guided sampling for discrete variable, discontinuous design space exploration: Convergence and computational performance

A classifier-guided sampling (CGS) method is introduced for solving engineering design optimization problems with discrete and/or continuous variables and continuous and/or discontinuous responses. The method merges concepts from metamodel-guided sampling and population-based optimization algorithms. The CGS method uses a Bayesian network classifier for predicting the performance of new designs based on a set of known observations or training points. Unlike most metamodeling techniques, however, the classifier assigns a categorical class label to a new design, rather than predicting the resulting response in continuous space, and thereby accommodates nondifferentiable and discontinuous functions of discrete or categorical variables. The CGS method uses these classifiers to guide a population-based sampling process towards combinations of discrete and/or continuous variable values with a high probability of yielding preferred performance. Accordingly, the CGS method is appropriate for discrete/discontinuous design problems that are ill-suited for conventional metamodeling techniques and too computationally expensive to be solved by population-based algorithms alone. In addition, the rates of convergence and computational properties of the CGS method are investigated when applied to a set of discrete variable optimization problems. Results show that the CGS method significantly improves the rate of convergence towards known global optima, on average, when compared to genetic algorithms.

42 ENGINEERING↗

American Gut: an Open Platform for Citizen Science Microbiome Research

Although much work has linked the human microbiome to specific phenotypes and lifestyle variables, data from different projects have been challenging to integrate and the extent of microbial and molecular diversity in human stool remains unknown. Using standardized protocols from the Earth Microbiome Project and sample contributions from over 10,000 citizen-scientists, together with an open research network, we compare human microbiome specimens primarily from the United States, United Kingdom, and Australia to one another and to environmental samples. Our results show an unexpected range of beta-diversity in human stool microbiomes compared to environmental samples; demonstrate the utility of procedures for removing the effects of overgrowth during room-temperature shipping for revealing phenotype correlations; uncover new molecules and kinds of molecular communities in the human stool metabolome; and examine emergent associations among the microbiome, metabolome, and the diversity of plants that are consumed (rather than relying on reductive categorical variables such as veganism, which have little or no explanatory power). We also demonstrate the utility of the living data resource and cross-cohort comparison to confirm existing associations between the microbiome and psychiatric illness and to reveal the extent of microbiome change within one individual during surgery, providing a paradigm for open microbiome research and education. We show that a citizen science, self-selected cohort shipping samples through the mail at room temperature recaptures many known microbiome results from clinically collected cohorts and reveals new ones. Of particular interest is integrating n = 1 study data with the population data, showing that the extent of microbiome change after events such as surgery can exceed differences between distinct environmental biomes, and the effect of diverse plants in the diet, which we confirm with untargeted metabolomics on hundreds of samples.

59 BASIC BIOLOGICAL SCIENCES↗

Partitioning assimilatory nitrogen uptake in streams: an analysis of stable isotope tracer additions across continents

Headwater streams remove, transform, and store inorganic nitrogen (N) delivered from surrounding watersheds, but excessive N inputs from human activity can saturate removal capacity. Most research has focused on quantifying N removal from the water column over short periods and in individual reaches, and these ecosystem-scale measurements suggest that assimilatory N uptake accounts for most N removal. However, cross-system comparisons addressing the relative role of particular biota responsible for incorporating inorganic N into biomass are lacking. In this paper, we assess the importance of different primary uptake compartments on reach-scale ammonium (NH 4 + -N) uptake and storage across a wide range of streams varying in abundance of biota and local environmental factors. We analyzed data from 17 15 N-NH 4 + tracer addition experiments globally, and found that assimilatory N uptake by autotrophic compartments (i.e., epilithic biofilm, filamentous algae, bryophytes/macrophytes) was higher but more variable than for heterotrophic microorganisms colonizing detrital organic matter (i.e., leaves, small wood, and fine particles). Autotrophic compartments played a disproportionate role in N uptake relative to their biomass, although uptake rates were similar when we rescaled heterotrophic assimilatory N uptake associated only with live microbial biomass. Assimilatory NH 4 + -N uptake, either estimated as removal from the water column or from the sum uptake of all individual compartments, was four times higher in open- than in closed-canopy streams. Using Bayesian Model Averaging, we found that canopy cover and gross primary production (GPP) controlled autotrophic assimilatory N uptake while ecosystem respiration (ER) was more important for the heterotrophic contribution. The ratio of autotrophic to heterotrophic N storage was positively correlated with metabolism (GPP: ER), which was also higher in open- than in closed-canopy streams. Our analysis shows riparian canopy cover influences the relative abundance of different biotic uptake compartments and thus GPP:ER. As such, the simple categorical variable of canopy cover explained differences in assimilatory N uptake among streams at the reach scale, as well as the relative roles of autotrophs and heterotrophs in N storage. In conclusion, this synthesis links cumulative N uptake by stream biota to reach-scale N demand and provides a mechanistic and predictive framework for estimating and modeling N cycling in other streams.

15N↗