FLUXNET and modelling the global carbon cycle

Measurements of the net CO₂ flux between terrestrial ecosystems and the atmosphere using the eddy covariance technique have the potential to underpin our interpretation of regional CO₂ source–sink patterns, CO₂ flux responses to forcings, and predictions of the future terrestrial C balance. Information contained in FLUXNET eddy covariance data has multiple uses for the development and application of global carbon models, including evaluation/validation, calibration, process parameterization, and data assimilation. This paper reviews examples of these uses, compares global estimates of the dynamics of the global carbon cycle, and suggests ways of improving the utility of such data for global carbon modelling. Net ecosystem exchange of CO₂ (NEE) predicted by different terrestrial biosphere models compares favourably with FLUXNET observations at diurnal and seasonal timescales. However, complete model validation, particularly over the full annual cycle, requires information on the balance between assimilation and decomposition processes, information not readily available for most FLUXNET sites. Site history, when known, can greatly help constrain the model‐data comparison. Flux measurements made over four vegetation types were used to calibrate the land‐surface scheme of the Goddard Institute for Space Studies global climate model, significantly improving simulated climate and demonstrating the utility of diurnal FLUXNET data for climate modelling. Land‐surface temperatures in many regions cool due to higher canopy conductances and latent heat fluxes, and the spatial distribution of CO₂ uptake provides a significant additional constraint on the realism of simulated surface fluxes. FLUXNET data are used to calibrate a global production efficiency model (PEM). This model is forced by satellite‐measured absorbed radiation and suggests that global net primary production (NPP) increased 6.2% over 1982–1999. Good agreement is found between global trends in NPP estimated by the PEM and a dynamic global vegetation model (DGVM), and between the DGVM and estimates of global NEE derived from a global inversion of atmospheric CO₂ measurements. Combining the PEM, DGVM, and inversion results suggests that CO₂ fertilization is playing a major role in current increases in NPP, with lesser impacts from increasing N deposition and growing season length. Both the PEM and the inversion identify the Amazon basin as a key region for the current net terrestrial CO₂ uptake (i.e. 33% of global NEE), as well as its interannual variability. The inversion's global NEE estimate of −1.2 Pg [C] yr⁻¹ for 1982–1995 is compatible with the PEM‐ and DGVM‐predicted trends in NPP. There is, thus, a convergence in understanding derived from process‐based models, remote‐sensing‐based observations, and inversion of atmospheric data. Future advances in field measurement techniques, including eddy covariance (particularly concerning the problem of night‐time fluxes in dense canopies and of advection or flow distortion over complex terrain), will result in improved constraints on land‐atmosphere CO₂ fluxes and the rigorous attribution of mechanisms to the current terrestrial net CO₂ uptake and its spatial and temporal heterogeneity. Global ecosystem models play a fundamental role in linking information derived from FLUXNET measurements to atmospheric CO₂ variability. A number of recommendations concerning FLUXNET data are made, including a request for more comprehensive site data (particularly historical information), more measurements in undisturbed ecosystems, and the systematic provision of error estimates. The greatest value of current FLUXNET data for global carbon cycle modelling is in evaluating process representations, rather than in providing an unbiased estimate of net CO₂ exchange.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

Integrated statistical analysis of cDNA microarray and NIR spectroscopic data applied to a hemp dataset

Both cDNA microarray and spectroscopic data provide indirect information about the chemical compounds present in the biological tissue under consideration. In this paper simple univariate and bivariate measures are used to investigate correlations between both types of high dimensional analyses. A large dataset of 42 hemp samples on which 3456 cDNA clones and 351 NIR wavelengths have been measured, was analyzed using graphical representations. For this purpose we propose clustered correlation and clustered discrimination images. Large, tissue-related differences are seen to dominate the cDNA-NIR correlation structure but smaller, more difficult to detect, variety-related differences can be found at specific cDNA clone/NIR wavelength combinations.     

Regional electricity consumption mixes using trade data for representative inventories

The International Journal of Life Cycle Assessment - Electricity flows are frequently used life cycle assessment modeling and are often a significant source of emissions so creating inventories...     

Peptide vaccine models using statistical data mining

Design and synthesis of peptide vaccines is of significant pharmaceutical importance. A knowledge based statistical model is fitted here for prediction of binding of an antigenic site of a protein or a B-cell epitope on a CDR (complementarity determining region) of an immunoglobulin. Linear analogues of the 3D structure of the epitopes are computed using this model. Extension for prediction of peptide epitopes from the protein sequence alone is also presented. Validation results show promising potential of this approach in computer-aided peptide vaccine production. The computed probabilities of binding also provide a pioneering approach for ab-initio prediction of 'potency' of protein or peptide vaccines modeled by this method.     

On the statistical assessment of classifiers using DNA microarray data

Background

In this paper we present a method for the statistical assessment of cancer predictors which make use of gene expression profiles. The methodology is applied to a new data set of microarray gene expression data collected in Casa Sollievo della Sofferenza Hospital, Foggia – Italy. The data set is made up of normal (22) and tumor (25) specimens extracted from 25 patients affected by colon cancer. We propose to give answers to some questions which are relevant for the automatic diagnosis of cancer such as: Is the size of the available data set sufficient to build accurate classifiers? What is the statistical significance of the associated error rates? In what ways can accuracy be considered dependant on the adopted classification scheme? How many genes are correlated with the pathology and how many are sufficient for an accurate colon cancer classification? The method we propose answers these questions whilst avoiding the potential pitfalls hidden in the analysis and interpretation of microarray data.

Results

We estimate the generalization error, evaluated through the Leave-K-Out Cross Validation error, for three different classification schemes by varying the number of training examples and the number of the genes used. The statistical significance of the error rate is measured by using a permutation test. We provide a statistical analysis in terms of the frequencies of the genes involved in the classification. Using the whole set of genes, we found that the Weighted Voting Algorithm (WVA) classifier learns the distinction between normal and tumor specimens with 25 training examples, providing e = 21% (p = 0.045) as an error rate. This remains constant even when the number of examples increases. Moreover, Regularized Least Squares (RLS) and Support Vector Machines (SVM) classifiers can learn with only 15 training examples, with an error rate of e = 19% (p = 0.035) and e = 18% (p = 0.037) respectively. Moreover, the error rate decreases as the training set size increases, reaching its best performances with 35 training examples. In this case, RLS and SVM have error rates of e = 14% (p = 0.027) and e = 11% (p = 0.019). Concerning the number of genes, we found about 6000 genes (p < 0.05) correlated with the pathology, resulting from the signal-to-noise statistic. Moreover the performances of RLS and SVM classifiers do not change when 74% of genes is used. They progressively reduce up to e = 16% (p < 0.05) when only 2 genes are employed. The biological relevance of a set of genes determined by our statistical analysis and the major roles they play in colorectal tumorigenesis is discussed.

Conclusions

The method proposed provides statistically significant answers to precise questions relevant for the diagnosis and prognosis of cancer. We found that, with as few as 15 examples, it is possible to train statistically significant classifiers for colon cancer diagnosis. As for the definition of the number of genes sufficient for a reliable classification of colon cancer, our results suggest that it depends on the accuracy required.     

Multivariate statistical and other approaches for the separation of cereal from wild Poaceae pollen using a large Holocene dataset

The separation of the pollen of wild Poaceae species from that of domesticated cereal crops is of considerable importance to palynologists studying Holocene vegetational and agricultural change. Studies of the characteristics of modern pollen populations indicate that it may be possible to distinguish cereal pollen from that of many (but not all) undomesticated Poaceae species, though there are few detailed investigations into the applicability of such studies to palaeoecological samples. This paper assesses the reliability of available keys for identifying sub-fossil grass pollen using a large Holocene dataset obtained from a series of well-dated profiles from lowland Yorkshire, England. Pollen within the dataset is classified using the keys of Andersen (Danmarks Geol Undersøgelse, Arbog, 1978, 69–92, 1979) and Küster (1988), and the resulting identifications are compared. The possibilities of combining the two approaches and employing the multivariate statistical techniques of principal component and discriminant analysis to achieve greater confidence of identification are then investigated. Finally, the findings of the above analyses are used to discuss the interpretation of incidences of large Poaceae pollen (i.e. >37 m grain diameter as measured in silicone oil) within the palynological record, particularly during prehistory. The outcomes of this study will be of relevance to other investigations in which careful identification of large grass pollen is desirable, but where preservation or other factors prohibit accurate or confident identification of pollen surface pattern.     

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.     

Estimation of forest-ecosystem site index using remote-sensed data

The estimation of site index and site quality forms the fundamental theory and basic tools in forest-ecosystem management and silviculture practice. The study on the spatial pattern and temporal dynamics of site index and site quality of forest ecosystem still lacks technological advancement. It is a novel approach for estimating forest productivity in large areas using satellite remote-sensed data. The site-index spatial distribution pattern of spruce (Picea asperata) forest in Songpan-Zhengjiangguan watershed, northwestern Sichuan Province, China, was described using the remote-sensing vegetation index application and the established inverse models. The application potential of the methodology in broad regions and forests using the accuracy assessment was evaluated. The results show that the site index of the spruce forest is in linear correlation with the remote-sensed vegetation indices (normalized difference vegetation index (NDVI) and soil adjust NDVI (TNDVI)), as well as with these inverse models with high accuracy. This study demonstrated that this approach can be used in similar estimation of different forest ecosystems.     

Estimation of forest-ecosystem site index using remote-sensed data

The estimation of site index and site quality forms the fundamental theory and basic tools in forest-ecosystem management and silviculture practice. The study on the spatial pattern and temporal dynamics of site index and site quality of forest ecosystem still lacks technological advancement. It is a novel approach for estimating forest productivity in large areas using satellite remote-sensed data. The site-index spatial distribution pattern of spruce (Picea asperata) forest in Songpan-Zhengjiangguan watershed, northwestern Sichuan Province, China, was described using the remote-sensing vegetation index application and the established inverse models. The application potential of the methodology in broad regions and forests using the accuracy assessment was evaluated. The results show that the site index of the spruce forest is in linear correlation with the remote-sensed vegetation indices (normalized difference vegetation index (NDVI) and soil adjust NDVI (TNDVI)), as well as with these inverse models with high accuracy. This study demonstrated that this approach can be used in similar estimation of different forest ecosystems.     

Overdispersed fungus germination data: statistical analysis using R

ABSTRACT

Proportion data from dose-response experiments are often overdispersed, characterised by a larger variance than assumed by the standard binomial model. Here, we present different models proposed in the literature that incorporate overdispersion. We also discuss how to select the best model to describe the data and present, using R software, specific code used to fit and interpret binomial, quasi-binomial, beta-binomial, and binomial-normal models, as well as to assess goodness-of-fit. We illustrate applications of these generalized linear models and generalized linear mixed models with a case study from a biological control experiment, where different isolates of Isaria fumosorosea (Hypocreales: Cordycipitaceae) were used to assess which ones presented higher resistance to UV-B radiation. We show how to test for differences between isolates and also how to statistically group isolates presenting a similar behaviour.     

A statistical framework for eQTL mapping using RNA-seq data

RNA-seq may replace gene expression microarrays in the near future. Using RNA-seq, the expression of a gene can be estimated using the total number of sequence reads mapped to that gene, known as the total read count (TReC). Traditional expression quantitative trait locus (eQTL) mapping methods, such as linear regression, can be applied to TReC measurements after they are properly normalized. In this article, we show that eQTL mapping, by directly modeling TReC using discrete distributions, has higher statistical power than the two-step approach: data normalization followed by linear regression. In addition, RNA-seq provides information on allele-specific expression (ASE) that is not available from microarrays. By combining the information from TReC and ASE, we can computationally distinguish cis- and trans-eQTL and further improve the power of cis-eQTL mapping. Both simulation and real data studies confirm the improved power of our new methods. We also discuss the design issues of RNA-seq experiments. Specifically, we show that by combining TReC and ASE measurements, it is possible to minimize cost and retain the statistical power of cis-eQTL mapping by reducing sample size while increasing the number of sequence reads per sample. In addition to RNA-seq data, our method can also be employed to study the genetic basis of other types of sequencing data, such as chromatin immunoprecipitation followed by DNA sequencing data. In this article, we focus on eQTL mapping of a single gene using the association-based method. However, our method establishes a statistical framework for future developments of eQTL mapping methods using RNA-seq data (e.g., linkage-based eQTL mapping), and the joint study of multiple genetic markers and/or multiple genes.     

Challenges and opportunities in synthesizing historical geospatial data using statistical models

We classified land cover types from 1940s historical aerial imagery using Object Based Image Analysis (OBIA) and compared these maps with data on recent cover. Few studies have used these kinds of maps to model drivers of cover change, partly due to two statistical challenges: 1) appropriately accounting for spatial autocorrelation and 2) appropriately modeling percent cover which is bounded between 0 and 100 and not normally distributed. We studied the change in woody cover at four sites in California's North Coast using historical (1948) and recent (2009) high spatial resolution imagery. We classified the imagery using eCognition Developer and aggregated the resulting maps to the scale of a Digital Elevation Model (DEM) in order to understand topographic drivers of woody cover change. We used Generalized Additive Models (GAMs) with a quasi-binomial probability distribution to account for spatial autocorrelation and the boundedness of the percent woody cover variable. We explored the relative influences on current percent woody cover of topographic variables (grouped using principal component analysis) reflecting water retention capacity, exposure, and within-site context, as well as historical percent woody cover and geographical coordinates. We estimated these models for pixel sizes of 20, 30, 40, 50, 60, 70, 80, 90, and 100 m, reflecting both tree neighborhood scales and stand scales. We found that historical woody cover had a consistent positive effect on current woody cover, and that the spatial autoregressive term in the model was significant even after controlling for historical cover. Specific topographic variables emerged as important for different sites at different scales, but no overall pattern emerged across sites or scales for any of the topographic variables we tested. This GAM framework for modeling historical data is flexible and could be used with more variables, more flexible relationships with predictor variables, and larger scales. Modeling drivers of woody cover change from historical ecology data sources can be a valuable way to plan restoration and enhance ecological insight into landscape change.     

Predicting the onset of net carbon uptake by deciduous forests with soil temperature and climate data: a synthesis of FLUXNET data

We tested the hypothesis that the date of the onset of net carbon uptake by temperate deciduous forest canopies corresponds with the time when the mean daily soil temperature equals the mean annual air temperature. The hypothesis was tested using over 30 site-years of data from 12 field sites where CO₂ exchange is being measured continuously with the eddy covariance method. The sites spanned the geographic range of Europe, North America and Asia and spanned a climate space of 16°C in mean annual temperature. The tested phenology rule was robust and worked well over a 75 day range of the initiation of carbon uptake, starting as early as day 88 near Ione, California to as late as day 147 near Takayama, Japan. Overall, we observed that 64% of variance in the timing when net carbon uptake started was explained by the date when soil temperature matched the mean annual air temperature. We also observed a strong correlation between mean annual air temperature and the day that a deciduous forest starts to be a carbon sink. Consequently we are able to provide a simple phenological rule that can be implemented in regional carbon balance models and be assessed with soil and temperature outputs produced by climate and weather models.     

Comparison of statistical population reconstruction using full and pooled adult age-class data

Background

Age-at-harvest data are among the most commonly collected, yet neglected, demographic data gathered by wildlife agencies. Statistical population construction techniques can use this information to estimate the abundance of wild populations over wide geographic areas and concurrently estimate recruitment, harvest, and natural survival rates. Although current reconstruction techniques use full age-class data (0.5, 1.5, 2.5, 3.5, … years), it is not always possible to determine an animal''s age due to inaccuracy of the methods, expense, and logistics of sample collection. The ability to inventory wild populations would be greatly expanded if pooled adult age-class data (e.g., 0.5, 1.5, 2.5+ years) could be successfully used in statistical population reconstruction.

Methodology/Principal Findings

We investigated the performance of statistical population reconstruction models developed to analyze full age-class and pooled adult age-class data. We performed Monte Carlo simulations using a stochastic version of a Leslie matrix model, which generated data over a wide range of abundance levels, harvest rates, and natural survival probabilities, representing medium-to-big game species. Results of full age-class and pooled adult age-class population reconstructions were compared for accuracy and precision. No discernible difference in accuracy was detected, but precision was slightly reduced when using the pooled adult age-class reconstruction. On average, the coefficient of variation increased by 0.059 when the adult age-class data were pooled prior to analyses. The analyses and maximum likelihood model for pooled adult age-class reconstruction are illustrated for a black-tailed deer (Odocoileus hemionus) population in Washington State.

Conclusions/Significance

Inventorying wild populations is one of the greatest challenges of wildlife agencies. These new statistical population reconstruction models should expand the demographic capabilities of wildlife agencies that have already collected pooled adult age-class data or are seeking a cost-effective method for monitoring the status and trends of our wild resources.     

Exploration of phylogenetic data using a global sequence analysis method

Background  

Molecular phylogenetic methods are based on alignments of nucleic or peptidic sequences. The tremendous increase in molecular data permits phylogenetic analyses of very long sequences and of many species, but also requires methods to help manage large datasets.     

A global prognostic scheme of leaf onset using satellite data

Leaf phenology describes the seasonal cycle of leaf functioning. Although it is essential for understanding the interactions between the biosphere, the climate, and biogeochemical cycles, it has received little attention in the modelling community at global scale. This article focuses on the prediction of spatial patterns of the climatological onset date of leaf growth for the decade 1983–93. It examines the possibility of extrapolating existing local models of leaf onset date to the global scale. Climate is the main variable that controls leaf phenology for a given biome at this scale, and satellite observations provide a unique means to study the seasonal cycle of canopies. We combine leaf onset dates retrieved from NOAA/AVHRR satellite NDVI with climate data and the DISCover land‐cover map to identify appropriate models, and determine their new parameters at a 0.5° spatial resolution. We define two main regions: at temperate and high latitudes leaf onset models are mainly dependent on temperature; at low latitudes they are controlled by water availability. Some local leaf onset models are no longer relevant at the global scale making their calibration impossible. Nevertheless, we define our unified model by retaining the model that best reproduced the spatial distribution of leaf onset dates for each biome. The main spatial patterns of leaf onset date are well simulated, such as the Sahelian gradient due to aridity and the high latitude gradient due to frost. At temperate and high latitudes, simulated onset dates are in good agreement with climatological observations; 62% of treated grid‐cells have a simulated leaf onset date within 10 days of the satellite observed onset date (which is also the temporal resolution of the NDVI data). In tropical areas, the subgrid heterogeneity of the phenology is larger and our model's predictive power is diminished. The difficulties encountered in the tropics are due to the ambiguity of the satellite signal interpretation and the low reliability of rainfall and soil moisture fields.