Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

A compositional approach to stable isotope data analysis

Isotopic data are currently becoming an important source of information regardingsources, evolution and mixing processes of water in hydrogeologic systems. However, itis not clear how to treat with statistics the geochemical data and the isotopic datatogether. We propose to introduce the isotopic information as new parts, and applycompositional data analysis with the resulting increased composition. Results areequivalent to downscale the classical isotopic delta variables, because they are alreadyrelative (as needed in the compositional framework) and isotopic variations are almostalways very small. This methodology is illustrated and tested with the study of theLlobregat River Basin (Barcelona, NE Spain), where it is shown that, though verysmall, isotopic variations comp lement geochemical principal components, and help inthe better identification of pollution sources

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts,which are difficult to use correctly in standard statistical packages. For this reason afreeware package, named CoDaPack was created. This software implements most of thebasic statistical methods suitable for compositional data.In this paper we describe the new version of the package that now is calledCoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©),Visual Basic and Open GL, and it is oriented towards users with a minimum knowledgeof computers with the aim at being simple and easy to use.This new version includes new graphical output in 2D and 3D. These outputs could bezoomed and, in 3D, rotated. Also a customization menu is included and outputs couldbe saved in jpeg format. Also this new version includes an interactive help and alldialog windows have been improved in order to facilitate its use.To use CoDaPack one has to access Excel© and introduce the data in a standardspreadsheet. These should be organized as a matrix where Excel© rows correspond tothe observations and columns to the parts. The user executes macros that returnnumerical or graphical results. There are two kinds of numerical results: new variablesand descriptive statistics, and both appear on the same sheet. Graphical output appearsin independent windows. In the present version there are 8 menus, with a total of 38submenus which, after some dialogue, directly call the corresponding macro. Thedialogues ask the user to input variables and further parameters needed, as well aswhere to put these results. The web site http://ima.udg.es/CoDaPack contains thisfreeware package and only Microsoft Excel© under Microsoft Windows© is required torun the software.Kew words: Compositional data Analysis, Software

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Compositional Time Series: An Application

The composition of the labour force is an important economic factor for a country.Often the changes in proportions of different groups are of interest.I this paper we study a monthly compositional time series from the Swedish LabourForce Survey from 1994 to 2005. Three models are studied: the ILR-transformed series,the ILR-transformation of the compositional differenced series of order 1, and the ILRtransformationof the compositional differenced series of order 12. For each of thethree models a VAR-model is fitted based on the data 1994-2003. We predict the timeseries 15 steps ahead and calculate 95 % prediction regions. The predictions of thethree models are compared with actual values using MAD and MSE and the predictionregions are compared graphically in a ternary time series plot.We conclude that the first, and simplest, model possesses the best predictive power ofthe three models

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Intragenomic variation in the second internal transcribed spacer of the ribosomal DNA of species of the genera Culex and Lutzia (Diptera: Culicidae)

Culex is the largest genus of Culicini and includes vectors of several arboviruses and filarial worms. Many species of Culex are morphologically similar, which makes their identification difficult, particularly when using female specimens. To aid evolutionary studies and species distinction, molecular techniques are often used. Sequences of the second internal transcribed spacer (ITS2) of ribosomal DNA (rDNA) from 16 species of the genus Culex and one of Lutzia were used to assess their genomic variability and to verify their applicability in the phylogenetic analysis of the group. The distance matrix (uncorrected p-distance) that was obtained revealed intragenomic and intraspecific variation. Because of the intragenomic variability, we selected ITS2 copies for use in distance analyses based on their secondary structures. Neighbour-joining topology was obtained with an uncorrected p-distance. Despite the heterogeneity observed, individuals of the same species were grouped together and correlated with the current, morphology-based classification, thereby showing that ITS2 is an appropriate marker to be used in the taxonomy of Culex.

Intra-individual variation in body temperature and pectoral muscle size in nestling Alpine swifts Apus melba in response to an episode of inclement weather

The Alpine swift (Apus melba) forages on insects caught exclusively on the wing, implying that dependent nestlings face acute food shortage in periods of cold and rainy weather. Therefore, there should be strong selection on nestling swifts to evolve physiological strategies to cope with periods of undernutrition. We have investigated intra-individual changes in nestling pectoral muscle and body temperature in response to a 1-week period of inclement weather. The pectoral muscle is the largest reserves of proteins, and nestlings have to devote a large amount of energy in the maintenance of body temperature. The results show that nestling pectoral muscle size and body temperature were significantly reduced during the episode of inclement weather. Assuming that these physiological changes are adaptive, our study suggests that nestling swifts spare energy by a pronounced reduction (up to 18 degrees C) in body temperature and use proteins from the pectoral muscle as a source of extra energy to survive prolonged periods of fasting.

Allelic variation in the VMD2 gene in best disease and age-related macular degeneration.

PURPOSE: To assess the allelic variation of the VMD2 gene in patients with Best disease and age-related macular degeneration (AMD). METHODS: Three hundred twenty-one AMD patients, 192 ethnically similar control subjects, 39 unrelated probands with familial Best disease, and 57 unrelated probands with the ophthalmoscopic findings of Best disease but no family history were screened for sequence variations in the VMD2 gene by single-strand conformation polymorphism (SSCP) analysis. Amplimers showing a bandshift were reamplified and sequenced bidirectionally. In addition, the coding regions of the VMD2 gene were completely sequenced in six probands with familial Best disease who showed no SSCP shift. RESULTS: Forty different probable or possible disease-causing mutations were found in one or more Best disease or AMD patients. Twenty-nine of these variations are novel. Of the 39 probands with familial Best disease, mutations were detected in all 39 (33 by SSCP and 6 by DNA sequencing). SSCP screening of the 57 probands with a clinical diagnosis of Best disease but no family history revealed 16 with mutations. Mutations were found in 5 of 321 AMD patients (1.5%), a fraction that was not significantly greater than in control individuals (0/192, 0%). CONCLUSIONS: Patients with the clinical diagnosis of Best disease are significantly more likely to have a mutation in the VMD2 gene if they also have a positive family history. These findings suggest that a small fraction of patients with the clinical diagnosis of AMD may actually have a late-onset variant of Best disease, whereas at the same time, a considerable fraction of isolated patients with the ophthalmoscopic features of Best disease are probably affected with some other macular disease.

Extensive natural variation for cellular hydrogen peroxide release is genetically controlled.

Natural variation in DNA sequence contributes to individual differences in quantitative traits. While multiple studies have shown genetic control over gene expression variation, few additional cellular traits have been investigated. Here, we investigated the natural variation of NADPH oxidase-dependent hydrogen peroxide (H(2)O(2) release), which is the joint effect of reactive oxygen species (ROS) production, superoxide metabolism and degradation, and is related to a number of human disorders. We assessed the normal variation of H(2)O(2) release in lymphoblastoid cell lines (LCL) in a family-based 3-generation cohort (CEPH-HapMap), and in 3 population-based cohorts (KORA, GenCord, HapMap). Substantial individual variation was observed, 45% of which were associated with heritability in the CEPH-HapMap cohort. We identified 2 genome-wide significant loci of Hsa12 and Hsa15 in genome-wide linkage analysis. Next, we performed genome-wide association study (GWAS) for the combined KORA-GenCord cohorts (n = 279) using enhanced marker resolution by imputation (>1.4 million SNPs). We found 5 significant associations (p<5.00×10-8) and 54 suggestive associations (p<1.00×10-5), one of which confirmed the linked region on Hsa15. To replicate our findings, we performed GWAS using 58 HapMap individuals and ∼2.1 million SNPs. We identified 40 genome-wide significant and 302 suggestive SNPs, and confirmed genome signals on Hsa1, Hsa12, and Hsa15. Genetic loci within 900 kb from the known candidate gene p67phox on Hsa1 were identified in GWAS in both cohorts. We did not find replication of SNPs across all cohorts, but replication within the same genomic region. Finally, a highly significant decrease in H(2)O(2) release was observed in Down Syndrome (DS) individuals (p<2.88×10-12). Taken together, our results show strong evidence of genetic control of H(2)O(2) in LCL of healthy and DS cohorts and suggest that cellular phenotypes, which themselves are also complex, may be used as proxies for dissection of complex disorders.

Genetic variability in a population of arbuscular mycorrhizal fungi causes variation in plant growth.

Different species of arbuscular mycorrhizal fungi (AMF) alter plant growth and affect plant coexistence and diversity. Effects of within-AMF species or within-population variation on plant growth have received less attention. High genetic variation exists within AMF populations. However, it is unknown whether genetic variation contributes to differences in plant growth. In our study, a population of AMF was cultivated under identical conditions for several generations prior to the experiments thus avoiding environmental maternal effects. We show that genetically different Glomus intraradices isolates from one AMF population significantly alter plant growth in an axenic system and in greenhouse experiments. Isolates increased or reduced plant growth meaning that plants potentially receive benefits or are subject to costs by forming associations with different individuals in the AMF population. This shows that genetic variability in AMF populations could affect host-plant fitness and should be considered in future research to understand these important soil organisms.