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In order to investigate the interaction of genotype × trait and relationships among agronomic traits on 12 maize hybrids, an experiment was conducted in a randomized complete block design (RCBD) with three replicates in four regions of Karaj, Birjand, Shiraz, and Arak. Results of analysis of variance indicated that most of the genotypes were significantly different in terms of agronomic traits. Mean comparison by Duncan's method showed that KSC705 genotype was more favorable than other genotypes in all studied regions. SC604 genotype in Birjand and Karaj regions and KSC707 genotype in Shiraz region have higher rank than other genotypes. Correlation analysis was used to investigate the relationships between traits. In most of the studied regions, traits of number of grains in row and number of rows per ear were positively and significantly correlated with grain width and grain weight with grain yield. Graphical analysis was used to further investigate. Genotypes–trait interaction graph explained 59.27%, 61.22%, 59.17%, and 61.95% of total variance in Karaj, Birjand, Shiraz, and Arak, respectively. Based on the multivariate graph, KSC705, KSC706, and SC647 genotypes were identified as superior genotypes in all studied regions and KSC400 genotype did not show much response to change in traits. Correlation between grain width and number of rows in ear, plant height and grain length, one thousand grain weight and grain thickness, and ear diameter with number of grains in row was positive and significant. The results of classification graph of genotypes also divided the cultivars in to three groups as follows: KSC703, KSC400, and KSC706 genotypes in the first group; DC370, SC604, and SC301 in the second group; and KSC260, KSC704, KSC707, and SC301 in the third group.

Pathological lesions of feet occur frequently in captive elephant populations. To improve foot health, it is important to identify risk factors associated with such pathologies. Several previous studies have analyzed potentially influencing factors but were limited, for example, by small sample sizes. This study analyzed the relationship between 87 independent variables and the foot health score of 204 Asian elephants (Elephas maximus) in European zoos using bivariate correlation, multivariable regression models, and principal component analysis (PCA). Correlation and regression tests revealed significant results for 30 different variables, mainly with small effect sizes. Only three variables were significant in more than one test: sex, time spent indoors, and time spent on hard ground, with lower scores (i.e. less or less severe pathological lesions) in females, and when less time is spent indoors or on hard ground. Due to small effect sizes and differing results of the statistical tests, it is difficult to determine which risk factors are most important. Instead, a holistic consideration appears more appropriate. A biplot of the PCA shows that factors representing more advanced husbandry conditions (e.g. large areas, high proportions of sand flooring) were associated with each other and with decreased foot scores, whereas indicators of more limited conditions (e.g. high proportions of hard ground, much time spent indoors) were also associated with each other but increased the foot score. In conclusion, instead of resulting from just one or two factors, reduced foot health might be an indicator of a generally poorer husbandry system.

Multienvironment trials (METs) are used to investigate the performance of crop genotypes. To efficiently generate reliable performance estimates, the magnitude and patterns of genotype × environment interaction (G×E) in MET data must be known. We quantified G×E in fall-planted common wheat (Triticum aestivum L.) in California, with the goal of increasing the reliability and efficiency of statewide variety testing activities. Linear mixed models and the genotype main effects plus G×E interaction effects (GGE) biplot method were used to analyze MET data for 211 common wheat genotypes, the MET consisted of 9 locations and 14 seasons. The representativeness and discriminating power of the MET locations were tested, and estimates of the optimum number of test locations were made. The analyses did not find evidence for significant, repeatable, crossover G×E. The genotype and G×E effects were of a similar magnitude, and the G×E effects were relatively strong compared with other sources of variance but were dominated by seasonal effects, with potentially repeatable genotype-by-location (G×L) effects being relatively weak. The GGE analyses did not detect repeatable G×L patterns across seasons. As a result, we conclude that the cereal production regions of California consist of a single, but unstable, mega-environment for common wheat grain yield. The test location evaluation found few significant differences between test locations in terms of how well they represent the target production environment. We estimate that the number of test locations could be reduced while maintaining trial accuracy, which would improve the resource use efficiency of statewide trial activities without sacrificing information about variety-specific common wheat yield performance.

Alliaria petiolata, a strict biennial in North America, can have an annual alternating high abundance of rosettes and flowering plants. We monitored changes in abundance of rosettes and flowering plants in permanent plots (2004–2014). Three times during our study, the alternating yearly cycle was not observed (2007–2008, 2008–2009, and 2013–2014). We concluded stochastic extreme climate events (ECEs), deviating from long‐term climatic data norms (10th or 90th percentile), likely caused negative organism responses. Long‐term data from a local NOAA station located 25 km from our study site included monthly data (1) total precipitation, (2) number of days with >0.13 cm precipitation, and (3) mean and minimum temperatures. September 2007 met the criteria for ECEs for all monthly variables. We first observed A. petiolata on our study site in 1988, and by the early 1990s, it was abundant. To determine whether September 2007 significantly differed from other September (1984–2014), we used six variables related to drought: (1) total precipitation, (2) number of days with precipitation, (3) number of contiguous days without precipitation, (4) mean monthly temperature, (5) mean maximum daily temperature, and (6) the number of days with temperatures >30°C. The first two variables likely increase plant stress as they decrease, whereas stress declines as the remaining variables decrease. We used the six variables to generate a principal component analysis (PCA) biplot. Axes 1 and 2 accounted for 74.3% of the variance. Record‐breaking minimum temperatures (ECEs) for January (2009) and February–March (2014) likely reduced rosette abundance and disrupted reestablishment of alternating high abundance of rosettes and flowering plants. Our data suggest that a single ECE variable, minimum temperature, and multiple ECE variables related to drought likely had negative effects on A. petiolata.

Premise Black Sigatoka is one of the most severe banana (Musa spp.) diseases worldwide, but no methods for the rapid early detection of this disease have been reported. This paper assesses the use of hyperspectral images for the development of a partial-least-squares penalized-logistic-regression (PLS-PLR) model and a hyperspectral biplot (HS biplot) as a visual tool for detecting the early stages of black Sigatoka disease. Methods Young (three-month-old) banana plants were inoculated with a conidia suspension of the black Sigatoka fungus (Pseudocercospora fijiensis). Selected infected and control plants were evaluated using a hyperspectral imaging system at wavelengths in the range of 386-1019 nm. PLS-PLR models were run on the hyperspectral data set. The prediction power was assessed using leave-one-out cross-validation as well as external validation. Results The PLS-PLR model was able to predict the presence of the disease with a 98% accuracy. The wavelengths with the highest contribution to the classification ranged from 577 to 651 nm and from 700 to 1019 nm. Discussion PLS-PLR and HS biplot effectively estimated the presence of black Sigatoka disease at the early stages and can be used to graphically represent the relationship between groups of leaves and both visible and near-infrared wavelengths.

Two-way tables of data, either observed or standardized in some way, are commonly analyzed by spectral decomposition or singular value decomposition, providing scores for both rows and columns of the two-way classification. Two of the most common examples in plant and crop research are sample × variable data (principal component analysis) and genotype × environment data, the latter either centered for environment only (genotype main effect plus genotype × environment interaction biplots) or doubly centered for both genotype and environment (genotype × environment interaction biplots based on the additive main effects and multiplicative interaction [AMMI] model). Results are often displayed by plotting the row scores, column scores, or both to visually study the structure of the data. Usually, arrows or lines are drawn from the origin to facilitate interpretation. Graphical features such as angles between arrows and distances between points, as well as graphical operations such as orthogonal projections, allow a number of useful interpretations. For the validity of such properties and operations, it is imperative that the two axes of a plot or biplot be equally scaled exactly (i.e., 1 cm on the vertical axis must represent the same number of units as 1 cm on the horizontal axis). Unfortunately, this important fact is often neglected by users when preparing such plots or integrating them into a text document for publication, rendering all of these features of a plot essentially meaningless. The purpose of the present note, therefore, is to highlight the importance of equal scaling using pertinent examples.

Principal component analysis (PCA) was carried out to study the relationship between 24 meat quality measurements taken from beef round samples that were injected with curing brines containing gum arabic (1%, 1.5%, 2%, 2.5%, and 3%) and soy protein concentrate (SPC) (3.5%) at two injection levels (30% and 35%). The measurements used to describe beef round quality were expressible moisture, moisture content, cook yield, possible injection, achieved gum arabic level in beef round, and protein content, as well as descriptive sensory attributes for flavor, texture, basic tastes, feeling factors, color, and overall acceptability. Several significant correlations were found between beef round quality parameters. The highest significant negative and positive correlations were recorded between color intensity and gray color and between color intensity and brown color, respectively. The first seven principal components (PCs) were extracted explaining over 95% of the total variance. The first PC was characterized by texture attributes (hardness and denseness), feeling factors (chemical taste and chemical burn), and two physicochemical properties (expressible moisture and achieved gum arabic level). Taste attribute (saltiness), physicochemical attributes (cook yield and possible injection), and overall acceptability were useful in defining the second PC, while the third PC was characterized by metallic taste, gray color, brown color, and physicochemical attributes (moisture and protein content). The correlation loading plot showed that the distribution of the samples on the axes of the first two PCs allowed for differentiation of samples injected to 30% injection level which were placed on the upper side of the biplot from those injected to 35% which were placed on the lower side. Similarly, beef samples extended with gum arabic and those containing SPC were also visible when scores for the first and third PCs were plotted. Thus, PCA was efficient in analyzing the quality characteristics of beef rounds extended with gum arabic.

Quinoa is a pseudocereal from South America known for its unique nutritional properties. Hundreds of varieties and experimental lines are currently either grown or in development in many countries around the world. There exists a lack of information about, and understanding of, the nutritional composition and processing characteristics of these varieties and their potential end-use applications. Twenty-eight quinoa varieties and experimental lines tested in the Washington State University breeding program were evaluated for their chemical composition and physicochemical characteristics. Both compositional and physicochemical analysis demonstrated wide variation in properties among the varieties. Analysis of flour swelling power, water absorption index, and differential scanning calorimetry further supported the differences hypothesized between varieties. Hierarchical cluster analysis grouped the varieties into four clusters. Principal component analysis was used to visually display the data on a biplot, r...

Emotions are often associated with colors, but what mediates color–emotion associations is not fully understood. This study examined associations between colors and emotions using correspondence analysis. The hypothesis that emotions are associated with colors through the correspondence between the hue circle and the circumplex model of emotion/affect was tested. Participants viewed 40 colors and reported a word that expressed an emotion that they associated with or felt in response to each color. Participants' responses were aggregated into a contingency table of colors and emotion words, and a correspondence analysis was conducted. An eight-dimensional biplot was obtained. The first and second dimensions were related to hue, and the hue configuration was similar to colors' spectral trajectory in the CIE xy space or the CIELAB a*b* color space. The configuration of emotions was not consistent with the circumplex model of emotion, which rejected the above hypothesis. The associations in dimensions 1 and 2 appeared to be mediated by the perceived temperature of colors and emotions. In dimensions 3–6, dimensions that seemed to reflect secondary associations based on cultural convention or personal experiences (such as white with emotionless and purity and blue with depression) were obtained. These results also demonstrated the usefulness of correspondence analysis for analyzing color–emotion associations due to its ability to reveal the underlying statistical structure of associations.

Free asparagine in wheat is known to be a precursor for the formation of acrylamide, which is unacceptable to consumers owing to its potential risks to human health. This research was performed to determine variation of free asparagine concentration (FAC) in hard red spring (HRS) wheat grown in North Dakota. Quality traits and FAC were analyzed for 75 HRS wheat genotypes grown at three locations. The ANOVA indicated that growing location had a strong effect on FAC. The main effect of genotype and interaction of genotype × location were also highly significant (P < 0.001). The genotype × location interaction was also explored graphically using a biplot of principal components calculated from the genotype and genotype × environment interaction model. The biplot analysis revealed that the pattern of interaction of genotype × location might be a noncrossover type. Certain HRS genotypes were identified to have consistently low FAC across growing locations. The FAC showed low genotypic correlations with quality...

Five maize inbred lines, 20 F1 diallel hybrids and two check genotypes were evaluated through genotype × environment interaction (GEI) and GGE biplot for earliness and yield traits at four locations.; Results: Genotype, environment and GEI showed highly significant differences for all the traits. In total sum of squares, environment and genotype played a primary role, followed by GEI. Larger effects of environment and genotype to total variation influence the earliness and yield traits. However, according to the GGE biplot, the first two principal components (PC1 and PC2) explained 95% of the variation caused by GEI. GGE biplot confirmed the differential response of genotypes across environments. F1 hybrid SWAJK-1 × FRHW-3 had better stability, with a good yield, and was considered an ideal genotype. F1 hybrid FRHW-2 × FRHW-1 showed more earliness at CCRI and Haripur, followed by PSEV3 × FRHW-2 and its reciprocal at Swat and Mansehra, respectively. F1 hybrids FRHW-1 × SWAJK-1, PSEV3 × SWAJK-1 and SWAJK-1 × FRHW-3 at Mansehra and Swat produced maximum grain yield, followed by SWAJK-1 × FRHW-1 and PSEV3 × FRHW-1 at Haripur and CCRI, respectively.; Conclusion: Overall, maize genotypes showed early maturity in plain areas (CCRI and Haripur) but higher yield in hilly areas (Mansehra and Swat). © 2017 Society of Chemical Industry.; © 2017 Society of Chemical Industry.

Yellow mosaic disease (YMD) is the major constraint of mungbean for realizing high productivity worldwide. Moreover, management of disease using YMD-resistant genotypes is the simplest approach. Therefore, based on a preliminary screening of 220 genotypes during the year 2010 and 2011 at 17 locations, a set of 25 genotypes was further selected to evaluate at six locations over 2 years for identification of more stable resistant genotypes. The genotype and genotype × environment (GGE) analysis indicated that the genotypes and environment effects were significant (P

Genotype by environment interaction (GE) is a reality in plant breeding and crop production, and has to be dealt with. There are but two viable options to deal with GE: to utilize it or to avoid it, depending on whether it is repeatable. Repeatable GE can be selected for (utilized) whereas unrepeatable GE has to be selected against (avoided). To utilize GE involves identifying repeatable GE, dividing the target region into subregions or megaenvironments (ME) based on the repeatable GE pattern, and selecting within ME. By definition, GE within ME is unrepeatable and has to be avoided. To avoid unrepeatable GE is to test in a sufficient number of environments (locations and years) representing the target ME and to select both high mean performance and high stability. My preferred analytic tool for identifying repeatable GE, ME analysis, representative test locations, and superior genotypes is GGE (genotypic main effect plus GE) biplots, which was demonstrated using oat (Avena sativa L.) yield data from multilocation multiyear trials. Some important issues on GE study, in relation to genotype evaluation, were discussed. These included the framework of multiyear multilocation trials, the distinction between repeatable and nonrepeatable components of GE, the need to consider both genotypic main effect (G) and GE, and the relative importance of mean performance (G) vs. stability (GE) in genotype evaluation.

In agriculture and plant breeding, multi-environment trials over multiple years are conducted to evaluate and predict genotypic performance under different environmental conditions, and to analyze, study, and interpret genotype × environment interaction (G×E). In this study, we propose a hierarchical Bayesian formulation of a linear-bilinear model, where the conditional conjugate prior for the bilinear (multiplicative) G×E interaction term is the matrix von Mises-Fisher distribution (with environments and sites defined as synonymous). A hierarchical normal structure is assumed for linear effects of genotypes and sites, and priors for precision parameters are assumed to follow gamma distributions. Bivariate Highest Posterior Density (HPD) regions for the posterior multiplicative components of the interaction are shown within the usual biplots. Simulated and real maize breeding multi-site data sets were analyzed. Results showed that the proposed model facilitates identifying groups of genotypes and sites that cause G×E across years and within years, since the hierarchical Bayesian structure allows using plant breeding data from different years by borrowing information among them. This model offers the researcher valuable information about the G×E interaction patterns not only for each one-year period of the breeding trials but also for the general process that originates the response across these periods.

The objectives of this study were to determine how U.S. consumers perceive 6 Korean traditional beverages (Bokbunja, Hongsaam, Korean date, Omija, Sansuyu and Yuja) and to find out the influence of extrinsic information (name, nutritional information, picture of raw material and stories related to each sample) on acceptability, liking and intensity appropriateness of sweetness and bitterness, and emotion when consuming novel beverages. Bokbunja, Yuja and Korean date were samples received high acceptability, had adequate intensity of sweetness and bitterness, and evoked positive emotions. When the extrinsic information of the samples was provided, acceptability of all six samples tended to increase. Percentage of consumers who perceived the intensity of sweetness and bitterness of products as “just about right” increased when evaluated the samples in the informed condition. Also principal component analysis (PCA) biplot of emotions revealed the influence of information during evaluation. When tested in the informed condition, samples evoked relatively positive emotion compare to samples tested in the blind condition. The disliked products showed the greater increase of acceptability from the blind to the informed conditions. Practical Applications There is not much research conducted to evaluate acceptability of Korean traditional beverages with foreign consumers. In our study, we used these traditional beverages, which were still novel to U.S. consumers, and measured overall acceptability, liking and intensity appropriateness of sweetness and bitterness, and emotion using EsSense Profile™. Among six beverage samples we used, three samples (Bokbunja, Yuja and Korean date) received positive scores for all measurements. Also by comparing the results of evaluations conducted in blind and informed conditions, importance of information when evaluating the samples was shown. Our work provided the basis of launching favored Korean traditional beverage products in the U.S. market and demonstrated importance of the information when introducing the novel products to consumers.

A previous paper, Biplots: Quantitative data, dealt exclusively with biplots for quantitative data. This paper is mainly concerned with qualitative data or data in the form of counts. Qualitative data can be nominal or ordinal, and it is usually reported in a coded numerical form. In the analysis of qualitative data, many methods can be grouped as quantification methods e.g., categorical principal component analysis, correspondence analysis, multiple correspondence analysis, homogeneity analysis: transforming qualities into quantitative values that may then be treated with quantitative methods. All the features of quantitative biplots are found in qualitative biplots, but calibrated interpolation axes become labeled category-level points and calibrated prediction axes become prediction regions. Interpretation remains in terms of distance, inner products, and sometimes area. WIREs Comput Stat 2016, 8:82-111. doi: 10.1002/wics.1377

High starch yield is the most important trait for commercialized cassava starch production. Furthermore, cyanide present in cassava roots poses a health challenge in the use of cassava for food. Cassava genotypes have varying maturity periods that are also environmental dependent. This study aimed at identifying suitable cultivars and optimum time of harvest to maximize starch production across three environments. The study found significant difference between genotypes, locations, harvest period, and all the interactions (P ≤ 0.001) for all traits analyzed. Kiroba recorded high starch yields of 17.4, 12.7, and 8.2 t ha−1 at Chambezi, Amani, and Magadu, respectively. Kilusungu recorded highest cyanide content of 300–400 ppm across all locations but Kiroba recorded highest values of 800 ppm, 15 months after planting at Chambezi. Genotype by environment (GGE) biplot analysis revealed that Kiroba was a superior cultivar in terms of starch yield. Kilusungu recorded highest cyanide content and average starch yield, therefore suitable for use in starch production. The study confirmed effect of genotype and genotype by environment interaction, Kiroba cultivar was superior in terms of starch yield and maximum starch yield was obtained at 9 months after planting. Nyamkagile and Kibandameno had the lowest cyanide content across all environments.

This study is conducted to characterize some nutritional attributes and starch properties of 156 Turkish sorghum populations and 4 standard cultivars (Sorghum bicolor L.). Crude protein contents of the populations vary between 6.67% and 14.33%, digestible protein ratios between 6.67% and 82.24%, crude oil contents between 2.15% and 6.40%, phytic acid contents between 0.37% and 4.09%, resistant starch between 1.10% and 34.23%, nonresistant starch between 10.79% and 79.61%, total starch between 15.42% and 85.54%, amylose between 5.67% and 43.48%, amylopectin between 9.45% and 65.67%, total phenolic between 0.19% and 5.06 mg GAE/g and antiradical activity between 3.72% and 91.48%. Significant differences are obtained from starch-based Rapid Visco Analyzer parameters of sorghum genotypes. As compared standard cultivars, several superior genotypes are identified in terms of nutritional characteristics. Genotype treatment (GT) biplot analysis revealed ideal genotypes for investigated parameters. Present findings confirmed that there are many genotypes with superior nutritional properties in local sorghum genotypes.

OBJECTIVES: We employed the correspondence analysis (CA) biplot to estimate correlations between gender–age levels of cardiovascular disease patients and their psychiatric and physical symptoms. Utilization of this correlation estimation can inform clinical practice by elucidating associations between certain psychiatric or physical symptoms and specific gender–age levels. METHOD: The CA biplot utilized here was designed to visually inspect row–column category associations in a 2‐dimensional plane and then to numerically estimate the category associations with correlations. To do so, we (a) estimated dimensions from row and column categories with CA; (b) verified statistical significance of dimensions with a permutation test; (c) projected row and column categories in a plan constructed with the first 2 dimensions that were statistically significant; (d) visually inspected category associations in the plane; and (e) numerically estimated category associations with correlations. RESULTS: Consistent with the previous results, female cardiovascular disease patients were more likely to experience psychiatric symptoms than the male patients. However, when examining the results by gender and age, both female and male patients in their 50s and 60s tended to experience elevated rates of the psychiatric symptoms. CONCLUSIONS: The CA biplot can be useful for isolating key clinical concerns among any medical populations.

Previous research has shown that progress in genetic yield potential is associated with adaptation to agronomic planting density, though its genetic basis has not been addressed before. In the current study, a wheat (Triticum aestivum L.) association mapping initiative (WAMI) panel of 287 elite lines was assessed for the effects of plant density on grain yield (YLD), 1000-kernel weight (TKW), and grain number (GNO) in yield plots consisting of four evenly spaced rows. The YLD and GNO of inner (high plant density) rows compared with outer rows (low plant density) indicated a consistent pattern: genotypes that performed best under intense competition (inner rows) responded less to reduced competition (outer rows) while being generally the best performers on aggregate (inner plus outer rows). However, TKW was not affected by plant density. To identify the genetic loci, an adaptation to density index (ADi) was computed as the scaled difference in trait values between inner and outer rows. Results on biplot analysis indicated that ADi was correlated with YLD in high-yielding environments, suggesting that it is a component of high yield potential. Genotyping of the WAMI panel was done through 90K Illumina Bead single nucleotide polymorphism (SNP) array. Association mapping employed using 18,104 SNP markers for ADi identified a major locus in chromosome 3B at 71 cM that explained 11.4% variation in ADi for YLD and GNO. Functional marker for ADi will enable identification of the trait in early generations—not otherwise possible in spaced plants typical of pedigree breeding approach—and to select parents for hybrid development.

The additive main effects and multiplicative interaction (AMMI) model is frequently applied in plant breeding for studying the genotype × environment (G × E) interaction. One of the main difficulties related to this method of analysis is the incorporation of inference to the bilinear terms that compose the biplot representation. This study aimed to incorporate credible intervals for the genotypic and environmental scores in the AMMI model by using an informative prior for the genotype effect. This approach differs from the Bayesian methods that have been presented so far, which assume the same restrictions as the fixed effects model. The method was exemplified by using data from a study with 55 maize hybrids in nine different environments for which variable being studied was the yield of unhusked ears. Our results demonstrated that the credible intervals allowed for the identification of genotypes and environments that did not contribute to the G × E interaction. In addition, it facilitated recognition of homogeneous subgroups of genotypes and environments (with respect to the effect of the interaction) and the adaptability of genotypes to specific environments of great interest to breeders. The posterior distributions of singular vectors were bimodal but with the same density peaks in absolute value. This reflects the arbitrary choice of signs of the main component that was used in different mathematical algorithms. Although our data set was based on unrelated single cross hybrids, the choice of genotypes as random effects enabled the Bayesian AMMI to accommodate the additive and nonadditive relationship matrices. Additionally, the flexibility of the analysis facilitated working with unbalanced data and the incorporation of heterogeneity of variances.

Summary Stable isotope analyses of carbon and nitrogen are widely used to study food web structure in ecosystems. However, isotopic signatures are affected by the often-needed chemical preservation of tissues in the field, which impedes or weakens the interpretation of results. The scarcely available correction factors for preserved fish samples are species specific and have so far not been validated for general use. Moreover, no studies have evaluated the effect of preservation on the estimation of metrics typically used in food web studies. We aimed to develop a general correction model suitable for a vast number of fish species and to test whether formalin-preserved fish muscle δ13C and δ15N values can be used in food web metrics estimations. For this purpose, we used paired formalin-preserved and fresh muscle samples of 116 fish individuals belonging to 17 species covering a wide range of fish trophic characteristics, from nine tropical streams. Formalin decreased δ13C values by 0·6–1·4‰ (0·94‰ on average) and increased δ15N values by 0·3–0·5‰ (0·33‰ on average). Preservation effect was ecologically significant for δ13C values (as it surpassed natural trophic fractionation) and less important for δ15N values (being minor than natural trophic fractionation). However, preservation did not affect estimation of community-wide food web metrics. The deviations in preserved samples varied among species and increased with increasing fresh sample C : N ratios and changes in carbon proportions after preservation and with increasing isotopic values (for δ13C). Despite these major deviations in δ13C values, we developed and validated a powerful general linear model to predict fresh fish muscle isotopic signatures from preserved samples. Formalin-preserved samples of fish can be used in food web studies, simplifying sampling logistics and allowing the use of museum and scientific collection specimens for historical food web reconstruction. Food web metrics based on δ13C vs. δ15N biplots can be directly estimated from preserved samples as the preservation effect seems overall consistent. When more detailed information is needed, or fresh and preserved samples are being simultaneously studied, formalin-preserved isotopic signatures can be corrected to fresh values using the model developed in this study.

The International Winter Wheat Improvement Program (IWWIP)—a collaboration between the government of Turkey, the International Maize and Wheat Improvement Center (CIMMYT), and the International Center for Agricultural Research in the Dry Areas (ICARDA)—develops and globally distributes improved winter wheat (Triticum aestivum L.) germplasm. The Winter Wheat Eastern European Regional Yield Trial was conducted by IWWIP during 1998–2005 using elite lines and varieties from IWWIP, Eastern Europe (EE), the United States, and Central and West Asia (CWA). This study analyzed data to identify superior genotypes and key locations that could be useful for future international collaboration on winter wheat. Grain yield and agronomic traits of 422 elite breeding lines and new varieties from 17 countries were evaluated across 39 locations. Superior genotypes and key environments for grain yield were determined using genotype and genotype × environment biplot analyses. Many superior genotypes were identified for both EE and CWA, and 11 geno types showed high, stable grain yield across the regions. The most representative and discriminating sites for grain yield were Konya and Eskisehir, Turkey (overall); Edirne, Turkey (CWA); and Dobrich, Bulgaria (EE). These findings rep resent a comprehensive analysis of yield and stability of a large, globally important set of winter wheat genotypes and growing locations, which may be useful for national and international winter wheat improvement programs.

The aim of this study was to investigate 6 cherry tomato varieties in terms of morphological, instrumental, and sensory attributes. Hungarian cherry tomato landraces have not been investigated in comparison with new commercial varieties for these traits. Parameters investigated were water-soluble antioxidant capacity (FRAP, DPPH, and TEAC), and total polyphenol, vitamin C, β-carotene, lycopene, total soluble solids, and acid contents. Colorimetric measurements as well as sensory analyses were conducted. It was concluded that varied antioxidant assays should be used in parallel to overcome the selectivity of any 1 method. Total phenolic content significantly contributed to results of antioxidant assays for the investigated varieties. The sensory profiles of the 6 cherry tomato varieties have been created. The differences between the products based on the 18 attributes were analyzed by Tukey post hoc test. The biplot of the principal component analysis showed that the sensory panel could discriminate the samples along the principal components. No correlation was found between colorimetric data a* and b* measured from pulp and lycopene, but a negative connection of β-carotene and hue was noted. Total polyphenol content showed correlations with colorimetric results, except for b*. The influence of tomato skin color on color perception is significant as in the present study instrumental data measured from pulp did not match that of the panelists evaluating intact fruit. Instrumental results of sugar content were supported by the ratings of the sensory panel. Practical Application The results will enhance the acceptance of different cherry-type tomatoes in the market, enrich the nutritional value knowledge of tomato varieties and landraces, and could support the work of tomato breeders as an instrumental and sensory feedback on their activity.

Biplots provide visualizations of two things, usually, but not necessarily, in two dimensions. This paper deals exclusively with biplots for quantitative data X; qualitative data or data in the form of counts will be addressed in a subsequent paper. Data X may represent either (1) a matrix with n rows representing samples/cases and columns representing p quantitative variables or (2) a two-way table whose rows and columns both represent classifying variables. Data sets of both types (1) and (2) are considered. Plotting symbols are usually points (typically for samples and distinguished by shape and/or color) and lines (typically for variables which may be calibrated or treated as arrowed vectors). Furthermore, variables may be nonlinear in both regularity of calibration and/or curvature. Interpretation is through distance, inner-products, and sometimes area. Biplots may be improved by judicious shifts of axes, by scaling and by rotation. Nearly always, biplots give approximations to X and measures, incorporated in the biplot, expressing the degree of approximation are discussed. These aspects are illustrated with reference to examples from principal component analysis, nonlinear biplots, biplots for biadditive models, canonical variate analysis and the analysis of distance between grouped samples. WIREs Comput Stat 2015, 7:42–62. doi: 10.1002/wics.1338 For further resources related to this article, please visit the WIREs website. Conflict of interest: The authors have declared no conflicts of interest for this article.

The objectives of this study were to investigate the pattern of genotype environment interaction and identify megaenvironments (ME), essential test locations, and suitable genotypes for each ME. The genotype plus genotype by environment interaction (GGE) biplot and additive main effects and multiplicative interaction analysis (AMMI) were used to demonstrate the potential of using a graphical biplot to analyze the genotype by environment interaction (GEI) in data of multienvironment trials (MET). These trials of the Central Cooperative Agricultural Research (COODETEC) evaluated 36 advanced breeding lines and 27 check cultivars for 3 years (2008– 2010) at 12 test locations. Yield data were analyzed using the genotype plus GGE and AMMI biplot methods. The test environments were classified into two ME (i.e. ME1: Castro, Gua rapuava, Nao-Me-Toque, Abelardo Luz, and Cachoeira do Sul; and ME2: Campo Mourao, Dourados, Palmital, Palotina, Ponta Pora ,and Rolândia. In ME1, the locations Guarapuava, Cachoeira do Sul, and Abelardo Luz were classified as ideal, while in ME2, Ponta Pora, Dou rados and Palotina were close to ideal. Guarapuava was the essential test location in ME1; however the identification of an essential test location in ME2 was unclear. Superior cultivars and advanced lines were identified in both ME that could be valuable for spring wheat (Triticum aestivum L.) improvement or cultivars released.

BACKGROUND Traditional internal and external preference mapping methods are based on principal component analysis (PCA). However, parallel factor analysis (PARAFAC) and Tucker-3 methods could be a better choice. To evaluate the methods, preference maps of sweet corn varieties will be introduced. RESULTS A preference map of eight sweet corn varieties was established using PARAFAC and Tucker-3 methods. Instrumental data were also integrated into the maps. The triplot created by the PARAFAC model explains better how odour is separated from texture or appearance, and how some varieties are separated from others. CONCLUSION Internal and external preference maps were created using parallel factor analysis (PARAFAC) and Tucker-3 models employing both sensory (trained panel and consumers) and instrumental parameters simultaneously. Triplots of the applied three-way models have a competitive advantage compared to the traditional biplots of the PCA-based external preference maps. The solution of PARAFAC and Tucker-3 is very similar regarding the interpretation of the first and third factors. The main difference is due to the second factor as it differentiated the attributes better. Consumers who prefer ‘super sweet’ varieties (they place great emphasis especially on taste) are much younger and have significantly higher incomes, and buy sweet corn products rarely (once a month). Consumers who consume sweet corn products mainly because of their texture and appearance are significantly older and include a higher ratio of men. © 2014 Society of Chemical Industry

Northern Hemisphere mean monthly temperature anomalies for the 1890 – 2010 period are examined for seasonality. The statistical method of biplotting visually synthesizes the major features of the time series for the 12 calendar months into a single plot. The common upward trend in all months and the winter – summer temperature contrast capture more than 80% of the total data variance. A temperature seasonalization is established: winter (January – March), summer (May – October) and transitional months (November, December and April). Two uncorrelated factors underlie this seasonality. The first is the North Atlantic thermohaline circulation, which is indicated by the Atlantic Multidecadal Oscillation and which statistically determines the summer temperature anomalies. The second is the cold ocean – warm land pattern, which is indicated by the hemispheric land – ocean temperature contrast and which statistically determines the winter anomalies. The interannual effect of the El Ni˜ – Southern Oscillation, volcanism and also the Arctic Oscillation/North Atlantic Oscillation mode compete with the background trend to produce a few extreme and outlier years.

A base index involving Striga damage, number of emerged Striga plants and ears per plant is used for selecting for maize (Zea mays L.) grain yield under Striga infestation. There are contradictory reports on the reliability of number of emerged Striga plants for selecting for Striga resistance. The objective of this study was to confirm reliability of the secondary traits for selecting for improved grain yield under Striga infestation. Ten Striga-resistant extra-early cultivars were evaluated for 3 years under artificial Striga-infested and Striga-free environments in Nigeria. Analysis of variance combined across years and locations showed significant mean squares for genotype, year, location and their interactions for most traits. Sequential path analysis identified ear aspect as the only trait with significant direct effect on yield under artificial Striga infestation, while GGE biplot confirmed ear aspect, ears per plant and Striga damage as the most reliable traits. Ear aspect should be included in the base index for selecting for improved grain yield of extra-early maize under Striga infestation, while the number of emerged Striga plants should be excluded.

BACKGROUND Information about the chemical profile of soybean seed is valuable for breeding programs aimed at obtaining value-added products to meet the demands of niche markets. The objective of this study was to determine seed composition of non-transgenic soybean genotypes with specialty characters in different environments of Argentina. RESULTS Protein and oil contents ranged from 396 to 424 g kg−1 and from 210 to 226 g kg−1, respectively. Oleic and linolenic acid ratio, the general indicator of oil quality, varied from 2.7 to 3.8. The oil contained high levels of total tocopherols (1429–1558 mg kg−1) and the meal exhibited high levels of total isoflavones (2.91–4.62 mg g−1). The biplot showed that oleic, linoleic and linolenic acids, γ-, δ- and total tocopherols, genistin, malonyl daidzin and genistin, acetyl daidzin and glycitin and total isoflavones allowed the greatest discrimination among the genotypes studied. CONCLUSION Different chemical profiles of each non-transgenic genotype analyzed were established and, therefore, their identity was defined. These results are important for breeders who intend to obtain new genotypes with improved meal and oil quality, as well as for processors and exporters, who could use them directly as raw material for soyfood processing for nutraceutical purposes. © 2013 Society of Chemical Industry

Pearl millet [Pennisetum glaucum (L.) R. Br.] is grown under a wide range of environmental conditions in India. The All India Coordinated Pearl Millet Improvement Project (AICPMIP) has the responsibility of testing and releasing pearl millet cultivars adapted to such conditions. As a part of this process, AICPMIP has divided the entire pearl millet growing regions into three different zones (A1, A, and B) based on the rainfall pattern and local adaptation of the crop. This study was conducted to define the presently used test locations into possible mega-environments and to identify essential test locations for cost-effective evaluation of pearl millet cultivars. Grain yield data of different sets of 34 to 45 medium-maturity pearl millet hybrids tested at 29 to 34 locations during 2006 to 2008 were analyzed using genotype main effects and genotype × environment interaction biplot method. Two distinct pearl millet mega-environments with consistent grouping of locations across the years and corresponding to AICPMIP’s designated A and B zones were identified. No such consistent grouping of locations corresponding to AICPMIP’s designated A1 zone was, however, observed. Based on the discriminating ability, uniqueness, and research resources, 13 locations were identified as essential test locations for evaluation across the two mega-environments. Testing at these locations appeared to provide good coverage of the whole pearl millet growing areas of India. Based on these findings, it is suggested to conduct initial yield trials at identified 13 locations across all the pearl millet growing zones represented by two mega-environments followed by testing of selected hybrids with specific adaptation in their respective adaptation zones.

In this article a trained sensory panel evaluated 6 flavored mineral water samples. The samples consisted of 3 different brands, each with 2 flavors (pear-lemon grass and josta berry). The applied sensory method was profile analysis. Our aim was to analyze the sensory profiles and to investigate the similarities between the sensitivity of the trained human panel and an electronic tongue device. Another objective was to demonstrate the possibilities for the prediction of sensory attributes from electronic tongue measurements using a multivariate statistical method (Partial Least Squares regression [PLS]). The results showed that the products manufactured under different brand name but with the same aromas had very similar sensory profiles. The panel performance evaluation showed that it is appropriate (discrimination ability, repeatability, and panel consensus) to compare the panel's results with the results of the electronic tongue. The samples can be discriminated by the electronic tongue and an accurate classification model can be built. Principal Component Analysis BiPlot diagrams showed that Brand A and B were similar because the manufacturers use the same aroma brands for their products. It can be concluded that Brand C was quite different compared to the other samples independently of the aroma content. Based on the electronic tongue results good prediction models can be obtained with high correlation coefficient (r(2) > 0.81) and low prediction error (RMSEP < 13.71 on the scale of the sensory evaluation from 0 to 100).

Superior genotypes are needed to give farmers a choice of improved cultivars of chickpea (Cicer arietinum L.) suitable for traditional spring sowing. From 1997 to 2010, 68 experiments comprising 404 elite chickpea lines were conducted for two seasons per year (spring and winter) at two locations—Tel Hadya, Syria (TH), and Terbol, Lebanon (TR). Genotypic differences were significant (P < 0.05) in 65 of 68 experiments. Genotype × season interaction was more important than the genotype × location. The predicted means in the two growing seasons were significantly correlated, implying the possibility of conducting yield trials in only one of the seasons, such as at TH. Stability analyses showed that S95082 (FLIP95-78C), with a predicted yield of 1725 kg ha−1, was the top yielding genotype at the TH spring sowing, with a temporal stability rank of 14. The line S95419 ranked second for yield (1633 kg ha−1) followed by S95335 (FLIP95-147C) with the spring yield at TH of 1583 kg ha−1. The genotype main effect plus genotype × environment interaction (GGE) biplot analyses showed that the FLIP95-78C and S95335 genotypes were high yielding at TH while FLIP98-91C and FLIP98-162C did better at TR in both seasons. Three lines, FLIP01-06C, FLIP01-30C, and FLIP01-49C, having high yields across locations and seasons and being tolerant to drought, were identified for dual season sowing. The findings show the potential to improve chickpea for spring sowing. The ICARDA breeding program is enriching the germplasm base with elite chickpea genotypes benefiting regional and international chickpea improvement programs.

Bibliometric mapping and visualization techniques represent one of the main pillars in the field of scientometrics. Traditionally, the main methodologies employed for representing data are Multi-Dimensional Scaling, Principal Component Analysis or Correspondence Analysis. In this paper we aim at presenting a visualization methodology known as Biplot analysis for representing bibliometric and science and technology indicators. A Biplot is a graphical representation of multivariate data, where the elements of a data matrix are represented according to dots and vectors associated with the rows and columns of the matrix. In this paper we explore the possibilities of applying the Biplot analysis in the research policy area. More specifically we will first describe and introduce the reader to this methodology and secondly, we will analyze its strengths and weaknesses through three different study cases: countries, universities and scientific fields. For this, we use a Biplot analysis known as JK-Biplot. Finally we compare the Biplot representation with other multivariate analysis techniques. We conclude that Biplot analysis could be a useful technique in scientometrics when studying multivariate data and an easy-to-read tool for research decision makers.

The Canonical Biplot method is used to deter- mine the magnitude of the effects on the D chromatic coor- dinates (DL*, Da*, Db*) and the parameter DE*, where (DL*, Da*, Db*) are the difference in the values of the sample after each aging cycle and the value of the untreated sample and DE* ¼ ((DL*) 2 þ (Da*) 2 þ (Db*) 2 ) 1/2 . We performed a study of the changes in color produced by two types of artificial aging procedures on four varieties of siliceous conglomerates from Zamora (Spain) that have traditionally been used in construction and later renovations in historical buildings in the zone. To accomplish this, 25 cycles of the following types of acceler- ated artificial aging were carried out: (a) freezing/thawing and cooling/heating (T1) and (b) combined freezing/thaw- ing and cooling/heating þ salt (phosphates) crystallization (T2).The results of the statistical study applied (Canonical Biplot) allowed us to differentiate the magnitude effect on the color of the surface brought about by T1 as compared with T2. These effects (p \ 0.05) were observed in all but one (ochre conglomerate) of the varieties, but mainly in the variable governing red hue (Da*) and yellow hue (Db*). 2012 Wiley Periodicals, Inc. Col Res Appl, 00, 000 - 000, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/col.21779

Grain yield of maize (Zea mays L.) has low heritability under low soil nitrogen (low-N) and drought, necessitating the use of secondary traits with strong associations with yield for selection. A base index involving anthesis-silking interval, plant and ear aspects, ears per plant, and stay green characteristic is used for selection for yield under drought and low-N stresses. Reports are contradictory on the reliability of stay green characteristic for selecting for yield under drought stress and ears per plant and anthesis-silking interval in selecting for low-N tolerance. Ninety extra-early inbreds were evaluated for 2 years at 3 locations in Nigeria under low-N and drought to confirm reliability of stay green characteristic for selecting for drought tolerance and ears per plant and anthesis-silking interval for low-N. Plant aspect, plant and ear heights were identified as the most reliable traits for simultaneous selection for yield under low- N and drought in the extra-early inbreds. Stay green characteristic was unreliable for selecting drought tolerant genotypes while ears per plant and anthesis-silking interval were not among the reliable traits for selecting low-N tolerant genotypes. Ear height, plant and ear aspects, and stay green characteristic were identified by both path–coefficient and GGE (genotype main effect plus genotype x environment) biplot analyses as reliable for selecting for low-N and ear aspect, plant height, and anthesis-silking interval for drought tolerance.

With 4 figures and 3 tables Abstract Soil salinity reduces crop yield in many areas of the world. Ninety-eight hexaploid wheat inbreds differing in geographic origin and belonging to six diverse adaptation groups were studied in control, EC-10 and EC-15 dS/m treatments to evaluate variability for salt tolerance and to assess the usefulness of early growth stage salinity assessment in the determination of adult plant salinity response. Significant differences (P ≤ 0.05) were observed among the 98 inbreds, three NaCl treatments and their interactions for relative growth rate (RGR), biomass, fertile tillers, grains/spike, 100-grain weight and grain yield. A range of responses were observed with an increasing salinity for most characters among the inbreds tested. The three evaluation systems (solution culture, raised beds in the field with added salt, naturally saline field conditions) were effective in assessing variability for salt tolerance in wheat germplasm. Assessment of salinity tolerance at the seedling stage correlated well with adult plant response under field conditions, and several highly stable sources of salinity tolerance were identified.

In semi-arid regions, particularly in the Sahel, water and high-temperature stress are serious constraints for groundnut production. Understanding of combined effects of heat and drought on physiological traits, yield and its attributes is of special significance for improving groundnut productivity. Two hundred and sixty-eight groundnut genotypes were evaluated in four trials under both intermittent drought and fully irrigated conditions, two of the trial being exposed to moderate temperature, while the two other trials were exposed to high temperature. The objectives were to analyse the component of the genetic variance and their interactions with water treatment, year and environment (temperature) for agronomic characteristics, to select genotypes with high pod yield under hot- and moderate-temperature conditions, or both, and to identify traits conferring heat and/or drought tolerance. Strong effects of water treatment (Trt), genotype (G) and genotype-by-treatment (GxTrt) interaction were observed for pod yield (Py), haulm yield (Hy) and harvest index (HI). The pod yield decrease caused by drought stress was 72 % at high temperature and 55 % at moderate temperature. Pod yield under well-watered (WW) conditions did not decrease under high-temperature conditions. Haulm yield decrease caused by water stress (WS) was 34 % at high temperature and 42 % under moderate temperature. Haulm yield tended to increase under high temperature, especially in one season. A significant year effect and genotype-by-environment interaction (GxE) effect were also observed for the three traits under WW and WS treatments. The GGE biplots confirmed these large interactions and indicated that high yielding genotypes under moderate temperature were different to those at high temperature. However, several genotypes with relatively high yield across years and temperature environments could be identified under both WW and WS conditions. Correlation analysis between pod weight and traits measured during plant growth showed that the partition rate, that is, the proportion of dry matter partitioned into pods, was contributing in heat and drought tolerance and could be a reliable selection criterion for groundnut breeding programme. Groundnut sensitivity to high-temperature stress was in part related to the sensitivity of reproduction.

Predictive biplots, as developed by J.C. Gower and coworkers, can be a very useful tool to aid the interpretation of the outcomes of multivariate analyses. This paper covers a statistical methodology that enables the automation of the construction of predictive biplots, as well as an R function, AutoBiplots.PCA( ), which applies the methodology to principal components analysis. A case study based on the sensory analysis of coffees is used to illustrate the methodology as well as the outputs of the R function. The method relies on the definition of a variable's mean standard predictive error, mspe, as the degree of accuracy in the process of predicting the original values from the biplots, which is compared with a predefined tolerance value (Taxis) to decide if the correspondent biplot axis is drawn in the biplot. Standard predictive errors, spe, are calculated for each unit in relation to each biplot axis in each two-dimensional plot and are compared with a predefined tolerance value (Tunits) to decide which units shall be faced as outliers. The R function automates the process, enabling the user to decide on the degree of precision of the actual analysis. Besides providing a solution for the automatic production of predictive biplots, the methodology offers new insights for the interpretation of multivariate analyses outputs on the basis of a sound principle, the degree of precision of the analysis. This provides an automatic way for the selection of variables that explain latent dimensions and also helps in deciding on the number of important latent dimensions for model developments. Copyright © 2012 John Wiley & Sons, Ltd.

The biplot is a generalization of a scatterplot for two variables to the case of many variables. Instead of having samples represented as points with respect to two perpendicular axes, as in a bivariate scatterplot, there are as many axes as variables pointing in different directions. Samples are then perpendicularly projected onto axes to obtain approximate values of the data. The word ‘approximate’ is important, because it is not possible to represent data on many variables exactly by this procedure, but the biplot arranges the axes to display the data as accurately as possible, usually by least-squares fitting. The ‘bi’ in biplot refers to the rows and columns of a multivariate data matrix, where the rows are usually cases and the columns are variables. Biplots are almost always displayed in a two-dimensional plot but can just as well be displayed in three-dimensions, with more accurate data representation, using suitable graphical software, for example dynamic rotation or conditioned plots. The usual linear biplot, using least-squares approximation, relies analytically on the singular value decomposition, which in turn can be thought of as a two-sided regression problem. Biplot geometry underlies many classical multivariate procedures, such as principal component analysis, simple and multiple correspondence analysis, discriminant analysis, and other variants of dimension reduction methods such as log-ratio analysis. WIREs Comput Stat 2012 doi: 10.1002/wics.1200

Cecere S, Leroy R, Groenen PJF, Lesaffre E, Declerck D. Estimating Emergence Sequences of Permanent Teeth in Flemish Schoolchildren using Interval-Censored Biplots: a graphical display of tooth emergence sequences. Community Dent Oral Epidemiol 2012; 40 (Suppl. 1): 49–55. © 2012 John Wiley & Sons A/S Abstract – Objectives: The aim of the present study was to investigate the pattern of emergence of permanent teeth using nonparametric techniques. Materials and methods: Data were obtained from the Signal-Tandmobiel® project, a 6-year prospective dental study conducted in Flanders (Belgium) in which 4468 primary school children born in 1989 were annually examined. A new exploratory method for interval-censored data, the IC-biplot, was applied to estimate individual sequences of emergence. In addition, the method renders a nice graphical representation of both children and teeth in the plane where the individual sequences of emergence can easily be visualized. On the basis of the estimated individual sequences, their corresponding prevalences were calculated. Results: The study revealed that between 7 and 13 different sequences of emergence can be expected depending on gender and quadrant. The prevalences of the most frequent sequences in girls varied from 35% to 85% depending on the quadrant, while in boys they varied from 28% to 32%. Most sequences in the maxilla start with 6-1-2 and in the mandible with 1-6-2. Conclusions: The IC-biplot is a flexible procedure that allows an easy visualization of the pattern of emergence of permanent teeth. Rank orders derived from the IC-biplot confirm rank orders suggested earlier in the literature.

This paper introduces a class of methods to infer the relationship between observations and variables in latent subspace models. The approach is a modification of the recently proposed missing data methods for exploratory data analysis (MEDA). MEDA is useful to identify the structure in the data and also to interpret the contribution of each latent variable. In this paper, MEDA is augmented with dummy variables to find the data variables related to a given deviation detected among observations, for instance, the difference between one cluster of observations and the bulk of the data. The MEDA extension, referred to as observation-based MEDA or oMEDA, can be performed in several ways, one of which is theoretically shown to be equivalent to a comparison of means between groups. The use of the proposed approach is demonstrated with a number of examples with simulated data and a real data set of archeological artifacts. Copyright © 2011 John Wiley & Sons, Ltd.

Compositional data are data that contain only relative information (see, e.g. Aitchison 1986)). Typical examples are data describing expenditures of persons on certain goods, or environmental data like the concentration of chemical elements in the soil. If all the compositional parts would be available, they would sum up to a total, like 100case of geochemical concentrations. Frequently, practical data sets include outliers, and thus a robust analysis is desirable. The R-package robCompositions (Templ et al., 2009) contains functions for robust statistical methods designed for compositional data, like principal component analysis (Filzmoser et al., 2009a) (including the robust compositional biplot), factor analysis (Filzmoser et al., 2009b), and discriminant analysis (Filzmoser et al., 2009c). Furthermore, methods to improve the quality of compositional data sets are implemented, like outlier detection (Filzmoser et al., 2008), and imputation of missing values (Hron et al, 2010). The latter one, based on a modified k-nearest neighbor algorithm and a model-based imputation, is also supported with measures of quality of imputation and diagnostic plots. The usage of the package will be illustrated on practical examples.