Abstract:
The aim of this study was to compare the multivariate methods GGE (Genotype main effects and Genotype xEnvironment interaction) and AMMI (Additive Main effects and Multiplicative Interaction) with the method of Eberhart andRussell for interpreting genotype x environment interaction. The AMMI and GGE analysis explained around 50% of the sumof squares of the genotype x environment interaction, whereas the method of Eberhart and Russell explained only 9.1 and15.8% each year. The cultivars classified as minor contribution to the genotype x environment interaction by methods ofAMMI and GGE were also the same classification method of Eberhart and Russell. The AMMI and the GGE biplot analysesare more efficient than the Eberhart and Russell. The GGE biplot explains a higher proportion of the sum of squares of theGxE interaction and is more informative with regards to environments and cultivar performance than the AMMI analysis.

Abstract:
Twelve rice varieties were cultivated in inland hydromorphic lowland over a four year-season period in tropical rainforest ecology to study the genotype x environment (GxE) interaction and yield stability and to determine the agronomic and environmental factors responsible for the interaction. Data on yield and agronomic characters and environmental variables were analyzed using the Additive Main Effect and Multiplicative Interaction (AMMI), Genotype and Genotype x Environment Interaction, GGE and the yield stability using the modified rank-sum statistic (YSi). AMMI analysis revealed environmental differences as accounting for 47.6% of the total variation. The genotype and GxE interaction accounted for 28.5% and 24% respectively. The first and second interaction axes captured 57% and 30% of the total variation due to GXE interaction. The analysis identified ‘TOX 3107’ as having a combination of stable and average yield. The GGE captured 85.8%of the total GxE. ‘TOX 3226-53-2-2-2’ and ‘ITA 230’ were high yielding but adjudged unstable by AMMI. These two varieties along with ‘WITA 1’ and ‘TOX 3180-32-2-1-3-5’ were identified with good inland swamp environment, which is essentially moisture based. The two varieties (‘TOX 3226-53-2-2-2’ and ‘ITA 230’), which were equally considered unstable in yield by the stability variance, σ2i, were selected by YSi in addition to ‘TOX 3107’, ‘WITA 1’, ‘IR 8’ and ‘M 55’. The statistic may positively complement AMMI and GGE in selecting varieties suited to specific locations with peculiar fluctuations in environmental indices. Correlation of PC scores with environmental and agronomic variables identified total rainfall up to the reproductive stage, variation in tillering ability and plant height as the most important factors underlying the GxE interaction. Additional information from the models can be positively utilized in varietal development for different ecologies.

Abstract:
The large amount of data on galaxies, up to higher and higher redshifts, asks for sophisticated statistical approaches to build adequate classifications. Multivariate cluster analyses, that compare objects for their global similarities, are still confidential in astrophysics, probably because their results are somewhat difficult to interpret. We believe that the missing key is the unavoidable characteristics in our Universe: evolution. Our approach, known as Astrocladistics, is based on the evolutionary nature of both galaxies and their properties. It gathers objects according to their "histories" and establishes an evolutionary scenario among groups of objects. In this presentation, I show two recent results on globular clusters and earlytype galaxies to illustrate how the evolutionary concepts of Astrocladistics can also be useful for multivariate analyses such as K-means Cluster Analysis.

Abstract:
Recent advances in neuroimaging technology and molecular genetics provide the unique opportunity to investigate genetic influence on the variation of brain attributes. Since the year 2000, when the initial publication on brain imaging and genetics was released, imaging genetics has been a rapidly growing research approach with increasing publications every year. Several reviews have been offered to the research community focusing on various study designs. In addition to study design, analytic tools and their proper implementation are also critical to the success of a study. In this review, we survey recent publications using data from neuroimaging and genetics, focusing on methods capturing multivariate effects accommodating the large number of variables from both imaging data and genetic data. We group the analyses of genetic or genomic data into either a priori driven or data driven approach, including gene-set enrichment analysis, multifactor dimensionality reduction, principal component analysis, independent component analysis (ICA), and clustering. For the analyses of imaging data, ICA and extensions of ICA are the most widely used multivariate methods. Given detailed reviews of multivariate analyses of imaging data available elsewhere, we provide a brief summary here that includes a recently proposed method known as independent vector analysis. Finally, we review methods focused on bridging the imaging and genetic data by establishing multivariate and multiple genotype-phenotype-associations, including sparse partial least squares, sparse canonical correlation analysis, sparse reduced rank regression and parallel ICA. These methods are designed to extract latent variables from both genetic and imaging data, which become new genotypes and phenotypes, and the links between the new genotype-phenotype pairs are maximized using different cost functions. The relationship between these methods along with their assumptions, advantages, and limitations are discussed.

Abstract:
although much appreciated in brazil, commercial popcorn is currently cropped on a fairly small scale. a number of problems need to be solved to increase production, notably the obtaintion of seeds with good agronomic traits and good culinary characteristics. with the objective of developing superior genotypes in popcorn, a second cycle of intrapopulation recurrent selection based on inbred s1 families was carried out. from the first cycle of selection over the unb-2u population, 222 s1 families were obtained, which were then divided into six sets and evaluated in a randomized complete block design with two replications within the sets. experiments were carried out in two brazilian localities. the analysis of variance revealed environmental effects for all evaluated traits, except popping and stand, showing that, for most traits, these environments affected genotype behavior in different ways. in addition, the set as source of variation was significant for most of the evaluated traits, indicating that dividing the families into sets was an efficient strategy. genotype-by-environment interaction was detected for most traits, except popping expansion and stand. differences among genotypes were also detected (1% f-test), making viable the proposition of using the genetic variability in the popcorn population as a basis for future recurrent selection cycles. superior families were selected using the smith and hazel classic index, with predicted genetic gains of 17.8% for popping expansion and 26.95% for yield.

Abstract:
Although much appreciated in Brazil, commercial popcorn is currently cropped on a fairly small scale. A number of problems need to be solved to increase production, notably the obtaintion of seeds with good agronomic traits and good culinary characteristics. With the objective of developing superior genotypes in popcorn, a second cycle of intrapopulation recurrent selection based on inbred S1 families was carried out. From the first cycle of selection over the UNB-2U population, 222 S1 families were obtained, which were then divided into six sets and evaluated in a randomized complete block design with two replications within the sets. Experiments were carried out in two Brazilian localities. The analysis of variance revealed environmental effects for all evaluated traits, except popping and stand, showing that, for most traits, these environments affected genotype behavior in different ways. In addition, the set as source of variation was significant for most of the evaluated traits, indicating that dividing the families into sets was an efficient strategy. Genotype-by-environment interaction was detected for most traits, except popping expansion and stand. Differences among genotypes were also detected (1% F-test), making viable the proposition of using the genetic variability in the popcorn population as a basis for future recurrent selection cycles. Superior families were selected using the Smith and Hazel classic index, with predicted genetic gains of 17.8% for popping expansion and 26.95% for yield.

Abstract:
Thirteen advance lines and three check varieties viz. , Chakwal-86, Pak-81 and Rawal-87 of wheat were planted at nine locations to estimate genotype x environment interaction. Both the linear and non-linear (pooled deviation) components were highly significant, indicating the presence of both predictable and un-predictable components of "G X E" interaction. The stability parameters for the individual genotype revealed that the genotypes, 89R-35 and 90R-36 showed the regression closer to unity along with low deviation from regression and thus may be stated as stable genotypes.

Abstract:
The aim of this literature review was to identify the existence and scope of genotype by environment interaction (G × E)from reports on dairy cattle populations in different management systems. Methods applied to deal with G × E (controlledexperiments and large data modeling) were discussed. A G × E was confirmed essentially when high differences betweenproduction environments and/or genotypes (genetically distant genotypes) were observed. Environmental effects wereaggregated in most studies and identification of the components of the environment was largely unresolved, with only a fewstudies based on more definite-descriptors of environment. The implications of G × E on breeding decisions are discussed.Breeders should select genotypes on production traits within environmental conditions comparable to where candidate animalsare intended to perform.

Abstract:
To date, the genome-wide association study (GWAS) is the primary tool to identify genetic variants that cause phenotypic variation. As GWAS analyses are generally univariate in nature, multivariate phenotypic information is usually reduced to a single composite score. This practice often results in loss of statistical power to detect causal variants. Multivariate genotype–phenotype methods do exist but attain maximal power only in special circumstances. Here, we present a new multivariate method that we refer to as TATES (Trait-based Association Test that uses Extended Simes procedure), inspired by the GATES procedure proposed by Li et al (2011). For each component of a multivariate trait, TATES combines p-values obtained in standard univariate GWAS to acquire one trait-based p-value, while correcting for correlations between components. Extensive simulations, probing a wide variety of genotype–phenotype models, show that TATES's false positive rate is correct, and that TATES's statistical power to detect causal variants explaining 0.5% of the variance can be 2.5–9 times higher than the power of univariate tests based on composite scores and 1.5–2 times higher than the power of the standard MANOVA. Unlike other multivariate methods, TATES detects both genetic variants that are common to multiple phenotypes and genetic variants that are specific to a single phenotype, i.e. TATES provides a more complete view of the genetic architecture of complex traits. As the actual causal genotype–phenotype model is usually unknown and probably phenotypically and genetically complex, TATES, available as an open source program, constitutes a powerful new multivariate strategy that allows researchers to identify novel causal variants, while the complexity of traits is no longer a limiting factor.

Abstract:
Random regression models are widely used to describe effects that change gradually over a continuous scale, for instance in genotype by environment interaction studies, where the genotype effect is modeled as a function of the environment [1]. A common measurement of the interaction is the variance in the slope of the sire reaction norms, i.e. sire breeding values regressed on an environmental variable. The interaction is regarded as significant if the slope variance is significant [e.g. [2,3,1]].For the estimation of genotype by environment interactions, both sire models or animal models are used, however sire models are computationally less demanding. Thus the sire model is preferred when the model is complex, the amount of data is large, or the analysis has to be repeated many times, as in QTL analyses in which testing many positions is necessary.Performing genetic analyses with a sire model gives an estimate of the "sire-variance", which is one fourth of the genetic variance. The remaining genetic variance (3/4) is modeled through the residual term together with the environmental variance. When the genetic variance is heterogeneous because of genotype by environment interactions, the residual variance will also be heterogeneous since part of it is genetic. Therefore, a random regression model that also accounts for heterogeneous residual variance is preferred [4,1].One way to account for heterogeneous residual variance over environments is to divide the environment into classes and to assume homogeneous variance within each environmental class, but with different residual variances across classes [1]. The drawbacks of this method are that classes have to be arbitrarily defined and that the number of classes increases with the number of parameters that need to be estimated [5]. A more advantageous approach would be to model the residual variance as a function of the environment in the mixed model, but commonly used software does not facilitate this option [6]. An