Multiple-to-multiple path analysis model.

One-to-multiple path analysis model describes the regulation mechanism of multiple independent variables to one dependent variable by dividing the correlation coefficient and the determination coefficient. How to analyse more complex regulation mechanisms of multiple independent variables to multiple dependent variables? Similarly, according to multiple-to-multiple linear regression analysis, multiple-to-multiple path analysis model was proposed in this paper and it demonstrated more complex regulation mechanisms among multiple independent variables and multiple dependent variables by dividing the generalized determination coefficient. Differently, three other types of paths were generated in multiple-to-multiple path analysis model in that the correlation among multiple dependent variables was considered. Then, the decision coefficient of each independent variable was constructed for dependent variables system, and its hypothesis testing statistics were given. Finally, the research example of the wheat breeding rules in arid area demonstrated that the multiple-to-multiple path analysis considering more correlation information can get better results.

Breeder friendly phenotyping.

The word phenotyping can nowadays invoke visions of a drone or phenocart moving swiftly across research plots collecting high-resolution data sets on a wide array of traits. This has been made possible by recent advances in sensor technology and data processing. Nonetheless, more comprehensive often destructive phenotyping still has much to offer in breeding as well as research. This review considers the 'breeder friendliness' of phenotyping within three main domains: (i) the 'minimum data set', where being 'handy' or accessible and easy to collect and use is paramount, visual assessment often being preferred; (ii) the high throughput phenotyping (HTP), relatively new for most breeders, and requiring significantly greater investment with technical hurdles for implementation and a steeper learning curve than the minimum data set; (iii) detailed characterization or 'precision' phenotyping, typically customized for a set of traits associated with a target environment and requiring significant time and resources. While having been the subject of debate in the past, extra investment for phenotyping is becoming more accepted to capitalize on recent developments in crop genomics and prediction models, that can be built from the high-throughput and detailed precision phenotypes. This review considers different contexts for phenotyping, including breeding, exploration of genetic resources, parent building and translational research to deliver other new breeding resources, and how the different categories of phenotyping listed above apply to each. Some of the same tools and rules of thumb apply equally well to phenotyping for genetic analysis of complex traits and gene discovery.

Statistical Approach for Improving Genomic Prediction Accuracy through Efficient Diagnostic Measure of Influential Observation.

It is expected the predictive performance of genomic prediction methods may be adversely affected in the presence of outliers. In agriculture science an outlier may arise due to wrong data imputation, outlying response, and in a series of trials over the time or location. Although several statistical procedures are already there in literature for identification of outlier but identification of true outlier is still a challenge especially in case of high dimensional genomic data. Here we have proposed an efficient approach for detecting outlier in high dimensional genomic data, our approach is p-value based combination methods to produce single p-value for detecting the outliers. Robustness of our approach has been tested using simulated data through the evaluation measures like precision, recall etc. It has been observed that significant improvement in the performance of genomic prediction has been obtained by detecting the outliers and handling them accordingly through our proposed approach using real data.

Bayesian factor analytic model: An approach in multiple environment trials.

One of the main challenges in plant breeding programs is the efficient quantification of the genotype-by-environment interaction (GEI). The presence of significant GEI may create difficulties for breeders in the selection and recommendation of superior genotypes for a wide environmental network. Among the diverse statistical procedures developed for this purpose, we highlight those based on mixed models and factor analysis that are called factor analytic (FA) models. However, some inferential issues are related to the factor analytic model, such as Heywood cases that make the model non-identifiable. Moreover, the representation of the loads and factors in the conventional biplot does not involve any measurement of uncertainty. In this work, we propose dealing with the FA model using the Bayesian framework with direct sampling of factor loadings via spectral decomposition; this guarantees identifiability in the estimation process and eliminates the need for the rotationality of factor loadings or imposition of any ad hoc constraints. We used simulated and real data to illustrate the method's application in multi-environment trials (MET) and to compare it with traditional FA mixed models on controlled unbalancing. In general, the Bayesian FA model was robust under different simulated unbalanced levels, presenting the superior predictive ability of missing data when compared to competing models, such as those based on FA mixed models. In addition, for some scenarios, the classical FA mixed model failed in estimating the full FA model, illustrating the parametric problems of convergence in these models. Our results suggest that Bayesian factorial models might be successfully used in plant breeding for MET analysis.

Evaluation of the micropropagation potential of curauá pineapple hybrids for fiber production / Avaliação do potencial de micropropagação de híbridos do abacaxi curauá para a produção de fibras

Plant fiber is a renewable and biodegradable material that can be used effectively to reinforce various composites. Pineapple hybrids selected for their fiber quality are in the phase of agronomic validation in Brazil by the Embrapa Cassava and Fruits research unit. The selection of a hybrid for large-scale fiber production depends on obtaining a large number of seedlings. This study evaluated the morphogenetic response and propagation potential of eight hybrids of Ananas comosus var. erectifolius, for the purpose of producing high-quality seedlings on a large scale. Stem and crown buds were reduced and placed in MS nutritive medium supplemented with BAP at 0.5 mg L-1, NAA at 0.01 mg L-1 and Phytagel® at 2.5 g L-1. After 45 days, the number of oxidized, contaminated and surviving buds was determined. Swollen buds and plantlets were transferred to a multiplication medium containing MS sucrose, salts and vitamins. The propagation potential was evaluated based on the geometric growth rate among sub-cultures. The FIB-NEG hybrid presented the best results for the establishment phase (40.28%). The best propagative potential was obtained from crown buds with the highest values for FIB-EST (3.93), FIB-MIN (3.91) and FIB-BOY (3.91) hybrids.

A fibra vegetal é uma fonte renovável, biodegradável e de excelente desempenho como reforço em compósitos variados. Híbridos selecionados pela qualidade de suas fibras estão em fase de validação agronômica na Embrapa Mandioca e Fruticultura e sua adoção para produção de fibra em larga escala depende de um elevado número de mudas. Este trabalho teve como objetivo avaliar a resposta morfogenética e o potencial propagativo de oito híbridos de Ananas comosus var. erectifolius, com a finalidade de produzir mudas de qualidade em larga escala. Gemas do caule e coroa foram reduzidas, introduzidas em meio nutritivo MS suplementado com BAP a 0,5 mg L-1, ANA a 0,01 mg L-1 e Phytagel® a 2,5 g L-1. Aos 45 dias foram avaliados o número de gemas oxidadas, contaminadas e sobreviventes. Gemas intumescidas e plantas formadas foram transferidas para o meio de multiplicação contendo sacarose, sais e vitaminas MS. Avaliou-se o potencial propagativo a partir de uma taxa de crescimento geométrico entre subcultivos. O híbrido FIB-NEG (40.28%) apresentou os melhores resultados em porcentagem para a fase de estabelecimento. O melhor potencial propagativo foi obtido a partir de gemas de coroa, com os valores mais elevados registrados para os híbridos FIB-EST (3.93), FIB-MIN (3.91) e FIB-BOY (3.91).

Improving Genomic Prediction in Cassava Field Experiments Using Spatial Analysis.

Cassava (Manihot esculenta Crantz) is an important staple food in sub-Saharan Africa. Breeding experiments were conducted at the International Institute of Tropical Agriculture in cassava to select elite parents. Taking into account the heterogeneity in the field while evaluating these trials can increase the accuracy in estimation of breeding values. We used an exploratory approach using the parametric spatial kernels Power, Spherical, and Gaussian to determine the best kernel for a given scenario. The spatial kernel was fit simultaneously with a genomic kernel in a genomic selection model. Predictability of these models was tested through a 10-fold cross-validation method repeated five times. The best model was chosen as the one with the lowest prediction root mean squared error compared to that of the base model having no spatial kernel. Results from our real and simulated data studies indicated that predictability can be increased by accounting for spatial variation irrespective of the heritability of the trait. In real data scenarios we observed that the accuracy can be increased by a median value of 3.4%. Through simulations, we showed that a 21% increase in accuracy can be achieved. We also found that Range (row) directional spatial kernels, mostly Gaussian, explained the spatial variance in 71% of the scenarios when spatial correlation was significant.

Minimum number of measurements for evaluating Bertholletia excelsa.

Repeatability studies on fruit species are of great importance to identify the minimum number of measurements necessary to accurately select superior genotypes. This study aimed to identify the most efficient method to estimate the repeatability coefficient (r) and predict the minimum number of measurements needed for a more accurate evaluation of Brazil nut tree (Bertholletia excelsa) genotypes based on fruit yield. For this, we assessed the number of fruits and dry mass of seeds of 75 Brazil nut genotypes, from native forest, located in the municipality of Itaúba, MT, for 5 years. To better estimate r, four procedures were used: analysis of variance (ANOVA), principal component analysis based on the correlation matrix (CPCOR), principal component analysis based on the phenotypic variance and covariance matrix (CPCOV), and structural analysis based on the correlation matrix (mean r - AECOR). There was a significant effect of genotypes and measurements, which reveals the need to study the minimum number of measurements for selecting superior Brazil nut genotypes for a production increase. Estimates of r by ANOVA were lower than those observed with the principal component methodology and close to AECOR. The CPCOV methodology provided the highest estimate of r, which resulted in a lower number of measurements needed to identify superior Brazil nut genotypes for the number of fruits and dry mass of seeds. Based on this methodology, three measurements are necessary to predict the true value of the Brazil nut genotypes with a minimum accuracy of 85%.

Bayesian Genomic Prediction with Genotype × Environment Interaction Kernel Models.

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects [Formula: see text] that can be assessed by the Kronecker product of variance-covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (genomic best linear unbiased predictors, GBLUP) and Gaussian (Gaussian kernel, GK). The other model has the same genetic component as the first model [Formula: see text] plus an extra component, F: , that captures random effects between environments that were not captured by the random effects [Formula: see text] We used five CIMMYT data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G × E always have superior prediction ability than single-environment models, and the higher prediction ability of multi-environment models with [Formula: see text] over the multi-environment model with only u occurred 85% of the time with GBLUP and 45% of the time with GK across the five data sets. The latter result indicated that including the random effect f is still beneficial for increasing prediction ability after adjusting by the random effect [Formula: see text].

Biplot analysis of strawberry genotypes recommended for the State of Espírito Santo.

Most strawberry genotypes grown commercially in Brazil originate from breeding programs in the United States, and are therefore not adapted to the various soil and climatic conditions found in Brazil. Thus, quantifying the magnitude of genotype x environment (GE) interactions serves as a primary means for increasing average Brazilian strawberry yields, and helps provide specific recommendations for farmers on which genotypes meet high yield and phenotypic stability thresholds. The aim of this study was to use AMMI (additive main effects and multiplicative interaction) and GGE biplot (genotype main effects + genotype x environment interaction) analyses to identify high-yield, stable strawberry genotypes grown at three locations in Espírito Santo for two agricultural years. We evaluated seven strawberry genotypes (Dover, Camino Real, Ventana, Camarosa, Seascape, Diamante, and Aromas) at three locations (Domingos Martins, Iúna, and Muniz Freire) in agricultural years 2006 and 2007, totaling six study environments. Joint analysis of variance was calculated using yield data (t/ha), and AMMI and GGE biplot analysis was conducted following the detection of a significant genotypes x agricultural years x locations (G x A x L) interaction. During the two agricultural years, evaluated locations were allocated to different regions on biplot graphics using both methods, indicating distinctions among them. Based on the results obtained from the two methods used in this study to investigate the G x A x L interaction, we recommend growing the Camarosa genotype for production at the three locations assessed due to the high frequency of favorable alleles, which were expressed in all localities evaluated regardless of the agricultural year.

Performance of genomic prediction within and across generations in maritime pine.

BACKGROUND: Genomic selection (GS) is a promising approach for decreasing breeding cycle length in forest trees. Assessment of progeny performance and of the prediction accuracy of GS models over generations is therefore a key issue. RESULTS: A reference population of maritime pine (Pinus pinaster) with an estimated effective inbreeding population size (status number) of 25 was first selected with simulated data. This reference population (n = 818) covered three generations (G0, G1 and G2) and was genotyped with 4436 single-nucleotide polymorphism (SNP) markers. We evaluated the effects on prediction accuracy of both the relatedness between the calibration and validation sets and validation on the basis of progeny performance. Pedigree-based (best linear unbiased prediction, ABLUP) and marker-based (genomic BLUP and Bayesian LASSO) models were used to predict breeding values for three different traits: circumference, height and stem straightness. On average, the ABLUP model outperformed genomic prediction models, with a maximum difference in prediction accuracies of 0.12, depending on the trait and the validation method. A mean difference in prediction accuracy of 0.17 was found between validation methods differing in terms of relatedness. Including the progenitors in the calibration set reduced this difference in prediction accuracy to 0.03. When only genotypes from the G0 and G1 generations were used in the calibration set and genotypes from G2 were used in the validation set (progeny validation), prediction accuracies ranged from 0.70 to 0.85. CONCLUSIONS: This study suggests that the training of prediction models on parental populations can predict the genetic merit of the progeny with high accuracy: an encouraging result for the implementation of GS in the maritime pine breeding program.

Evaluation of soybean lines and environmental stratification using the AMMI, GGE biplot, and factor analysis methods.

In the final phases of new soybean cultivar development, lines are cultivated in several locations across multiple seasons with the intention of identifying and selecting superior genotypes for quantitative traits. In this context, this study aimed to study the genotype-by-environment interaction for the trait grain yield (kg/ha), and to evaluate the adaptability and stability of early-cycle soybean genotypes using the additive main effects and multiplicative interaction (AMMI) analysis, genotype main effects and genotype x environment interaction (GGE) biplot, and factor analysis methods. Additionally, the efficiency of these methods was compared. The experiments were carried out in five cities in the State of Mato Grosso: Alto Taquari, Lucas do Rio Verde, Sinop, Querência, and Rondonópolis, in the 2011/2012 and 2012/2013 seasons. Twenty-seven early-cycle soybean genotypes were evaluated, consisting of 22 lines developed by Universidade Federal de Uberlândia (UFU) soybean breeding program, and five controls: UFUS Carajás, MSOY 6101, MSOY 7211, UFUS Guarani, and Riqueza. Significant and complex genotype-by-environment interactions were observed. The AMMI model presented greater efficiency by retaining most of the variation in the first two main components (61.46%), followed by the GGE biplot model (57.90%), and factor analysis (54.12%). Environmental clustering among the methodologies was similar, and was composed of one environmental group from one location but from different seasons. Genotype G5 presented an elevated grain yield, and high adaptability and stability as determined by the AMMI, factor analysis, and GGE biplot methodologies.

Estiva de Ca E Mg foliares por meio de Ca E Mg do solo em bananeira 'Prata Anã' utilizando cokrigagem / Estimation of nutrients foliar of tree banana 'Prata Anã' using cokrigagem

O objetivo deste trabalho foi investigar a eficiência do método estatístico da cokrigagem na estimativa do Ca e Mg foliares da bananeira 'Prata Anã', utilizando os teores de Ca e Mg do solo como variáveis auxiliares. Foram coletadas em torno de cada planta quatro amostras de solo na camada de 0 ­ 0,2 m e em seguida homogeneizadas formando uma amostra composta. Para análise foliar foram coletadas de 10 a 25 cm da parte interna mediana do limbo foliar, na terceira folha a contar do ápice eliminando-se a nervura central, no período de inflorescência da planta, em uma malha regular, totalizando 100 pontos amostrais espaçados de 6 x 4 m. Obteve-se as margens de erros associadas à cokrigagem por comparação dos valores estimados com aqueles determinados em laboratório. Os resultados mostraram que a técnica foi capaz de estimar os nutrientes foliares com eficiência.

The objective of this study was to investigate the efficiency of the cokrigagem statistical method to estimate the Ca and Mg leaf of tree banana 'Prata Anã', using the Ca and Mg in the soil as auxiliary variables. Were collected around each plant four samples of soil layer from 0 - 0.2 m then homogenised to form a composite sample. For leaf analysis were collected from 10 to 25 cm from the inner leaf of the median, the third leaf from apex eliminating the midrib, from inflorescence of the plant in a regular grid, totaling 100 sampling points spaced 6 x 4 m. Obtained the margins of error associated with cokrigagem by comparing the estimated values with those determined in the laboratory. The results showed that the technique was able to estimate the nutrient content efficiently