The Beta function, commonly used as a skewed probability density function in statistics, was introduced to describe the effect of temperature on the rate of crop development. The framework is set by three cardinal temperatures, namely the base (Tb), the optimum (T 0 ) and the ceiling (T,) temperature. The model parameters T b and 7;; and three other coefficients JJ., a and {3 can be used to derive the value of T 0 and the maximum developmem rate. Parameter a also characterizes the curvature of the relationship with temperatures between Tb and T 0 , and parameter {3 describes the curvature between T 0 and T..,. The model has one parameter less than the Rice Clock Model (RCM); and in contrast to the RCM, it ensures that the maximum development rate occurs exactly at 7;,. The model accurately described the response to temperature of several developmental processes, and was superior to two widely used thermal time approaches in predicting rice flowering time.
In plant breeding, multienvironment trials (MET) may include sets of related genetic strains. In self‐pollinated species the covariance matrix of the breeding values of these genetic strains is equal to the additive genetic covariance among them. This can be expressed as an additive relationship matrix, A, multiplied by the additive genetic variance. Using Mixed Model Methodology, the genetic covariance matrix can be estimated and Best Linear Unbiased Predictors (BLUPs) of the breeding values obtained. The effectiveness of exploiting relationships among strains tested in METs and usefulness of these BLUPs of breeding values for simultaneously modeling the main effects of genotypes and genotype × environment interaction (GE) have not been thoroughly studied. In this study, we obtained BLUPs of breeding values using genetic variance–covariance structures constructed as the Kroneker product (direct product) of a structured matrix of genetic variances and covariances for sites and a matrix of genetic relationships between strains, A. Results are compared with those from traditional fixed effects and random effects models for studying GE ignoring genetic relationships. A CIMMYT international wheat trial was used for illustration. Results showed that direct products of factor analytic structures with matrix A efficiently model the main effects of genotypes and GE. These models showed the lowest standard error of the BLUPs [SE(BLUP)] of breeding values. Genotypes that were related to other genotypes had small SE(BLUP). Related genotypes can clearly be visualized in biplots.
Rice double-haploid (DH) lines of an indica and japonica cross were grown at nine different locations across four countries in Asia. Genotype-by-environment (G x E) interaction analysis for 11 growth- and grain yield-related traits in nine locations was estimated by AMMI analysis. Maximum G x E interaction was exhibited for fertility percentage number of spikelets and grain yield. Plant height was least affected by environment, and the AMMI model explained a total of 76.2% of the interaction effect. Mean environment was computed by averaging the nine environments and subsequently analyzed with other environments to map quantitative trait loci (QTL). QTL controlling the 11 traits were detected by interval analysis using mapmaker/qtl. A threshold LOD of >/=3.20 was used to identify significant QTL. A total of 126 QTL were identified for the 11 traits across nine locations. Thirty-four QTL common in more than one environment were identified on ten chromosomes. A maximum of 44 QTL were detected for panicle length, and the maximum number of common QTL were detected for days to heading detected. A single locus for plant height (RZ730-RG810) had QTL common in all ten environments, confirming AMMI results that QTL for plant height were affected the least by environment, indicating the stability of the trait. Two QTL were detected for grain yield and 19 for thousand-grain weight in all DH lines. The number of QTL per trait per location ranged from zero to four. Clustering of the QTL for different traits at the same marker intervals was observed for plant height, panicle number, panicle length and spikelet number suggesting that pleiotropism and or tight linkage of different traits could be the possible reason for the congruence of several QTL. The many QTL detected by the same marker interval across environments indicate that QTL for most traits are stable and not essentially affected by environmental factors.
The Crop Ontology (CO) of the Generation Challenge Program (GCP) (http://cropontology.org/) is developed for the Integrated Breeding Platform (IBP) (http://www.integratedbreeding.net/) by several centers of The Consultative Group on International Agricultural Research (CGIAR): bioversity, CIMMYT, CIP, ICRISAT, IITA, and IRRI. Integrated breeding necessitates that breeders access genotypic and phenotypic data related to a given trait. The CO provides validated trait names used by the crop communities of practice (CoP) for harmonizing the annotation of phenotypic and genotypic data and thus supporting data accessibility and discovery through web queries. The trait information is completed by the description of the measurement methods and scales, and images. The trait dictionaries used to produce the Integrated Breeding (IB) fieldbooks are synchronized with the CO terms for an automatic annotation of the phenotypic data measured in the field. The IB fieldbook provides breeders with direct access to the CO to get additional descriptive information on the traits. Ontologies and trait dictionaries are online for cassava, chickpea, common bean, groundnut, maize, Musa, potato, rice, sorghum, and wheat. Online curation and annotation tools facilitate (http://cropontology.org) direct maintenance of the trait information and production of trait dictionaries by the crop communities. An important feature is the cross referencing of CO terms with the Crop database trait ID and with their synonyms in Plant Ontology (PO) and Trait Ontology (TO). Web links between cross referenced terms in CO provide online access to data annotated with similar ontological terms, particularly the genetic data in Gramene (University of Cornell) or the evaluation and climatic data in the Global Repository of evaluation trials of the Climate Change, Agriculture and Food Security programme (CCAFS). Cross-referencing and annotation will be further applied in the IBP.
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