Spatial Models for Field Trials

An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product Penalized splines (P-splines). A special ANOVA-type reformulation leads to five smooth additive spatial components, which form the basis of a mixed model with five unknown variance components. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. We show the relation between several definitions of heritability and the effective dimension or the effective degrees of freedom associated to the genetic component. The approach is illustrated with large-scale field trial experiments. An R-package is provided

A New Method to Infer Causal Phenotype Networks Using QTL and Phenotypic Information

In the context of genetics and breeding research on multiple phenotypic traits, reconstructing the directional or causal structure between phenotypic traits is a prerequisite for quantifying the effects of genetic interventions on the traits. Current approaches mainly exploit the genetic effects at quantitative trait loci (QTLs) to learn about causal relationships among phenotypic traits. A requirement for using these approaches is that at least one unique QTL has been identified for each trait studied. However, in practice, especially for molecular phenotypes such as metabolites, this prerequisite is often not met due to limited sample sizes, high noise levels and small QTL effects. Here, we present a novel heuristic search algorithm called the QTL+phenotype supervised orientation (QPSO) algorithm to infer causal directions for edges in undirected phenotype networks. The two main advantages of this algorithm are: first, it does not require QTLs for each and every trait; second, it takes into account associated phenotypic interactions in addition to detected QTLs when orienting undirected edges between traits. We evaluate and compare the performance of QPSO with another state-of-the-art approach, the QTL-directed dependency graph (QDG) algorithm. Simulation results show that our method has broader applicability and leads to more accurate overall orientations. We also illustrate our method with a real-life example involving 24 metabolites and a few major QTLs measured on an association panel of 93 tomato cultivars. Matlab source code implementing the proposed algorithm is freely available upon request

Phenomics data processing: A plot-level model for repeated measurements to extract the timing of key stages and quantities at defined time points

Decision-making in breeding increasingly depends on the ability to capture and predict crop responses to changing environmental factors. Advances in crop modeling as well as high-throughput eld phenotyping (HTFP) hold promise to provide such insights. Processing HTFP data is an interdisciplinary task that requires broad knowledge on experimental design, measurement techniques, feature extraction, dynamic trait modeling, and prediction of genotypic values using statistical models. To get an overview of sources of variation in HTFP, we develop a general plot-level model for repeated measurements. Based on this model, we propose a seamless step-wise procedure that allows for carry on of estimated means and variances from stage to stage. The process builds on the extraction of three intermediate trait categories; (1) timing of key stages, (2) quantities at de ned time points or periods, and (3) dose-response curves. In a rst stage, these intermediate traits are extracted from low-level traits’ time series (e.g., canopy height) using P-splines and the quarter of maximum elongation rate method (QMER), as well as nal height percentiles. In a second and third stage, extracted traits are further processed using a stage-wise linear mixed model analysis. Using a wheat canopy growth simulation to generate canopy height time series, we demonstrate the suitability of the stage-wise process for traits of the rst two above-mentioned categories. Results indicate that, for the rst stage, the P-spline/QMER method was more robust than the percentile method. In the subsequent two-stage linear mixed model processing, weighting the second and third stage with error variance estimates from the previous stages improved the root mean squared error. We conclude that processing phenomics data in stages represents a feasible approach if estimated means and variances are carried forward from one processing stage to the next. P-splines in combination with the QMER method are suitable tools to extract timing of key stages and quantities at de ned time points from HTFP data

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

Adjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.MTM2014-55966-P Grains Research and Development Corporation (GRDC) of Australia National Institute of Agricultural Technology (INTA) of Argentina, Res. DN 1126/13 Integrated Breeding Progra

Determinants of barley grain yield in drought-prone Mediterranean environments

The determinants of barley grain yield in drought-prone Mediterranean environments have been studied in the Nure x Tremois (NT) population. A large set of yield and other morpho-physiological data were recorded in 118 doubled haploid (DH) lines of the population, in multi-environment field trials (18 site-year combination). Agrometeorological variables have been recorded and calculated at each site too. Four main periods of barley development were considered, vegetative, reproductive early and late grain filling phases, to dissect the effect on yield traits of the growth phases. Relationships between agrometeorological variables, grain yield (GY) and its main components (GN and GW) were also investigated by correlation. Results firstly gave a clear indication of the involvement of water consumption in determining GY and GW (r2=0.616, P=0.007 and r2=0.703, P=0.005, respectively) calculated from sowing to the early grain filling period, while GN showed its highest correlation with the total photothermal quotient (PQ) calculated for the same period (r2=0.646, P=0.013). With the only exception of total PQ calculated during the vegetative period, all significant correlations with GY were associated to water-dependent agrometeorological parameters. As a second result, the NT segregating population allowed us to weight the amount of interaction due to genotypes over environments or to environments in relation to genotypes by a GGE analysis; 47.67% of G+GE sum of squares was explained by the first two principal components. Then, the introduction of genomic information at major barley genes regulating the length of growth cycle allowed us to explain patterns of adaptation of different groups of NT lines according to the variants (alleles) harbored at venalization (Vrn-H1) in combination with earliness (Eam6) genes. The superiority of the lines carrying the Nure allele at Eam6 was confirmed by factorial ANOVA testing the four possible haplotypes obtained combining alternative alleles at Eam6 and Vrn-H1. Maximum yield potential and differentials among the NT genotypes was finally explored through Finlay-Wilkinson model to interpret grain yield of NT genotypes together with yield adaptability (Ya), as the regression coefficient bi; Ya ranged from 0.71 for NT77 to 1.20 for NT19. Lines simply harboring the Nure variants at the two genes behaved as highest yielding (3.04 t ha-1), and showed the highest yield adaptability (bi=1.05). The present study constitutes a starting point towards the introduction of genomic variables in agronomic models for barley grain yield in Mediterranean environments

Το λογισμικό SpatialAnalyzer & εφαρμογές του σε προβλήματα βιομηχανικής γεωδαισίας

This paper reports a first study exploring genomic prediction for adaptation of sorghum [Sorghum bicolor (L.) Moench] to drought-stress (D-ET) and nonstress (W-ET) environment types. The objective was to evaluate the impact of both modeling genotype × environment interaction (G×E) and accounting for heterogeneous variances of marker effects on genomic prediction of parental breeding values for grain yield within and across environment types (ETs). For this aim, different genetic covariance structures and different weights for individual markers were investigated in best linear unbiased prediction (BLUP)-based prediction models. The BLUP models used a kinship matrix combining pedigree and genomic information, termed K-BLUP. The dataset comprised testcross yield performances under D-ET and W-ET as well as pedigree and genomic data. In general, modeling G×E increased predictive ability and reduced empirical bias of genomic predictions for broad adaptation across both ETs vs. models that ignored G×E by fitting a main genetic effect only. Genomic predictions for specific adaptation to D-ET or W-ET were also improved by K-BLUP models that explicitly accommodated G×E and used data from both ETs relative to prediction models that used data from the targeted ET exclusively or models that used all the data but assumed no G×E. Allowing for heterogeneous marker variances through weighted K-BLUP produced clear increments (43–72%) in predictive ability of genomic prediction for grain yield in all adaptation scenarios. We conclude that G×E as well as locus-specific genetic variances should be accommodated in genomic prediction models to improve adaptability of sorghum to variable environmental conditions

Natural variation for seed longevity and seed dormancy are negatively correlated in Arabidopsis

Dormancy is a state of metabolic arrest that facilitates the survival of organisms during environmental conditions incompatible with their regular course of life. Many organisms have deep dormant stages to promote an extended life span (increased longevity). In contrast, plants have seed dormancy and seed longevity described as two traits. Seed dormancy is defined as a temporary failure of a viable seed to germinate in conditions that favor germination, whereas seed longevity is defined as seed viability after dry storage (storability). In plants, the association of seed longevity with seed dormancy has not been studied in detail. This is surprising given the ecological, agronomical, and economic importance of seed longevity. We studied seed longevity to reveal its genetic regulators and its association with seed dormancy in Arabidopsis (Arabidopsis thaliana). Integrated quantitative trait locus analyses for seed longevity, in six recombinant inbred line populations, revealed five loci: Germination Ability After Storage1 (GAAS1) to GAAS5. GAAS loci colocated with seed dormancy loci, Delay Of Germination (DOG), earlier identified in the same six recombinant inbred line populations. Both GAAS loci and their colocation with DOG loci were validated by near isogenic lines. A negative correlation was observed, deep seed dormancy correlating with low seed longevity and vice versa. Detailed analysis on the collocating GAAS5 and DOG1 quantitative trait loci revealed that the DOG1-Cape Verde Islands allele both reduces seed longevity and increases seed dormancy. To our knowledge, this study is the first to report a negative correlation between seed longevity and seed dormancy

Dynamics of senescence-related QTLs in potato

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