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

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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Dynamics of senescence-related QTLs in potato

The study of quantitative trait's expression over time helps to understand developmental processes which occur in the course of the growing season. Temperature and other environmental factors play an important role. The dynamics of haulm senescence was observed in a diploid potato mapping population in two consecutive years (2004 and 2005) under field conditions in Finland. The available time series data were used in a smoothed generalized linear model to characterize curves describing the senescence development in terms of its onset, mean and maximum progression rate and inflection point. These characteristics together with the individual time points were used in a Quantitative trait loci (QTL) analysis. Although QTLs occurring early in the sene

Interpreting genotype × environment interaction in tropical maize using linked molecular markers and environmental covariables

An understanding of the genetic and environmental basis of genotype´environment interaction (GEI) is of fundamental importance in plant breeding. In mapping quantitative trait loci (QTLs), suitable genetic populations are grown in different environments causing QTLs´environment interaction (QEI). The main objective of the present study is to show how Partial Least Squares (PLS) regression and Factorial Regression (FR) models using genetic markers and environmental covariables can be used for studying QEI related to GEI. Biomass data were analyzed from a multi-environment trial consisting of 161 lines from a F3:4 maize segregating population originally created with the purpose of mapping QTLs loci and investigating adaptation differences between highland and lowland tropical maize. PLS and FR methods detected 30 genetic markers (out of 86) that explained a sizeable proportion of the interaction of maize lines over four contrasting environments involving two low-altitude sites, one intermediate-altitude site, and one high-altitude site for biomass production. Based on a previous study, most of the 30 markers were associated with QTLs for biomass and exhibited significant QEI. It was found that marker loci in lines with positive GEI for the highland environments contained more highland alleles, whereas marker loci in lines with positive GEI for intermediate and lowland environments contained more lowland alleles. In addition, PLS and FR models identified maximum temperature as the most-important environmental covariable for GEI. Using a stepwise variable selection procedure, a FR model was constructed for GEI and QEI that exclusively included cross products between genetic markers and environmental covariables. Higher maximum temperature in low- and intermediatealtitude sites affected the expression of some QTLs, while minimum temperature affected the expression of other QTLs