FieldSimR: an R package for simulating plot data in multi-environment field trials

This paper presents a general framework for simulating plot data in multi-environment field trials with one or more traits. The framework is embedded within the R package FieldSimR, whose core function generates plot errors that capture global field trend, local plot variation, and extraneous variation at a user-defined ratio. FieldSimR's capacity to simulate realistic plot data makes it a flexible and powerful tool for a wide range of improvement processes in plant breeding, such as the optimisation of experimental designs and statistical analyses of multi-environment field trials. FieldSimR provides crucial functionality that is currently missing in other software for simulating plant breeding programmes and is available on CRAN. The paper includes an example simulation of field trials that evaluate 100 maize hybrids for two traits in three environments. To demonstrate FieldSimR's value as an optimisation tool, the simulated data set is then used to compare several popular spatial models for their ability to accurately predict the hybrids' genetic values and reliably estimate the variance parameters of interest. FieldSimR has broader applications to simulating data in other agricultural trials, such as glasshouse experiments.

Genome-wide association mapping for pre-harvest sprouting in European winter wheat detects novel resistance QTL, pleiotropic effects, and structural variation in multiple genomes

Pre-harvest sprouting (PHS), germination of seeds before harvest, is a major problem in global wheat (Triticum aestivum L.) production, and leads to reduced bread-making quality in affected grain. Breeding for PHS resistance can prevent losses under adverse conditions. Selecting resistant lines in years lacking pre-harvest rain, requires challenging of plants in the field or in the laboratory or using genetic markers. Despite the availability of a wheat reference and pan-genome, linking markers, genes, allelic, and structural variation, a complete understanding of the mechanisms underlying various sources of PHS resistance is still lacking. Therefore, we challenged a population of European wheat varieties and breeding lines with PHS conditions and phenotyped them for PHS traits, grain quality, phenological and agronomic traits to conduct genome-wide association mapping. Furthermore, we compared these marker-trait associations to previously reported PHS loci and evaluated their usefulness for breeding. We found markers associated with PHS on all chromosomes, with strong evidence for novel quantitative trait locus/loci (QTL) on chromosome 1A and 5B. The QTL on chromosome 1A lacks pleiotropic effect, for the QTL on 5B we detected pleiotropic effects on phenology and grain quality. Multiple peaks on chromosome 4A co-located with the major resistance locus Phs-A1, for which two causal genes, TaPM19 and TaMKK3, have been proposed. Mapping markers and genes to the pan-genome and chromosomal alignments provide evidence for structural variation around this major PHS-resistance locus. Although PHS is controlled by many loci distributed across the wheat genome, Phs-A1 on chromosome 4A seems to be the most effective and widely deployed source of resistance, in European wheat varieties.

Genomic prediction for root and yield traits of barley under a water availability gradient: a case study comparing different spatial adjustments

BACKGROUND

In drought periods, water use efficiency depends on the capacity of roots to extract water from deep soil. A semi-field phenotyping facility (RadiMax) was used to investigate above-ground and root traits in spring barley when grown under a water availability gradient. Above-ground traits included grain yield, grain protein concentration, grain nitrogen removal, and thousand kernel weight. Root traits were obtained through digital images measuring the root length at different depths. Two nearest-neighbor adjustments (M1 and M2) to model spatial variation were used for genetic parameter estimation and genomic prediction (GP). M1 and M2 used (co)variance structures and differed in the distance function to calculate between-neighbor correlations. M2 was the most developed adjustment, as accounted by the Euclidean distance between neighbors.

RESULTS

The estimated heritabilities ([Formula: see text]) ranged from low to medium for root and above-ground traits. The genetic coefficient of variation ([Formula: see text]) ranged from 3.2 to 7.0% for above-ground and 4.7 to 10.4% for root traits, indicating good breeding potential for the measured traits. The highest [Formula: see text] observed for root traits revealed that significant genetic change in root development can be achieved through selection. We studied the genotype-by-water availability interaction, but no relevant interaction effects were detected. GP was assessed using leave-one-line-out (LOO) cross-validation. The predictive ability (PA) estimated as the correlation between phenotypes corrected by fixed effects and genomic estimated breeding values ranged from 0.33 to 0.49 for above-ground and 0.15 to 0.27 for root traits, and no substantial variance inflation in predicted genetic effects was observed. Significant differences in PA were observed in favor of M2.

CONCLUSIONS

The significant [Formula: see text] and the accurate prediction of breeding values for above-ground and root traits revealed that developing genetically superior barley lines with improved root systems is possible. In addition, we found significant spatial variation in the experiment, highlighting the relevance of correctly accounting for spatial effects in statistical models. In this sense, the proposed nearest-neighbor adjustments are flexible approaches in terms of assumptions that can be useful for semi-field or field experiments.

Mr.Bean: a comprehensive statistical and visualization application for modeling agricultural field trials data

Crop improvement efforts have exploited new methods for modeling spatial trends using the arrangement of the experimental units in the field. These methods have shown improvement in predicting the genetic potential of evaluated genotypes. However, the use of these tools may be limited by the exposure and accessibility to these products. In addition, these new methodologies often require plant scientists to be familiar with the programming environment used to implement them; constraints that limit data analysis efficiency for decision-making. These challenges have led to the development of Mr.Bean, an accessible and user-friendly tool with a comprehensive graphical visualization interface. The application integrates descriptive analysis, measures of dispersion and centralization, linear mixed model fitting, multi-environment trial analysis, factor analytic models, and genomic analysis. All these capabilities are designed to help plant breeders and scientist working with agricultural field trials make informed decisions more quickly. Mr.Bean is available for download at https://github.com/AparicioJohan/MrBeanApp.

Empirical comparison of time series models and tensor product penalised splines for modelling spatial dependence in plant breeding field trials

Plant breeding field trials are typically arranged as a row by column rectangular lattice. They have been widely analysed using linear mixed models in which low order autoregressive integrated moving average (ARIMA) time series models, and the subclass of separable lattice processes, are used to account for two-dimensional spatial dependence between the plot errors. A separable first order autoregressive model has been shown to be particularly useful in the analysis of plant breeding trials. Recently, tensor product penalised splines (TPS) have been proposed to model two-dimensional smooth variation in field trial data. This represents a non-stochastic smoothing approach which is in contrast to the autoregressive (AR) approach which models a stochastic covariance structure between the lattice of errors. This paper compares the AR and TPS methods empirically for a large set of early generation plant breeding trials. Here, the fitted models include information on genetic relatedness among the entries being evaluated. This provides a more relevant framework for comparison than the assumption of independent genetic effects. Judged by Akaike Information Criteria (AIC), the AR models were a better fit than the TPS model for more than 80% of trials. In the cases where the TPS model provided a better fit it did so by only a small amount whereas the AR models made a substantial improvement across a range of trials. When the AR and TPS models differ, there can be marked differences in the ranking of genotypes between the two methods of analysis based on their predicted genetic effects. Using the best fitting model for a trial as the benchmark, the rate of mis-classification of entries for selection was greater for the TPS model than the AR models. This has important practical implications for breeder selection decisions.

A two-stage approach for the spatio-temporal analysis of high-throughput phenotyping data

High throughput phenotyping (HTP) platforms and devices are increasingly used for the characterization of growth and developmental processes for large sets of plant genotypes. Such HTP data require challenging statistical analyses in which longitudinal genetic signals need to be estimated against a background of spatio-temporal noise processes. We propose a two-stage approach for the analysis of such longitudinal HTP data. In a first stage, we correct for design features and spatial trends per time point. In a second stage, we focus on the longitudinal modelling of the spatially corrected data, thereby taking advantage of shared longitudinal features between genotypes and plants within genotypes. We propose a flexible hierarchical three-level P-spline growth curve model, with plants/plots nested in genotypes, and genotypes nested in populations. For selection of genotypes in a plant breeding context, we show how to extract new phenotypes, like growth rates, from the estimated genotypic growth curves and their first-order derivatives. We illustrate our approach on HTP data from the PhenoArch greenhouse platform at INRAE Montpellier and the outdoor Field Phenotyping platform at ETH Zürich.

Preparation and Curation of Multiyear, Multilocation, Multitrait Datasets

Genome-wide association studies (GWAS) are a powerful approach to dissect genotype-phenotype associations and identify causative regions. However, this power is highly influenced by the accuracy of the phenotypic data. To obtain accurate phenotypic values, the phenotyping should be achieved through multienvironment trials (METs). In order to avoid any technical errors, the required time needs to be spent on exploring, understanding, curating and adjusting the phenotypic data in each trial before combining them using an appropriate linear mixed model (LMM). The LMM is chosen to minimize as much as possible any effect that can lead to misestimation of the phenotypic values. The purpose of this chapter is to explain a series of important steps to explore and analyze data from METs used to characterize an association panel. Two datasets are used to illustrate two different scenarios.

Accounting for spatial trends in multi-environment diallel analysis in maize breeding

Spatial trends represent an obstacle to genetic evaluation in maize breeding. Spatial analyses can correct spatial trends, which allow for an increase in selective accuracy. The objective of this study was to compare the spatial (SPA) and non-spatial (NSPA) models in diallel multi-environment trial analyses in maize breeding. The trials consisted of 78 inter-populational maize hybrids, tested in four environments (E1, E2, E3, and E4), with three replications, under a randomized complete block design. The SPA models accounted for autocorrelation among rows and columns by the inclusion of first-order autoregressive matrices (AR1 ⊗ AR1). Then, the rows and columns factors were included in the fixed and random parts of the model. Based on the Bayesian information criteria, the SPA models were used to analyze trials E3 and E4, while the NSPA model was used for analyzing trials E1 and E2. In the joint analysis, the compound symmetry structure for the genotypic effects presented the best fit. The likelihood ratio test showed that some effects changed regarding significance when the SPA and NSPA models were used. In addition, the heritability, selective accuracy, and selection gain were higher when the SPA models were used. This indicates the power of the SPA model in dealing with spatial trends. The SPA model exhibits higher reliability values and is recommended to be incorporated in the standard procedure of genetic evaluation in maize breeding. The analyses bring the parents 2, 10 and 12, as potential parents in this microregion.

Plant Variety Selection Using Interaction Classes Derived From Factor Analytic Linear Mixed Models: Models With Independent Variety Effects

A major challenge in the analysis of plant breeding multi-environment datasets is the provision of meaningful and concise information for variety selection in the presence of variety by environment interaction (VEI). This is addressed in the current paper by fitting a factor analytic linear mixed model (FALMM) then using the fundamental factor analytic parameters to define groups of environments in the dataset within which there is minimal crossover VEI, but between which there may be substantial crossover VEI. These groups are consequently called interaction classes (iClasses). Given that the environments within an iClass exhibit minimal crossover VEI, it is then valid to obtain predictions of overall variety performance (across environments) for each iClass. These predictions can then be used not only to select the best varieties within each iClass but also to match varieties in terms of their patterns of VEI across iClasses. The latter is aided with the use of a new graphical tool called an iClass Interaction Plot. The ideas are introduced in this paper within the framework of FALMMs in which the genetic effects for different varieties are assumed independent. The application to FALMMs which include information on genetic relatedness is the subject of a subsequent paper.

Spatial kernel models capturing field heterogeneity for accurate estimation of genetic potential

According to Fisher's principles, an experimental field is typically divided into multiple blocks for local control. Although homogeneity is supposed within a block, this assumption may not be practical for large blocks, such as those including hundreds of plots. In line evaluation trials, which are essential in plant breeding, field heterogeneity must be carefully treated, because it can cause bias in the estimation of genetic potential. To more accurately estimate genotypic values in a large field trial, we developed spatial kernel models incorporating genome-wide markers, which consider continuous heterogeneity within a block and over the field. In the simulation study, the spatial kernel models were robust under various conditions. Although heritability, spatial autocorrelation range, replication number, and missing plots directly affected the estimation accuracy of genotypic values, the spatial kernel models always showed superior performance over the classical block model. We also employed these spatial kernel models for quantitative trait locus mapping. Finally, using field experimental data of bioenergy sorghum lines, we validated the performance of the spatial kernel models. The results suggested that a spatial kernel model is effective for evaluating the genetic potential of lines in a heterogeneous field.

Novel Sources of Tolerance to Aluminium Toxicity in Wild Cicer (Cicer reticulatum and Cicer echinospermum) Collections

In acid soils, the toxic form of aluminium, Al³⁺, significantly inhibits root growth and elongation, leading to less water and nutrient uptake. Previous research had shown differential Al toxicity tolerance among cultivated Cicer arietinum L. (chickpea); however, the potential for developing tolerant cultivars is limited by the narrow genetic diversity of cultivated chickpeas. Recent collections from Turkey of wild Cicer species, Cicer reticulatum, and Cicer echinospermum, have increased the available gene pool significantly, but there has been no large-scale screening of wild Cicer for acid tolerance or Al³⁺ toxicity tolerance. This study evaluated 167 wild Cicer and 17 Australian chickpea cultivars in a series of screenings under controlled growth conditions. The pH of 4.2 and Al concentrations of 15 and 60 μM Al were selected for large-scale screening based on dose response experiments in a low ionic strength nutrient solution. The change in root length showed better discrimination between tolerant and sensitive lines when compared with shoot and root dry weights and was used as a selection criterion. In a large-scale screening, 13 wild Cicer reticulatum accessions had a higher root tolerance index (≥50%), and eight had higher relative change in root length (≥40%) compared with PBA Monarch, which showed greater tolerance among the Australian domestic cultivars screened. In general, C. reticulatum species were found to be more tolerant than C. echinospermum, while genetic population groups Ret_5, Ret_6, and Ret_7 from Diyarbakir and Mardin Province were more tolerant than other groups. Among C. echinospermum, Ech_6 from the Siv-Diyar collection site of the Urfa Province showed better tolerance than other groups. In this first detailed screening of aluminium toxicity tolerance in the new wild Cicer collections, we identified accessions that were more tolerant than current domestic cultivars, providing promising germplasm for breeding programs to expand chickpea adaptation to acid soils.

A Systematic Narration of Some Key Concepts and Procedures in Plant Breeding

The goal of a plant breeding program is to develop new cultivars of a crop kind with improved yield and quality for a target region and end-use. Improved yield across locations and years means better adaptation to the climatic, soil, and management conditions in the target region. Improved or maintained quality renders and adds value to the improved yield. Both yield and quality must be considered simultaneously, which constitutes the greatest challenge to successful cultivar development. Cultivar development consists of two stages: the development of a promising breeding population and the selection of the best genotypes out of it. A complete breeder's equation was presented to cover both stages, which consists of three key parameters for a trait of interest: the population mean (μ), the population variability (σ _G ), and the achieved heritability (h ² or H), under the multi-location, multi-year framework. Population development is to maximize μσ _G and progeny selection is to improve H. Approaches to improve H include identifying and utilizing repeatable genotype by environment interaction (GE) through mega-environment analysis, accommodating unrepeatable GE through adequate testing, and reducing experimental error via replication and spatial analysis. Related concepts and procedures were critically reviewed, including GGE (genotypic main effect plus genotype by environment interaction) biplot analysis, GGE + GGL (genotypic main effect plus genotype by location interaction) biplot analysis, LG (location-grouping) biplot analysis, stability analysis, spatial analysis, adequate testing, and optimum replication. Selection on multiple traits includes independent culling and index selection, for the latter GYT (genotype by yield^*trait) biplot analysis was recommended. Genomic selection may provide an alternative and potentially more effective approach in all these aspects. Efforts were made to organize and comment on these concepts and procedures in a systematic manner.

Adaptability and stability analyses of plants using random regression models

The evaluation of cultivars using multi-environment trials (MET) is an important step in plant breeding programs. One of the objectives of these evaluations is to understand the genotype by environment interaction (GEI). A method of determining the effect of GEI on the performance of cultivars is based on studies of adaptability and stability. Initial studies were based on linear regression; however, these methodologies have limitations, mainly in trials with genetic or statistical unbalanced, heterogeneity of residual variances, and genetic covariance. An alternative would be the use of random regression models (RRM), in which the behavior of the genotypes is characterized as a reaction norm using longitudinal data or repeated measurements and information regarding a covariance function. The objective of this work was the application of RRM in the study of the behavior of common bean cultivars using a MET, based on Legendre polynomials and genotype-ideotype distances. We used a set of 13 trials, which were classified as unfavorable or favorable environments. The results revealed that RRM enables the prediction of the genotypic values of cultivars in environments where they were not evaluated with high accuracy values, thereby circumventing the unbalanced of the experiments. From these values, it was possible to measure the genotypic adaptability according to ideotypes, according to their reaction norms. In addition, the stability of the cultivars can be interpreted as variation in the behavior of the ideotype. The use of ideotypes based on real data allowed a better comparison of the performance of cultivars across environments. The use of RRM in plant breeding is a good alternative to understand the behavior of cultivars in a MET, especially when we want to quantify the adaptability and stability of genotypes.

Do Spatial Designs Outperform Classic Experimental Designs?

Controlling spatial variation in agricultural field trials is the most important step to compare treatments efficiently and accurately. Spatial variability can be controlled at the experimental design level with the assignment of treatments to experimental units and at the modeling level with the use of spatial corrections and other modeling strategies. The goal of this study was to compare the efficiency of methods used to control spatial variation in a wide range of scenarios using a simulation approach based on real wheat data. Specifically, classic and spatial experimental designs with and without a two-dimensional autoregressive spatial correction were evaluated in scenarios that include differing experimental unit sizes, experiment sizes, relationships among genotypes, genotype by environment interaction levels, and trait heritabilities. Fully replicated designs outperformed partially and unreplicated designs in terms of accuracy; the alpha-lattice incomplete block design was best in all scenarios of the medium-sized experiments. However, in terms of response to selection, partially replicated experiments that evaluate large population sizes were superior in most scenarios. The AR1 $$\times $$ ×  AR1 spatial correction had little benefit in most scenarios except for the medium-sized experiments with the largest experimental unit size and low GE. Overall, the results from this study provide a guide to researchers designing and analyzing large field experiments.

Supplementary materials accompanying this paper appear online.

Flexible modelling of spatial variation in agricultural field trials with the R package INLA

KEY MESSAGE

Established spatial models improve the analysis of agricultural field trials with or without genomic data and can be fitted with the open-source R package INLA. The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ([Formula: see text]) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the [Formula: see text] and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA.

Average information residual maximum likelihood in practice

Gilmour, Thompson, and Cullis (Biometrics, 1995, 51, 1440) presented the average information residual maximum likelihood (REML) algorithm for efficient variance parameter estimation in the linear mixed model. That paper dealt specifically with traditional variance component models, but the algorithm was quickly applied to more general models and implemented in several REML packages including ASReml (Gilmour et al., Biometrics, 2015, 51, 1440). This paper outlines the theory with respect to these more general models, describes the main issues encountered in fitting these models and how they have been addressed in the ASReml software. The issues covered are the basics steps in the implementation of the algorithm, keeping parameters within the parameter space, maximizing sparsity, avoiding issues associated with unstructured variance matrices by using the factor-analytic structure and handling singularities in marker-based relationship matrices and current work.

Genome Wide Associations of Growth, Phenology, and Plasticity Traits in Willow [Salix viminalis (L.)]

The short rotation biomass crop willow (Salix genera) has been of interest for bioenergy but recently also for biofuel production. For a faster development of new varieties molecular markers could be used as selection tool in an early stage of the breeding cycle. To identify markers associated with growth traits, genome-wide association mapping was conducted using a population of 291 Salix viminalis accessions collected across Europe and Russia and a large set of genotyping-by-sequencing markers. The accessions were vegetatively propagated and planted in replicated field experiments, one in Southern Sweden and one in Central Sweden. Phenology data, including bud burst and leaf senescence, as well as different growth traits were collected and measured repeatedly between 2010 and 2017 at both field environments. A value of the plasticity for each accession was calculated for all traits that were measured the same year in both environments as the normalized accession value in one environment subtracted by the corresponding value in the other environment. Broad-sense accession heritabilities and narrow-sense chip heritabilities ranged from 0.68 to 0.95 and 0.45 to 0.99, respectively for phenology traits and from 0.56 to 0.85 and 0.24 to 0.97 for growth traits indicating a considerable genetic component for most traits. Population structure and kinship between accessions were taken into account in the association analyses. In total, 39 marker-trait associations were found where four were specifically connected to plasticity and interestingly one particular marker was associated to several different plasticity growth traits. Otherwise association consistency was poor, possibly due to accession by environment interactions which were demonstrated by the low structure adjusted accession correlations across environments (ranging from 0.40 to 0.58). However, one marker association with biomass fresh weight was repeatedly observed in the same environment over two harvest years. For some traits where several associations were found, the markers jointly explained over 20% of the accession variation. The result from this study using a population of unrelated accessions has given useful information about marker-trait associations especially highlighting marker-plasticity associations and genotype-by-environment interactions as important factors to take account of in future strategies of Salix breeding.

A guide to using a multiple-matrix animal model to disentangle genetic and nongenetic causes of phenotypic variance

Non-genetic influences on phenotypic traits can affect our interpretation of genetic variance and the evolutionary potential of populations to respond to selection, with consequences for our ability to predict the outcomes of selection. Long-term population surveys and experiments have shown that quantitative genetic estimates are influenced by nongenetic effects, including shared environmental effects, epigenetic effects, and social interactions. Recent developments to the "animal model" of quantitative genetics can now allow us to calculate precise individual-based measures of non-genetic phenotypic variance. These models can be applied to a much broader range of contexts and data types than used previously, with the potential to greatly expand our understanding of nongenetic effects on evolutionary potential. Here, we provide the first practical guide for researchers interested in distinguishing between genetic and nongenetic causes of phenotypic variation in the animal model. The methods use matrices describing individual similarity in nongenetic effects, analogous to the additive genetic relatedness matrix. In a simulation of various phenotypic traits, accounting for environmental, epigenetic, or cultural resemblance between individuals reduced estimates of additive genetic variance, changing the interpretation of evolutionary potential. These variances were estimable for both direct and parental nongenetic variances. Our tutorial outlines an easy way to account for these effects in both wild and experimental populations. These models have the potential to add to our understanding of the effects of genetic and nongenetic effects on evolutionary potential. This should be of interest both to those studying heritability, and those who wish to understand nongenetic variance.

The stationary regions for the parameter space of unilateral second-order spatial AR model

The analysis of spatial models has received much attention in the last three decades. It involves methods which take into account the data location for exploring and modelling spatial data. Spatial modelling has its applications in many fields like geology, geography, agriculture, meteorology, economics etc. In this paper, the unilateral second-order spatial autoregressive model, denoted as {\operatorname{SAR}(2,1)} model, is introduced. Then the necessary conditions for casual solutions of this model will be given. Since each casual model is a stationary model, these conditions will be stationary regions for the parameter space of the {\operatorname{SAR}(2,1)} model. Under the stationary conditions, we can estimate the model parameters.

Genomic relationships reveal significant dominance effects for growth in hybrid Eucalyptus

Non-additive genetic effects can be effectively exploited in control-pollinated families with the availability of genome-wide markers. We used 41,304 SNP markers and compared pedigree vs. marker-based genetic models by analysing height, diameter, basic density and pulp yield for Eucalyptus urophylla × E.grandis control-pollinated families represented by 949 informative individuals. We evaluated models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance). We showed that the models can capture a large proportion of the genetic variance from dominance and epistasis for growth traits as those components are typically not independent. We also showed that we could partition genetic variances more precisely when using relationship matrices derived from markers compared to using only pedigree information. In addition, phenotypic prediction accuracies were only slightly increased by including dominance effects for growth traits since estimates of non-additive variances yielded rather high standard errors. This novel result improves our current understanding of the architecture of quantitative traits and recommends accounting for dominance variance when developing genomic selection strategies in hybrid Eucalyptus.

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.

Genomic prediction ability for yield-related traits in German winter barley elite material

Genomic prediction was evaluated in German winter barley breeding lines. In this material, prediction ability is strongly influenced by population structure and main determinant of prediction ability is the close genetic relatedness of the breeding material. To ensure breeding progress under changing environmental conditions the implementation and evaluation of new breeding methods is of crucial importance. Modern breeding approaches like genomic selection may significantly accelerate breeding progress. We assessed the potential of genomic prediction in a training population of 750 genotypes, consisting of multiple six-rowed winter barley (Hordeum vulgare L.) elite material families and old cultivars, which reflect the breeding history of barley in Germany. Crosses of parents selected from the training set were used to create a set of double-haploid families consisting of 750 genotypes. Those were used to confirm prediction ability estimates based on a cross-validation with the training set material using 11 different genomic prediction models. Population structure was inferred with dimensionality reduction methods like discriminant analysis of principle components and the influence of population structure on prediction ability was investigated. In addition to the size of the training set, marker density is of crucial importance for genomic prediction. We used genome-wide linkage disequilibrium and persistence of linkage phase as indicators to estimate that 11,203 evenly spaced markers are required to capture all QTL effects. Although a 9k SNP array does not contain a sufficient number of polymorphic markers for long-term genomic selection, we obtained fairly high prediction accuracies ranging from 0.31 to 0.71 for the traits earing, hectoliter weight, spikes per square meter, thousand kernel weight and yield and show that they result from the close genetic relatedness of the material. Our work contributes to designing long-term genetic prediction programs for barley breeding.

Genetics of phenotypic plasticity and biomass traits in hybrid willows across contrasting environments and years

BACKGROUND AND AIMS

Phenotypic plasticity can affect the geographical distribution of taxa and greatly impact the productivity of crops across contrasting and variable environments. The main objectives of this study were to identify genotype-phenotype associations in key biomass and phenology traits and the strength of phenotypic plasticity of these traits in a short-rotation coppice willow population across multiple years and contrasting environments to facilitate marker-assisted selection for these traits.

METHODS

A hybrid Salix viminalis  × ( S. viminalis × Salix schwerinii ) population with 463 individuals was clonally propagated and planted in three common garden experiments comprising one climatic contrast between Sweden and Italy and one water availability contrast in Italy. Several key phenotypic traits were measured and phenotypic plasticity was estimated as the trait value difference between experiments. Quantitative trait locus (QTL) mapping analyses were conducted using a dense linkage map and phenotypic effects of S. schwerinii haplotypes derived from detected QTL were assessed.

KEY RESULTS

Across the climatic contrast, clone predictor correlations for biomass traits were low and few common biomass QTL were detected. This indicates that the genetic regulation of biomass traits was sensitive to environmental variation. Biomass QTL were, however, frequently shared across years and across the water availability contrast. Phenology QTL were generally shared between all experiments. Substantial phenotypic plasticity was found among the hybrid offspring, that to a large extent had a genetic origin. Individuals carrying influential S. schwerinii haplotypes generally performed well in Sweden but less well in Italy in terms of biomass production.

CONCLUSIONS

The results indicate that specific genetic elements of S. schwerinii are more suited to Swedish conditions than to those of Italy. Therefore, selection should preferably be conducted separately for such environments in order to maximize biomass production in admixed S. viminalis × S. schwerinii populations.

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

A flexible and user-friendly spatial method called SpATS performed comparably to more elaborate and trial-specific spatial models in a series of sorghum breeding trials. 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.

Accounting for female space sharing in St. Kilda Soay sheep (Ovis aries) results in little change in heritability estimates

When estimating heritability in free-living populations, it is common practice to account for common environment effects, because of their potential to generate phenotypic covariance among relatives thereby biasing heritability estimates. In quantitative genetic studies of natural populations, however, philopatry, which results in relatives being clustered in space, is rarely accounted for. The two studies that have been carried out so far suggest absolute declines in heritability estimates of up to 43% when accounting for space sharing by relatives. However, due to methodological limitations these estimates may not be representative. We used data from the St. Kilda Soay sheep population to estimate heritabilities with and without accounting for space sharing for five traits for which there is evidence for additive genetic variance (birthweight, birth date, lamb August weight, and female post-mortem jaw and metacarpal length). We accounted for space sharing by related females by separately incorporating spatial autocorrelation, and a home range similarity matrix. Although these terms accounted for up to 18% of the variance in these traits, heritability estimates were only reduced by up to 7%. Our results suggest that the bias caused by not accounting for space sharing may be lower than previously thought. This suggests that philopatry does not inevitably lead to a large bias if space sharing by relatives is not accounted for. We hope our work stimulates researchers to model shared space when relatives in their study population share space, as doing so will enable us to better understand when bias may be of particular concern.

Association mapping in Salix viminalis L. (Salicaceae) - identification of candidate genes associated with growth and phenology

Willow species (Salix) are important as short-rotation biomass crops for bioenergy, which creates a demand for faster genetic improvement and breeding through deployment of molecular marker-assisted selection (MAS). To find markers associated with important adaptive traits, such as growth and phenology, for use in MAS, we genetically dissected the trait variation of a Salix viminalis (L.) population of 323 accessions. The accessions were sampled throughout northern Europe and were established at two field sites in Pustnäs, Sweden, and at Woburn, UK, offering the opportunity to assess the impact of genotype-by-environment interactions (G × E) on trait-marker associations. Field measurements were recorded for growth and phenology traits. The accessions were genotyped using 1536 SNP markers developed from phenology candidate genes and from genes previously observed to be differentially expressed in contrasting environments. Association mapping between 1233 of these SNPs and the measured traits was performed taking into account population structure and threshold selection bias. At a false discovery rate (FDR) of 0.2, 29 SNPs were associated with bud burst, leaf senescence, number of shoots or shoot diameter. The percentage of accession variation (Radj2) explained by these associations ranged from 0.3% to 4.4%, suggesting that the studied traits are controlled by many loci of limited individual impact. Despite this, a SNP in the EARLY FLOWERING 3 gene was repeatedly associated (FDR < 0.2) with bud burst. The rare homozygous genotype exhibited 0.4-1.0 lower bud burst scores than the other genotype classes on a five-grade scale. Consequently, this marker could be promising for use in MAS and the gene deserves further study. Otherwise, associations were less consistent across sites, likely due to their small Radj2 estimates and to considerable G × E interactions indicated by multivariate association analyses and modest trait accession correlations across sites (0.32-0.61).

Genome wide association study for drought, aflatoxin resistance, and important agronomic traits of maize hybrids in the sub-tropics

The primary maize (Zea mays L.) production areas are in temperate regions throughout the world and this is where most maize breeding is focused. Important but lower yielding maize growing regions such as the sub-tropics experience unique challenges, the greatest of which are drought stress and aflatoxin contamination. Here we used a diversity panel consisting of 346 maize inbred lines originating in temperate, sub-tropical and tropical areas testcrossed to stiff-stalk line Tx714 to investigate these traits. Testcross hybrids were evaluated under irrigated and non-irrigated trials for yield, plant height, ear height, days to anthesis, days to silking and other agronomic traits. Irrigated trials were also inoculated with Aspergillus flavus and evaluated for aflatoxin content. Diverse maize testcrosses out-yielded commercial checks in most trials, which indicated the potential for genetic diversity to improve sub-tropical breeding programs. To identify genomic regions associated with yield, aflatoxin resistance and other important agronomic traits, a genome wide association analysis was performed. Using 60,000 SNPs, this study found 10 quantitative trait variants for grain yield, plant and ear height, and flowering time after stringent multiple test corrections, and after fitting different models. Three of these variants explained 5-10% of the variation in grain yield under both water conditions. Multiple identified SNPs co-localized with previously reported QTL, which narrows the possible location of causal polymorphisms. Novel significant SNPs were also identified. This study demonstrated the potential to use genome wide association studies to identify major variants of quantitative and complex traits such as yield under drought that are still segregating between elite inbred lines.

Efficiency of augmented p-rep designs in multi-environmental trials

The paper shows that unreplicated designs in multi-environmental trials are most efficient. If replication per environment is needed then augmented p-rep designs outperform augmented and replicated designs in triticale and maize. In plant breeding, augmented designs with unreplicated entries are frequently used for early generation testing. With limited amount of seed, this design allows to use a maximum number of environments in multi-environmental trials (METs). Check plots enable the estimation of block effects, error variances and a connection of otherwise unconnected trials in METs. Cullis et al. (J Agri Biol Environ Stat 11:381-393, 2006) propose to replace check plots from a grid-plot design by plots of replicated entries leading to partially replicated (p-rep) designs. Williams et al. (Biom J 53:19-27, 2011) apply this idea to augmented designs (augmented p-rep designs). While p-rep designs are increasingly used in METs, a comparison of the efficiency of augmented p-rep designs and augmented designs in the range between replicated and unreplicated designs in METs is lacking. We simulated genetic effects and allocated them according to these four designs to plot yields of a triticale and a maize uniformity trial. The designs varied in the number of environments, but have a fixed number of entries and total plots. The error model and the assumption of fixed or random entry effects were varied in simulations. We extended our simulation for the triticale data by including correlated entry effects which are common in genomic selection. Results show an advantage of unreplicated and augmented p-rep designs and a preference for using random entry effects, especially in case of correlated effects reflecting relationships among entries. Spatial error models had minor advantages compared to purely randomization-based models.

QTL dissection of the loss of green colour during post-anthesis grain maturation in two-rowed barley

Ability to genetically manipulate the loss of green colour during grain maturation has potentials for increasing productivity, disease resistance, and drought and heat tolerance in crop plants. Two doubled haploid, two-rowed barley populations (Vlamingh × Buloke and VB9524 × ND11231*12) were monitored over 2 years for loss of green colour during grain filling using a portable active sensor. The aims were to determine the genomic regions that control trait heritability by quantitative trait locus (QTL) analysis, and to examine patterns of QTL-environment interactions under different conditions of water stress. In the Vlamingh × Buloke cross, broad-sense heritability estimate for loss of green colour (measured as the difference in sensor readings taken at anthesis and maturity, ∆SRI) was 0.68, and 0.78 for the VB9524 × ND11231*12 population. In the VB9524 × ND11231*12 population, rapid loss of green colour was positively associated with grain yield and percent plump grains, but in the Vlamingh × Buloke population, a slower loss of green colour (low ∆SRI) was associated with increased grain plumpness. With the aid of a dense array of single nucleotide polymorphisms (SNPs) and EST-derived SSR markers, a total of nine QTLs were detected across the two populations. Of these, a single major locus on the short arm of barley chromosome 5H was consistently linked with trait variation across the populations and multiple environments. The QTL was independent of flowering time and explained between 5.4 and 15.4 % of the variation observed in both populations, depending on the environment, and although a QTL × E interaction was detected, it was largely due to a change in the magnitude of the effect, rather than a change in direction. The results suggest that loss of green colour during grain maturation may be under the control of a simple genetic architecture, but a careful study of target populations and environments would be required for breeding purposes.

Shared spatial effects on quantitative genetic parameters: accounting for spatial autocorrelation and home range overlap reduces estimates of heritability in wild red deer

Social structure, limited dispersal, and spatial heterogeneity in resources are ubiquitous in wild vertebrate populations. As a result, relatives share environments as well as genes, and environmental and genetic sources of similarity between individuals are potentially confounded. Quantitative genetic studies in the wild therefore typically account for easily captured shared environmental effects (e.g., parent, nest, or region). Fine-scale spatial effects are likely to be just as important in wild vertebrates, but have been largely ignored. We used data from wild red deer to build "animal models" to estimate additive genetic variance and heritability in four female traits (spring and rut home range size, offspring birth weight, and lifetime breeding success). We then, separately, incorporated spatial autocorrelation and a matrix of home range overlap into these models to estimate the effect of location or shared habitat on phenotypic variation. These terms explained a substantial amount of variation in all traits and their inclusion resulted in reductions in heritability estimates, up to an order of magnitude up for home range size. Our results highlight the potential of multiple covariance matrices to dissect environmental, social, and genetic contributions to phenotypic variation, and the importance of considering fine-scale spatial processes in quantitative genetic studies.

The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population

Appropriate selection of parents for the development of mapping populations is pivotal to maximizing the power of quantitative trait loci detection. Trait genotypic variation within a family is indicative of the family's informativeness for genetic studies. Accurate prediction of the most useful parental combinations within a species would help guide quantitative genetics studies. We tested the reliability of genotypic and phenotypic distance estimators between pairs of maize inbred lines to predict genotypic variation for quantitative traits within families derived from biparental crosses. We developed 25 families composed of ~200 random recombinant inbred lines each from crosses between a common reference parent inbred, B73, and 25 diverse maize inbreds. Parents and families were evaluated for 19 quantitative traits across up to 11 environments. Genetic distances (GDs) among parents were estimated with 44 simple sequence repeat and 2303 single-nucleotide polymorphism markers. GDs among parents had no predictive value for progeny variation, which is most likely due to the choice of neutral markers. In contrast, we observed for about half of the traits measured a positive correlation between phenotypic parental distances and within-family genetic variance estimates. Consequently, the choice of promising segregating populations can be based on selecting phenotypically diverse parents. These results are congruent with models of genetic architecture that posit numerous genes affecting quantitative traits, each segregating for allelic series, with dispersal of allelic effects across diverse genetic material. This architecture, common to many quantitative traits in maize, limits the predictive value of parental genotypic or phenotypic values on progeny variance.

Experimental designs for evaluation of genetic variability and selection of ancient grapevine varieties: a simulation study

Classical methodologies for grapevine selection used in the vine-growing world are generally based on comparisons among a small number of clones. This does not take advantage of the entire genetic variability within ancient varieties, and therefore limits selection challenges. Using the general principles of plant breeding and of quantitative genetics, we propose new breeding strategies, focussed on conservation and quantification of genetic variability by performing a cycle of mass genotypic selection prior to clonal selection. To exploit a sufficiently large amount of genetic variability, initial selection trials must be generally very large. The use of experimental designs adequate for those field trials has been intensively recommended for numerous species. However, their use in initial trials of grapevines has not been studied. With the aim of identifying the most suitable experimental designs for quantification of genetic variability and selection of ancient varieties, a study was carried out to assess through simulation the comparative efficiency of various experimental designs (randomized complete block design, alpha design and row-column (RC) design). The results indicated a greater efficiency for alpha and RC designs, enabling more precise estimates of genotypic variance, greater precision in the prediction of genetic gain and consequently greater efficiency in genotypic mass selection.