The importance of phenotypic data analysis for genomic prediction - a case study comparing different spatial models in rye

Background

Genomic prediction is becoming a daily tool for plant breeders. It makes use of genotypic information to make predictions used for selection decisions. The accuracy of the predictions depends on the number of genotypes used in the calibration; hence, there is a need of combining data across years. A proper phenotypic analysis is a crucial prerequisite for accurate calibration of genomic prediction procedures. We compared stage-wise approaches to analyse a real dataset of a multi-environment trial (MET) in rye, which was connected between years only through one check, and used different spatial models to obtain better estimates, and thus, improved predictive abilities for genomic prediction. The aims of this study were to assess the advantage of using spatial models for the predictive abilities of genomic prediction, to identify suitable procedures to analyse a MET weakly connected across years using different stage-wise approaches, and to explore genomic prediction as a tool for selection of models for phenotypic data analysis.

Results

Using complex spatial models did not significantly improve the predictive ability of genomic prediction, but using row and column effects yielded the highest predictive abilities of all models. In the case of MET poorly connected between years, analysing each year separately and fitting year as a fixed effect in the genomic prediction stage yielded the most realistic predictive abilities. Predictive abilities can also be used to select models for phenotypic data analysis. The trend of the predictive abilities was not the same as the traditionally used Akaike information criterion, but favoured in the end the same models.

Conclusions

Making predictions using weakly linked datasets is of utmost interest for plant breeders. We provide an example with suggestions on how to handle such cases. Rather than relying on checks we show how to use year means across all entries for integrating data across years. It is further shown that fitting of row and column effects captures most of the heterogeneity in the field trials analysed.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-646) contains supplementary material, which is available to authorized users.     

Exome sequences and multi‐environment field trials elucidate the genetic basis of adaptation in barley

Broadening the genetic base of crops is crucial for developing varieties to respond to global agricultural challenges such as climate change. Here, we analysed a diverse panel of 371 domesticated lines of the model crop barley to explore the genetics of crop adaptation. We first collected exome sequence data and phenotypes of key life history traits from contrasting multi‐environment common garden trials. Then we applied refined statistical methods, including some based on exomic haplotype states, for genotype‐by‐environment (G×E) modelling. Sub‐populations defined from exomic profiles were coincident with barley's biology, geography and history, and explained a high proportion of trial phenotypic variance. Clear G×E interactions indicated adaptation profiles that varied for landraces and cultivars. Exploration of circadian clock‐related genes, associated with the environmentally adaptive days to heading trait (crucial for the crop's spread from the Fertile Crescent), illustrated complexities in G×E effect directions, and the importance of latitudinally based genic context in the expression of large‐effect alleles. Our analysis supports a gene‐level scientific understanding of crop adaption and leads to practical opportunities for crop improvement, allowing the prioritisation of genomic regions and particular sets of lines for breeding efforts seeking to cope with climate change and other stresses.     

Repeatability for Gaussian and non‐Gaussian data: a practical guide for biologists

Repeatability (more precisely the common measure of repeatability, the intra‐class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy of phenotypes. It is the proportion of phenotypic variation that can be attributed to between‐subject (or between‐group) variation. As a consequence, the non‐repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non‐Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non‐Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation‐based, analysis of variance (ANOVA)‐based and linear mixed‐effects model (LMM)‐based methods, while for non‐Gaussian data, we focus on generalised linear mixed‐effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM‐ and GLMM‐based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow‐sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non‐Gaussian data.     

Using conditional power of network meta‐analysis (NMA) to inform the design of future clinical trials

Clinical trials are typically designed with an aim to reach sufficient power to test a hypothesis about relative effectiveness of two or more interventions. Their role in informing evidence‐based decision‐making demands, however, that they are considered in the context of the existing evidence. Consequently, their planning can be informed by characteristics of relevant systematic reviews and meta‐analyses. In the presence of multiple competing interventions the evidence base has the form of a network of trials, which provides information not only about the required sample size but also about the interventions that should be compared in a future trial. In this paper we present a methodology to evaluate the impact of new studies, their information size, the comparisons involved, and the anticipated heterogeneity on the conditional power (CP) of the updated network meta‐analysis. The methods presented are an extension of the idea of CP initially suggested for a pairwise meta‐analysis and we show how to estimate the required sample size using various combinations of direct and indirect evidence in future trials. We apply the methods to two previously published networks and we show that CP for a treatment comparison is dependent on the magnitude of heterogeneity and the ratio of direct to indirect information in existing and future trials for that comparison. Our methodology can help investigators calculate the required sample size under different assumptions about heterogeneity and make decisions about the number and design of future studies (set of treatments compared).     

A matrix‐based method of moments for fitting the multivariate random effects model for meta‐analysis and meta‐regression

Multivariate meta‐analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between‐study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta‐regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example.     

A modular toolbox for Golden‐Gate‐based plasmid assembly streamlines the generation of Ralstonia solanacearum species complex knockout strains and multi‐cassette complementation constructs

Members of the Ralstonia solanacearum species complex (Rssc) cause bacterial wilt, a devastating plant disease that affects numerous economically important crops. Like other bacterial pests, Rssc injects a cocktail of effector proteins via the bacterial type III secretion system into host cells that collectively promote disease. Given their functional relevance in disease, the identification of Rssc effectors and the investigation of their in planta function are likely to provide clues on how to generate pest‐resistant crop plants. Accordingly, molecular analysis of effector function is a focus of Rssc research. The elucidation of effector function requires corresponding gene knockout strains or strains that express the desired effector variants. The cloning of DNA constructs that facilitate the generation of such strains has hindered the investigation of Rssc effectors. To overcome these limitations, we have designed, generated and functionally validated a toolkit consisting of DNA modules that can be assembled via Golden‐Gate (GG) cloning into either desired gene knockout constructs or multi‐cassette expression constructs. The Ralstonia‐GG‐kit is compatible with a previously established toolkit that facilitates the generation of DNA constructs for in planta expression. Accordingly, cloned modules, encoding effectors of interest, can be transferred to vectors for expression in Rssc strains and plant cells. As many effector genes have been cloned in the past as GATEWAY entry vectors, we have also established a conversion vector that allows the implementation of GATEWAY entry vectors into the Ralstonia‐GG‐kit. In summary, the Ralstonia‐GG‐kit provides a valuable tool for the genetic investigation of genes encoding effectors and other Rssc genes.     

A quantitative anharmonic analysis of the amide A band in α‐helical poly(L‐alanine)

Polarized ir spectra of oriented films of α‐helical poly(l ‐alanine) (α‐PLA) have been obtained as a function of residual solvent dichloroacetic acid (DCA). The amide A, B, II, and V regions exhibit multiple bands whose structure depends on the residual DCA content, and those associated with the α_I‐PLA structure have been identified. A calculation of the relevant cubic anharmonic force constants indicates that, contrary to previous assignments, the overtone of amide II(A) is in Fermi resonance with the NH stretch fundamental, whose unperturbed frequency we now find to be at 3314 cm⁻¹, significantly higher than the previously suggested 3279 cm⁻¹. The presence of a structure in addition to the standard α_I‐PLA is indicated by our analysis. © 1999 John Wiley & Sons, Inc. Biopoly 49: 195–207, 1999     

A likelihood‐based approach for assessment of extra‐pair paternity and conspecific brood parasitism in natural populations

Genotypes are frequently used to assess alternative reproductive strategies such as extra‐pair paternity and conspecific brood parasitism in wild populations. However, such analyses are vulnerable to genotyping error or molecular artefacts that can bias results. For example, when using multilocus microsatellite data, a mismatch at a single locus, suggesting the offspring was not directly related to its putative parents, can occur quite commonly even when the offspring is truly related. Some recent studies have advocated an ad‐hoc rule that offspring must differ at more than one locus in order to conclude that they are not directly related. While this reduces the frequency with which true offspring are identified as not directly related young, it also introduces bias in the opposite direction, wherein not directly related young are categorized as true offspring. More importantly, it ignores the additional information on allele frequencies which would reduce overall bias. In this study, we present a novel technique for assessing extra‐pair paternity and conspecific brood parasitism using a likelihood‐based approach in a new version of program cervus . We test the suitability of the technique by applying it to a simulated data set and then present an example to demonstrate its influence on the estimation of alternative reproductive strategies.     

A large‐scale genomic association analysis identifies the candidate causal genes conferring stripe rust resistance under multiple field environments

The incorporation of resistance genes into wheat commercial varieties is the ideal strategy to combat stripe or yellow rust (YR). In a search for novel resistance genes, we performed a large‐scale genomic association analysis with high‐density 660K single nucleotide polymorphism (SNP) arrays to determine the genetic components of YR resistance in 411 spring wheat lines. Following quality control, 371 972 SNPs were screened, covering over 50% of the high‐confidence annotated gene space. Nineteen stable genomic regions harbouring 292 significant SNPs were associated with adult‐plant YR resistance across nine environments. Of these, 14 SNPs were localized in the proximity of known loci widely used in breeding. Obvious candidate SNP variants were identified in certain confidence intervals, such as the cloned gene Yr18 and the major locus on chromosome 2BL, despite a large extent of linkage disequilibrium. The number of causal SNP variants was refined using an independent validation panel and consideration of the estimated functional importance of each nucleotide polymorphism. Interestingly, four natural polymorphisms causing amino acid changes in the gene TraesCS2B01G513100 that encodes a serine/threonine protein kinase (STPK) were significantly involved in YR responses. Gene expression and mutation analysis confirmed that STPK played an important role in YR resistance. PCR markers were developed to identify the favourable TraesCS2B01G513100 haplotype for marker‐assisted breeding. These results demonstrate that high‐resolution SNP‐based GWAS enables the rapid identification of putative resistance genes and can be used to improve the efficiency of marker‐assisted selection in wheat disease resistance breeding.     

Environmental Footprints and Scenario Analysis for Assessing the Impacts of the Agri‐Food Industry on a Regional Economy: A Case Study in Spain

The study of the environmental footprints of various sectors and industries is increasingly demanded by institutions and by society. In this context, the regional perspective is becoming particularly important, and even more so in countries such as Spain, where the autonomous communities have the primary responsibility for implementing measures to combat environmental degradation and promote sustainable development, in coordination with national strategies. Taking as a case study a Spanish region, Aragon, and significant economic sectors, including agriculture and the food industry, the aim of this work is twofold. First, we calculate the associated environmental footprints (of emissions and water) from the dual perspectives of production (local impacts) and consumption (final destination of the goods produced by the agri‐food industry). Second, through a scenarios analysis, based on a general equilibrium model designed and calibrated specifically for the region, we evaluate the environmental implications of changes in the agri‐food industry (changes in the export and import pattern, as well as in consumer behavior). This model provides a flexible approximation to the environmental impacts, controlling for a wider range of behavioral and economic interactions. Our results indicate that the agri‐food industry has a significant impact on the environment, especially on water resources, which must be responsibly managed in order to maintain the differential advantage that a regional economy can have, compared to other territories.     

Identification and analysis of residues contained on β → α loops of the dual‐substrate (βα)8 phosphoribosyl isomerase A specific for its phosphoribosyl anthranilate isomerase activity

A good model to experimentally explore evolutionary hypothesis related to enzyme function is the ancient‐like dual‐substrate (βα)₈ phosphoribosyl isomerase A (PriA), which takes part in both histidine and tryptophan biosynthesis in Streptomyces coelicolor and related organisms. In this study, we determined the Michaelis–Menten enzyme kinetics for both isomerase activities in wild‐type PriA from S. coelicolor and in selected single‐residue monofunctional mutants, identified after Escherichia coli in vivo complementation experiments. Structural and functional analyses of a hitherto unnoticed residue contained on the functionally important β → α loop 5, namely, Arg¹³⁹, which was postulated on structural grounds to be important for the dual‐substrate specificity of PriA, is presented for the first time. Indeed, enzyme kinetics analyses done on the mutant variants PriA_Ser⁸¹Thr and PriA_Arg¹³⁹Asn showed that these residues, which are contained on β → α loops and in close proximity to the N‐terminal phosphate‐binding site, are essential solely for the phosphoribosyl anthranilate isomerase activity of PriA. Moreover, analysis of the X‐ray crystallographic structure of PriA_Arg¹³⁹Asn elucidated at 1.95 Å herein strongly implicates the occurrence of conformational changes in this β → α loop as a major structural feature related to the evolution of the dual‐substrate specificity of PriA. It is suggested that PriA has evolved by tuning a fine energetic balance that allows the sufficient degree of structural flexibility needed for accommodating two topologically dissimilar substrates—within a bifunctional and thus highly constrained active site—without compromising its structural stability.