Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within-and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.KEYWORDS marker-based estimation of heritability; GWAS; genomic prediction; Arabidopsis thaliana; one-vs. two-stage approaches N ARROW-SENSE heritability is an important parameter in quantitative genetics, determining the response to selection and representing the proportion of phenotypic variance that is due to additive genetic effects (Jacquard 1983;Ritland 1996;Visscher et al. 2006Visscher et al. , 2008Holland et al. 2010;Sillanpaa 2011). This definition of heritability goes back to Fisher (1918) and Wright (1920) almost a century ago. In plant species for which replicates of the same genotype are available (inbred lines, doubled haploids, clones), a different form of heritability, broadsense heritability, is traditionally estimated by the intraclass correlation coefficient for genotypic effects, using estimates for within-and between-genotype variance. Broad-sense heritability is also referred to as repeatability and gives the proportion of phenotypic variance explained by heritable (additive) and nonheritable (dominance, epistasis) genetic variance.With the arrival of high-density genotyping there is growing interest in marker-based estimation of narrow-sense heritability (WTCCC 2007;Yang et al. 2010Yang et al. , 2011Vatti...

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Epigenetics is receiving growing attention in the plant science community. Epigenetic modifications are thought to play a particularly important role in fluctuating environments. It is hypothesized that epigenetics contributes to plant phenotypic plasticity because epigenetic modifications, in contrast to DNA sequence variation, are more likely to be reversible. The population of decrease in DNA methylation 1-2 (ddm1-2)-derived epigenetic recombinant inbred lines (epiRILs) in Arabidopsis thaliana is well suited for studying this hypothesis, as DNA methylation differences are maximized and DNA sequence variation is minimized. Here, we report on the extensive heritable epigenetic variation in plant growth and morphology in neutral and saline conditions detected among the epiRILs. Plant performance, in terms of branching and leaf area, was both reduced and enhanced by different quantitative trait loci (QTLs) in the ddm1-2 inherited epigenotypes. The variation in plasticity associated significantly with certain genomic regions in which the ddm1-2 inherited epigenotypes caused an increased sensitivity to environmental changes, probably due to impaired genetic regulation in the epiRILs. Many of the QTLs for morphology and plasticity overlapped, suggesting major pleiotropic effects. These findings indicate that epigenetics contributes substantially to variation in plant growth, morphology, and plasticity, especially under stress conditions.

IntroductionBatch effects in large untargeted metabolomics experiments are almost unavoidable, especially when sensitive detection techniques like mass spectrometry (MS) are employed. In order to obtain peak intensities that are comparable across all batches, corrections need to be performed. Since non-detects, i.e., signals with an intensity too low to be detected with certainty, are common in metabolomics studies, the batch correction methods need to take these into account. ObjectivesThis paper aims to compare several batch correction methods, and investigates the effect of different strategies for handling non-detects.MethodsBatch correction methods usually consist of regression models, possibly also accounting for trends within batches. To fit these models quality control samples (QCs), injected at regular intervals, can be used. Also study samples can be used, provided that the injection order is properly randomized. Normalization methods, not using information on batch labels or injection order, can correct for batch effects as well. Introducing two easy-to-use quality criteria, we assess the merits of these batch correction strategies using three large LC–MS and GC–MS data sets of samples from Arabidopsis thaliana.ResultsThe three data sets have very different characteristics, leading to clearly distinct behaviour of the batch correction strategies studied. Explicit inclusion of information on batch and injection order in general leads to very good corrections; when enough QCs are available, also general normalization approaches perform well. Several approaches are shown to be able to handle non-detects—replacing them with very small numbers such as zero seems the worst of the approaches considered.ConclusionThe use of quality control samples for batch correction leads to good results when enough QCs are available. If an experiment is properly set up, batch correction using the study samples usually leads to a similar high-quality correction, but has the advantage that more metabolites are corrected. The strategy for handling non-detects is important: choosing small values like zero can lead to suboptimal batch corrections.