We identify three major components of spatial variation in plot errors from eld experiments and extend the two-dimensional spatial procedures of Cullis and Gleeson (1991) to account for them. The components are non-stationary large scale (global) variation across the eld, stationary variation within the trial (natural variation or local trend) and extraneous variation which is often induced by experimental procedures and is predominantly aligned with rows and columns. We present a strategy for identifying a model for the plot errors which uses a trellis plot of residuals, a perspective plot of the sample variogram and, where possible, likelihood ratio tests to identify which components are present. We demonstrate the strategy using two illustrative examples. We conclude that while there is no one model that adequately ts all eld experiments, the separable autoregressive model is dominant. However, there is often additional identi able variation present.

In designed experiments and in particular longitudinal studies, the aim may be to assess the effect of a quantitative variable such as time on treatment effects. Modelling treatment effects can be complex in the presence of other sources of variation. Three examples are presented to illustrate an approach to analysis in such cases. The ®rst example is a longitudinal experiment on the growth of cows under a factorial treatment structure where serial correlation and variance heterogeneity complicate the analysis. The second example involves the calibration of optical density and the concentration of a protein DNase in the presence of sampling variation and variance heterogeneity. The ®nal example is a multienvironment agricultural ®eld experiment in which a yield±seeding rate relationship is required for several varieties of lupins. Spatial variation within environments, heterogeneity between environments and variation between varieties all need to be incorporated in the analysis. In this paper, the cubic smoothing spline is used in conjunction with ®xed and random effects, random coef®cients and variance modelling to provide simultaneous modelling of trends and covariance structure. The key result that allows coherent and¯exible empirical model building in complex situations is the linear mixed model representation of the cubic smoothing spline. An extension is proposed in which trend is partitioned into smooth and nonsmooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented.1999 Royal Statistical Society 0035±9254/99/48269 Appl. Statist. (1999) 48, Part 3, pp. 269^311 treatments, e.g. time in the longitudinal setting, the interaction of treatments with the quantitative variable is generally of interest. The following experiments illustrate such situations and provide the motivation for the methods discussed in this paper. Data sets for the examples can be accessed at http://www.blackwellpublishers.co.uk/rss/ 1.1. Example 1: live-weights of cows An experiment was carried out to study the eects of altered dietary iron intake in dairy cattle infected with Mycobacterium paratuberculosis (see Lepper et al. (1989)). Previous studies on mice had established that the multiplication of the organism was inhibited by low rather than high dietary iron intake. The aim of the study on cows was to examine the long-term eects of iron dosing on the progress of the organism. Several variables were measured in the experiment, with the focus on the live-weight data in this paper. At the start of the experiment, 28 female calves, at most 2 weeks old, were subdivided into two groups of eight and 20 animals and accommodated in two yards. 4 weeks later, the group of 20 was inoculated with the organism (the infected group) and this is taken as time 0. The ®rst live-weights were taken 122 days later and were recorded to the nearest 5 kg. Iron dosing began on day 155 (5 days after the second measurement of live-weight). The two groups were subdivi...

A statistical approach is presented for selection of best performing lines for commercial release and best parents for future breeding programs from standard agronomic trials. The method involves the partitioning of the genetic effect of a line into additive and non-additive effects using pedigree based inter-line relationships, in a similar manner to that used in animal breeding. A difference is the ability to estimate non-additive effects. Line performance can be assessed by an overall genetic line effect with greater accuracy than when ignoring pedigree information and the additive effects are predicted breeding values. A generalized definition of heritability is developed to account for the complex models presented.

MAGIC populations present novel challenges and opportunities in crops due to their complex pedigree structure. They offer great potential both for dissecting genomic structure and for improving breeding populations. The past decade has seen the rise of multiparental populations as a study design offering great advantages for genetic studies in plants. The genetic diversity of multiple parents, recombined over several generations, generates a genetic resource population with large phenotypic diversity suitable for high-resolution trait mapping. While there are many variations on the general design, this review focuses on populations where the parents have all been inter-mated, typically termed Multi-parent Advanced Generation Intercrosses (MAGIC). Such populations have already been created in model animals and plants, and are emerging in many crop species. However, there has been little consideration of the full range of factors which create novel challenges for design and analysis in these populations. We will present brief descriptions of large MAGIC crop studies currently in progress to motivate discussion of population construction, efficient experimental design, and genetic analysis in these populations. In addition, we will highlight some recent achievements and discuss the opportunities and advantages to exploit the unique structure of these resources post-QTL analysis for gene discovery.

BackgroundNext-generation sequencing technologies provide new opportunities to identify the genetic components responsible for trait variation. However, in species with large polyploid genomes, such as bread wheat, the ability to rapidly identify genes underlying quantitative trait loci (QTL) remains non-trivial. To overcome this, we introduce a novel pipeline that analyses, by RNA-sequencing, multiple near-isogenic lines segregating for a targeted QTL.ResultsWe use this approach to characterize a major and widely utilized seed dormancy QTL located on chromosome 4AL. It exploits the power and mapping resolution afforded by large multi-parent mapping populations, whilst reducing complexity by using multi-allelic contrasts at the targeted QTL region. Our approach identifies two adjacent candidate genes within the QTL region belonging to the ABA-induced Wheat Plasma Membrane 19 family. One of them, PM19-A1, is highly expressed during grain maturation in dormant genotypes. The second, PM19-A2, shows changes in sequence causing several amino acid alterations between dormant and non-dormant genotypes. We confirm that PM19 genes are positive regulators of seed dormancy.ConclusionsThe efficient identification of these strong candidates demonstrates the utility of our transcriptomic pipeline for rapid QTL to gene mapping. By using this approach we are able to provide a comprehensive genetic analysis of the major source of grain dormancy in wheat. Further analysis across a diverse panel of bread and durum wheats indicates that this important dormancy QTL predates hexaploid wheat. The use of these genes by wheat breeders could assist in the elimination of pre-harvest sprouting in wheat.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-015-0665-6) contains supplementary material, which is available to authorized users.

Worldwide, dryland salinity is a major limitation to crop production. Breeding for salinity tolerance could be an effective way of improving yield and yield stability on saline-sodic soils of dryland agriculture. However, this requires a good understanding of inheritance of this quantitative trait. In the present study, a doubled-haploid bread wheat population (Berkut/Krichauff) was grown in supported hydroponics to identify quantitative trait loci (QTL) associated with salinity tolerance traits commonly reported in the literature (leaf symptoms, tiller number, seedling biomass, chlorophyll content, and shoot Na(+) and K(+) concentrations), understand the relationships amongst these traits, and determine their genetic value for marker-assisted selection. There was considerable segregation within the population for all traits measured. With a genetic map of 527 SSR-, DArT- and gene-based markers, a total of 40 QTL were detected for all seven traits. For the first time in a cereal species, a QTL interval for Na(+) exclusion (wPt-3114-wmc170) was associated with an increase (10%) in seedling biomass. Of the five QTL identified for Na(+) exclusion, two were co-located with seedling biomass (2A and 6A). The 2A QTL appears to coincide with the previously reported Na(+) exclusion locus in durum wheat that hosts one active HKT1;4 (Nax1) and one inactive HKT1;4 gene. Using these sequences as template for primer design enabled mapping of at least three HKT1;4 genes onto chromosome 2AL in bread wheat, suggesting that bread wheat carries more HKT1;4 gene family members than durum wheat. However, the combined effects of all Na(+) exclusion loci only accounted for 18% of the variation in seedling biomass under salinity stress indicating that there were other mechanisms of salinity tolerance operative at the seedling stage in this population. Na(+) and K(+) accumulation appear under separate genetic control. The molecular markers wmc170 (2A) and cfd080 (6A) are expected to facilitate breeding for salinity tolerance in bread wheat, the latter being associated with seedling vigour.

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An extension of interval mapping is presented that incorporates all intervals on the linkage map simultaneously. The approach uses a working model in which the sizes of putative QTL for all intervals across the genome are random effects. An outlier detection method is used to screen for possible QTL. Selected QTL are subsequently fitted as fixed effects. This screening and selection approach is repeated until the variance component for QTL sizes is not statistically significant. A comprehensive simulation study is conducted in which map uncertainty is included. The proposed method is shown to be superior to composite interval mapping in terms of power of detection of QTL. There is an increase in the rate of false positive QTL detected when using the new approach, but this rate decreases as the population size increases. The new approach is much simpler computationally. The analysis of flour milling yield in a doubled haploid population illustrates the improved power of detection of QTL using the approach, and also shows how vital it is to allow for sources of non-genetic variation in the analysis.