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Large agricultural field trials may display irregular spatial trends that cannot be fully captured by a purely randomization-based analysis. For this reason, paralleling the development of analysis-of-variance procedures for randomized field trials, there is a long history of spatial modeling for field trials, starting with the early work of Papadakis on nearest neighbor analysis, which can be cast in terms of first or second differences among neighboring plot values. This kind of spatial modeling is amenable to a natural extension using splines, as has been demonstrated in recent publications in the field. Here, we consider the P-spline framework, focusing on model options that are easy to implement in linear mixed model packages. Two examples serve to illustrate and evaluate the methods. A key conclusion is that first differences are rather competitive with second differences. A further key observation is that second differences require special attention regarding the representation of the null space of the smooth terms for spatial interaction, and that an unstructured variance–covariance structure is required to ensure invariance to translation and rotation of eigenvectors associated with that null space. We develop a strategy that permits fitting this model with ease, but the approach is more demanding than that needed for fitting models using first differences. Hence, even though in other areas, second differences are very commonly used in the application of P-splines, our conclusion is that with field trials, first differences have advantages for routine use.

A novel case of developing a portable spectral imaging device for kiwifruit analysis is presented. Furthermore, a new complementary spectral image processing strategy combining deep learning and advanced chemometric is proposed for processing the spectral images. The deep learning was used for detection and localisation of harvested fruit in the spectral image while the chemometric modelling was used to predict multiple fruit quality related properties i.e., dry matter and soluble solids content. The developed models were independently validated on fruit harvested from a different orchard as well as on a different variety. The one touch spectral imaging presented in this paper can allow widespread usage of spectral imaging for fresh fruit analysis, particularly benefitting non-experts in spectral imaging and chemometrics to routinely use the spectral imaging for fresh fruit analysis.

Temperature response of stem elongation in wheat grown under field conditions indicated that temperature response is highly heritable and linked to the flowering pathway., In wheat, temperature affects the timing and intensity of stem elongation. Genetic variation for this process is therefore important for adaptation. This study investigates the genetic response to temperature fluctuations during stem elongation and its relationship to phenology and height. Canopy height of 315 wheat genotypes (GABI wheat panel) was scanned twice weekly in the field phenotyping platform (FIP) of ETH Zurich using a LIDAR. Temperature response was modelled using linear regressions between stem elongation and mean temperature in each measurement interval. This led to a temperature-responsive (slope) and a temperature-irresponsive (intercept) component. The temperature response was highly heritable (H2=0.81) and positively related to a later start and end of stem elongation as well as final height. Genome-wide association mapping revealed three temperature-responsive and four temperature-irresponsive quantitative trait loci (QTLs). Furthermore, putative candidate genes for temperature-responsive QTLs were frequently related to the flowering pathway in Arabidopsis thaliana, whereas temperature-irresponsive QTLs corresponded to growth and reduced height genes. In combination with Rht and Ppd alleles, these loci, together with the loci for the timing of stem elongation, accounted for 71% of the variability in height. This demonstrates how high-throughput field phenotyping combined with environmental covariates can contribute to a smarter selection of climate-resilient crops.

Key messageWe evaluate self-organizing maps (SOM) to identify adaptation zones and visualize multi-environment genotypic responses. We apply SOM to multiple traits and crop growth model output of large-scale European sunflower data.AbstractGenotype-by-environment interactions (G × E) complicate the selection of well-adapted varieties. A possible solution is to group trial locations into adaptation zones with G × E occurring mainly between zones. By selecting for good performance inside those zones, response to selection is increased. In this paper, we present a two-step procedure to identify adaptation zones that starts from a self-organizing map (SOM). In the SOM, trials across locations and years are assigned to groups, called units, that are organized on a two-dimensional grid. Units that are further apart contain more distinct trials. In an iterative process of reweighting trial contributions to units, the grid configuration is learnt simultaneously with the trial assignment to units. An aggregation of the units in the SOM by hierarchical clustering then produces environment types, i.e. trials with similar growing conditions. Adaptation zones can subsequently be identified by grouping trial locations with similar distributions of environment types across years. For the construction of SOMs, multiple data types can be combined. We compared environment types and adaptation zones obtained for European sunflower from quantitative traits like yield, oil content, phenology and disease scores with those obtained from environmental indices calculated with the crop growth model Sunflo. We also show how results are affected by input data organization and user-defined weights for genotypes and traits. Adaptation zones for European sunflower as identified by our SOM-based strategy captured substantial genotype-by-location interaction and pointed to trials in Spain, Turkey and South Bulgaria as inducing different genotypic responses.

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., Scientific Reports, 12 (1), ISSN:2045-2322

Motivation Multi-parent populations (MPPs) are popular for QTL mapping because they combine wide genetic diversity in parents with easy control of population structure, but a limited number of software tools for QTL mapping are specifically developed for general MPP designs. Results We developed an R package called statgenMPP, adopting a unified identity-by-descent (IBD)-based mixed model approach for QTL analysis in MPPs. The package offers easy-to-use functionalities of IBD calculations, mixed model solutions and visualizations for QTL mapping in a wide range of MPP designs, including diallele, nested-association mapping populations, multi-parent advanced genetic inter-cross populations and other complicated MPPs with known crossing schemes. Availability and implementation The R package statgenMPP is open-source and freely available on CRAN at https://CRAN.R-project.org/package=statgenMPP Supplementary information Supplementary data are available at Bioinformatics online.

Construction of genetic linkage maps has become a routine step for mapping quantitative trait loci (QTL), particularly in animal and plant breeding populations. Many multiparental populations have recently been produced to increase genetic diversity and QTL mapping resolution. However, few software packages are available for map construction in these populations. In this paper, we build a general framework for the construction of genetic linkage maps from genotypic data in diploid populations, including bi- and multiparental populations, cross-pollinated (CP) populations, and breeding pedigrees. The framework is implemented as an automatic pipeline called magicMap, where the maximum multilocus likelihood approach utilizes genotypic information efficiently. We evaluate magicMap by extensive simulations and eight real datasets: one biparental, one CP, four multiparent advanced generation intercross (MAGIC), and two nested association mapping (NAM) populations, the number of markers ranging from a few hundred to tens of thousands. Not only is magicMap the only software capable of accommodating all of these designs, it is more accurate and robust to missing genotypes and genotyping errors than commonly used packages.

Yield is a function of environmental quality and the sensitivity with which genotypes react to that. Environmental quality is characterized by meteorological data, soil and agronomic management, whereas genotypic sensitivity is embodied by combinations of physiological traits that determine the crop capture and partitioning of environmental resources over time. This paper illustrates how environmental quality and genotype responses can be studied by a combination of crop simulation and statistical modelling. We characterized the genotype by environment interaction for grain yield of a wheat population segregating for flowering time by simulating it using the the Agricultural Production Systems sIMulator (APSIM) cropping systems model. For sites in the NE Australian wheat-belt, we used meteorological information as integrated by APSIM to classify years according to water, heat and frost stress. Results highlight that the frequency of years with more severe water and temperature stress has largely increased in recent years. Consequently, it is likely that future varieties will need to cope with more stressful conditions than in the past, making it important to select for flowering habits contributing to temperature and water-stress adaptation. Conditional on year types, we fitted yield response surfaces as functions of genotype, latitude and longitude to virtual multi-environment trials. Response surfaces were fitted by two-dimensional P-splines in a mixed-model framework to predict yield at high spatial resolution. Predicted yields demonstrated how relative genotype performance changed with location and year type and how genotype by environment interactions can be dissected. Predicted response surfaces for yield can be used for performance recommendations, quantification of yield stability and environmental characterization.

The aim of this study was to compare a laboratory-based and a pocket-sized near-infrared (NIR) spectrophotometer (SCiO) to predict mango fruit firmness. Three batches of mango fruit were measured to explore batch specific and global models. To gain insight to useful wavelengths important for predicting mango firmness variables, the bootstrapping soft shrinkage (BOSS) variable selection routine was used. Modelling was performed with partial least-squares regression (PLSR). The reference firmness measurements were performed with AWETA acoustic firmness analyser. The SCiO and the laboratory-based instrument showed similar performances predicting the reference firmness in terms of prediction coefficient of determination (R2). However, the root mean squared error of prediction (RMSEP) was slightly lower for the laboratory-based instrument compared to the SCiO, likely because a broader spectral region was used. The performance of the batch specific models was improved by up to 8 % in R2 with a 13 % reduction in RMSEP when BOSS was applied. For both laboratory based and SCiO, the global models based on combined data from the three batches, showed good performance (R2 0.74-0.93, RMSEP 4.8 – 8.2 Hz2g2/3 depending on the batch) to predict the firmness. Due to comparable performance of the SCiO compared to the laboratory-based spectrophotometer, the pocket-sized SCiO NIR sensor has the potential to become a low-cost, easy to use non-destructive tool to measure firmness in mango fruit.

Key message The identity-by-descent (IBD)-based mixed model approach introduced in this study can detect quantitative trait loci (QTLs) referring to the parental origin and simultaneously account for multilevel relatedness of individuals within and across families. This unified approach is proved to be a powerful approach for all kinds of multiparental population (MPP) designs. Abstract Multiparental populations (MPPs) have become popular for quantitative trait loci (QTL) detection. Tools for QTL mapping in MPPs are mostly developed for specific MPPs and do not generalize well to other MPPs. We present an IBD-based mixed model approach for QTL mapping in all kinds of MPP designs, e.g., diallel, Nested Association Mapping (NAM), and Multiparental Advanced Generation Intercross (MAGIC) designs. The first step is to compute identity-by-descent (IBD) probabilities using a general Hidden Markov model framework, called reconstructing ancestry blocks bit by bit (RABBIT). Next, functions of IBD information are used as design matrices, or genetic predictors, in a mixed model approach to estimate variance components for multiallelic genetic effects associated with parents. Family-specific residual genetic effects are added, and a polygenic effect is structured by kinship relations between individuals. Case studies of simulated diallel, NAM, and MAGIC designs proved that the advanced IBD-based multi-QTL mixed model approach incorporating both kinship relations and family-specific residual variances (IBD.MQMkin_F) is robust across a variety of MPP designs and allele segregation patterns in comparison to a widely used benchmark association mapping method, and in most cases, outperformed or behaved at least as well as other tools developed for specific MPP designs in terms of mapping power and resolution. Successful analyses of real data cases confirmed the wide applicability of our IBD-based mixed model methodology.

International audience; Close-range spectral imaging (SI) of agricultural plants is widely performed for digital plant phenotyping. A key task in digital plant phenotyping is the non-destructive and rapid identification of drought stress in plants so as to allow plant breeders to select potential genotypes for breeding drought-resistant plant varieties. Visible and near-infrared SI is a key sensing technique that allows the capture of physicochemical changes occurring in the plant under drought stress. The main challenges are in processing the massive spectral images to extract information relevant for plant breeders to support genotype selection. Hence, this study presents a generic data processing workflow for analysing SI data generated in real-world digital phenotyping experiments to extract meaningful information for decision making by plant breeders. The workflow is a combination of chemometric approaches and deep learning. The usefulness of the proposed workflow is demonstrated on a real-life experiment related to drought stress detection and quantification in Arabidopsis thaliana plants grown in a semi-controlled environment. The results show that the proposed approach is able to detect the presence of drought just 3 days after its induction compared to the well-watered plants. Furthermore, the unsupervised clustering approach provides detailed time-series images where the drought-related changes in plants can be followed visually along the time course. The developed approach facilitates digital phenotyping and can thus accelerate breeding of drought-tolerant plant varieties.

Many different types of multiparental populations have recently been produced to increase genetic diversity and resolution in QTL mapping. Low-coverage, genotyping-by-sequencing (GBS) technology has become a cost-effective tool in these populations, despite large amounts of missing data in offspring and founders. In this work, we present a general statistical framework for genotype imputation in such experimental crosses from low-coverage GBS data. Generalizing a previously developed hidden Markov model for calculating ancestral origins of offspring DNA, we present an imputation algorithm that does not require parental data and that is applicable to bi- and multiparental populations. Our imputation algorithm allows heterozygosity of parents and offspring as well as error correction in observed genotypes. Further, our approach can combine imputation and genotype calling from sequencing reads, and it also applies to called genotypes from SNP array data. We evaluate our imputation algorithm by simulated and real data sets in four different types of populations: the F2, the advanced intercross recombinant inbred lines, the multiparent advanced generation intercross, and the cross-pollinated population. Because our approach uses marker data and population design information efficiently, the comparisons with previous approaches show that our imputation is accurate at even very low (

The study of gene flow in pedigrees is of strong interest for the development of quantitative trait loci (QTL) mapping methods in multiparental populations. We developed a Markovian framework for modeling ancestral origins along two homologous chromosomes within individuals in fixed pedigrees. A highly beneficial property of our method is that the size of state space depends linearly or quadratically on the number of pedigree founders, whereas this increases exponentially with pedigree size in alternative methods. To calculate the parameter values of the Markov process, we describe two novel recursive algorithms that differ with respect to the pedigree founders being assumed to be exchangeable or not. Our algorithms apply equally to autosomes and sex chromosomes, another desirable feature of our approach. We tested the accuracy of the algorithms by a million simulations on a pedigree. We demonstrated two applications of the recursive algorithms in multiparental populations: design a breeding scheme for maximizing the overall density of recombination breakpoints and thus the QTL mapping resolution, and incorporate pedigree information into hidden Markov models in ancestral inference from genotypic data; the conditional probabilities and the recombination breakpoint data resulting from ancestral inference can facilitate follow-up QTL mapping. The results show that the generality of the recursive algorithms can greatly increase the application range of genetic analysis such as ancestral inference in multiparental populations.

Nearest-neighbour methods based on first differences are an approach to spatial analysis of field trials with a long history, going back to the early work by Papadakis first published in 1937. These methods are closely related to a geostatistical model that assumes spatial covariance to be a linear function of distance. Recently, P-splines have been proposed as a flexible alternative to spatial analysis of field trials. On the surface, P-splines may appear like a completely new type of method, but closer scrutiny reveals intimate ties with earlier proposals based on first differences and the linear variance model. This paper studies these relations in detail, first focussing on one-dimensional spatial models and then extending to the two-dimensional case. Two yield trial datasets serve to illustrate the methods and their equivalence relations. Parsimonious linear variance and random walk models are suggested as a good point of departure for exploring possible improvements of model fit via the flexible P-spline framework.

Genomic prediction of complex traits, say yield, benefits from including information on correlated component traits. Statistical criteria to decide which yield components to consider in the prediction model include the heritability of the component traits and their genetic correlation with yield. Not all component traits are easy to measure. Therefore, it may be attractive to include proxies to yield components, where these proxies are measured in (high-throughput) phenotyping platforms during the growing season. Using the Agricultural Production Systems Simulator (APSIM)-wheat cropping systems model, we simulated phenotypes for a wheat diversity panel segregating for a set of physiological parameters regulating phenology, biomass partitioning, and the ability to capture environmental resources. The distribution of the additive quantitative trait locus effects regulating the APSIM physiological parameters approximated the same distribution of quantitative trait locus effects on real phenotypic data for yield and heading date. We use the crop growth model APSIM-wheat to simulate phenotypes in three Australian environments with contrasting water deficit patterns. The APSIM output contained the dynamics of biomass and canopy cover, plus yield at the end of the growing season. Each water deficit pattern triggered different adaptive mechanisms and the impact of component traits differed between drought scenarios. We evaluated multiple phenotyping schedules by adding plot and measurement error to the dynamics of biomass and canopy cover. We used these trait dynamics to fit parametric models and P-splines to extract parameters with a larger heritability than the phenotypes at individual time points. We used those parameters in multi-trait prediction models for final yield. The combined use of crop growth models and multi-trait genomic prediction models provides a procedure to assess the efficiency of phenotyping strategies and compare methods to model trait dynamics. It also allows us to quantify the impact of yield components on yield prediction accuracy even in different environment types. In scenarios with mild or no water stress, yield prediction accuracy benefitted from including biomass and green canopy cover parameters. The advantage of the multi-trait model was smaller for the early-drought scenario, due to the reduced correlation between the secondary and the target trait. Therefore, multi-trait genomic prediction models for yield require scenario-specific correlated traits.

Key message Awn length was mapped using a multiparent population derived from cv. Morex and four wild accessions. One QTL was fine mapped and candidate genes were identified in NILs by RNA-seq. Abstract Barley awns are photosynthetically active and contribute to grain yield. Awn length is variable among both wild and cultivated barley genotypes and many mutants with alterations in awn length have been identified. Here, we used a multiparent mapping population derived from cv. Morex and four genetically diverse wild barley lines to detect quantitative trait loci (QTLs) for awn length. Twelve QTLs, distributed over the barley genome, were identified with the most significant one located on chromosome arm 7HL (QTL AL7.1). The effect of AL7.1 was confirmed using near isogenic lines (NILs) and fine-mapped in two independent heterogeneous inbred families to a

Genotype by environment interaction (G×E) for the target trait, e.g. yield, is an emerging property of agricultural systems and results from the interplay between a hierarchy of secondary traits involving the capture and allocation of environmental resources during the growing season. This hierarchy of secondary traits ranges from basic traits that correspond to response mechanisms/sensitivities, to intermediate traits that integrate a larger number of processes over time and therefore show a larger amount of G×E. Traits underlying yield differ in their contribution to adaptation across environmental conditions and have different levels of G×E. Here, we provide a framework to study the performance of genotype to phenotype (G2P) modeling approaches. We generate and analyze response surfaces, or adaptation landscapes, for yield and yield related traits, emphasizing the organization of the traits in a hierarchy and their development and interactions over time. We use the crop growth model APSIM-wheat with genotype-dependent parameters as a tool to simulate non-linear trait responses over time with complex trait dependencies and apply it to wheat crops in Australia. For biological realism, APSIM parameters were given a genetic basis of 300 QTLs sampled from a gamma distribution whose shape and rate parameters were estimated from real wheat data. In the simulations, the hierarchical organization of the traits and their interactions over time cause G×E for yield even when underlying traits do not show G×E. Insight into how G×E arises during growth and development helps to improve the accuracy of phenotype predictions within and across environments and to optimize trial networks. We produced a tangible simulated adaptation landscape for yield that we first investigated for its biological credibility by statistical models for G×E that incorporate genotypic and environmental covariables. Subsequently, the simulated trait data were used to evaluate statistical genotype-to-phenotype models for multiple traits and environments and to characterize relationships between traits over time and across environments, as a way to identify traits that could be useful to select for specific adaptation. Designed appropriately, these types of simulated landscapes might also serve as a basis to train other, more deep learning methodologies in order to transfer such network models to real-world situations.

New types of phenotyping tools generate large amounts of data on many aspects of plant physiology and morphology with high spatial and temporal resolution. These new phenotyping data are potentially useful to improve understanding and prediction of complex traits, like yield, that are characterized by strong environmental context dependencies, i.e., genotype by environment interactions. For an evaluation of the utility of new phenotyping information, we will look at how this information can be incorporated in different classes of genotype-to-phenotype (G2P) models. G2P models predict phenotypic traits as functions of genotypic and environmental inputs. In the last decade, access to high-density single nucleotide polymorphism markers (SNPs) and sequence information has boosted the development of a class of G2P models called genomic prediction models that predict phenotypes from genome wide marker profiles. The challenge now is to build G2P models that incorporate simultaneously extensive genomic information alongside with new phenotypic information. Beyond the modification of existing G2P models, new G2P paradigms are required. We present candidate G2P models for the integration of genomic and new phenotyping information and illustrate their use in examples. Special attention will be given to the modelling of genotype by environment interactions. The G2P models provide a framework for model based phenotyping and the evaluation of the utility of phenotyping information in the context of breeding programs. ispartof: Plant Science vol:282 pages:23-39 ispartof: location:MEXICO, Int Maize & Wheat Improvement Ctr status: Published online

An important aim of the analysis of agricultural field experiments is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper explores the use of two-dimensional smooth surfaces to model random spatial variation. We propose the use of anisotropic tensor product P-splines to explicitly model large-scale (global trend) and small-scale (local trend) spatial dependence. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. Each component in the model is shown to have an effective dimension. They are closely related to variance estimation, and helpful for characterising the importance of model components. An important result of this paper is the formal proof of the relation between several definitions of heritability and the effective dimension associated with the genetic component. The practical value of our approach is illustrated by simulations and analyses of large-scale plant breeding experiments. An \texttt{R}-package, \texttt{SpATS}, is provided

Heritability is a central parameter in quantitative genetics, both from 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 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 G-BLUP and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at 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 GWAS 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., 6 figures. Contains all the supplementary information (p. 30-54)

Molecular BioSystems 11(11), 3101-3110 (2015). doi:10.1039/C5MB00477B, Published by Royal Society of Chemistry, Cambridge

The potential for using whole genome sequencing (WGS) data in microbiological risk assessment (MRA) has been discussed on several occasions since the beginning of this century. Still, the proposed heuristic approaches have never been applied in a practical framework. This is due to the non-trivial problem of mapping microbial information consisting of thousands of loci onto a probabilistic scale for risks. The paradigm change for MRA involves translation of multidimensional microbial genotypic information to much reduced (integrated) phenotypic information and onwards to a single measure of human risk (i.e. probability of illness). In this paper a first approach in methodology development is described for the application of WGS data in MRA; this is supported by a practical example. That is, combining genetic data (single nucleotide polymorphisms; SNPs) for Shiga toxin-producing Escherichia coli (STEC) O157 with phenotypic data (in vitro adherence to epithelial cells as a proxy for virulence) leads to hazard identification in a Genome Wide Association Study (GWAS). This application revealed practical implications when using SNP data for MRA. These can be summarized by considering the following main issues: optimum sample size for valid inference on population level, correction for population structure, quantification and calibration of results, reproducibility of the analysis, links with epidemiological data, anchoring and integration of results into a systems biology approach for the translation of molecular studies to human health risk. Future developments in genetic data analysis for MRA should aim at resolving the mapping problem of processing genetic sequences to come to a quantitative description of risk. The development of a clustering scheme focusing on biologically relevant information of the microbe involved would be a useful approach in molecular data reduction for risk assessment.

Linkage disequilibrium decay in sugar beet is strongly affected by the breeding history, and varies extensively between and along chromosomes, allowing identification of known and unknown signatures of selection. Genetic diversity and linkage disequilibrium (LD) patterns were investigated in 233 elite sugar beet breeding lines and 91 wild beet accessions, using 454 single nucleotide polymorphisms (SNPs) and 418 SNPs, respectively. Principal coordinate analysis suggested the existence of three groups of germplasm, corresponding to the wild beets, the seed parent and the pollen parent breeding pool. LD was investigated in each of these groups, with and without correction for genetic relatedness. Without correction for genetic relatedness, in the pollen as well as the seed parent pool, LD persisted beyond 50 centiMorgan (cM) on four (2, 3, 4 and 5) and three chromosomes (2, 4 and 6), respectively; after correction for genetic relatedness, LD decayed after

Adjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials., MTM2014-55966-P Grains Research and Development Corporation (GRDC) of Australia National Institute of Agricultural Technology (INTA) of Argentina, Res. DN 1126/13 Integrated Breeding Program

The common assumption in quantitative trait locus (QTL) linkage mapping studies that parents of multiple connected populations are unrelated is unrealistic for many plant breeding programs. We remove this assumption and propose a Bayesian approach that clusters the alleles of the parents of the current mapping populations from locus-specific identity by descent (IBD) matrices that capture ancestral marker and pedigree information. Moreover, we demonstrate how the parental IBD data can be incorporated into a QTL linkage analysis framework by using two approaches: a Threshold IBD model (TIBD) and a Latent Ancestral Allele Model (LAAM). The TIBD and LAAM models are empirically tested via numerical simulation based on the structure of a commercial maize breeding program. The simulations included a pilot dataset with closely linked QTL on a single linkage group and 100 replicated datasets with five linkage groups harboring four unlinked QTL. The simulation results show that including parental IBD data (similarly for TIBD and LAAM) significantly improves the power and particularly accuracy of QTL mapping, e.g., position, effect size and individuals’ genotype probability without significantly increasing computational demand.

25 Pag., 5 Tabl., 6 Fig. The definitive version is available at: www.springerlink.com, Quantitative trait locus (QTL) detection is commonly performed by analysis of designed segregating populations derived from two inbred parental lines, where absence of selection, mutation and genetic drift is assumed. Even for designed populations, selection cannot always be avoided, with as consequence varying correlation between genotypes instead of uniform correlation. Akin to linkage disequilibrium mapping, ignoring this type of genetic relatedness will increase the rate of false-positives. In this paper, we advocate using mixed models including genetic relatedness, or ‘kinship’ information for QTL detection in populations where selection forces operated. We demonstrate our case with a three-way barley cross, designed to segregate for dwarfing, vernalization and spike morphology genes, in which selection occurred. The population of 161 inbred lines was screened with 1,536 single nucleotide polymorphisms (SNPs), and used for gene and QTL detection. The coefficient of coancestry matrix was estimated based on the SNPs and imposed to structure the distribution of random genotypic effects. The model incorporating kinship, coancestry, information was consistently superior to the one without kinship (according to the Akaike information criterion). We show, for three traits, that ignoring the coancestry information results in an unrealistically high number of marker–trait associations, without providing clear conclusions about QTL locations. We used a number of widely recognized dwarfing and vernalization genes known to segregate in the studied population as landmarks or references to assess the agreement of the mapping results with a priori candidate gene expectations. Additional QTLs to the major genes were detected for all traits as well., We want to thank INIA (MICINN) for partially funding this work through different grants. The Centre UdL-IRTA forms part of the Centre CONSOLIDER on Agrigenomics funded by the Spanish Ministry of Education and Science and acknowledges partial funding from grant AGL2005-07195-C02-02. Genotyping of the RIL population with BOPA1 was funded by the Spanish Ministry of Science and Innovation, project GEN2006-28560-E. The work of M.M. and FvE was partially financed by the Generation Challenge Programme, through the Integrated Breeding Platform projects ‘2.2.1. Develop and deploy statistical and genetic analysis methodology for molecular breeding’ and ‘3.2.4. Design and Analysis’. The research of FvE was partly financed by project BB9 of the Centre for Bio-Systems Genomics (CBSG), which is part of the Netherlands Genomics Initiative/Netherlands Organization for Scientific Research. This work was carried out within the research programme of the Netherlands Consortium for Systems Biology (NCSB), which is part of the Netherlands Genomics Initiative / Netherlands Organization for Scientific Research.

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models. © 2010 Elsevier Inc.

Genetic linkage and association studies are empowered by proper modeling of relatedness among individuals. Such relatedness can be inferred from marker and/or pedigree information. In this study, the genetic relatedness among n inbred individuals at a particular locus is expressed as an n × n square matrix Q. The elements of Q are identity-by-descent probabilities, that is, probabilities that two individuals share an allele descended from a common ancestor. In this representation the definition of the ancestral alleles and their number remains implicit. For human inspection and further analysis, an explicit representation in terms of the ancestral allele origin and the number of alleles is desirable. To this purpose, we decompose the matrix Q by a latent class model with K classes (latent ancestral alleles). Let P be an n × K matrix with assignment probabilities of n individuals to K classes constrained such that every element is nonnegative and each row sums to 1. The problem then amounts to approximating Q by PPT, while disregarding the diagonal elements. This is not an eigenvalue problem because of the constraints on P. An efficient algorithm for calculating P is provided. We indicate the potential utility of the latent ancestral allele model. For representative locus-specific Q matrices constructed for a set of maize inbreds, the proposed model recovered the known ancestry.

A Bayesian approach to analyze complex traits is presented that can help plant eneticists and breeders in exploiting the marker and phenotypic data on pedigreed populations as available from ongoing breeding programs. The statistical model for the quantitative trait may include non-genetic and genetic components. The latter component can be divided into QTL on known marker linkage groups, major genes and a polygenic component. The full probability model, prior assumptions on model variables are presented and criterion for model selection and posterior inferences are given. Simulated data on a known pedigreed population structure of the EU project HiDRAS was used to illustrate the use of the Bayesian approach to analyze complex traits. It was shown that estimates for QTL parameters were more accurate when non-genetic factors were included in the model and when a polygenic component was included when not all linkage groups were analyzed simultaneously. The Bayesian approach has been implemented into the software package FlexQTL and allows plant breeders explore their pedigreed populations for segregating QTL alleles that are relevant in their breeding program.

Prediction of the phenotypes for a set of genotypes across multiple environments is a fundamental task in any plant breeding program. Genomic prediction (GP) can assist selection decisions by combining incomplete phenotypic information over multiple environments (MEs) with dense sets of markers. We compared a range of ME-GP models differing in the way environment-specific genetic effects were modeled. Information among environments was shared either implicitly via the response variable, or by the introduction of explicit environmental covariables. We discuss the models not only in the light of their accuracy, but also in their ability to predict the different parts of the incomplete genotype × environment interaction (G × E) table: (G t ; E t ), (G u ; E t ), (G t ; E u ), and (G u ; E u ), where G is genotype, E is environment, both tested (t; in one or more instances) and untested (u). Using the ‘Steptoe’ × ‘Morex’ barley (Hordeum vulgare L.) population as an example, we show the advantage of ME-GP models that account for G × E. In addition, for our example data set, we show that for prediction in the most challenging scenario of untested environments (E u ), the use of explicit environmental information is preferable over the simpler approach of predicting from a main effects model. Besides producing the most general ME-GP model, the use of environmental covariables naturally links with ecophysiological and crop-growth models (CGMs) for G × E. We conclude with a list of future research topics in ME-GP, where we see CGMs playing a central role.

We present a general hidden Markov model framework called reconstructing ancestry blocks bit by bit (RABBIT) for reconstructing genome ancestry blocks from single-nucleotide polymorphism (SNP) array data, a required step for quantitative trait locus (QTL) mapping. The framework can be applied to a wide range of mapping populations such as the Arabidopsis multiparent advanced generation intercross (MAGIC), the mouse Collaborative Cross (CC), and the diversity outcross (DO) for both autosomes and X chromosomes if they exist. The model underlying RABBIT accounts for the joint pattern of recombination breakpoints between two homologous chromosomes and missing data and allelic typing errors in the genotype data of both sampled individuals and founders. Studies on simulated data of the MAGIC and the CC and real data of the MAGIC, the DO, and the CC demonstrate that RABBIT is more robust and accurate in reconstructing recombination bin maps than some commonly used methods.

In 2003, Xu obtained remarkably precise estimates of QTL positions despite the many markers simultaneously in his Bayesian model. We extend his model and Gibbs algorithm to ensure a valid posterior distribution and convergence to it, without changing the attractiveness of the method.

The next generation of QTL (quantitative trait loci) mapping populations have been designed with multiple founders, where one to a number of generations of intercrossing are introduced prior to the inbreeding phase to increase accumulated recombinations and thus mapping resolution. Examples of such populations are Collaborative Cross (CC) in mice and Multiparent Advanced Generation Inter-Cross (MAGIC) lines in Arabidopsis. The genomes of the produced inbred lines are fine-grained random mosaics of the founder genomes. In this article, we present a novel framework for modeling ancestral origin processes along two homologous autosomal chromosomes from mapping populations, which is a major component in the reconstruction of the ancestral origins of each line for QTL mapping. We construct a general continuous time Markov model for ancestral origin processes, where the rate matrix is deduced from the expected densities of various types of junctions (recombination breakpoints). The model can be applied to monoecious populations with or without self-fertilizations and to dioecious populations with two separate sexes. The analytic expressions for map expansions and expected junction densities are obtained for mapping populations that have stage-wise constant mating schemes, such as CC and MAGIC. Our studies on the breeding design of MAGIC populations show that the intercross mating schemes do not matter much for large population size and that the overall expected junction density, and thus map resolution, are approximately proportional to the inverse of the number of founders.

Managed environments in the form of well watered and water stressed trials were performed to study the genetic basis of grain yield and stay green in sorghum with the objective of validating previously detected QTL. As variations in phenology and plant height may influence QTL detection for the target traits, QTL for flowering time and plant height were introduced as cofactors in QTL analyses for yield and stay green. All but one of the flowering time QTL were detected near yield and stay green QTL. Similar co-localization was observed for two plant height QTL. QTL analysis for yield, using flowering time/plant height cofactors, led to yield QTL on chromosomes 2, 3, 6, 8 and 10. For stay green, QTL on chromosomes 3, 4, 8 and 10 were not related to differences in flowering time/plant height. The physical positions for markers in QTL regions projected on the sorghum genome suggest that the previously detected plant height QTL, Sb-HT9-1, and Dw2, in addition to the maturity gene, Ma5, had a major confounding impact on the expression of yield and stay green QTL. Co-localization between an apparently novel stay green QTL and a yield QTL on chromosome 3 suggests there is potential for indirect selection based on stay green to improve drought tolerance in sorghum. Our QTL study was carried out with a moderately sized population and spanned a limited geographic range, but still the results strongly emphasize the necessity of corrections for phenology in QTL mapping for drought tolerance traits in sorghum. Made available in DSpace on 2020-08-24T04:11:26Z (GMT). No. of bitstreams: 1 Studying-genetic.pdf: 478153 bytes, checksum: ed67faaaf2dbb17ce8ce6d332df279a2 (MD5) Previous issue date: 2012

To exploit the diversity in Arabidopsis thaliana , eight founder accessions were crossed to produce six recombinant inbred line (RIL) subpopulations, together called an Arabidopsis multiparent RIL (AMPRIL) population. Founders were crossed pairwise to produce four F1 hybrids. These F1s were crossed according to a diallel scheme. The resulting offspring was then selfed for three generations. The F4 generation was genotyped with SNP and microsatellite markers. Data for flowering time and leaf morphology traits were determined in the F5 generation. Quantitative trait locus (QTL) analysis for these traits was performed using especially developed mixed-model methodology, allowing tests for QTL main effects, QTL by background interactions, and QTL by QTL interactions. Because RILs were genotyped in the F4 generation and phenotyped in the F5 generation, residual heterozygosity could be used to confirm and fine-map a number of the QTLs in the selfed progeny of lines containing such heterozygosity. The AMPRIL population is an attractive resource for the study of complex traits.

To improve QTL detection power for QTL main effects and interactions and QTL mapping resolution, new types of multi-founder crossing populations are created in plants and animals. Some recent examples are complex intercrossed populations in mice and Arabidopsis thaliana. For the latter, a set of eight accessions was intercrossed to produce four two-way hybrids that were subsequently intercrossed again in a half diallel fashion leading to six subpopulations of four-way hybrids, each subpopulation containing 100 individuals. Within each subpopulation, individuals were inbred for four generations via single seed descent. QTL mapping in the complex crosses requires new statistical tools. We present a first sketch of a QTL mapping methodology for the complex cross in Arabidopsis based on mixed model analyses. As experimental data were not yet available, we illustrate our methodology on simulated but realistic data.

Species establishment in a model system in a homogeneous environment can be dependent not only on the parameter setting, but also on the initial conditions of the system. For instance, predator invasion into an established prey population can fail and lead to system collapse, an event referred to as overexploitation. This phenomenon occurs in models with bistability properties, such as strong Allee effects. The Allee effect then prevents easy re-establishment of the prey species. In this paper, we deal with the bifurcation analyses of two previously published predator-prey models with strong Allee effects. We expand the analyses to include not only local, but also global bifurcations. We show the existence of a point-to-point heteroclinic cycle in these models, and discuss numerical techniques for continuation in parameter space. The continuation of such a cycle in two-parameter space forms the boundary of a region in parameter space where the system collapses after predator invasion, i.e. where overexploitation occurs. We argue that the detection and continuation of global bifurcations in these models are of vital importance for the understanding of the model dynamics. © 2007 Elsevier Inc. All rights reserved.

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F5 maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.

Two outlines for mixed model based approaches to quantitative trait locus (QTL) mapping in existing maize hybrid selection programs are presented: a restricted maximum likelihood (REML) and a Bayesian Markov Chain Monte Carlo (MCMC) approach. The methods use the in-silico-mapping procedure developed by Parisseaux and Bernardo (2004) as a starting point. The original single-point approach is extended to a multi-point approach that facilitates interval mapping procedures. For computational and conceptual reasons, we partition the full set of relationships from founders to parents of hybrids into two types of relations by defining so-called intermediate founders. QTL effects are defined in terms of those intermediate founders. Marker based identity by descent relationships between intermediate founders define structuring matrices for the QTL effects that change along the genome. The dimension of the vector of QTL effects is reduced by the fact that there are fewer intermediate founders than parents. Furthermore, additional reduction in the number of QTL effects follows from the identification of founder groups by various algorithms. As a result, we obtain a powerful mixed model based statistical framework to identify QTLs in genetic backgrounds relevant to the elite germplasm of a commercial breeding program. The identification of such QTLs will provide the foundation for effective marker assisted and genome wide selection strategies. Analyses of an example data set show that QTLs are primarily identified in different heterotic groups and point to complementation of additive QTL effects as an important factor in hybrid performance.