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1AbstractGenetic improvements of discrete characteristics such as flower color, the genetic improvements are obvious and easy to demonstrate; however, for characteristics that are measured on continuous scales, the genetic contributions are incremental and less obvious. Reliable and accurate methods are required to disentangle the confounding genetic and non-genetic components of quantitative traits. Stochastic simulations of soybean (Glycine max (L.) Merr.) breeding programs were performed to evaluate models to estimate the realized genetic gain (RGG) from 30 years of multi-environment trials (MET). True breeding values were simulated under an infinitesimal model to represent the genetic contributions to soybean seed yield under various MET conditions. Estimators were evaluated using objective criteria of bias and linearity. Results indicated all estimation models were biased. Covariance modeling as well as direct versus indirect estimation resulted in substantial differences in RGG estimation. Although there were no unbiased models, the three best-performing models resulted in an average bias of ±7.41 kg/ha−1/yr−1(±0.11 bu/ac−1/yr−1). Rather than relying on a single model to estimate RGG, we recommend the application of multiple models and consider the range of the estimated values. Further, based on our simulations parameters, we do not think it is appropriate to use any single models to compare breeding programs or quantify the efficiency of proposed new breeding strategies. Lastly, for public soybean programs breeding for maturity groups II and III in North America from 1989 to 2019, the range of estimated RGG values was from 18.16 to 39.68 kg/ha−1/yr−1(0.27 to 0.59 bu/ac−1/yr−1).

Photosynthesis is a key target to improve crop production in many species including soybean [Glycine max (L.) Merr.]. A challenge is that phenotyping photosynthetic traits by traditional approaches is slow and destructive. There is proof-of-concept for leaf hyperspectral reflectance as a rapid method to model photosynthetic traits. However, the crucial step of demonstrating that hyperspectral approaches can be used to advance understanding of the genetic architecture of photosynthetic traits is untested. To address this challenge, we used full-range (500–2,400 nm) leaf reflectance spectroscopy to build partial least squares regression models to estimate leaf traits, including the rate-limiting processes of photosynthesis, maximum Rubisco carboxylation rate, and maximum electron transport. In total, 11 models were produced from a diverse population of soybean sampled over multiple field seasons to estimate photosynthetic parameters, chlorophyll content, leaf carbon and leaf nitrogen percentage, and specific leaf area (with R2 from 0.56 to 0.96 and root mean square error approximately

The Beavis effect in quantitative trait locus (QTL) mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners’ curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners’ curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated noncentral Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated noncentral Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300 k single nucleotide polymorphism markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction.

Maize has for many decades been both one of the most important crops worldwide and one of the primary genetic model organisms. More recently, maize breeding has been impacted by rapid technological advances in sequencing and genotyping technology, transformation including genome editing, doubled haploid technology, parallelled by progress in data sciences and the development of novel breeding approaches utilizing genomic information. Herein, we report on past, current and future developments relevant for maize breeding with regard to (1) genome analysis, (2) germplasm diversity characterization and utilization, (3) manipulation of genetic diversity by transformation and genome editing, (4) inbred line development and hybrid seed production, (5) understanding and prediction of hybrid performance, (6) breeding methodology and (7) synthesis of opportunities and challenges for future maize breeding.

Plant breeding is a decision making discipline based on understanding project objectives. Genetic improvement projects can have two competing objectives: maximize rate of genetic improvement and minimize loss of useful genetic variance. For commercial plant breeders competition in the marketplace forces greater emphasis on maximizing immediate genetic improvements. In contrast public plant breeders have an opportunity, perhaps an obligation, to place greater emphasis on minimizing loss of useful genetic variance while realizing genetic improvements. Considerable research indicates that short term genetic gains from Genomic Selection (GS) are much greater than Phenotypic Selection (PS), while PS provides better long term genetic gains because PS retains useful genetic diversity during the early cycles of selection. With limited resources must a soybean breeder choose between the two extreme responses provided by GS or PS? Or is it possible to develop novel breeding strategies that will provide a desirable compromise between the competing objectives? To address these questions, we decomposed breeding strategies into decisions about selection methods, mating designs and whether the breeding population should be organized as family islands. For breeding populations organized into islands decisions about possible migration rules among family islands were included. From among 60 possible strategies, genetic improvement is maximized for the first five to ten cycles using GS, a hub network mating design in breeding populations organized as fully connected family islands and migration rules allowing exchange of two lines among islands every other cycle of selection. If the objectives are to maximize both short-term and long-term gains, then the best compromise strategy is similar except a genomic mating design, instead of a hub networked mating design, is used. This strategy also resulted in realizing the greatest proportion of genetic potential of the founder populations. Weighted genomic selection applied to both non-isolated and island populations also resulted in realization of the greatest proportion of genetic potential of the founders, but required more cycles than the best compromise strategy.

Selection of markers linked to alleles at quantitative trait loci (QTL) for tolerance to Iron Deficiency Chlorosis (IDC) has not been successful. Genomic selection has been advocated for continuous numeric traits such as yield and plant height. For ordinal data types such as IDC, genomic prediction models have not been systematically compared. The objectives of research reported in this manuscript were to evaluate the most commonly used genomic prediction method, ridge regression and it’s equivalent logistic ridge regression method, with algorithmic modeling methods including random forest, gradient boosting, support vector machine, K-nearest neighbors, Naïve Bayes, and artificial neural network using the usual comparator metric of prediction accuracy. In addition we compared the methods using metrics of greater importance for decisions about selecting and culling lines for use in variety development and genetic improvement projects. These metrics include specificity, sensitivity, precision, decision accuracy, and area under the receiver operating characteristic curve. We found that Support Vector Machine provided the best specificity for culling IDC susceptible lines, while Random Forest GP models provided the best combined set of decision metrics for retaining IDC tolerant and culling IDC susceptible lines.

Models have been developed to account for heterogeneous spatial variation in field trials. These spatial models have been shown to successfully increase the quality of phenotypic data resulting in improved effectiveness of selection by plant breeders. The models were developed for continuous data types such as grain yield and plant height, but data for most traits, such as in iron deficiency chlorosis (IDC), are recorded on ordinal scales. Is it reasonable to make spatial adjustments to ordinal data by simply applying methods developed for continuous data? The objective of the research described herein is to evaluate methods for spatial adjustment on ordinal data, using soybean IDC as an example. Spatial adjustment models are classified into three different groups: group I, moving average grid adjustment; group II, geospatial autoregressive regression (SAR) models; and group III, tensor product penalized P-splines. Comparisons of eight models sampled from these three classes demonstrate that spatial adjustments depend on severity of field heterogeneity, the irregularity of the spatial patterns, and the model used. SAR models generally produce better performance metrics than other classes of models. However, none of the eight evaluated models fully removed spatial patterns indicating that there is a need to either adjust existing models or develop novel models for spatial adjustments of ordinal data collected in fields exhibiting discontinuous transitions between heterogeneous patches.

Herein we report the impacts of applying five selection methods across 40 cycles of recurrent selection and identify interactions among factors that affect genetic responses in sets of simulated families of recombinant inbred lines derived from 21 homozygous soybean lines. Our use of recurrence equation to model response from recurrent selection allowed us to estimate the half-lives, asymptotic limits to recurrent selection for purposes of assessing the rates of response and future genetic potential of populations under selection. The simulated factors include selection methods, training sets, and selection intensity that are under the control of the plant breeder as well as genetic architecture and heritability. A factorial design to examine and analyze the main and interaction effects of these factors showed that both the rates of genetic improvement in the early cycles and limits to genetic improvement in the later cycles are significantly affected by interactions among all factors. Some consistent trends are that genomic selection methods provide greater initial rates of genetic improvement (per cycle) than phenotypic selection, but phenotypic selection provides the greatest long term responses in these closed genotypic systems. Model updating with training sets consisting of data from prior cycles of selection significantly improved prediction accuracy and genetic response with three parametric genomic prediction models. Ridge Regression, if updated with training sets consisting of data from prior cycles, achieved better rates of response than BayesB and Bayes LASSO models. A Support Vector Machine method, with a radial basis kernel, had the worst estimated prediction accuracies and the least long term genetic response. Application of genomic selection in a closed breeding population of a self-pollinated crop such as soybean will need to consider the impact of these factors on trade-offs between short term gains and conserving useful genetic diversity in the context of the goals for the breeding program.

Soybean is the world’s leading source of vegetable protein and demand for its seed continues to grow. Breeders have successfully increased soybean yield, but the genetic architecture of yield and key agronomic traits is poorly understood. We developed a 40-mating soybean nested association mapping (NAM) population of 5,600 inbred lines that were characterized by single nucleotide polymorphism (SNP) markers and six agronomic traits in field trials in 22 environments. Analysis of the yield, agronomic, and SNP data revealed 23 significant marker-trait associations for yield, 19 for maturity, 15 for plant height, 17 for plant lodging, and 29 for seed mass. A higher frequency of estimated positive yield alleles was evident from elite founder parents than from exotic founders, although unique desirable alleles from the exotic group were identified, demonstrating the value of expanding the genetic base of US soybean breeding.

SummaryWe present GWASpro, a high-performance web server for the analyses of large-scale genome-wide association studies (GWAS). GWASpro was developed to provide data analyses for large-scale molecular genetic data, coupled with complex replicated experimental designs such as found in plant science investigations and to overcome the steep learning curves of existing GWAS software tools. GWASpro supports building complex design matrices, by which complex experimental designs that may include replications, treatments, locations and times, can be accounted for in the linear mixed model. GWASpro is optimized to handle GWAS data that may consist of up to 10 million markers and 10 000 samples from replicable lines or hybrids. GWASpro provides an interface that significantly reduces the learning curve for new GWAS investigators.Availability and implementationGWASpro is freely available at https://bioinfo.noble.org/GWASPRO.Supplementary informationSupplementary data are available at Bioinformatics online.

An epistatic genetic architecture can have a significant impact on prediction accuracies of genomic prediction (GP) methods. Machine learning methods predict traits comprised of epistatic genetic architectures more accurately than statistical methods based on additive mixed linear models. The differences between these types of GP methods suggest a diagnostic for revealing genetic architectures underlying traits of interest. In addition to genetic architecture, the performance of GP methods may be influenced by the sample size of the training population, the number of QTL, and the proportion of phenotypic variability due to genotypic variability (heritability). Possible values for these factors and the number of combinations of the factor levels that influence the performance of GP methods can be large. Thus, efficient methods for identifying combinations of factor levels that produce most accurate GPs is needed. Herein, we employ response surface methods (RSMs) to find the experimental conditions that produce the most accurate GPs. We illustrate RSM with an example of simulated doubled haploid populations and identify the combination of factors that maximize the difference between prediction accuracies of best linear unbiased prediction (BLUP) and support vector machine (SVM) GP methods. The greatest impact on the response is due to the genetic architecture of the population, heritability of the trait, and the sample size. When epistasis is responsible for all of the genotypic variance and heritability is equal to one and the sample size of the training population is large, the advantage of using the SVM method vs. the BLUP method is greatest. However, except for values close to the maximum, most of the response surface shows little difference between the methods. We also determined that the conditions resulting in the greatest prediction accuracy for BLUP occurred when genetic architecture consists solely of additive effects, and heritability is equal to one.

Key message Using an Operations Research approach, we demonstrate design of optimal trait introgression projects with respect to competing objectives. Abstract We demonstrate an innovative approach for designing Trait Introgression (TI) projects based on optimization principles from Operations Research. If the designs of TI projects are based on clear and measurable objectives, they can be translated into mathematical models with decision variables and constraints that can be translated into Pareto optimality plots associated with any arbitrary selection strategy. The Pareto plots can be used to make rational decisions concerning the trade-offs between maximizing the probability of success while minimizing costs and time. The systematic rigor associated with a cost, time and probability of success (CTP) framework is well suited to designing TI projects that require dynamic decision making. The CTP framework also revealed that previously identified ‘best’ strategies can be improved to be at least twice as effective without increasing time or expenses. Electronic supplementary material The online version of this article (doi:10.1007/s00122-017-2938-9) contains supplementary material, which is available to authorized users.

The development of ubiquitous polymorphic genetic markers that span the genome have made it possible for quantitative and molecular geneticists to investigate what M. D. Edwards et al. referred to as the numbers, magnitudes, and distributions of quantitative trait loci (QTL). QTL are identified as significant statistical associations between genotypic values and phenotypic variability among the segregating progeny. Magnitude of QTL effects are reported as the minimum and maximum percent of phenotypic variability explained by the significant QTL. Genomic locations of the QTL with estimated large effects mapped to syntenic regions across all three genera. Identification of QTL for agronomically important traits has been pursued through progeny derived from intraspecific crosses of adapted inbred lines. There is a tendency to make the inferential leap from QTL to physiology of gene effects at genetic loci, but QTL are, by definition, merely significant statistical associations.

SIGNIFICANCE Vertically yoked prisms have been used in treatment of binocular vision dysfunction despite minimal supporting evidence. In people with normal binocular vision, the impact on phorias has been assessed but not the impact on accommodation, accommodation vergence interactions, or the horopter. We found that vertically yoked prisms have minor effects during short-term wear in young adults. PURPOSE The purpose of this study was to determine effects of vertically yoked prisms on accommodative response and several binocular vision tasks. METHODS There were 45 participants aged 18 to 24 years. The 23 myopes wore distance-corrected soft contact lenses. In a random arrangement, each person wore spectacles containing planopower lenses with either 8 Δ base-up, 4 Δ base-up, zero, 4 Δ base-down, and 8 Δ base-down prisms. Before spectacle wear, baseline measurements of near heterophoria, accommodation response, negative and positive relative accommodations, fusional vergence, and Nonius-horopter spatial perception were taken. Measurements were repeated after a 40-minute wear, spectacles were removed, and tests were performed 20 minutes later. On a 22-participant subset, on a separate occasion, measurements of heterophoria, accommodation response, and relative accommodation were made immediately after spectacles were fitted. RESULTS Most changes relative to baseline were not significant. Where effects occurred, these were nearly all associated with prism presence rather than adaptation. There were significant effects on accommodation response, but these seem to be refraction effects produced by pantoscopic tilt-induced power changes rather than perceptual effects altering accommodation. There were statistically significant effects on negative relative accommodation (P < .01), with zero prism giving more negative relative accommodation than 8 Δ base-down prisms. Tendencies were noted for prisms to move horopter limits toward the observer. Effects were small and likely not of clinical relevance. CONCLUSIONS Vertically yoked prisms have minor effects on accommodation and binocular vision, at least during short-term wear in young adults with normal binocular vision.

Soybean, Glycine max (L.) Merr., has been grown as a forage and as an important protein and oil crop for thousands of years. Domestication, breeding improvements and enhanced cropping systems have made soybeans the most cultivated and utilized oilseed crop globally. Soybeans provide a high-quality protein source for livestock and aquaculture, oil for industrial uses and a valued component of human diets. Originating in China and Eastern Asia, today 80–85% of the world’s soybeans, approximately 88 million ha, are grown in the Western Hemisphere. United States soybean breeding and development efforts for over 80 years have transitioned from primarily universities and United States Department of Agriculture (USDA) programs to private company-led investments in commercial cultivar development. Soybean breeders continuously adapt tools and technologies that encompass classical breeding, mutation breeding and marker-assisted selection, biotechnology and transgenic approaches, gene silencing, and genome editing. In addition to breeding technologies, improved agronomics, precision agriculture and digital agriculture have advanced soybean production and profitability. The primary goals of soybean breeding and cropping systems advances include yield improvement, increased seed protein and oil composition and quality, and yield preservation through weed, pathogen, insect pest and abiotic stress resistance and management. This chapter primarily describes the introduction and improvement of soybeans in the United States. Contributing authors describe classical and molecular breeding, biotechnology, biotic and abiotic stress management, and soybean agronomics and cropping systems improvements that maximize soybean productivity, profitability and sustainability to supply a continually increasing world demand for protein and oil for feed, fuel and food.

We present the generalized numerator relationship matrix (GNRM) algorithm and Numericware N as a software tool for calculating the numerator relationship matrix (NRM). The GNRM algorithm aims to build the NRM based on plant pedigrees. Customary plant pedigrees have a sparse format representing multiple ancestors and offspring. Applying the existing NRM algorithm to plant pedigrees requires transforming the pedigree statements from sparse (multi-founders to offspring) to dense (bi-parents to offspring). The GNRM algorithm enables the computation of the NRM using sparse pedigrees. Because sparse pedigrees can be used, Numericware N produces smaller dimensions of the NRM, thus making computing time much faster. Moreover, Numericware N enables expansion of identical by state (IBS) matrix for scheduled pedigrees, which allows prediction of IBS matrix.

The purpose of breeding programs is to obtain sustainable gains in multiple traits while controlling the loss of genetic variation. The decisions at each breeding cycle involve multiple, usually competing, objectives; these complex decisions can be supported by the insights that are gained by applying multi-objective optimization principles to breeding. The discussion in this manuscript includes the definition of several multi-objective optimized breeding approaches within the phenotypic or genomic breeding frameworks and the comparison of these approaches with the standard multi-trait breeding schemes such as tandem selection, independent culling and index selection. Proposed methods are demonstrated with two empirical data sets and simulations. In addition, we have described several graphical tools that can aid breeders in arriving at a compromise decision. The results show that the proposed methodology is a viable approach to answer several real breeding problems. In simulations, the newly proposed methods resulted in gains larger than the methods previously proposed including index selection: Compared to the best alternative breeding strategy, the gains from multi-objective optimized parental proportions approaches were about 20–30% higher at the end of long-term simulations of breeding cycles. In addition, the flexibility of the multi-objective optimized breeding strategies were displayed with methods and examples covering non-dominated selection, assignment of optimal parental proportions, using genomewide marker effects in producing optimal mating designs, and finally in selection of training populations for genomic prediction.

87 INTRODUCTION 88 MATERIALS AND METHODS 90 Materials 90 Field Evaluation 93 Statistical Analyses 94 RESULTS 97 DISCUSSION 104 REFERENCES CITED 109 GENERAL CONCLUSIONS 111 ADDITIONAL REFERENCES CITED 115 ACKNOWLEDGMENTS 125

Genetic improvement toward optimized and stable agronomic performance of soybean genotypes is desirable for food security. Understanding how genotypes perform in different environmental conditions helps breeders develop sustainable cultivars adapted to target regions. Complex traits of importance are known to be controlled by a large number of genomic regions with small effects whose magnitude and direction are modulated by environmental factors. Knowledge of the constraints and undesirable effects resulting from genotype by environmental interactions is a key objective in improving selection procedures in soybean breeding programs. In this study, the genetic basis of soybean grain yield responsiveness to environmental factors was examined in a large soybean nested association population. For this, a genome-wide association to performance stability estimates generated from a Finlay-Wilkinson analysis and the inclusion of the interaction between marker genotypes and environmental factors was implemented. Genomic footprints were investigated by analysis and meta-analysis using a recently published multiparent model. Results indicated that specific soybean genomic regions were associated with stability, and that multiplicative interactions were present between environments and genetic background. Seven genomic regions in six chromosomes were identified as being associated with genotype-by-environment interactions. This study provides insight into genomic assisted breeding aimed at achieving a more stable agronomic performance of soybean, and documented opportunities to exploit genomic regions that were specifically associated with interactions involving environments and subpopulations.

A set of nested association mapping (NAM) families was developed by crossing 40 diverse soybean [ (L.) Merr.] genotypes to the common cultivar. The 41 parents were deeply sequenced for SNP discovery. Based on the polymorphism of the single-nucleotide polymorphisms (SNPs) and other selection criteria, a set of SNPs was selected to be included in the SoyNAM6K BeadChip for genotyping the parents and 5600 RILs from the 40 families. Analysis of the SNP profiles of the RILs showed a low average recombination rate. We constructed genetic linkage maps for each family and a composite linkage map based on recombinant inbred lines (RILs) across the families and identified and annotated 525,772 high confidence SNPs that were used to impute the SNP alleles in the RILs. The segregation distortion in most families significantly favored the alleles from the female parent, and there was no significant difference of residual heterozygosity in the euchromatic vs. heterochromatic regions. The genotypic datasets for the RILs and parents are publicly available and are anticipated to be useful to map quantitative trait loci (QTL) controlling important traits in soybean.

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE.

The use of nonlinear functions provides a concise measure of a variety of physiological traits associated with growth and development that would otherwise be difficult to observe. Maize kernel growth and development is a complex process, and the description of the processes involved benefits from the application of a nonlinear function to the process over growing degree days (GDD), a measure of heat accumulation over a period of development. The objective of this study was to compare and contrast canonical models of growth and development to determine which provided the best description of maize kernel biomass accumulation. Observations of kernel dry weights starting shortly after pollination through maturity were regressed onto a measure of thermal time. Observations from differing maize hybrids taken in two years with significantly different weather patterns were used to construct the model. Of the four nonlinear functions described, the Weibull and Gompertz functions were found to describe the pattern of biomass accumulation best. The Gompertz function was selected to describe kernel growth based on information criteria, biological interpretation of the parameters, and computational ease. Tests of autocorrelation and homogeneity of errors determined that the errors were heteroscedastic but autocorrelation was not an issue. The application of a variance function, which models the residuals as a function of the variance, was used to account for heteroscedastic errors. While the Gompertz function was selected as the best fit for use with this data set, it is suggested that future studies use the selection process described herein to determine the most appropriate function.

b-glucan, a soluble fiber found in oat ( Avena sativa L.) grain, is good for human health, and selection for higher levels of this compound is regarded as an important breeding objective. recent advances in oat DNA markers pres - ent an opportunity to investigate new selection methods for polygenic traits such as b -glucan concentration. our objectives in this study were to compare genomic, marker-assisted, and best linear unbiased prediction (BLUp )-based phe- notypic selection for short-term response to selection and ability to maintain genetic variance for b-glucan concentration. Starting with a col - lection of 446 elite oat lines from North America, each method was conducted for two cycles. The average b-glucan concentration increased from 4.57 g/100 g in Cycle 0 to between 6.66 and 6.88 g/100 g over the two cycles. The aver - ages of marker-based selection methods in Cycle 2 were greater than those of phenotypic selection (0.08). progenies with the highest b-glucan came from the marker-based selection methods. Marker-assisted selection (MAS) for higher b-glucan concentration resulted in a later heading date. We also found that marker-based selection methods maintained greater genetic variance than did BLUp phenotypic selection, potentially enabling greater future selection gains. overall, the results of these experiments suggest that genomic selection is a superior method for selecting a polygenic complex trait like b-glucan concentration.

Han et al. introduce a new metric, the Predicted Cross Value (PCV), for selecting breeding parents. Unlike estimated breeding values, which represent... We consider the plant genetic improvement challenge of introgressing multiple alleles from a homozygous donor to a recipient. First, we frame the project as an algorithmic process that can be mathematically formulated. We then introduce a novel metric for selecting breeding parents that we refer to as the predicted cross value (PCV). Unlike estimated breeding values, which represent predictions of general combining ability, the PCV predicts specific combining ability. The PCV takes estimates of recombination frequencies as an input vector and calculates the probability that a pair of parents will produce a gamete with desirable alleles at all specified loci. We compared the PCV approach with existing estimated-breeding-value approaches in two simulation experiments, in which 7 and 20 desirable alleles were to be introgressed from a donor line into a recipient line. Results suggest that the PCV is more efficient and effective for multi-allelic trait introgression. We also discuss how operations research can be used for other crop genetic improvement projects and suggest several future research directions.

Herein we introduce software, Numericware i to compute a matrix consisting of all pairwise identical in state (IIS) coefficients from genotypic data. Since the emergence of high throughput technology for genotyping, calculating an IIS matrix between many pairs of entities has required large computer memory and lengthy processing times. Numericware i addresses these limitations with two algorithmic methods: multithreading and forward chopping. The multithreading feature allows computational routines to concurrently run on multiple CPU processors. The forward chopping addresses memory limitations by dividing the genotypic data into appropriately sized subsets. Numericware i allows researchers who need to estimate an IIS matrix for big genotypes to use typical laptop/desktop computers. For comparison with different software, we calculated genetic relationship matrices using Numericware i, SPAGeDi and TASSEL with the same small-sized data set. Numericware i measured kinship coefficients between zero and two, while the matrices from SPAGeDi and TASSEL produced different ranges of values, including negative values. The Pearson correlation coefficient between the matrices from Numericware i and TASSEL was high at 0.993, while SPAGeDi rarely showed correlation with Numericware i (0.088) and TASSEL (0.087). To compare the capacity with high dimensional data, we applied the three software to a simulated data set consisted of 500 entities by 1,000,000 SNPs. Numericware i spent 71 minutes using seven CPU cores on a laptop (DELL LATITUDE E6540), while SPAGeDi and TASSEL failed to start. Numericware i is freely available for Windows and Linux under CC-BY license at https://figshare.com/s/f100f33a8857131eb2db.

Previously we reported the inability of genomic prediction methods based on linear models to accurately predict trait values composed of an epistatic genetic architecture. We also reported non-parametric genomic prediction methods applied to the same data produced reasonably accurate predictions. The difference led us to propose analyses by paired parametric and non-parametric methods to the same data could be used as a diagnostic for epistatic genetic architectures in typical plant breeding populations. The suggested computational diagnostic was based on evaluation of 14 genomic prediction methods applied to eight sets of simulated conditions consisting of three factors, each with two levels. Because the potential set of factors that might affect accuracies of genomic predictions is unknown, there is a need for a systematic approach to identify combinations of factors that impact estimates of accuracy. Herein we propose the application of response surface methods to systematically identify conditions that maximize the difference between estimated accuracies of genomic prediction methods. The results indicate that genetic architecture and repeatability at their upper boundaries for complete epistasis and repeatability have the greatest influence on the differences between parametric and non-parametric estimated prediction accuracies. Further, the surface is very steep in the vicinity of the boundary conditions, indicating that the proposed diagnostic is of limited value for discovery of epistatic genetic architectures.

We present a multi-objective integer programming model for the gene stacking problem, which is to bring desirable alleles found in multiple inbred lines to a single target genotype. Pareto optimal solutions from the model provide strategic stacking schemes to maximize the likelihood of successfully creating the target genotypes and to minimize the number of generations associated with a stacking strategy. A consideration of genetic diversity is also incorporated in the models to preserve all desirable allelic variants in the target population. Although the gene stacking problem is proved to be NP-hard, we have been able to obtain Pareto frontiers for smaller sized instances within one minute using the state-of-the-art commercial computer solvers in our computational experiments.

Genomic selection (GS) is a method to estimate the breeding values of individuals by using markers throughout the genome. We evaluated the accuracies of GS using data from fi ve traits on 446 oat (Avena sativa L.) lines genotyped with 1005 Diversity Array Technology (DArT) markers and two GS methods (ridge regression–best linear unbiased prediction [RR-BLUP] and BayesCπ) under various training designs. Our objectives were to (i) determine accuracy under increasing marker density and training population size, (ii) assess accuracies when data is divided over time, and (iii) examine accuracy in the presence of population structure. Accuracy increased as the number of markers and training size become larger. Including older lines in the training population increased or maintained accuracy, indicating that older generations retained information useful for predicting validation populations. The presence of population structure affected accuracy: when training and validation subpopulations were closely related accuracy was greater than when they were distantly related, implying that linkage disequilibrium (LD) relationships changed across subpopulations. Across many scenarios involving large training populations, the accuracy of BayesCπ and RR-BLUP did not differ. This empirical study provided evidence regarding the application of GS to hasten the delivery of cultivars through the use of inexpensive and abundant molecular markers available to the public sector. T HE DECREASING COST of high-density molecular markers allows saturation of crop genomes with genetic markers and off ers an approach to predict genetic merit. Th ese markers can help capture the eff ects of many quantitative trait loci (QTL) controlling polygenic traits regardless of location of the QTL in the genome by using linkage disequilibrium (LD), the nonrandom association of alleles at diff erent loci (Falconer and Mackay, 1996). Meuwissen et al. (2001) proposed genomic selection (GS) based on prediction of the genetic value of individuals or the genomic estimated breeding values (GEBV) from high-density markers positioned throughout the genome. Because GS includes all markers, major and polygenic eff ects can be captured, potentially explaining more genetic variance (Solberg et al., 2008). Th erefore, the objective of GS is to predict the breeding value of each individual instead of identifying QTL for use in a tradi

Identification of functional markers (FMs) provides information about the genetic architecture underlying complex traits. An approach that combines the strengths of linkage and association mapping, referred to as nested association mapping (NAM), has been proposed to identify FMs in many plant species. The ability to identify and resolve FMs for complex traits depends upon a number of factors including frequency of FM alleles, magnitudes of their genetic effects, disequilibrium among functional and nonfunctional markers, statistical analysis methods, and mating design. The statistical characteristics of power, accuracy, and precision to identify FMs with a NAM population were investigated using three simulation studies. The simulated data sets utilized publicly available genetic sequences and simulated FMs were identified using least-squares variable selection methods. Results indicate that FMs with simple additive genetic effects that contribute at least 5% to the phenotypic variability in at least five segregating families of a NAM population consisting of recombinant inbred progeny derived from 28 matings with a single reference inbred will have adequate power to accurately and precisely identify FMs. This resolution and power are possible even for genetic architectures consisting of disequilibrium among multiple functional and nonfunctional markers in the same genomic region, although the resolution of FMs will deteriorate rapidly if more than two FMs are tightly linked within the same amplicon. Finally, nested mating designs involving several reference parents will have a greater likelihood of resolving FMs than single reference designs.

Nested Association Mapping (NAM) has been proposed as a means to combine the power of linkage mapping with the resolution of association mapping. It is enabled through sequencing or array genotyping of parental inbred lines while using low-cost, low-density genotyping technologies for their segregating progenies. For purposes of data analyses of NAM populations, parental genotypes at a large number of Single Nucleotide Polymorphic (SNP) loci need to be projected to their segregating progeny. Herein we demonstrate how approximately 0.5 million SNPs that have been genotyped in 26 parental lines of the publicly available maize NAM population can be projected onto their segregating progeny using only 1,106 SNP loci that have been genotyped in both the parents and their 5,000 progeny. The challenge is to estimate both the genotype and genetic location of the parental SNP genotypes in segregating progeny. Both challenges were met by estimating their expected genotypic values conditional on observed flanking markers through the use of both physical and linkage maps. About 90%, of 500,000 genotyped SNPs from the maize HapMap project, were assigned linkage map positions using linear interpolation between the maize Accessioned Gold Path (AGP) and NAM linkage maps. Of these, almost 70% provided high probability estimates of genotypes in almost 5,000 recombinant inbred lines.

The analysis of gene expression microarrays plays an important role in elucidating the functionality of genes, including the discovery of genetic interactions that regulate gene expression. Several methods for modeling such gene regulatory networks exist, including a variety of continuous and discrete models. Methods based on fuzzy logic provide an interesting alternative. However, the guidelines for modeling gene expression with fuzzy logic are fairly open, and the need arises to investigate how adjustments in the modeling scheme will affect the results. In this work, we modify an existing fuzzy logic algorithm to involve an arbitrary number of classification states, and investigate the limiting behavior as the number of states tends to infinity. We also propose a probabilistic model as an alternative to the fuzzy logic model. We investigate the behavior of both models using yeast cell-cycle data and the simulated data of Werhli et al. [A.V. Werhli, M. Grzegorczyk, D. Husmeier, Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models, and Bayesian networks, Bioinformatics 22 (2006) 2523-2531]. We found that altering the number of classification states in both the fuzzy logic and probability models can influence which networks are predicted by both models. As the number of states tends to infinity, the predictions made by both models converge to those of a regression model. Models with a small to moderate number of classification states produced better results from a biological standpoint, compared to models with higher numbers of states. In simulated data, models with differing numbers of classification states produced similar overall results. Thus, increasing the complexity of the models has no apparent benefit, and models with smaller numbers of classification states are therefore preferred based on their ease of linguistic interpretation. The software used in this paper is freely available for non-commercial use at http://louisville.edu/~g0broc01.

Infection is a leading cause of neonatal morbidity and mortality worldwide. Premature neonates are particularly susceptible to infection because of physiologic immaturity, comorbidity, and extraneous medical interventions. Additionally premature infants are at higher risk of progression to sepsis or severe sepsis, adverse outcomes, and antimicrobial toxicity. Currently initial diagnosis is based upon clinical suspicion accompanied by nonspecific clinical signs and is confirmed upon positive microbiologic culture results several days after institution of empiric therapy. There exists a significant need for rapid, objective, in vitro tests for diagnosis of infection in neonates who are experiencing clinical instability. We used immunoassays multiplexed on microarrays to identify differentially expressed serum proteins in clinically infected and non-infected neonates. Immunoassay arrays were effective for measurement of more than 100 cytokines in small volumes of serum available from neonates. Our analyses revealed significant alterations in levels of eight serum proteins in infected neonates that are associated with inflammation, coagulation, and fibrinolysis. Specifically P- and E-selectins, interleukin 2 soluble receptor alpha, interleukin 18, neutrophil elastase, urokinase plasminogen activator and its cognate receptor, and C-reactive protein were observed at statistically significant increased levels. Multivariate classifiers based on combinations of serum analytes exhibited better diagnostic specificity and sensitivity than single analytes. Multiplexed immunoassays of serum cytokines may have clinical utility as an adjunct for rapid diagnosis of infection and differentiation of etiologic agent in neonates with clinical decompensation.

It has been well established that gene expression data contain large amounts of random variation that affects both the analysis and the results of microarray experiments. Typically, microarray data are either tested for differential expression between conditions or grouped on the basis of profiles that are assessed temporally or across genetic or environmental conditions. While testing differential expression relies on levels of certainty to evaluate the relative worth of various analyses, cluster analysis is exploratory in nature and has not had the benefit of any judgment of statistical inference. By using a novel dissimilarity function to ascertain gene expression clusters and conditional randomization of the data space to illuminate distinctions between statistically significant clusters of gene expression patterns, we aim to provide a level of confidence to inferred clusters of gene expression data. We apply both permutation and convex hull approaches for randomization of the data space and show that both methods can provide an effective assessment of gene expression profiles whose coregulation is statistically different from that expected by random chance alone.

On December 14 to 15, 2004, some 50 legume researchers and funding agency representatives (the latter as observers) met in Santa Fe, New Mexico, to develop a plan for cross-legume genomics research. This conference was one of the outcomes of the Legume Crops Genome Initiative (LCGI), an organization

The goal of the Complex Trait Consortium is to promote the development of resources that can be used to understand, treat and ultimately prevent pervasive human diseases. Existing and proposed mouse resources that are optimized to study the actions of isolated genetic loci on a fixed background are less effective for studying intact potygenic networks and interactions among genes, environments, pathogens and other factors. The Collaborative Cross will provide a common reference panel specifically designed for the integrative analysis of complex systems and will change the way we approach human health and disease.

Particle production of charged kaons in central Au+Au collisions at has been studied as a function of rapidity by the BRAHMS collaboration at RHIC. The kaon spectral shapes are described well by an exponential in transverse mass for the rapidity range of 0 ≤ yK ≤ 3.3 with smoothly decreasing inverse slopes as the rapidity increases. For the charged kaon to pion ratios, while there is no significant rapidity dependence for the K+/π+ ratio, the K−/π− ratio shows a significant decrease from y ≈ 1 towards higher rapidities. The systematics of K−/K+ and ratios in the measured rapidity range demonstrates a strongly correlated behaviour which can be described by thermal–statistical models.