Computer simulation permits answering theoretical and applied questions in animal and plant breeding. Blib is a novel multi-module simulation platform, which is able to handle more complicated genetic effects and models than most existing tools. In this study, we describe one major and unified application module of Blib, i.e., ISB (abbreviated from in silico breeding), for simulating the three categories of breeding programs for developing clonal, pure-line and hybrid cultivars in plants. Genetic models on environments and breeding-targeted traits, one or several parental populations, and a number of breeding methods are key elements to run simulation experiments in ISB, which are arranged in three external input files by given formats. Applications of ISB are illustrated by three case studies, representing the three categories of plant breeding programs. Under the condition that 5000 F₁ progenies were generated and tested from 50 heterozygous parents, Case study Ⅰ showed that 50 crosses, each of 100 progenies, made the best balance between genetic achievement and field cost. In Case study Ⅱ, one optimum breeding method was identified by which the pure lines with high yield and medium maturity could be developed. Case study Ⅲ investigated the genetic consequence in hybrid breeding from five testers. One tester was identified for the simultaneous improvement in F₁ hybrids and inbred lines. In summary, ISB identified a balanced crossing scheme, an optimum pure-line selection method, and an optimized tester in three case studies which are relevant to plant breeding. We believe the prediction by simulation would be highly required in front of the next generation of breeding to be driven by informatics and intelligence.

A large amount of genome-wide association study (GWAS) panels together with quantitative-trait locus (QTL) information associated with breeding-targeted traits have been described in wheat (Triticum aestivum L.). However, the application of mapping results from a GWAS panel to conventional wheat breeding remains a challenge. In this study, we first report a general genetic map which was constructed from 44 published linkage maps. It permits the estimation of genetic distances between any two genetic loci with physical map positions, thereby unifying the linkage relationships between QTL, genes, and genomic markers from multiple genetic populations. Second, we describe QTL mapping in a wheat GWAS panel of 688 accessions, identifying 77 QTL associated with 12 yield and grain-quality traits. Because these QTL have known physical map positions, they could be mapped onto the general map. Finally, we present a design approach to wheat breeding by using known QTL information and computer simulation. Potential crosses between parents in the GWAS panel may be evaluated by the relative frequency of the target genotype, trait correlations in simulated progeny populations, and genetic gain of selected progenies. It is possible to simultaneously improve yield and grain quality by suitable parental selection, progeny population size, and progeny selection scheme. Applying the design approach will allow identifying the most promising crosses and selection schemes in advance of the field experiment, increasing predictability and efficiency in wheat breeding.

Construction of accurate and high-density linkage maps is a key research area of genetics. We investigated the efficiency of genetic map construction (MAP) using modifications of the k-Optimal (k-Opt) algorithm for solving the traveling-salesman problem (TSP). For TSP, different initial routes resulted in different optimal solutions. The most optimal solution could be found only by use of as many initial routes as possible. But for MAP, a large number of initial routes resulted in one optimal order. k-Opt using open route length gave a slightly higher proportion of correct orders than the method of adding one virtual marker and using closed route length. Recombination frequency (REC) and logarithm of odds (LOD) score gave similar proportions of correct order, higher than that given by genetic distance. Both missing markers and genotyping error reduced ordering accuracy, but the best order was still achieved with high probability by comparison of the optimal orders from multiple initial routes. Computation time increased rapidly with marker number, and 2-Opt took much less time than 3-Opt. The 2-Opt algorithm was compared with ordering methods used in two other software packages. The best method was 2-Opt using open route length as the criterion to identify the optimal order and using REC or LOD as the measure of distance between markers. We describe a unified software interface for using k-Opt in high-density linkage map construction for a wide range of genetic populations.

Pure lines derived from multiple parents provide abundant variation for genetic study. However, efficient genetic analysis methods and user-friendly software are still lacking. In this study, we developed linkage analysis methods and integrated analysis software for pure-line populations derived from four-way and eight-way crosses. First, polymorphic markers are classified into different categories according to the number of identifiable alleles in the inbred parents. Expected genotypic probability is then derived for each pair of complete markers, and based on them a maximum likelihood estimate (MLE) of recombination frequency is calculated. An EM algorithm is proposed for calculating recombination frequencies in scenarios that at least one marker is incomplete. A linkage map can thus be constructed using estimated recombination frequencies. We describe a software package called GAPL for recombination frequency estimation and linkage map construction in multi-parental pure-line populations. Both simulation studies and results from a reported four-way cross recombinant inbred line population demonstrate that the proposed method and software can build more accurate linkage maps in shorter times than other published software packages. The GAPL software is freely available from www.isbreeding.net and can also be used for QTL mapping in multi-parental populations.

In wheat breeding, it is a difficult task to select the most suitable parents for making crosses aimed at the improvement of both grain yield and grain quality. By quantitative genetics theory, the best cross should have high progeny mean and large genetic variance, and ideally yield and quality should be less negatively or positively correlated. Usefulness is built on population mean and genetic variance, which can be used to select the best crosses or populations to achieve the breeding objective. In this study, we first compared five models (RR-BLUP, Bayes A, Bayes B, Bayes ridge regression, and Bayes LASSO) for genomic selection (GS) with respect to prediction of usefulness of a biparental cross and two criteria for parental selection, using simulation. The two parental selection criteria were usefulness and midparent genomic estimated breeding value (GEBV). Marginal differences were observed among GS models. Parental selection with usefulness resulted in higher genetic gain than midparent GEBV. In a population of 57 wheat fixed lines genotyped with 7588 selected markers, usefulness of each biparental cross was calculated to evaluate the cross performance, a key target of breeding programs aimed at developing pure lines. It was observed that progeny mean was a major determinant of usefulness, but the usefulness ratings of quality traits were more influenced by their genetic variances in the progeny population. Near-zero or positive correlations between yield and major quality traits were found in some crosses, although they were negatively correlated in the population of parents. A selection index incorporating yield, extensibility, and maximum resistance was formed as a new trait and its usefulness for selecting the crosses with the best potential to improve yield and quality simultaneously was calculated. It was shown that applying the selection index improved both yield and quality while retaining more genetic variance in the selected progenies than the individual trait selection. It was concluded that combining genomic selection with simulation allows the prediction of cross performance in simulated progenies and thereby identifies candidate parents before crosses are made in the field for pure-line breeding programs.