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This paper introduces AlphaSimR, an R package for stochastic simulations of plant and animal breeding programs. AlphaSimR is a highly flexible software package able to simulate a wide range of plant and animal breeding programs for diploid and autopolyploid species. AlphaSimR is ideal for testing the overall strategy and detailed design of breeding programs. AlphaSimR utilizes a scripting approach to building simulations that is particularly well suited for modeling highly complex breeding programs, such as commercial breeding programs. The primary benefit of this scripting approach is that it frees users from preset breeding program designs and allows them to model nearly any breeding program design. This paper lists the main features of AlphaSimR and provides a brief example simulation to show how to use the software.

Invasive species are among the major driving forces behind biodiversity loss. Gene drive technology may offer a humane, efficient and cost-effective method of control. For safe and effective deployment it is vital that a gene drive is both self-limiting and can overcome evolutionary resistance. We present HD-ClvR in this modelling study, a novel combination of CRISPR-based gene drives that eliminates resistance and localises spread. As a case study, we model HD-ClvR in the grey squirrel ( Sciurus carolinensis ), which is an invasive pest in the UK and responsible for both biodiversity and economic losses. HD-ClvR combats resistance allele formation by combining a homing gene drive with a cleave-and-rescue gene drive. The inclusion of a self-limiting daisyfield gene drive allows for controllable localisation based on animal supplementation. We use both randomly mating and spatial models to simulate this strategy. Our findings show that HD-ClvR could effectively control a targeted grey squirrel population, with little risk to other populations. HD-ClvR offers an efficient, self-limiting and controllable gene drive for managing invasive pests.

Core Ideas Genomic selection applied for wheat quality in CIMMYT spring bread wheat breeding program. All wheat quality traits predicted and validated using forward genomic selection. Dough and loaf traits have moderately high predictive ability in CIMMYT breeding program. Genomic selection genetic gain 1.4 to 2.7 times higher than phenotypic selection. Wheat (Triticum aestivum L.) cultivars must possess suitable end‐use quality for release and consumer acceptability. However, breeding for quality traits is often considered a secondary target relative to yield largely because of amount of seed needed and expense. Without testing and selection, many undesirable materials are advanced, expending additional resources. Here, we develop and validate whole‐genome prediction models for end‐use quality phenotypes in the CIMMYT bread wheat breeding program. Model accuracy was tested using forward prediction on breeding lines (n = 5520) tested in unbalanced yield trials from 2009 to 2015 at Ciudad Obregon, Sonora, Mexico. Quality parameters included test weight, 1000‐kernel weight, hardness, grain and flour protein, flour yield, sodium dodecyl sulfate sedimentation, Mixograph and Alveograph performance, and loaf volume. In general, prediction accuracy substantially increased over time as more data was available to train the model. Reflecting practical implementation of genomic selection (GS) in the breeding program, forward prediction accuracies (r) for quality parameters were assessed in 2015 and ranged from 0.32 (grain hardness) to 0.62 (mixing time). Increased selection intensity was possible with GS since more entries can be genotyped than phenotyped and expected genetic gain was 1.4 to 2.7 times higher across all traits than phenotypic selection. Given the limitations in measuring many lines for quality, we conclude that GS is a powerful tool to facilitate early generation selection for end‐use quality in wheat, leaving larger populations for selection on yield during advanced testing and leading to better gain for both quality and yield in bread wheat breeding programs.

Over the last two decades, the application of genomic selection has been extensively studied in various crop species, and it has become a common practice to report prediction accuracies using cross validation. However, genomic prediction accuracies obtained from random cross validation can be strongly inflated due to population or family structure, a characteristic shared by many breeding populations. An understanding of the effect of population and family structure on prediction accuracy is essential for the successful application of genomic selection in plant breeding programs. The objective of this study was to make this effect and its implications for practical breeding programs comprehensible for breeders and scientists with a limited background in quantitative genetics and genomic selection theory. We, therefore, compared genomic prediction accuracies obtained from different random cross validation approaches and within-family prediction in three different prediction scenarios. We used a highly structured population of 940 Brassica napus hybrids coming from 46 testcross families and two subpopulations. Our demonstrations show how genomic prediction accuracies obtained from among-family predictions in random cross validation and within-family predictions capture different measures of prediction accuracy. While among-family prediction accuracy measures prediction accuracy of both the parent average component and the Mendelian sampling term, within-family prediction only measures how accurately the Mendelian sampling term can be predicted. With this paper we aim to foster a critical approach to different measures of genomic prediction accuracy and a careful analysis of values observed in genomic selection experiments and reported in literature.

Background Accurate assignment of breed origin of alleles (BOA) at a heterozygote locus may help to introduce a resilient or adaptive haplotype in crossbreeding. In this study, we developed and tested a method to assign breed of origin for individual alleles in crossbred dairy cattle. After generations of mating within and between local breeds as well as the importation of exotic bulls, five rounds of selected crossbred cows were simulated to mimic a dairy breeding program in the low- and middle-income countries (LMICs). In each round of selection, the alleles of those crossbred animals were phased and assigned to their breed of origin (being either local or exotic). Results Across all core lengths and modes of phasing (with offset—move 50% of the core length forward or no-offset), the average percentage of alleles correctly assigned a breed origin was 95.76%, with only 1.39% incorrectly assigned and 2.85% missing or unassigned. On consensus, the average percentage of alleles correctly assigned a breed origin was 93.21%, with only 0.46% incorrectly assigned and 6.33% missing or unassigned. This high proportion of alleles correctly assigned a breed origin resulted in a high core-based mean accuracy of 0.99 and a very high consensus-based (most frequently observed assignment across all the scenarios) mean accuracy of 1.00. The algorithm’s assignment yield and accuracy were affected by the choice of threshold levels for the best match of assignments. The threshold level had the opposite effect on assignment yield and assignment accuracy. A less stringent threshold generated higher assignment yields and lower assignment accuracy. Conclusions We developed an algorithm that accurately assigns a breed origin to alleles of crossbred animals designed to represent breeding programs in the LMICs. The developed algorithm is straightforward in its application and does not require prior knowledge of pedigree, which makes it more relevant and applicable in LMICs breeding programs.

Core Ideas Incorporating environmental covariates increases genomic selection accuracy. G × E models can impute known lines into known environments with good accuracy. Breeding programs may exploit genomic selection cross‐validation schemes in trial designs. Wheat (Triticum aestivum L.) breeding programs test experimental lines in multiple locations over multiple years to get an accurate assessment of grain yield and yield stability. Selections in early generations of the breeding pipeline are based on information from only one or few locations and thus materials are advanced with little knowledge of the genotype × environment interaction (G × E) effects. Later, large trials are conducted in several locations to assess the performance of more advanced lines across environments. Genomic selection (GS) models that include G × E covariates allow us to borrow information not only from related materials, but also from historical and correlated environments to better predict performance within and across specific environments. We used reaction norm models with several cross‐validation schemes to demonstrate the increased breeding efficiency of Kansas State University's hard red winter wheat breeding program. The GS reaction norm models line effect (L) + environment effect (E), L + E + genotype environment (G), and L + E + G + (G × E) effects) showed high accuracy values (>0.4) when predicting the yield performance in untested environments, sites or both. The GS model L + E + G + (G × E) presented the highest prediction ability (r = 0.54) when predicting yield in incomplete field trials for locations with a moderate number of lines. The difficulty of predicting future years (forward prediction) is indicated by the relatively low accuracy (r = 0.171) seen even when environments with 300+ lines were included.

Genetic variance is a central parameter in quantitative genetics and breeding. Assessing changes in genetic variance over time as well as the genome is therefore of high interest. Here, we extend a previously proposed framework for temporal analysis of genetic variance using the pedigree-based model, to a new framework for temporal and genomic analysis of genetic variance using marker-based models. To this end, we describe the theory of partitioning genetic variance into genic variance and within-chromosome and between-chromosome linkage-disequilibrium, and how to estimate these variance components from a marker-based model fitted to observed phenotype and marker data. The new framework involves three steps: (i) fitting a marker-based model to data, (ii) sampling realisations of marker effects from the fitted model and for each sample calculating realisations of genetic values and (iii) calculating the variance of sampled genetic values by time and genome partitions. Analysing time partitions indicates breeding programme sustainability, while analysing genome partitions indicates contributions from chromosomes and chromosome pairs and linkage-disequilibrium. We demonstrate the framework with a simulated breeding programme involving a complex trait. Results show good concordance between simulated and estimated variances, provided that the fitted model is capturing genetic complexity of a trait. We observe a reduction of genetic variance due to selection and drift changing allele frequencies, and due to selection inducing negative linkage-disequilibrium.

Hybrid vigour has the potential to substantially increase the yield of self-pollinating crops such as wheat and rice, but future hybrid performance may depend on the initial strategy to form heterotic pools. We used in silico stochastic simulation of future hybrid performance in a self-pollinating crop to evaluate three strategies of forming heterotic pools in the founder population. The model included either 500, 2000 or 8000 quantitative trait nucleotides (QTN) across 10 chromosomes that contributed to a quantitative trait with population mean 100 and variance 10. The average degree of dominance at each QTN was either 0.2, 0.4 or 0.8 with variance 0.2. Three strategies for splitting the founder population into two heterotic pools were compared: (i) random split; (ii) split based on genetic distance according to principal component analysis of SNP genotypes; and (iii) optimized split based on F 1 hybrid performance in a diallel cross among the founders. Future hybrid performance was stochastically simulated over 30 cycles of reciprocal recurrent selection based on true genetic values for additive and dominance effects. The three strategies of forming heterotic pools produced similar future hybrid performance, and superior future hybrids to a control population selected on inbred line performance when the number of quantitative trait nucleotides was ≥2000 and/or the average degree of dominance was ≥0.4.

Intercrop breeding programs using genomic selection can produce faster genetic gain than intercrop breeding programs using phenotypic selection. Intercropping is an agricultural practice in which two or more component crops are grown together. It can lead to enhanced soil structure and fertility, improved weed suppression, and better control of pests and diseases. Especially in subsistence agriculture, intercropping has great potential to optimize farming and increase profitability. However, breeding for intercrop varieties is complex as it requires simultaneous improvement of two or more component crops that combine well in the field. We hypothesize that genomic selection can significantly simplify and accelerate the process of breeding crops for intercropping. Therefore, we used stochastic simulation to compare four different intercrop breeding programs implementing genomic selection and an intercrop breeding program entirely based on phenotypic selection. We assumed three different levels of genetic correlation between monocrop grain yield and intercrop grain yield to investigate how the different breeding strategies are impacted by this factor. We found that all four simulated breeding programs using genomic selection produced significantly more intercrop genetic gain than the phenotypic selection program regardless of the genetic correlation with monocrop yield. We suggest a genomic selection strategy which combines monocrop and intercrop trait information to predict general intercropping ability to increase selection accuracy in the early stages of a breeding program and to minimize the generation interval.

Key messageOptimal cross selection increases long-term genetic gain of two-part programs with rapid recurrent genomic selection. It achieves this by optimising efficiency of converting genetic diversity into genetic gain through reducing the loss of genetic diversity and reducing the drop of genomic prediction accuracy with rapid cycling.This study evaluates optimal cross selection to balance selection and maintenance of genetic diversity in two-part plant breeding programs with rapid recurrent genomic selection. The two-part program reorganises a conventional breeding program into a population improvement component with recurrent genomic selection to increase the mean value of germplasm and a product development component with standard methods to develop new lines. Rapid recurrent genomic selection has a large potential, but is challenging due to genotyping costs or genetic drift. Here we simulate a wheat breeding program for 20 years and compare optimal cross selection against truncation selection in the population improvement component with one to six cycles per year. With truncation selection we crossed a small or a large number of parents. With optimal cross selection we jointly optimised selection, maintenance of genetic diversity, and cross allocation with AlphaMate program. The results show that the two-part program with optimal cross selection delivered the largest genetic gain that increased with the increasing number of cycles. With four cycles per year optimal cross selection had 78% (15%) higher long-term genetic gain than truncation selection with a small (large) number of parents. Higher genetic gain was achieved through higher efficiency of converting genetic diversity into genetic gain; optimal cross selection quadrupled (doubled) efficiency of truncation selection with a small (large) number of parents. Optimal cross selection also reduced the drop of genomic selection accuracy due to the drift between training and prediction populations. In conclusion optimal cross selection enables optimal management and exploitation of population improvement germplasm in two-part programs.