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In recent years, breeding programs have become increasingly larger and more structurally complex, with various highly interdependent parameters and contrasting breeding goals. Therefore, resource allocation in a breeding program has become more complex, and the derivation of an optimal breeding strategy has become more and more challenging. As a result, it is a common practice to reduce the optimization problem to a set of scenarios that are only changed in a few parameters and, in turn, can be deeply analyzed in detail. This paper aims to provide a framework for the numerical optimization of breeding programs beyond just comparing scenarios. For this, we first determine the space of potential breeding programs that is only limited by basic constraints like the budget and housing capacities. Subsequently, the goal is to identify the optimal breeding program by finding the parametrization that maximizes the target function, as a combination of the different breeding goals. To assess the value of the target function for a parametrization, we propose the use of stochastic simulations and the subsequent use of a kernel regression method to cope with the stochasticity of simulation outcomes. This procedure is performed iteratively to narrow down the most promising areas of the search space and perform more and more simulations in these areas of interest. The developed concept was applied to a dairy cattle program with a target function aiming at genetic gain and genetic diversity conservation limited by budget constraints.

High-throughput genotyping of large numbers of lines remains a key challenge in plant genetics, requiring geneticists and breeders to find a balance between data quality and the number of genotyped lines under a variety of different existing technologies when resources are limited. In this work, we are proposing a new imputation pipeline (“HBimpute”) that can be used to generate high-quality genomic data from low read-depth whole-genome-sequence data. The key idea of the pipeline is the use of haplotype blocks from the software HaploBlocker to identify locally similar lines and merge their reads locally. The effectiveness of the pipeline is showcased on a dataset of 321 doubled haploid lines of a European maize landrace, which were sequenced with 0.5X read-depth. Overall imputing error rates are cut in half compared to the state-of-the-art software BEAGLE, while the average read-depth is increased to 83X, thus enabling the calling of structural variation. The usefulness of the obtained imputed data panel is further evaluated by comparing the performance in common breeding applications to that of genomic data from a 600k array. In particular for genome-wide association studies, the sequence data is shown to be performing slightly better. Furthermore, genomic prediction based on the overlapping markers from the array and sequence is leading to a slightly higher predictive ability for the imputed sequence data, thereby indicating that the data quality obtained from low read-depth sequencing is on par or even slightly higher than high-density array data. When including all markers for the sequence data, the predictive ability is slightly reduced indicating overall lower data quality in non-array markers.Author summaryHigh-throughput genotyping of large numbers of lines remains a key challenge in plant genetics and breeding. Cost, precision, and throughput must be balanced to achieve optimal efficiencies given available technologies and finite resources. Although genotyping arrays are still considered the gold standard in high-throughput quantitative genetics, recent advances in sequencing provide new opportunities for this. Both the quality and cost of genomic data generated based on sequencing are highly dependent on the used read depth. In this work, we are proposing a new imputation pipeline (“HBimpute”) that uses haplotype blocks to detect individuals of the same genetic origin and subsequently uses all reads of those individuals in the variant calling. Thus, the obtained virtual read depth is artificially increased, leading to higher calling accuracy, coverage, and the ability to all copy number variation based on relatively cheap low-read depth sequencing data. Thus, our approach makes sequencing a cost-competitive alternative to genotyping arrays with the additional benefit of the potential use of structural variation.

Selective breeding is a continued element of both crop and livestock breeding since early prehistory. In this work, we are proposing a new web-based simulation framework (“MoBPSweb”) that is combining a unified language to describe breeding programs with the simulation software MoBPS, standing for ‘Modular Breeding Program Simulator’. Thereby, MoBPSweb is providing a flexible environment to enter, simulate, evaluate and compare breeding programs. Inputs can be provided via modules ranging from a Vis.js-based flash environment for “drawing” the breeding program to a variety of modules to provide phenotype information, economic parameters and other relevant information. Similarly, results of the simulation study can be extracted and compared to other scenarios via output modules (e.g. observed phenotypes, accuracy of breeding value estimation, inbreeding rates). Usability of the framework is showcased along a toy example of a dairy cattle breeding program on farm level, with comparing scenarios differing in implemented breeding value estimation, selection index and selection intensity being considered. Comparisons are made considering both short and long-term effects of the different scenarios in terms of genomic gains, rates of inbreeding and the accuracy of the breeding value estimation. Lastly, general applicability of the MoBPSweb framework and the general potential for simulation studies for genetics and in particular in breeding are discussed.

Modern animal breeding programs are constantly evolving with advances in breeding theory, biotechnology and genetics. Surprisingly, there seems to be no generally accepted succinct definition of what exactly a breeding program is, neither is there a unified language to describe breeding programs in a comprehensive, unambiguous and reproducible way. In this work, we try to fill this gap by suggesting a general definition of breeding programs that also pertains to cases where genetic progress is not achieved through selection, but e.g. through transgenic technologies, or the aim is not to generate genetic progress, but e.g. to maintain genetic diversity. The key idea of the underlying concept is to represent a breeding program in modular form as a directed graph that is composed of nodes and edges, where nodes represent cohorts of breeding units, usually individuals, and edges represent breeding activities, like ‘selection’ or ‘reproduction’. We claim, that by defining a comprehensive set of nodes and edges it is possible to represent any breeding program of arbitrary complexity by such a graph, which thus comprises a full description of the breeding program. This concept is implemented in a web-based tool (MoBPSweb, available at www.mobps.de) which is described in a companion paper, and has a link to the R-package MoBPS (Modular Breeding Program Simulator) to simulate the described breeding programs. The approach is illustrated by showcasing three different breeding programs of increasing complexity. Finally, potential limitations of the concept are indicated and extensions to other fields, like plant breeding, are discussed.

Migration of populations from their founder population is expected to cause a reduction in genetic diversity and facilitates population differentiation between the populations and their founder population as predicted by the theory of genetic isolation by distance. Consistent with that, a model of expansion from a single founder predicts that patterns of genetic diversity in populations can be well explained by their geographic expansion from the founders, which is correlated to the genetic differentiation. To investigate this in the chicken, we have estimated the relationship between the genetic diversity in 172 domesticated chicken populations and their genetic distances to wild populations. We have found a strong inverse relationship whereby 87.5% of the variation in the overall genetic diversity of domesticated chicken can be explained by the genetic distance to the wild populations. We also investigated if different types of SNPs and genes present similar patterns of genetic diversity as the overall genome. Among different SNP classes, the non-synonymous ones were the most deviating from the overall genome. However, the genetic distances to wild populations still explained more variation in domesticated chicken diversity in all SNP classes ranging from 81.7 to 88.7%. The genetic diversity seemed to change at a faster rate within the chicken in genes that are associated with transmembrane transport, protein transport and protein metabolic processes, and lipid metabolic processes. In general, such genes are flexible to be manipulated according to the population needs. On the other hand, genes which the genetic diversity hardly changes despite the genetic distance to the wild populations are associated with major functions e.g. brain development. Therefore, changes in the genes may be detrimental to the chickens. These results contribute to the knowledge of different evolutionary patterns of different functional genomic regions in the chicken.Author summaryThe chicken was first domesticated about 6000 B.C. in Asia from the jungle fowl. Following domestication, chickens were taken to different parts of the world mainly by humans. Evolutionary forces such as selection and genetic drift have shaped diversification within the chicken species. In addition, new breeds or strains have been developed from crossbreeding programs facilitated by man. These events, together with other breeding practices, have led to genomic alterations causing genetic differentiation between the domesticated chickens and their ancestral/wild population as well as manipulation of the genetic diversity within the domesticated chickens. We investigated the relationship between 172 domesticated chicken populations from different selection, breeding and management backgrounds and their genetic distance to the wild type chickens. We found that the genetic diversity within the populations decreases with the increasing genetic distances to the wild types. Human manipulation of chicken genetic diversity has more effect on the genetic differentiation than simple geographic separations (through migrations) do. We further found that some genes associated with vital functions show evolutionary constraints or persistent selection across the populations and do not comply with this relationship i.e. the genetic diversity within the populations is constant despite the change in the genetic distance to the wild types.

Single nucleotide polymorphisms (SNPs), genotyped with SNP arrays, have become a widely used marker type in population genetic analyses over the last 10 years. However, compared to whole genome re-sequencing data, arrays are known to lack a substantial proportion of globally rare variants and tend to be biased towards variants present in populations involved in the development process of the respective array. This affects population genetic estimators and is known as SNP ascertainment bias. We investigated factors contributing to ascertainment bias in array development by redesigning the Axiom™ Genome-Wide Chicken Array in silico and evaluating changes in allele frequency spectra and heterozygosity estimates in a stepwise manner. A sequential reduction of rare alleles during the development process was shown with main influencing factors being the identification of SNPs in a limited set of populations and a within-population selection of common SNPs when aiming for equidistant spacing. These effects were shown to be less severe with a larger discovery panel. Additionally, a generally massive overestimation of expected heterozygosity for the ascertained SNP sets was shown. This overestimation was 24% higher for populations involved in the discovery process than not involved populations in case of the original array. The same was observed after the SNP discovery step in the redesign. However, an unequal contribution of populations during the SNP selection can mask this effect but also adds uncertainty. Finally, we make suggestions for the design of specialized arrays for large scale projects where whole genome re-sequencing techniques are still too expensive.

The concept of haplotype blocks has been shown to be useful in genetics. Fields of application range from the detection of regions under positive selection to statistical methods that make use of dimension reduction. We propose a novel approach ("HaploBlocker") for defining and inferring haplotype blocks that focuses on linkage instead of the commonly used population-wide measures of linkage disequilibrium (LD) which fail to identify segments shared by individuals in only a subset of the population. We define a haplotype block as a sequence of alleles that has a predefined minimum frequency in the population and only haplotypes with a similar sequence of alleles are considered to be carrying that block, effectively screening a dataset for group-wise identity-by-descent (IBD). Different to most other approaches these blocks are not restricted to shared start or end positions, but can overlap or even contain each other. From these haplotype blocks we construct a haplotype library that represents a large proportion of genetic variability of a population with a limited number of blocks. Our method is implemented in the associated R-package HaploBlocker and provides flexibility to not only optimize the structure of the obtained haplotype library for subsequent analyses (e.g., identification of shared segments between different populations), but is also able to handle datasets of different marker density and genetic diversity. By using haplotype blocks instead of SNPs, local epistatic interactions can be naturally modelled and the reduced number of parameter enables a wide variety of new methods for further genomic analyses. We illustrate our methodology with a dataset comprising 501 doubled haploid lines in a European maize landrace genotyped at 5019124 SNPs. With the suggested approach, we identified 29851 haplotype blocks with an average length of 29633 SNPs (compared to 27.8 SNPs per block in HaploView) that together represent 94% of the dataset.

Important traits in agricultural, natural, and human populations are increasingly being shown to be under the control of many genes that individually contribute only a small proportion of genetic variation. However, the majority of modern tools in quantitative and population genetics, including genome wide association studies and selection mapping protocols, are designed to identify individual genes with large effects. We have developed an approach to identify traits that have been under selection and are controlled by large numbers of loci. In contrast to existing methods, our technique utilizes additive effects estimates from all available markers, and relates these estimates to allele frequency change over time. Using this information, we generate a composite statistic, denoted Ĝ, which can be used to test for significant evidence of selection on a trait. Our test requires pre- and post-selection genotypic data but only a single time point with phenotypic information. Simulations demonstrate that Ĝ is powerful for identifying selection, particularly in situations where the trait being tested is controlled by many genes, which is precisely the scenario where classical approaches for selection mapping are least powerful. We apply this test to breeding populations of maize and chickens, where we demonstrate the successful identification of selection on traits that are documented to have been under selection.