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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.

Context Breeding programs aim at improving the genetic characteristics of livestock populations with respect to productivity, fitness and adaptation, while controlling negative effects such as inbreeding or health and welfare issues. As breeding is affected by a variety of interdependent factors, the analysis of the effect of certain breeding actions and the optimisation of a breeding program are highly complex tasks. Aims This study was conducted to display the potential of using stochastic simulation to analyse, evaluate and compare breeding programs and to show how the Modular Breeding Program Simulator (MoBPS) simulation framework can further enhance this. Methods In this study, a simplified version of the breeding program of Göttingen Minipigs was simulated to analyse the impact of genotyping and optimum contribution selection in regard to both genetic gain and diversity. The software MoBPS was used as the backend simulation software and was extended to allow for a more realistic modelling of pig breeding programs. Among others, extensions include the simulation of phenotypes with discrete observations (e.g. teat count), variable litter sizes, and a breeding value estimation in the associated R-package miraculix that utilises a graphics processing unit. Key results Genotyping with the subsequent use of genomic best linear unbiased prediction (GBLUP) led to substantial increases in genetic gain (15.3%) compared with a pedigree-based BLUP, while reducing the increase of inbreeding by 24.8%. The additional use of optimum genetic selection was shown to be favourable compared with the plain selection of top boars. The use of graphics processing unit-based breeding value estimation with known heritability was ~100 times faster than the state-of-the-art R-package rrBLUP. Conclusions The results regarding the effect of both genotyping and optimal contribution selection are in line with well established results. Paired with additional new features such as the modelling of discrete phenotypes and adaptable litter sizes, this confirms MoBPS to be a unique tool for the realistic modelling of modern breeding programs. Implications The MoBPS framework provides a powerful tool for scientists and breeders to perform stochastic simulations to optimise the practical design of modern breeding programs to secure standardised breeding of high-quality animals and answer associated research questions.

We introduce the R-package learnMET, developed as a flexible framework to enable a collection of analyses on multi-environment trial (MET) breeding data with machine learning-based models. learnMET allows the combination of genomic information with environmental data such as climate and/or soil characteristics. Notably, the package offers the possibility of incorporating weather data from field weather stations, or can retrieve global meteorological datasets from a NASA database. Daily weather data can be aggregated over specific periods of time based on naive (for instance, non-overlapping 10-day windows) or phenological approaches. Different machine learning methods for genomic prediction are implemented, including gradient boosted trees, random forests, stacked ensemble models, and multi-layer perceptrons. These prediction models can be evaluated via a collection of cross-validation schemes that mimic typical scenarios encountered by plant breeders working with MET experimental data in a user-friendly way. The package is fully open source and accessible on GitHub.

The plasticity of sexual phenotype in response to environmental conditions results in biased sex ratios, and their variation has an effect on population dynamics. Epigenetic modifications can modulate sex ratio variation in species, where sex is determined by genetic and environmental factors. However, the role of epigenetic mechanisms underlying skewed sex ratios is far from being clear and is still an object of debate in evolutionary developmental biology. In this study, we used zebrafish as a model animal to investigate the effect of DNA methylation on sex ratio variation in sex-biased families in response to environmental temperature. Two sex-biased families with a significant difference in sex ratio were selected for genome-wide DNA methylation analysis using reduced representation bisulfite sequencing (RRBS). The results showed significant genome-wide methylation differences between male-biased and female-biased families, with a greater number of methylated CpG sites in testes than ovaries. Likewise, pronounced differences between testes and ovaries were identified within both families, where the male-biased family exhibited a higher number of methylated sites than the female-biased family. The effect of temperature showed more methylated positions in the high incubation temperature than the control temperature. We found differential methylation of many reproduction-related genes (e.g., sox9a, nr5a2, lhx8a, gata4) and genes involved in epigenetic mechanisms (e.g., dnmt3bb.1, dimt1l, hdac11, h1m) in both families. We conclude that epigenetic modifications can influence the sex ratio variation in zebrafish families and may generate skewed sex ratios, which could have a negative consequence for population fitness in species with genotype-environment interaction sex-determining system under rapid environmental changes.

The importance of accurate genomic prediction of phenotypes in plant breeding is undeniable, as higher prediction accuracy can increase selection responses. In this regard, epistasis models have shown to be capable of increasing the prediction accuracy while their high computational load is challenging. In this study, we investigated the predictive ability obtained in additive and epistasis models when utilizing haplotype blocks versus pruned sets of SNPs by including phenotypic information from the last growing season. This was done by considering a single biological trait in two growing seasons (2017 and 2018) as separate traits in a multi-trait model. Thus, bivariate variants of the Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) and selective Epistatic Random Regression BLUP (sERRBLUP) as epistasis models were compared with respect to their prediction accuracies for the second year. The prediction accuracies of bivariate GBLUP, ERRBLUP and sERRBLUP were assessed with eight phenotypic traits for 471/402 doubled haploid lines in the European maize landrace Kemater Landmais Gelb/Petkuser Ferdinand Rot. The results indicate that the obtained prediction accuracies are similar when utilizing a pruned set of SNPs or haplotype blocks, while utilizing haplotype blocks reduces the computational load significantly compared to the pruned sets of SNPs. The number of interactions considered in the model was reduced from 323.5/456.4 million for the pruned SNP panel to 4.4/5.5 million in the haplotype block dataset for Kemater and Petkuser landraces, respectively. Since the computational load scales linearly with the number of parameters in the model, this leads to a reduction in computational time of 98.9% from 13.5 hours for the pruned set of markers to 9 minutes for the haplotype block dataset. We further investigated the impact of genomic correlation, phenotypic correlation and trait heritability as factors affecting the bivariate models’ prediction accuracy, identifying the genomic correlation between years as the most influential one. As computational load is substantially reduced, while the accuracy of genomic prediction is unchanged, the here proposed framework to use haplotype blocks in sERRBLUP provided a solution for the practical implementation of sERRBLUP in real breeding programs. Furthermore, our results indicate that sERRBLUP is not only suitable for prediction across different locations, but also for the prediction across growing seasons.

Background Structural variants (SV) are causative for some prominent phenotypic traits of livestock as different comb types in chickens or color patterns in pigs. Their effects on production traits are also increasingly studied. Nevertheless, accurately calling SV remains challenging. It is therefore of interest, whether close-by single nucleotide polymorphisms (SNPs) are in strong linkage disequilibrium (LD) with SVs and can serve as markers. Literature comes to different conclusions on whether SVs are in LD to SNPs on the same level as SNPs to other SNPs. The present study aimed to generate a precise SV callset from whole-genome short-read sequencing (WGS) data for three commercial chicken populations and to evaluate LD patterns between the called SVs and surrounding SNPs. It is thereby the first study that assessed LD between SVs and SNPs in chickens. Results The final callset consisted of 12,294,329 bivariate SNPs, 4,301 deletions (DEL), 224 duplications (DUP), 218 inversions (INV) and 117 translocation breakpoints (BND). While average LD between DELs and SNPs was at the same level as between SNPs and SNPs, LD between other SVs and SNPs was strongly reduced (DUP: 40%, INV: 27%, BND: 19% of between-SNP LD). A main factor for the reduced LD was the presence of local minor allele frequency differences, which accounted for 50% of the difference between SNP – SNP and DUP – SNP LD. This was potentially accompanied by lower genotyping accuracies for DUP, INV and BND compared with SNPs and DELs. An evaluation of the presence of tag SNPs (SNP in highest LD to the variant of interest) further revealed DELs to be slightly less tagged by WGS SNPs than WGS SNPs by other SNPs. This difference, however, was no longer present when reducing the pool of potential tag SNPs to SNPs located on four different chicken genotyping arrays. Conclusions The results implied that genomic variance due to DELs in the chicken populations studied can be captured by different SNP marker sets as good as variance from WGS SNPs, whereas separate SV calling might be advisable for DUP, INV, and BND effects.

The R-package MoBPS provides a computationally efficient and flexible framework to simulate complex breeding programs and compare their economic and genetic impact. Simulations are performed on the base of individuals. MoBPS utilizes a highly efficient implementation with bit-wise data storage and matrix multiplications from the associated R-package miraculix allowing to handle large scale populations. Individual haplotypes are not stored but instead automatically derived based on points of recombination and mutations. The modular structure of MoBPS allows to combine rather coarse simulations, as needed to generate founder populations, with a very detailed modeling of todays’ complex breeding programs, making use of all available biotechnologies. MoBPS provides pre-implemented functions for common breeding practices such as optimum genetic contributions and single-step GBLUP but also allows the user to replace certain steps with personalized and/or self-written solutions.

Imputation is one of the key steps in the preprocessing and quality control protocol of any genetic study. Most imputation algorithms were originally developed for the use in human genetics and thus are optimized for a high level of genetic diversity. Different versions of BEAGLE were evaluated on genetic datasets of doubled haploids of two European maize landraces, a commercial breeding line and a diversity panel in chicken, respectively, with different levels of genetic diversity and structure which can be taken into account in BEAGLE by parameter tuning. Especially for phasing BEAGLE 5.0 outperformed the newest version (5.1) which in turn also lead to improved imputation. Earlier versions were far more dependent on the adaption of parameters in all our tests. For all versions, the parameter ne (effective population size) had a major effect on the error rate for imputation of ungenotyped markers, reducing error rates by up to 98.5%. Further improvement was obtained by tuning of the parameters affecting the structure of the haplotype cluster that is used to initialize the underlying Hidden Markov Model of BEAGLE. The number of markers with extremely high error rates for the maize datasets were more than halved by the use of a flint reference genome (F7, PE0075 etc.) instead of the commonly used B73. On average, error rates for imputation of ungenotyped markers were reduced by 8.5% by excluding genetically distant individuals from the reference panel for the chicken diversity panel. To optimize imputation accuracy one has to find a balance between representing as much of the genetic diversity as possible while avoiding the introduction of noise by including genetically distant individuals.

Identifying selection on polygenic complex traits in crops and livestock is important for understanding evolution and helps prioritize important characteristics for breeding. Quantitative trait loci (QTL) that contribute to polygenic trait variation often exhibit small or infinitesimal effects. This hinders the ability to detect QTL-controlling polygenic traits because enormously high statistical power is needed for their detection. Recently, we circumvented this challenge by introducing a method to identify selection on complex traits by evaluating the relationship between genome-wide changes in allele frequency and estimates of effect size. The approach involves calculating a composite statistic across all markers that capture this relationship, followed by implementing a linkage disequilibrium-aware permutation test to evaluate if the observed pattern differs from that expected due to drift during evolution and population stratification. In this manuscript, we describe “Ghat,” an R package developed to implement this method to test for selection on polygenic traits. We demonstrate the package by applying it to test for polygenic selection on 15 published European wheat traits including yield, biomass, quality, morphological characteristics, and disease resistance traits. Moreover, we applied Ghat to different simulated populations with different breeding histories and genetic architectures. The results highlight the power of Ghat to identify selection on complex traits. The Ghat package is accessible on CRAN, the Comprehensive R Archival Network, and on GitHub.

Made available in DSpace on 2020-12-12T01:38:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-09-11 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) BACKGROUND: The cattle introduced by European conquerors during the Brazilian colonization period were exposed to a process of natural selection in different types of biomes throughout the country, leading to the development of locally adapted cattle breeds. In this study, whole-genome re-sequencing data from indicine and Brazilian locally adapted taurine cattle breeds were used to detect genomic regions under selective pressure. Within-population and cross-population statistics were combined separately in a single score using the de-correlated composite of multiple signals (DCMS) method. Putative sweep regions were revealed by assessing the top 1% of the empirical distribution generated by the DCMS statistics. RESULTS: A total of 33,328,447 biallelic SNPs with an average read depth of 12.4X passed the hard filtering process and were used to access putative sweep regions. Admixture has occurred in some locally adapted taurine populations due to the introgression of exotic breeds. The genomic inbreeding coefficient based on runs of homozygosity (ROH) concurred with the populations' historical background. Signatures of selection retrieved from the DCMS statistics provided a comprehensive set of putative candidate genes and revealed QTLs disclosing cattle production traits and adaptation to the challenging environments. Additionally, several candidate regions overlapped with previous regions under selection described in the literature for other cattle breeds. CONCLUSION: The current study reported putative sweep regions that can provide important insights to better understand the selective forces shaping the genome of the indicine and Brazilian locally adapted taurine cattle breeds. Such regions likely harbor traces of natural selection pressures by which these populations have been exposed and may elucidate footprints for adaptation to the challenging climatic conditions. São Paulo State University (Unesp) School of Agricultural and Veterinarian Sciences Animal Breeding and Genetics Group Department of Animal Sciences University of Goettingen, Albrecht-Thaer-Weg 3 Center for Integrated Breeding Research University of Goettingen, Albrecht-Thaer-Weg 3 National Council for Scientific and Technological Development (CNPq) Embrapa Dairy Cattle Embrapa Beef Cattle São Paulo State University (Unesp) School of Agricultural and Veterinarian Sciences

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..., 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. We define a haplotype block as a sequence of genetic markers that has a predefined minimum frequency in the population, and only haplotypes with a similar sequence of markers are considered to carry that block, effectively screening a dataset for group-wise identity-by-descent. From these haplotype blocks, we construct a haplotype library that represents a large proportion of genetic variability with a limited number of blocks. Our method is implemented in the associated R-package HaploBlocker, and provides flexibility not only to optimize the structure of the obtained haplotype library for subsequent analyses, but also to handle datasets of different marker density and genetic diversity. By using haplotype blocks instead of single nucleotide polymorphisms (SNPs), local epistatic interactions can be naturally modeled, and the reduced number of parameters enables a wide variety of new methods for further genomic analyses such as genomic prediction and the detection of selection signatures. We illustrate our methodology with a dataset comprising 501 doubled haploid lines in a European maize landrace genotyped at 501,124 SNPs. With the suggested approach, we identified 2991 haplotype blocks with an average length of 2685 SNPs that together represent 94% of the dataset.

The importance of accurate genomic prediction of phenotypes in plant breeding is undeniable, as higher prediction accuracy can increase selection responses. In this study, we investigated the ability of three models to improve prediction accuracy by including phenotypic information from the last growing season. This was done by considering a single biological trait in two growing seasons (2017 and 2018) as separate traits in a multi-trait model. Thus, bivariate variants of the Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) and selective Epistatic Random Regression BLUP (sERRBLUP) as epistasis models were compared with respect to their prediction accuracies for the second year. The results indicate that bivariate ERRBLUP is almost identical to bivariate GBLUP in prediction accuracy, while bivariate sERRBLUP has the highest prediction accuracy in most cases. The obtained prediction accuracies were similar when utilizing pruned sets of SNPs and haplotype blocks, while utilizing haplotype blocks reduces the computational load significantly compared to utilizing pruned sets of SNPs. The prediction accuracies of bivariate GBLUP, ERRBLUP and sERRBLUP have been assessed across eight phenotypic traits and studied datasets from 471/402 doubled haploid lines in the European maize landrace Kemater Landmais Gelb/Petkuser Ferdinand Rot. We further investigated the genomic correlation, phenotypic correlation and trait heritability as factors affecting the bivariate models’ prediction accuracy, with genetic correlation between growing seasons being the most important one. For all three considered model architectures results were far worse when using a univariate version of the model.

Background Population genetic studies based on genotyped single nucleotide polymorphisms (SNPs) are influenced by a non-random selection of the SNPs included in the used genotyping arrays. The resulting bias in the estimation of allele frequency spectra and population genetics parameters like heterozygosity and genetic distances relative to whole genome sequencing (WGS) data is known as SNP ascertainment bias. Full correction for this bias requires detailed knowledge of the array design process, which is often not available in practice. This study suggests an alternative approach to mitigate ascertainment bias of a large set of genotyped individuals by using information of a small set of sequenced individuals via imputation without the need for prior knowledge on the array design. Results The strategy was first tested by simulating additional ascertainment bias with a set of 1566 chickens from 74 populations that were genotyped for the positions of the Affymetrix Axiom™ 580 k Genome-Wide Chicken Array. Imputation accuracy was shown to be consistently higher for populations used for SNP discovery during the simulated array design process. Reference sets of at least one individual per population in the study set led to a strong correction of ascertainment bias for estimates of expected and observed heterozygosity, Wright’s Fixation Index and Nei’s Standard Genetic Distance. In contrast, unbalanced reference sets (overrepresentation of populations compared to the study set) introduced a new bias towards the reference populations. Finally, the array genotypes were imputed to WGS by utilization of reference sets of 74 individuals (one per population) to 98 individuals (additional commercial chickens) and compared with a mixture of individually and pooled sequenced populations. The imputation reduced the slope between heterozygosity estimates of array data and WGS data from 1.94 to 1.26 when using the smaller balanced reference panel and to 1.44 when using the larger but unbalanced reference panel. This generally supported the results from simulation but was less favorable, advocating for a larger reference panel when imputing to WGS. Conclusions The results highlight the potential of using imputation for mitigation of SNP ascertainment bias but also underline the need for unbiased reference sets. Supplementary Information The online version contains supplementary material available at 10.1186/s12864-021-07663-6.

Reliable methods of phenotype prediction from genomic data play an increasingly important role in many areas of plant and animal breeding. Thus, developing methods that enhance prediction accuracy is of major interest. Here, we provide three methods for this purpose: (1) Genomic Best Linear Unbiased Prediction (GBLUP) as a model just accounting for additive SNP effects; (2) Epistatic Random Regression BLUP (ERRBLUP) as a full epistatic model which incorporates all pairwise SNP interactions, and (3) selective Epistatic Random Regression BLUP (sERRBLUP) as an epistatic model which incorporates a subset of pairwise SNP interactions selected based on their absolute effect sizes or the effect variances, which is computed based on solutions from the ERRBLUP model. We compared the predictive ability obtained from GBLUP, ERRBLUP, and sERRBLUP with genotypes from a publicly available wheat dataset and respective simulated phenotypes. Results showed that sERRBLUP provides a substantial increase in prediction accuracy compared to the other methods when the optimal proportion of SNP interactions is kept in the model, especially when an optimal proportion of SNP interactions is selected based on the SNP interaction effect sizes. All methods described here are implemented in the R-package EpiGP, which is able to process large-scale genomic data in a computationally efficient way.

Background Population genetic studies based on genotyped single nucleotide polymorphisms (SNPs) are influenced by a non-random selection of the SNPs included in the used genotyping arrays. The resulting bias relative to whole genome sequencing (WGS) data is known as SNP ascertainment bias. Correction for this bias requires detailed knowledge of the array design process which is often not available in practice. This study intends to investigate an alternative approach to mitigate ascertainment bias of a large set of genotyped individuals by using information of a small set of sequenced individuals via imputation without the need for prior knowledge on the array design. Results The strategy was first tested by simulating additional ascertainment bias with a set of 1,566 chickens from 74 populations that were genotyped for the positions of the Affymetrix Axiom™ 580k Genome-Wide Chicken Array. Imputation accuracy was shown to be consistently higher for populations used for SNP discovery during the simulated array design process. Reference sets of at least one individual per population in the study set led to a strong correction of ascertainment bias for estimates of expected and observed heterozygosity, Wrights Fixation Index and Nei’s Standard Genetic Distance. In contrast, unbalanced reference sets introduced a new bias towards the reference populations. Finally, the array genotypes were imputed to WGS by utilization of reference sets of 74 individuals (one per population) to 98 individuals (additional commercial chickens) and compared with a mixture of individually and pooled sequenced populations. The imputation reduced the slope between heterozygosity estimates of array data and WGS data from 1.94 to 1.26 when using the smaller balanced reference panel and to 1.44 when using the larger but unbalanced reference panel. This generally supported the results from simulation but was less favorable, advocating for a larger reference panel when imputing to WGS. Conclusions The results highlight the potential of using imputation for mitigation of SNP ascertainment bias but also underline the need for unbiased reference sets.

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.

Reliable methods of phenotype prediction from genomic data play an increasingly important role in many areas of plant and animal breeding. Thus, developing methods that enhance prediction accuracy is of major interest. Here, we provide three methods for this purpose: (1) Genomic Best Linear Unbiased Prediction (GBLUP) as a model just accounting for additive SNP effects; (2) Epistatic Random Regression BLUP (ERRBLUP) as a full epistatic model which incorporates all pairwise SNP interactions, and (3) selective Epistatic Random Regression BLUP (sERRBLUP) as an epistatic model which incorporates a subset of pairwise SNP interactions selected based on their absolute effect sizes or the effect variances, which is computed based on solutions from the ERRBLUP model. We compared the predictive ability obtained from GBLUP, ERRBLUP, and sERRBLUP with genotypes from a publicly available wheat dataset and respective simulated phenotypes. Results showed that sERRBLUP provides a substantial increase in prediction accuracy compared to the other methods when the optimal proportion of SNP interactions is kept in the model, especially when an optimal proportion of SNP interactions is selected based on the SNP interaction effect sizes. All methods described here are implemented in the R-package EpiGP, which is able to process large-scale genomic data in a computationally efficient way.

Key Message The accuracy of genomic prediction of phenotypes can be increased by including the top-ranked pairwise SNP interactions into the prediction model. Abstract We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from two European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested at six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings for predictions within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Across all studied traits, locations and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from −0.3 to + 27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP, with an average increase of 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for “sparse testing” approaches in which only a subset of the lines/hybrids of interest is observed at each location.

Single nucleotide polymorphisms (SNPs), genotyped with 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. This was mainly caused by 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.

Modern animal breeding programmes 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 programme is, neither is there a unified language to describe breeding programmes in a comprehensive, unambiguous and reproducible way. In this work, we try to fill this gap by suggesting a general definition of breeding programmes that also pertains to cases where genetic progress is not achieved through selection, but, for example, through transgenic technologies, or the aim is not to generate genetic progress, but, for example, to maintain genetic diversity. The key idea of the underlying concept is to represent a breeding programme 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 programme of arbitrary complexity by such a graph, which thus comprises a full description of the breeding programme. This concept is implemented in a web-based tool (MoBPSweb, available at www.mobps.de) and has a link to the R-package MoBPS (Modular Breeding Program Simulator) to simulate the described breeding programmes. The approach is illustrated by showcasing three different breeding programmes of increasing complexity. The concept allows a formal description of breeding programmes, which is requested, for example, in legal regulations of the European Union, but so far cannot be provided in a standardized format. In the discussion, we point out potential limitations of the concept and argue that the general approach can be easily extended to account for novel breeding technologies, to breeding of crops or experimental species, but also to modelling diversity dynamics in natural populations.

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.

Gao et al. propose several approaches to incorporate gene annotation into genomic prediction and evaluate these new methods on populations..... Today, genomic prediction (GP) is an established technology in plant and animal breeding programs. Current standard methods are purely based on statistical considerations but do not make use of the abundant biological knowledge, which is easily available from public databases. Major questions that have to be answered before biological prior information can be used routinely in GP approaches are which types of information can be used, and at which points they can be incorporated into prediction methods. In this study, we propose a novel strategy to incorporate gene annotation into GP of complex phenotypes by defining haploblocks according to gene positions. Haplotype effects are then modeled as categorical or as numerical allele dosage variables. The underlying concept of this approach is to build the statistical model on variables representing the biologically functional units. We evaluate the new methods with data from a heterogeneous stock mouse population, the Drosophila Genetic Reference Panel (DGRP), and a rice breeding population from the Rice Diversity Panel. Our results show that using gene annotation to define haploblocks often leads to a comparable, but for some traits to a higher, predictive ability compared to SNP-based models or to haplotype models that do not use gene annotation information. Modeling gene interaction effects can further improve predictive ability. We also illustrate that the additional use of markers that have not been mapped to any gene in a second separate relatedness matrix does in many cases not lead to a relevant additional increase in predictive ability when the first matrix is based on haploblocks defined with gene annotation data, suggesting that intergenic markers only provide redundant information on the considered data sets. Therefore, gene annotation information seems to be appropriate to perceive the importance of DNA segments. Finally, we discuss the effects of gene annotation quality, marker density, and linkage disequilibrium on the performance of the new methods. To our knowledge, this is the first work that incorporates epistatic interaction or gene annotation into haplotype-based prediction approaches.

Summary Selection decisions in genomic selection schemes are made based on genomic breeding values (GBV) of candidates. Thus, the accuracy of GBV is a relevant parameter, as it reflects the stability of prediction and the possibility that the GBV might change when more information becomes available. Accuracy of genomic prediction defined as the correlation between GBV and true breeding values (TBV), however, is difficult to assess, considering TBV of the candidates are not available in reality. In previous studies, several methods were proposed to assess the accuracy of GBV including methods using population parameters or parameters inferred from mixed-model equations. In practice, most approaches tended to overestimate the accuracy of genomic prediction. We thus tested approaches used in previous studies in order to assess the magnitude of bias. Analyses were performed based on simulated data under a variety of scenarios mimicking different livestock breeding programmes. Furthermore, we proposed a novel method and tested it both with simulated data and in a real Holstein data set. The new method provided a better prediction for the accuracy of GBV in the simulated scenarios.

Due to the discrepancy of the high energy demand for rapidly increasing milk production and limited feed intake in the transition period around parturition, dairy cows require considerable metabolic adaptations. We hypothesize that some cows are genetically less suited to cope with these metabolic needs than others, leading to adverse follow-up effects on longevity. To test this, we designed a reaction norm model in which functional lifetime was linked to the metabolic challenge in the beginning of the first lactation. As challenge variables, we used either the sum of milk yield or the accumulated fat-to-protein ratio of the first 3 test-days (

Currently used multi-step methods to incorporate genomic information in the prediction of breeding values (BV) implicitly involve many assumptions which, if violated, may result in loss of information, inaccuracies and bias. To overcome this, single-step genomic best linear unbiased prediction (ssGBLUP) was proposed combining pedigree, phenotype and genotype of all individuals for genetic evaluation. Our objective was to implement ssGBLUP for genomic predictions in pigs and to compare the accuracy of ssGBLUP with that of multi-step methods with empirical data of moderately sized pig breeding populations. Different predictions were performed: conventional parent average (PA), direct genomic value (DGV) calculated with genomic BLUP (GBLUP), a GEBV obtained by blending the DGV with PA, and ssGBLUP. Data comprised individuals from a German Landrace (LR) and Large White (LW) population. The trait 'number of piglets born alive' (NBA) was available for 182,054 litters of 41,090 LR sows and 15,750 litters from 4534 LW sows. The pedigree contained 174,021 animals, of which 147,461 (26,560) animals were LR (LW) animals. In total, 526 LR and 455 LW animals were genotyped with the Illumina PorcineSNP60 BeadChip. After quality control and imputation, 495 LR (424 LW) animals with 44,368 (43,678) SNP on 18 autosomes remained for the analysis. Predictive abilities, i.e., correlations between de-regressed proofs and genomic BV, were calculated with a five-fold cross validation and with a forward prediction for young genotyped validation animals born after 2011. Generally, predictive abilities for LR were rather small (0.08 for GBLUP, 0.19 for GEBV and 0.18 for ssGBLUP). For LW, ssGBLUP had the greatest predictive ability (0.45). For both breeds, assessment of reliabilities for young genotyped animals indicated that genomic prediction outperforms PA with ssGBLUP providing greater reliabilities (0.40 for LR and 0.32 for LW) than GEBV (0.35 for LR and 0.29 for LW). Grouping of animals according to information sources revealed that genomic prediction had the highest potential benefit for genotyped animals without their own phenotype. Although, ssGBLUP did not generally outperform GBLUP or GEBV, the results suggest that ssGBLUP can be a useful and conceptually convincing approach for practical genomic prediction of NBA in moderately sized LR and LW populations.

The authors wish to make the following corrections to this paper [...]

Models based on additive marker effects and on epistatic interactions can be translated into genomic relationship models. This equivalence allows to perform predictions based on complex gene interaction models and reduces computational effort significantly. In the theory of genome-assisted prediction, the equivalence of a linear model based on independent and identically normally distributed marker effects and a model based on multivariate Gaussian distributed breeding values with genomic relationship as covariance matrix is well known. In this work, we demonstrate equivalences of marker effect models incorporating epistatic interactions and corresponding mixed models based on relationship matrices and show how to exploit these equivalences computationally for genome-assisted prediction. In particular, we show how models with epistatic interactions of higher order (e.g., three-factor interactions) translate into linear models with certain covariance matrices and demonstrate how to construct epistatic relationship matrices for the linear mixed model, if we restrict the model to interactions defined a priori. We illustrate the practical relevance of our results with a publicly available data set on grain yield of wheat lines growing in four different environments. For this purpose, we select important interactions in one environment and use this knowledge on the network of interactions to increase predictive ability of grain yield under other environmental conditions. Our results provide a guide for building relationship matrices based on knowledge on the structure of trait-related gene networks.

Longevity of dairy cows is determined by culling. Previous studies have shown that culling of dairy cows is not an unambiguous trait but rather the result of several reasons including diseases and selection decisions. The relative importance of these reasons is not stable over time, implying that genetic background of culling may vary over lifetime. Data of 7.6 million German Holstein cows were used to assess the detailed genetic correlation structure among 18 survival traits defined for the first 3 parities. Differences of genetic factors which determine survival of different production periods were found, showing a pattern with 3 genetically distinct periods within each parity: early lactation (calving until d 59), mid lactation (d 60 to 299), and late lactation (d 300 until next calving). Survival in first and later parities were found to be slightly genetically different from each other. The identified patterns were in good accordance with distributions of reasons for disposal, and correlations of estimated breeding values of survival traits for different periods to production and functional traits were generally plausible compared with literature regarding effects on the risk of culling. The study shows that genetic background of survival is variable not only across but also within parities. The results of the study can help developing more accurate models for routine genetic evaluations of longevity that account for nonunity genetic correlations between survival of different periods.

In most countries and for most livestock species, genomic evaluations are obtained from within-breed analyses. To achieve reliable breeding values, however, a sufficient reference sample size is essential. To increase this size, the use of multibreed reference populations for small populations is considered a suitable option in other species. Over decades, the separate breeding work of different pig breeding organizations in Germany has led to stratified subpopulations in the breed German Large White. Due to this fact and the limited number of Large White animals available in each organization, there was a pressing need for ascertaining if multi-subpopulation genomic prediction is superior compared with within-subpopulation prediction in pigs. Direct genomic breeding values were estimated with genomic BLUP for the trait "number of piglets born alive" using genotype data (Illumina Porcine 60K SNP BeadChip) from 2,053 German Large White animals from five different commercial pig breeding companies. To assess the prediction accuracy of within- and multi-subpopulation reference sets, a random 5-fold cross-validation with 20 replications was performed. The five subpopulations considered were only slightly differentiated from each other. However, the prediction accuracy of the multi-subpopulations approach was not better than that of the within-subpopulation evaluation, for which the predictive ability was already high. Reference sets composed of closely related multi-subpopulation sets performed better than sets of distantly related subpopulations but not better than the within-subpopulation approach. Despite the low differentiation of the five subpopulations, the genetic connectedness between these different subpopulations seems to be too small to improve the prediction accuracy by applying multi-subpopulation reference sets. Consequently, resources should be used for enlarging the reference population within subpopulation, for example, by adding genotyped females.

This study focused on a reintroduced population of south-western common brushtail possum (Trichosurus vulpecula hypoleucus) to assess genetic variability and inform future management strategies. Individuals were translocated to Matuwa Kurarra-Kurarra Indigenous Protected Area, Western Australia, from four source populations, but subsequent monitoring has indicated a 50% reduction in population size from original founder numbers in the eight years since establishment. Tissue samples from three of the four source populations and an additional four comparative sites (n=140 animals total) were analysed using 13 microsatellite loci. Inbreeding was lower and heterozygosity was higher in the translocated Matuwa population than in two of the source populations studied, highlighting the benefits of promoting outbreeding through the use of multiple source populations in translocations. However, allelic richness at Matuwa is low relative to two of the source populations, suggesting the impact of population bottlenecks on genetic diversity, which was supported by significant allele frequency mode shift and Wilcoxon rank sign test for heterozygosity excess tests for genetic bottlenecks. Despite the genetic health of the population being stronger than predicted, this population is still at risk due to environmental factors, small size and fragmentation. This is the first study to document patterns of genetic diversity and to highlight issues with translocation for this subspecies and adds to the limited literature illustrating how outbreeding can be used for conservation purposes.

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.

A whole-genome scan for identifying selection acting on pairs of linked loci is proposed and implemented. The scan is based on , one of Ohta's 1982 measures of between-population linkage disequilibrium (LD). An approximate empirical null distribution for the statistic is suggested. Although the partitioning of LD into between-population components was originally used to investigate epistatic selection, we demonstrate that values of may also be influenced by single-locus selective sweeps with linkage but no epistasis. The proposed scan is implemented in a diverse panel of chickens including 72 distinct breeds genotyped at 538 298 single-nucleotide polymorphisms. In all, 1723 locus pairs are identified as putatively corresponding to a selective sweep or epistatic selection. These pairs of loci generally cluster to form overlapping or neighboring signals of selection. Known variants that were expected to have been under selection in the panel are identified, as well as an assortment of novel regions that have putatively been under selection in chickens. Notably, a promising pair of genes located 8 MB apart on chromosome 9 are identified based on as demonstrating strong evidence of dispersive epistatic selection between populations.

This study presents an approach combining phenotypes from novel traits, deterministic equations from cattle nutrition, and stochastic simulation techniques from animal breeding to generate test-day methane emissions (MEm) of dairy cows. Data included test-day production traits (milk yield, fat percentage, protein percentage, milk urea nitrogen), conformation traits (wither height, hip width, body condition score), female fertility traits (days open, calving interval, stillbirth), and health traits (clinical mastitis) from 961 first lactation Brown Swiss cows kept on 41 low-input farms in Switzerland. Test-day MEm were predicted based on the traits from the current data set and 2 deterministic prediction equations, resulting in the traits labeled MEm1 and MEm2. Stochastic simulations were used to assign individual concentrate intake in dependency of farm-type specifications (requirement when calculating MEm2). Genetic parameters for MEm1 and MEm2 were estimated using random regression models. Predicted MEm had moderate heritabilities over lactation and ranged from 0.15 to 0.37, with highest heritabilities around DIM 100. Genetic correlations between MEm1 and MEm2 ranged between 0.91 and 0.94. Antagonistic genetic correlations in the range from 0.70 to 0.92 were found for the associations between MEm2 and milk yield. Genetic correlations between MEm with days open and with calving interval increased from 0.10 at the beginning to 0.90 at the end of lactation. Genetic relationships between MEm2 and stillbirth were negative (0 to -0.24) from the beginning to the peak phase of lactation. Positive genetic relationships in the range from 0.02 to 0.49 were found between MEm2 with clinical mastitis. Interpretation of genetic (co)variance components should also consider the limitations when using data generated by prediction equations. Prediction functions only describe that part of MEm which is dependent on the factors and effects included in the function. With high probability, there are more important effects contributing to variations of MEm that are not explained or are independent from these functions. Furthermore, autocorrelations exist between indicator traits and predicted MEm. Nevertheless, this integrative approach, combining information from dairy cattle nutrition with dairy cattle genetics, generated novel traits which are difficult to record on a large scale. The simulated data basis for MEm was used to determine the size of a cow calibration group for genomic selection. A calibration group including 2,581 cows with MEm phenotypes was competitive with conventional breeding strategies.

The aim of this study was to investigate the maternal genealogical pattern of chicken breeds sampled in Europe. Sequence polymorphisms of 1256 chickens of the hypervariable region (D-loop) of mitochondrial DNA (mtDNA) were used. Median-joining networks were constructed to establish evolutionary relationships among mtDNA haplotypes of chickens, which included a wide range of breeds with different origin and history. Chicken breeds which have had their roots in Europe for more than 3000 years were categorized by their founding regions, encompassing Mediterranean type, East European type and Northwest European type. Breeds which were introduced to Europe from Asia since the mid-19th century were classified as Asian type, and breeds based on crossbreeding between Asian breeds and European breeds were classified as Intermediate type. The last group, Game birds, included fighting birds from Asia. The classification of mtDNA haplotypes was based on Liu et al.'s (2006) nomenclature. Haplogroup E was the predominant clade among the European chicken breeds. The results showed, on average, the highest number of haplotypes, highest haplotype diversity, and highest nucleotide diversity for Asian type breeds, followed by Intermediate type chickens. East European and Northwest European breeds had lower haplotype and nucleotide diversity compared to Mediterranean, Intermediate, Game and Asian type breeds. Results of our study support earlier findings that chicken breeds sampled in Europe have their roots in the Indian subcontinent and East Asia. This is consistent with historical and archaeological evidence of chicken migration routes to Europe.

Obtaining accurate predictions of unobserved genetic or phenotypic values for complex traits in animal, plant, and human populations is possible through whole-genome prediction (WGP), a combined analysis of genotypic and phenotypic data. Because the underlying genetic architecture of the trait of interest is an important factor affecting model selection, we propose a new strategy, termed BLUP|GA (BLUP-given genetic architecture), which can use genetic architecture information within the dataset at hand rather than from public sources. This is achieved by using a trait-specific covariance matrix (T), which is a weighted sum of a genetic architecture part (S matrix) and the realized relationship matrix (G). The algorithm of BLUP|GA (BLUP-given genetic architecture) is provided and illustrated with real and simulated datasets. Predictive ability of BLUP|GA was validated with three model traits in a dairy cattle dataset and 11 traits in three public datasets with a variety of genetic architectures and compared with GBLUP and other approaches. Results show that BLUP|GA outperformed GBLUP in 20 of 21 scenarios in the dairy cattle dataset and outperformed GBLUP, BayesA, and BayesB in 12 of 13 traits in the analyzed public datasets. Further analyses showed that the difference of accuracies for BLUP|GA and GBLUP significantly correlate with the distance between the T and G matrices. The new strategy applied in BLUP|GA is a favorable and flexible alternative to the standard GBLUP model, allowing to account for the genetic architecture of the quantitative trait under consideration when necessary. This feature is mainly due to the increased similarity between the trait-specific relationship matrix (T matrix) and the genetic relationship matrix at unobserved causal loci. Applying BLUP|GA in WGP would ease the burden of model selection.

1. Bone stability of five purebred layer lines differing in performance efficiency and phylogenetic origin was investigated within two housing systems. 2. Hens were kept in single cages or floor pens until the end of the 74 th week of age. At that time, they were sacrificed and examined for humeral and tibial traits. 3. Within a phylogenetic group, hens of the low performing lines had higher bone breaking strengths compared to their high performing counterparts. The bone mineral density of the tibia was significantly lower in the high performing brown egg layers than in the low performing ones. 4. Within and among layer lines, birds in floor housing had significantly higher tibia and humerus breaking strengths as well as higher bone weights than caged hens. 5. The differences between the high and low performing layer lines suggest a negative association between egg laying performance and bone stability in laying hens, irrespective of their phylogenetic origin. Moreover, the results confirm the already known effect of the housing system on bone strength.

Background The single-step covariance matrix H combines the pedigree-based relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {A}}$$\end{document}A with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {G}}$$\end{document}G. 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In a joint discussion, we considered the question of the shape of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {H}}$$\end{document}H for non-trivial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document}ω. 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In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ or by decreasing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document}ω.

Basiswissen für das Grundstudium Dieses Buch bietet Studierenden der Agrarwissenschaften und Veterinärmedizin ohne Vorkenntnisse eine kompakte und leicht verständliche Einführung in das Fachgebiet der Tierzucht. Das Basiswissen wurde aktualisiert und in bewährter Form didaktisch aufbereitet. Aus dem Inhalt: • Einführung • Tierische Leistungen • Molekulargenetische und züchterische Grundlagen • Zuchtfortschritt • Selektion • Zuchtmethoden und Zuchtprogramme • Nutzungsrichtungen und Rassen Neu in der 2. Auflage: • Genomweite Sequenzierung • Genomische Zuchtwertschätzung • Genomisch-unterstützte Selektion und deren Anwendung in Zuchtprogrammen

The aim of this study was to answer the question whether models for genetic evaluations of longevity should include a correction for age at first calving (AFC). For this purpose, phenotypic and genetic relationships between AFC, its component traits age at first insemination (AFI) and interval from first to last insemination (FLI), and survival of different periods of the first lactation (S1: 0 to 49 d, S2: 50 to 249 d, S3: 250 d to second calving) were investigated. Data of 721,919 German Holstein heifers, being inseminated for the first time during the years from 2003 to 2012, were used for the analyses. Phenotypic correlations of AFI, FLI, and AFC to S1 to S3 were negative. Mean estimated heritabilities were 0.239 (AFI), 0.007 (FLI), and 0.103 (AFC) and 0.023 (S1), 0.016 (S2), and 0.028 (S3) on the observed scale. The genetic correlation between AFI and FLI was close to zero. Genetic correlations between AFI and the survival traits were -0.08 (S1), -0.02 (S2), and -0.10 (S3); those between FLI and the survival traits were -0.14 (S1), -0.20 (S2), and -0.44 (S3); and those between AFC and the survival traits were -0.09 (S1), -0.06 (S2), and -0.20 (S3). Some of these genetic correlations were different from zero, which suggests that correcting for AFC in genetic evaluations for longevity in dairy cows might remove functional genetic variance and should be reconsidered.

Maize (Zea mays L.) serves as model plant for heterosis research and is the crop where hybrid breeding was pioneered. We analyzed genomic and phenotypic data of 1254 hybrids of a typical maize hybrid breeding program based on the important Dent × Flint heterotic pattern. Our main objectives were to investigate genome properties of the parental lines (e.g., allele frequencies, linkage disequilibrium, and phases) and examine the prospects of genomic prediction of hybrid performance. We found high consistency of linkage phases and large differences in allele frequencies between the Dent and Flint heterotic groups in pericentromeric regions. These results can be explained by the Hill–Robertson effect and support the hypothesis of differential fixation of alleles due to pseudo-overdominance in these regions. In pericentromeric regions we also found indications for consistent marker–QTL linkage between heterotic groups. With prediction methods GBLUP and BayesB, the cross-validation prediction accuracy ranged from 0.75 to 0.92 for grain yield and from 0.59 to 0.95 for grain moisture. The prediction accuracy of untested hybrids was highest, if both parents were parents of other hybrids in the training set, and lowest, if none of them were involved in any training set hybrid. Optimizing the composition of the training set in terms of number of lines and hybrids per line could further increase prediction accuracy. We conclude that genomic prediction facilitates a paradigm shift in hybrid breeding by focusing on the performance of experimental hybrids rather than the performance of parental lines in testcrosses.

Human driven selection during domestication and subsequent breed formation and breeding has left detectable signatures within the genome of livestock breeds. The elucidation of these signatures of selection is of interest from the perspective of evolutionary biology and for identifying selected genes that ultimately may help to further genetically improve these economically important species. Genome-wide screenings based on population techniques provide analytical tools to detect these signatures in relation to the act of selection. This review outlines a nonmathematical treatment of the theories and approaches available to scan the genome for evidence of positive selection and is intended for readers who are little or not familiar with population genetics theory. We discuss the genetics underlying phenotypic variation and adaptation and highlight molecular pattern that positive selection leaves behind along with the statistical approaches that are developed to detect such signatures. We describe some of the relative strengths and weaknesses of different strategies and also the challenges with identifying signatures of selection. Ascertainment bias with widely used SNP arrays is also a topic of interest. Finally we review approaches to assess the statistical significance of a signal at a particular locus or window and discuss factors affecting the statistical power to detect selective sweeps.

Genetic parameters were inferred for the health traits mastitis, metritis, retained placenta, ovarian cysts and acetonemia from 1247 Brown Swiss cows in first parity kept in 53 organic and low input farms in Switzerland. For genetic analyses, univariate animal and sire models, repeatability animal and sire models, and random regression sire models (RRM) in a “generalized linear mixed model (GLMM) context” were applied. The five health traits were defined as binary data, count data, and longitudinal binary data in the interval between −1 and 120 d in milk (DIM). Firstly, binary data were analyzed by applying linear animal and sire models, and threshold animal and sire models with a probit link function. Secondly, data of total number of disease cases recorded within the defined time span were analyzed by using GLMM animal and sire models with a log link function for Poisson distributed count data. Thirdly, for longitudinal health data, linear repeatability animal and sire models, linear sire RRM, threshold animal and sire repeatability models, and threshold sire RRM with a probit link function were applied. Disease incidences of the five health disorders in organic farms were on a generally low level, with a highest incidence of 5.78% for mastitis within the time span of 120 d. With regard to mastitis, moderate heritabilities with an average value of 0.15 were realized from univariate models and binary data, and from GLMM with the log link function and count data. Heritabilities for mastitis were smaller (

Designing strategies for conservation and improvement livestock should be based on assessment of genetic characteristics of populations under consideration. In Oman, conservation programs for local livestock breeds have been started. The current study assessed the genetic diversity and conservation potential of local chickens from Oman. Twenty-nine microsatellite markers were analyzed in 158 birds from six agro-ecological zones: Batinah, Dhofar, North Hajar, East Hajar, Musandam, and East Coast. Overall, a total of 217 alleles were observed. Across populations, the average number of alleles per locus was 7.48 and ranged from 2 (MCW98 and MCW103) to 20 (LEI094). The mean expected heterozygosity (H E) was 0.62. Average fixation index among populations (F ST) was 0.034, indicating low population differentiation, while the mean global deficit of heterozygotes across populations (F IT) was 0.159. Based on Nei's genetic distance, a neighbor-joining tree was constructed for the populations, which clearly identified the Dhofar population as the most distant one of the Omani chicken populations. The analysis of conservation priorities identified Dhofar and Musandam populations as the ones that largely contribute to the maximal genetic diversity of the Omani chicken gene pool.

This paper undertakes an exploration of the potential application of the Weitzman prioritisation approach to the conservation of plant genetic resources (PGR). Using a case study approach and assuming limited conservation resources, this approach is applied to calculate the maximum diversity which can be conserved based on a clustering of cacao species (Theobroma cacao L.). A conservation budget allocation model applied across a set of ten clusters and nine subclusters of cacao, together with the use of alternative diversity and risk measures, allowed for an evaluation of a range of potential conservation outcomes. Alternative risk measures generally resulted in the allocation of conservation funds to the same priority clusters of cacao (Criollo and Curaray). However, the use of the number of locally common alleles as an alternative to the original Weitzman diversity measure produced a markedly different result, prioritising the Purus cluster in Western Amazonia. The Curaray cluster was highly prioritised under both diversity measures, indicating its distinctiveness relative to both the Criollo and Purus clusters. We conclude that the Weitzman approach can indeed allow diversity comparisons to be made between the outcomes of different PGR conservation strategies, although subjective decisions regarding the choice of diversity and risk measures remain.

The aim of this study was to estimate genetic parameters and accuracies of breeding values for a set of functional, behavior, and conformation traits in Brown Swiss cattle. These traits were milking speed, udder depth, position of labia, rank order in herd, general temperament, aggressiveness, milking temperament, and days to first heat. Data of 1,799 phenotyped Brown Swiss cows from 40 Swiss dairy herds were analyzed taking the complete pedigree into account. Estimated heritabilities were within the ranges reported in literature, with results at the high end of the reported values for some traits (e.g., milking speed: 0.42±0.06, udder depth: 0.42±0.06), whereas other traits were of low heritability and heritability estimates were of low accuracy (e.g., milking temperament: 0.04±0.04, days to first heat: 0.02±0.04). For most behavior traits, we found relatively high heritabilities (general temperament: 0.38±0.07, aggressiveness: 0.12±0.08, and rank order in herd: 0.16±0.06). Position of labia, arguably an indicator trait for pathological urovagina, was genetically analyzed in this study for the first time, and a moderate heritability (0.28±0.06) was estimated.