Uncertainty in the mating strategy of honeybees causes bias and unreliability in the estimates of genetic parameters.

BACKGROUND: Breeding queens may be mated with drones that are produced by a single drone-producing queen (DPQ), or a group of sister-DPQs, but often only the dam of the DPQ(s) is reported in the pedigree. Furthermore, datasets may include colony phenotypes from DPQs that were open-mated at different locations, and thus to a heterogeneous drone population. METHODS: Simulation was used to investigate the impact of the mating strategy and its modelling on the estimates of genetic parameters and genetic trends when the DPQs are treated in different ways in the statistical evaluation model. We quantified the bias and standard error of the estimates when breeding queens were mated to one DPQ or a group of DPQs, assuming that this information was known or not. We also investigated four alternative strategies to accommodate the phenotypes of open-mated DPQs in the genetic evaluation: excluding their phenotypes, adding a dummy pseudo-sire in the pedigree, or adding a non-genetic (fixed or random) effect to the statistical evaluation model to account for the origin of the mates. RESULTS: The most precise estimates of genetic parameters and genetic trends were obtained when breeding queens were mated with drones of single DPQs that are correctly assigned in the pedigree. However, when they were mated with drones from one or a group of DPQs, and this information was not known, erroneous assumptions led to considerable bias in these estimates. Furthermore, genetic variances were considerably overestimated when phenotypes of colonies from open-mated DPQs were adjusted for their mates by adding a dummy pseudo-sire in the pedigree for each subpopulation of open-mating drones. On the contrary, correcting for the heterogeneous drone population by adding a non-genetic effect in the evaluation model produced unbiased estimates. CONCLUSIONS: Knowing only the dam of the DPQ(s) used in each mating may lead to erroneous assumptions on how DPQs were used and severely bias the estimates of genetic parameters and trends. Thus, we recommend keeping track of DPQs in the pedigree, and not only of the dams of DPQ(s). Records from DPQ colonies with queens open-mated to a heterogeneous drone population can be integrated by adding non-genetic effects to the statistical evaluation model.

Improving selection decisions with mating information by accounting for Mendelian sampling variances looking two generations ahead.

BACKGROUND: Breeding programs are judged by the genetic level of animals that are used to disseminate genetic progress. These animals are typically the best ones of the population. To maximise the genetic level of very good animals in the next generation, parents that are more likely to produce top performing offspring need to be selected. The ability of individuals to produce high-performing progeny differs because of differences in their breeding values and gametic variances. Differences in gametic variances among individuals are caused by differences in heterozygosity and linkage. The use of the gametic Mendelian sampling variance has been proposed before, for use in the usefulness criterion or Index5, and in this work, we extend existing approaches by not only considering the gametic Mendelian sampling variance of individuals, but also of their potential offspring. Thus, the criteria developed in this study plan one additional generation ahead. For simplicity, we assumed that the true quantitative trait loci (QTL) effects, genetic map and the haplotypes of all animals are known. RESULTS: In this study, we propose a new selection criterion, ExpBVSelGrOff, which describes the genetic level of selected grand-offspring that are produced by selected offspring of a particular mating. We compare our criterion with other published criteria in a stochastic simulation of an ongoing breeding program for 21 generations for proof of concept. ExpBVSelGrOff performed better than all other tested criteria, like the usefulness criterion or Index5 which have been proposed in the literature, without compromising short-term gains. After only five generations, when selection is strong (1%), selection based on ExpBVSelGrOff achieved 5.8% more commercial genetic gain and retained 25% more genetic variance without compromising inbreeding rate compared to selection based only on breeding values. CONCLUSIONS: Our proposed selection criterion offers a new tool to accelerate genetic progress for contemporary genomic breeding programs. It retains more genetic variance than previously published criteria that plan less far ahead. Considering future gametic Mendelian sampling variances in the selection process also seems promising for maintaining more genetic variance.

Towards genetic improvement of social behaviours in livestock using large-scale sensor data: data simulation and genetic analysis.

BACKGROUND: Harmful social behaviours, such as injurious feather pecking in poultry and tail biting in swine, reduce animal welfare and production efficiency. While these behaviours are heritable, selective breeding is still limited due to a lack of individual phenotyping methods for large groups and proper genetic models. In the near future, large-scale longitudinal data on social behaviours will become available, e.g. through computer vision techniques, and appropriate genetic models will be needed to analyse such data. In this paper, we investigated prospects for genetic improvement of social traits recorded in large groups by (1) developing models to simulate and analyse large-scale longitudinal data on social behaviours, and (2) investigating required sample sizes to obtain reasonable accuracies of estimated genetic parameters and breeding values (EBV). RESULTS: Latent traits were defined as representing tendencies of individuals to be engaged in social interactions by distinguishing between performer and recipient effects. Animal movement was assumed random and without genetic variation, and performer and recipient interaction effects were assumed constant over time. Based on the literature, observed-scale heritabilities ([Formula: see text]) of performer and recipient effects were both set to 0.05, 0.1, or 0.2, and the genetic correlation ([Formula: see text]) between those effects was set to - 0.5, 0, or 0.5. Using agent-based modelling, we simulated ~ 200,000 interactions for 2000 animals (~ 1000 interactions per animal) with a half-sib family structure. Variance components and breeding values were estimated with a general linear mixed model. The estimated genetic parameters did not differ significantly from the true values. When all individuals and interactions were included in the analysis, the accuracy of EBV was 0.61, 0.70, and 0.76 for [Formula: see text] = 0.05, 0.1, and 0.2, respectively (for [Formula: see text]= 0). Including 2000 individuals each with only ~ 100 interactions, already yielded promising accuracies of 0.47, 0.60, and 0.71 for [Formula: see text] = 0.05, 0.1, and 0.2, respectively (with [Formula: see text] = 0). Similar results were found with [Formula: see text] of - 0.5 or 0.5. CONCLUSIONS: We developed models to simulate and genetically analyse social behaviours for animals that are kept in large groups, anticipating the availability of large-scale longitudinal data in the near future. We obtained promising accuracies of EBV with ~ 100 interactions per individual, which would correspond to a few weeks of recording. Therefore, we conclude that animal breeding can be a promising strategy to improve social behaviours in livestock.

Predicting the impact of genotype-by-genotype interaction on the purebred-crossbred genetic correlation from phenotype and genotype marker data of parental lines.

BACKGROUND: The genetic correlation between purebred (PB) and crossbred (CB) performances ([Formula: see text]) partially determines the response in CB when selection is on PB performance in the parental lines. An earlier study has derived expressions for an upper and lower bound of [Formula: see text], using the variance components of the parental purebred lines, including e.g. the additive genetic variance in the sire line for the trait expressed in one of the dam lines. How to estimate these variance components is not obvious, because animals from one parental line do not have phenotypes for the trait expressed in the other line. Thus, the aim of this study was to propose and compare three methods for approximating the required variance components. The first two methods are based on (co)variances of genomic estimated breeding values (GEBV) in the line of interest, either accounting for shrinkage (VCGEBV-S) or not (VCGEBV). The third method uses restricted maximum likelihood (REML) estimates directly from univariate and bivariate analyses (VCREML) by ignoring that the variance components should refer to the line of interest, rather than to the line in which the trait is expressed. We validated these methods by comparing the resulting predicted bounds of [Formula: see text] with the [Formula: see text] estimated from PB and CB data for five traits in a three-way cross in pigs. RESULTS: With both VCGEBV and VCREML, the estimated [Formula: see text] (plus or minus one standard error) was between the upper and lower bounds in 14 out of 15 cases. However, the range between the bounds was much smaller with VCREML (0.15-0.22) than with VCGEBV (0.44-0.57). With VCGEBV-S, the estimated [Formula: see text] was between the upper and lower bounds in only six out of 15 cases, with the bounds ranging from 0.21 to 0.44. CONCLUSIONS: We conclude that using REML estimates of variance components within and between parental lines to predict the bounds of [Formula: see text] resulted in better predictions than methods based on GEBV. Thus, we recommend that the studies that estimate [Formula: see text] with genotype data also report estimated genetic variance components within and between the parental lines.

Predictions of the accuracy of genomic prediction: connecting R2, selection index theory, and Fisher information.

BACKGROUND: Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) when combining information sources have been developed based on selection index theory (SIT) and on Fisher information (FI). These two approaches have resulted in slightly different results when considering the combination of pedigree and genomic information. Here, we clarify this apparent contradiction, both for the combination of pedigree and genomic information and for the combination of subpopulations into a joint reference population. RESULTS: First, we show that existing expressions for the squared accuracy of GEBV can be understood as a proportion of the variance explained. Next, we show that the apparent discrepancy that has been observed between accuracies based on SIT vs. FI originated from two sources. First, the FI referred to the genetic component that is captured by the marker genotypes, rather than the full genetic component. Second, the common SIT-based derivations did not account for the increase in the accuracy of GEBV due to a reduction of the residual variance when combining information sources. The SIT and FI approaches are equivalent when these sources are accounted for. CONCLUSIONS: The squared accuracy of GEBV can be understood as a proportion of the variance explained. The SIT and FI approaches for combining information for GEBV are equivalent and provide identical accuracies when the underlying assumptions are equivalent.

Can breeders prevent pathogen adaptation when selecting for increased resistance to infectious diseases?

BACKGROUND: Recent research shows that genetic selection has high potential to reduce the prevalence of infectious diseases in livestock. However, like all interventions that target infectious diseases, genetic selection of livestock can exert selection pressure on pathogen populations. Such selection on the pathogen may lead to escape strategies and reduce the effect of selection of livestock for disease resistance. Thus, to successfully breed livestock for lower disease prevalence, it is essential to develop strategies that prevent the invasion of pathogen mutants that escape host resistance. Here we investigate the conditions under which such "escape mutants" can replace wild-type pathogens in a closed livestock population using a mathematical model of disease transmission. RESULTS: Assuming a single gene that confers sufficient resistance, results show that genetic selection for resistance in livestock typically leads to an "invasion window" within which an escape mutant of the pathogen can invade. The bounds of the invasion window are determined by the frequency of resistant hosts in the population. The lower bound occurs when the escape mutant has an advantage over the wild-type pathogen in the population. The upper bound occurs when local eradication of the pathogen is expected. The invasion window is smallest when host resistance is strong and when infection with the wild-type pathogen provides cross immunity to infection with the escape mutant. CONCLUSIONS: To minimise opportunities for pathogens to adapt, under the assumptions of our model, the aim of disease control through genetic selection should be to achieve herd-level eradication of the infection faster than the rate of emergence of escape mutants of the pathogen. Especially for microparasitic infections, this could be achieved by placing animals into herds according to their genetic resistance, such that these herds stay completely out of the invasion window. In contrast to classical breeding theory, our model suggests that multi-trait selection with gradual improvement of each trait of the breeding goal might not be the best strategy when resistance to infectious disease is part of the breeding goal. Temporally, combining genetic selection with other interventions helps to make the invasion window smaller, and thereby reduces the risk of invasion of escape mutants.

The long-term effects of genomic selection: 1. Response to selection, additive genetic variance, and genetic architecture.

BACKGROUND: Genomic selection has revolutionized genetic improvement in animals and plants, but little is known about its long-term effects. Here, we investigated the long-term effects of genomic selection on response to selection, genetic variance, and the genetic architecture of traits using stochastic simulations. We defined the genetic architecture as the set of causal loci underlying each trait, their allele frequencies, and their statistical additive effects. We simulated a livestock population under 50 generations of phenotypic, pedigree, or genomic selection for a single trait, controlled by either only additive, additive and dominance, or additive, dominance, and epistatic effects. The simulated epistasis was based on yeast data. RESULTS: Short-term response was always greatest with genomic selection, while response after 50 generations was greater with phenotypic selection than with genomic selection when epistasis was present, and was always greater than with pedigree selection. This was mainly because loss of genetic variance and of segregating loci was much greater with genomic and pedigree selection than with phenotypic selection. Compared to pedigree selection, selection response was always greater with genomic selection. Pedigree and genomic selection lost a similar amount of genetic variance after 50 generations of selection, but genomic selection maintained more segregating loci, which on average had lower minor allele frequencies than with pedigree selection. Based on this result, genomic selection is expected to better maintain genetic gain after 50 generations than pedigree selection. The amount of change in the genetic architecture of traits was considerable across generations and was similar for genomic and pedigree selection, but slightly less for phenotypic selection. Presence of epistasis resulted in smaller changes in allele frequencies and less fixation of causal loci, but resulted in substantial changes in statistical additive effects across generations. CONCLUSIONS: Our results show that genomic selection outperforms pedigree selection in terms of long-term genetic gain, but results in a similar reduction of genetic variance. The genetic architecture of traits changed considerably across generations, especially under selection and when non-additive effects were present. In conclusion, non-additive effects had a substantial impact on the accuracy of selection and long-term response to selection, especially when selection was accurate.

Comparison of linkage disequilibrium estimated from genotypes versus haplotypes for crossbred populations.

BACKGROUND: Linkage disequilibrium (LD) is commonly measured based on the squared coefficient of correlation [Formula: see text] between the alleles at two loci that are carried by haplotypes. LD can also be estimated as the [Formula: see text] between unphased genotype dosage at two loci when the allele frequencies and inbreeding coefficients at both loci are identical for the parental lines. Here, we investigated whether [Formula: see text] for a crossbred population (F1) can be estimated using genotype data. The parental lines of the crossbred (F1) can be purebred or crossbred. METHODS: We approached this by first showing that inbreeding coefficients for an F1 crossbred population are negative, and typically differ in size between loci. Then, we proved that the expected [Formula: see text] computed from unphased genotype data is expected to be identical to the [Formula: see text] computed from haplotype data for an F1 crossbred population, regardless of the inbreeding coefficients at the two loci. Finally, we investigated the bias and precision of the [Formula: see text] estimated using unphased genotype versus haplotype data in stochastic simulation. RESULTS: Our findings show that estimates of [Formula: see text] based on haplotype and unphased genotype data are both unbiased for different combinations of allele frequencies, sample sizes (900, 1800, and 2700), and levels of LD. In general, for any allele frequency combination and [Formula: see text] value scenarios considered, and for both methods to estimate [Formula: see text], the precision of the estimates increased, and the bias of the estimates decreased as sample size increased, indicating that both estimators are consistent. For a given scenario, the [Formula: see text] estimates using haplotype data were more precise and less biased using haplotype data than using unphased genotype data. As sample size increased, the difference in precision and biasedness between the [Formula: see text] estimates using haplotype data and unphased genotype data decreased. CONCLUSIONS: Our theoretical derivations showed that estimates of LD between loci based on unphased genotypes and haplotypes in F1 crossbreds have identical expectations. Based on our simulation results, we conclude that the LD for an F1 crossbred population can be accurately estimated from unphased genotype data. The results also apply for other crosses (F2, F3, Fn, BC1, BC2, and BCn), as long as (selected) individuals from the two parental lines mate randomly.

Predicting the purebred-crossbred genetic correlation from the genetic variance components in the parental lines.

BACKGROUND: The genetic correlation between purebred and crossbred performance ([Formula: see text]) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of [Formula: see text] when selection is based on purebred (PB) performance. The value of [Formula: see text] can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between [Formula: see text] and parental allele frequencies suggests that [Formula: see text] can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for [Formula: see text] based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The expressions were derived for a genetic model with additive and dominance effects (D), and additive and epistatic additive-by-additive effects (EAA). We validated our expressions using simulations of purebred parental lines and their crosses, where the parental lines were either selected or not. Finally, using these simulations, we investigated the value of [Formula: see text] for genetic models with both dominance and epistasis or with other types of epistasis, for which expressions could not be derived. RESULTS: Our simulations show that when non-additive effects are present, [Formula: see text] decreases with increasing differences in allele frequencies between the parental lines. Genetic models that involve dominance result in lower values of [Formula: see text] than genetic models that involve epistasis only. Using information of parental lines only, our expressions provide exact estimates of [Formula: see text] for models D and EAA, and accurate upper and lower bounds of [Formula: see text] for two other genetic models. CONCLUSION: This work lays the foundation to enable estimation of [Formula: see text] from information collected in PB parental lines only.

On the origin of the genetic variation in infectious disease prevalence: Genetic analysis of disease status versus infections for Digital Dermatitis in Dutch dairy cattle.

The purpose of this study was to investigate the origin of the genetic variation in the prevalence of bovine digital dermatitis (DD) by comparing a genetic analysis of infection events to a genetic analysis of disease status. DD is an important endemic infectious disease affecting the claws of cattle. For disease status, we analysed binary data on individual disease status (0,1; indicating being free versus infected), whereas for infections, we analysed binary data on disease transmission events (1,0; indicating becoming infected or not). The analyses of the two traits were compared using cross-validation. The analysis of disease status captures a combination of genetic variation in disease susceptibility and the ability of individuals to recover, whereas the analysis of infections captures genetic variation in susceptibility only. Estimated genetic variances for both traits indicated substantial genetic variation. The GEBV for disease status and infections correlated with only 0.60, indicating that both models indeed capture distinct information. Together, these results suggest the presence of genetic variation not only in disease susceptibility, but also in the ability of individuals to recover from DD. We argue that the presence of genetic variation in recovery implies that breeders should distinguish between infected individuals versus infectious individuals. This is because epidemiological theory shows that selection for recovery is effective only when it targets recovery from being infectious.

Quantitative genetics of wing morphology in the parasitoid wasp Nasonia vitripennis: hosts increase sibling similarity.

The central aim of evolutionary biology is to understand patterns of genetic variation between species and within populations. To quantify the genetic variation underlying intraspecific differences, estimating quantitative genetic parameters of traits is essential. In Pterygota, wing morphology is an important trait affecting flight ability. Moreover, gregarious parasitoids such as Nasonia vitripennis oviposit multiple eggs in the same host, and siblings thus share a common environment during their development. Here we estimate the genetic parameters of wing morphology in the outbred HVRx population of N. vitripennis, using a sire-dam model adapted to haplodiploids and disentangled additive genetic and host effects. The results show that the wing-size traits have low heritability (h2 ~ 0.1), while most wing-shape traits have roughly twice the heritability compared with wing-size traits. However, the estimates increased to h2 ~ 0.6 for wing-size traits when omitting the host effect from the statistical model, while no meaningful increases were observed for wing-shape traits. Overall, host effects contributed to ~50% of the variation in wing-size traits. This indicates that hosts have a large effect on wing-size traits, about fivefold more than genetics. Moreover, bivariate analyses were conducted to derive the genetic relationships among traits. Overall, we demonstrate the evolutionary potential for morphological traits in the N. vitripennis HVRx-outbred population, and report the host effects on wing morphology. Our findings can contribute to a further dissection of the genetics underlying wing morphology in N. vitripennis, with relevance for gregarious parasitoids and possibly other insects as well.

The economic value of R0 for selective breeding against microparasitic diseases.

BACKGROUND: Microparasitic diseases are caused by bacteria and viruses. Genetic improvement of resistance to microparasitic diseases in breeding programs is desirable and should aim at reducing the basic reproduction ratio [Formula: see text]. Recently, we developed a method to derive the economic value of [Formula: see text] for macroparasitic diseases. In epidemiological models for microparasitic diseases, an animal's disease status is treated as infected or not infected, resulting in a definition of [Formula: see text] that differs from that for macroparasitic diseases. Here, we extend the method for the derivation of the economic value of [Formula: see text] to microparasitic diseases. METHODS: When [Formula: see text], the economic value of [Formula: see text] is zero because the disease is very rare. When [Formula: see text]. is higher than 1, genetic improvement of [Formula: see text] can reduce expenditures on vaccination if vaccination induces herd immunity, or it can reduce production losses due to disease. When vaccination is used to achieve herd immunity, expenditures are proportional to the critical vaccination coverage, which decreases with [Formula: see text]. The effect of [Formula: see text] on losses is considered separately for epidemic and endemic disease. Losses for epidemic diseases are proportional to the probability and size of major epidemics. Losses for endemic diseases are proportional to the infected fraction of the population at the endemic equilibrium. RESULTS: When genetic improvement reduces expenditures on vaccination, expenditures decrease with [Formula: see text] at an increasing rate. When genetic improvement reduces losses in epidemic or endemic diseases, losses decrease with [Formula: see text] at an increasing rate. Hence, in all cases, the economic value of [Formula: see text] increases as [Formula: see text] decreases towards 1. DISCUSSION: [Formula: see text] and its economic value are more informative for potential benefits of genetic improvement than heritability estimates for survival after a disease challenge. In livestock, the potential for genetic improvement is small for epidemic microparasitic diseases, where disease control measures limit possibilities for phenotyping. This is not an issue in aquaculture, where controlled challenge tests are performed in dedicated facilities. If genetic evaluations include infectivity, genetic gain in [Formula: see text] can be accelerated but this would require different testing designs. CONCLUSIONS: When [Formula: see text], its economic value is zero. The economic value of [Formula: see text] is highest at low values of [Formula: see text] and approaches zero at high values of [Formula: see text].

Optimizing genomic reference populations to improve crossbred performance.

BACKGROUND: In pig and poultry breeding, the objective is to improve the performance of crossbred production animals, while selection takes place in the purebred parent lines. One way to achieve this is to use genomic prediction with a crossbred reference population. A crossbred reference population benefits from expressing the breeding goal trait but suffers from a lower genetic relatedness with the purebred selection candidates than a purebred reference population. Our aim was to investigate the benefit of using a crossbred reference population for genomic prediction of crossbred performance for: (1) different levels of relatedness between the crossbred reference population and purebred selection candidates, (2) different levels of the purebred-crossbred correlation, and (3) different reference population sizes. We simulated a crossbred breeding program with 0, 1 or 2 multiplication steps to generate the crossbreds, and compared the accuracy of genomic prediction of crossbred performance in one generation using either a purebred or a crossbred reference population. For each scenario, we investigated the empirical accuracy based on simulation and the predicted accuracy based on the estimated effective number of independent chromosome segments between the reference animals and selection candidates. RESULTS: When the purebred-crossbred correlation was 0.75, the accuracy was highest for a two-way crossbred reference population but similar for purebred and four-way crossbred reference populations, for all reference population sizes. When the purebred-crossbred correlation was 0.5, a purebred reference population always resulted in the lowest accuracy. Among the different crossbred reference populations, the accuracy was slightly lower when more multiplication steps were used to create the crossbreds. In general, the benefit of crossbred reference populations increased when the size of the reference population increased. All predicted accuracies overestimated their corresponding empirical accuracies, but the different scenarios were ranked accurately when the reference population was large. CONCLUSIONS: The benefit of a crossbred reference population becomes larger when the crossbred population is more related to the purebred selection candidates, when the purebred-crossbred correlation is lower, and when the reference population is larger. The purebred-crossbred correlation and reference population size interact with each other with respect to their impact on the accuracy of genomic estimated breeding values.

Inbreeding depression across the genome of Dutch Holstein Friesian dairy cattle.

BACKGROUND: Inbreeding depression refers to the decrease in mean performance due to inbreeding. Inbreeding depression is caused by an increase in homozygosity and reduced expression of (on average) favourable dominance effects. Dominance effects and allele frequencies differ across loci, and consequently inbreeding depression is expected to differ along the genome. In this study, we investigated differences in inbreeding depression across the genome of Dutch Holstein Friesian cattle, by estimating dominance effects and effects of regions of homozygosity (ROH). METHODS: Genotype (75 k) and phenotype data of 38,792 cows were used. For nine yield, fertility and udder health traits, GREML models were run to estimate genome-wide inbreeding depression and estimate additive, dominance and ROH variance components. For this purpose, we introduced a ROH-based relationship matrix. Additive, dominance and ROH effects per SNP were obtained through back-solving. In addition, a single SNP GWAS was performed to identify significant additive, dominance or ROH associations. RESULTS: Genome-wide inbreeding depression was observed for all yield, fertility and udder health traits. For example, a 1% increase in genome-wide homozygosity was associated with a decrease in 305-d milk yield of approximately 99 kg. For yield traits only, including dominance and ROH effects in the GREML model resulted in a better fit (P < 0.05) than a model with only additive effects. After correcting for the effect of genome-wide homozygosity, dominance and ROH variance explained less than 1% of the phenotypic variance for all traits. Furthermore, dominance and ROH effects were distributed evenly along the genome. The most notable region with a favourable dominance effect for yield traits was on chromosome 5, but overall few regions with large favourable dominance effects and significant dominance associations were detected. No significant ROH-associations were found. CONCLUSIONS: Inbreeding depression was distributed quite equally along the genome and was well captured by genome-wide homozygosity. These findings suggest that, based on 75 k SNP data, there is little benefit of accounting for region-specific inbreeding depression in selection schemes.

Bayesian neural networks with variable selection for prediction of genotypic values.

BACKGROUND: Estimating the genetic component of a complex phenotype is a complicated problem, mainly because there are many allele effects to estimate from a limited number of phenotypes. In spite of this difficulty, linear methods with variable selection have been able to give good predictions of additive effects of individuals. However, prediction of non-additive genetic effects is challenging with the usual prediction methods. In machine learning, non-additive relations between inputs can be modeled with neural networks. We developed a novel method (NetSparse) that uses Bayesian neural networks with variable selection for the prediction of genotypic values of individuals, including non-additive genetic effects. RESULTS: We simulated several populations with different phenotypic models and compared NetSparse to genomic best linear unbiased prediction (GBLUP), BayesB, their dominance variants, and an additive by additive method. We found that when the number of QTL was relatively small (10 or 100), NetSparse had 2 to 28 percentage points higher accuracy than the reference methods. For scenarios that included dominance or epistatic effects, NetSparse had 0.0 to 3.9 percentage points higher accuracy for predicting phenotypes than the reference methods, except in scenarios with extreme overdominance, for which reference methods that explicitly model dominance had 6 percentage points higher accuracy than NetSparse. CONCLUSIONS: Bayesian neural networks with variable selection are promising for prediction of the genetic component of complex traits in animal breeding, and their performance is robust across different genetic models. However, their large computational costs can hinder their use in practice.

A note on genetic parameters and accuracy of estimated breeding values in honey bees.

BACKGROUND: In honey bees, observations are usually made on colonies. The phenotype of a colony is affected by the average breeding value for the worker effect of the thousands of workers in the colony (the worker group) and by the breeding value for the queen effect of the queen of the colony. Because the worker group consists of multiple individuals, interpretation of the variance components and heritabilities of phenotypes observed on the colony and of the accuracy of selection is not straightforward. The additive genetic variance among worker groups depends on the additive genetic relationship between the drone-producing queens (DPQ) that produce the drones that mate with the queen. RESULTS: Here, we clarify how the relatedness between DPQ affects phenotypic variance, heritability and accuracy of the estimated breeding values of replacement queens. Second, we use simulation to investigate the effect of assumptions about the relatedness between DPQ in the base population on estimates of genetic parameters. Relatedness between DPQ in the base generation may differ considerably between populations because of their history. CONCLUSIONS: Our results show that estimates of (co)variance components and derived genetic parameters were seriously biased (25% too high or too low) when assumptions on the relationship between DPQ in the statistical analysis did not agree with reality.

Genetic parameters and genomic breeding values for digital dermatitis in Holstein Friesian dairy cattle: host susceptibility, infectivity and the basic reproduction ratio.

BACKGROUND: For infectious diseases, the probability that an animal gets infected depends on its own susceptibility, and on the number of infectious herd mates and their infectivity. Together with the duration of the infectious period, susceptibility and infectivity determine the basic reproduction ratio of the disease ([Formula: see text]). [Formula: see text] is the average number of secondary cases caused by a typical infectious individual in an otherwise uninfected population. An infectious disease dies out when [Formula: see text] is lower than 1. Thus, breeding strategies that aim at reducing disease prevalence should focus on reducing [Formula: see text], preferably to a value lower than 1. In animal breeding, however, [Formula: see text] has received little attention. Here, we estimate the additive genetic variance in host susceptibility, host infectivity, and [Formula: see text] for the endemic claw disease digital dermatitis (DD) in Holstein Friesian dairy cattle, and estimate genomic breeding values (GEBV) for these traits. We recorded DD disease status of both hind claws of 1513 cows from 12 Dutch dairy farms, every 2 weeks, 11 times. The genotype data consisted of 75,904 single nucleotide polymorphisms (SNPs) for 1401 of the cows. We modelled the probability that a cow got infected between recordings, and compared four generalized linear mixed models. All models included a genetic effect for susceptibility; Models 2 and 4 also included a genetic effect for infectivity, while Models 1 and 2 included a farm*period interaction. We corrected for variation in exposure to infectious herd mates via an offset. RESULTS: GEBV for [Formula: see text] from the model that included genetic effects for susceptibility only had an accuracy of ~ 0.39 based on cross-validation between farms, which is very high given the limited amount of data and the complexity of the trait. Models with a genetic effect for infectivity showed a larger bias, but also a slightly higher accuracy of GEBV. Additive genetic standard deviation for [Formula: see text] was large, i.e. ~ 1.17, while the mean [Formula: see text] was 2.36. CONCLUSIONS: GEBV for [Formula: see text] showed substantial variation. The mean [Formula: see text] was only about one genetic standard deviation greater than 1. These results suggest that lowering DD prevalence by selective breeding is promising.

Estimating the purebred-crossbred genetic correlation of body weight in broiler chickens with pedigree or genomic relationships.

BACKGROUND: In pig and poultry breeding programs, the breeding goal is to improve crossbred (CB) performance, whereas selection in the purebred (PB) lines is often based on PB performance. Thus, response to selection may be suboptimal, because the genetic correlation between PB and CB performance ([Formula: see text]) is generally lower than 1. Accurate estimates of the [Formula: see text] are needed, so that breeders can decide if they should collect data from CB animals. [Formula: see text] can be estimated either from pedigree or genomic relationships, which may produce different results. With genomic relationships, the [Formula: see text] estimate could be improved when relationships between purebred and crossbred animals are based only on the alleles that originate from the PB line of interest. This work presents the first comparison of estimated [Formula: see text] and variance components of body weight in broilers, using pedigree-based or genotype-based models, where the breed-of-origin of alleles was either ignored or considered. We used genotypes and body weight measurements of PB and CB animals that have a common sire line. RESULTS: Our results showed that the [Formula: see text] estimates depended on the relationship matrix used. Estimates were 5 to 25% larger with genotype-based models than with pedigree-based models. Moreover, [Formula: see text] estimates were similar (max. 7% difference) regardless of whether the model considered breed-of-origin of alleles or not. Standard errors of [Formula: see text] estimates were smaller with genotype-based than with pedigree-based methods, and smaller with models that ignored breed-of-origin than with models that considered breed-of-origin. CONCLUSIONS: We conclude that genotype-based models can be useful for estimating [Formula: see text], even when the PB and CB animals that have phenotypes are closely related. Considering breed-of-origin of alleles did not yield different estimates of [Formula: see text], probably because the parental breeds of the CB animals were distantly related.

Validation of genomic predictions for body weight in broilers using crossbred information and considering breed-of-origin of alleles.

BACKGROUND: Pig and poultry breeding programs aim at improving crossbred (CB) performance. Selection response may be suboptimal if only purebred (PB) performance is used to compute genomic estimated breeding values (GEBV) because the genetic correlation between PB and CB performance ([Formula: see text]) is often lower than 1. Thus, it may be beneficial to use information on both PB and CB performance. In addition, the accuracy of GEBV of PB animals for CB performance may improve when the breed-of-origin of alleles (BOA) is considered in the genomic relationship matrix (GRM). Thus, our aim was to compare scenarios where GEBV are computed and validated by using (1) either CB offspring averages or individual CB records for validation, (2) either a PB or CB reference population, and (3) a GRM that either accounts for or ignores BOA in the CB individuals. For this purpose, we used data on body weight measured at around 7 (BW7) or 35 (BW35) days in PB and CB broiler chickens and evaluated the accuracy of GEBV based on the correlation GEBV with phenotypes in the validation population (validation correlation). RESULTS: With validation on CB offspring averages, the validation correlation of GEBV of PB animals for CB performance was lower with a CB reference population than with a PB reference population for BW35 ([Formula: see text] = 0.96), and about equal for BW7 ([Formula: see text] = 0.80) when BOA was ignored. However, with validation on individual CB records, the validation correlation was higher with a CB reference population for both traits. The use of a GRM that took BOA into account increased the validation correlation for BW7 but reduced it for BW35. CONCLUSIONS: We argue that the benefit of using a CB reference population for genomic prediction of PB animals for CB performance should be assessed either by validation on CB offspring averages, or by validation on individual CB records while using a GRM that accounts for BOA in the CB individuals. With this recommendation in mind, our results show that the accuracy of GEBV of PB animals for CB performance was equal to or higher with a CB reference population than with a PB reference population for a trait with an [Formula: see text] of 0.8, but lower for a trait with an [Formula: see text] of 0.96. In addition, taking BOA into account was beneficial for a trait with an [Formula: see text] of 0.8 but not for a trait with an [Formula: see text] of 0.96.

Models with indirect genetic effects depending on group sizes: a simulation study assessing the precision of the estimates of the dilution parameter.

BACKGROUND: In settings with social interactions, the phenotype of an individual is affected by the direct genetic effect (DGE) of the individual itself and by indirect genetic effects (IGE) of its group mates. In the presence of IGE, heritable variance and response to selection depend on size of the interaction group (group size), which can be modelled via a 'dilution' parameter (d) that measures the magnitude of IGE as a function of group size. However, little is known about the estimability of d and the precision of its estimate. Our aim was to investigate how precisely d can be estimated and what determines this precision. METHODS: We simulated data with different group sizes and estimated d using a mixed model that included IGE and d. Schemes included various average group sizes (4, 6, and 8), variation in group size (coefficient of variation (CV) ranging from 0.125 to 1.010), and three values of d (0, 0.5, and 1). A design in which individuals were randomly allocated to groups was used for all schemes and a design with two families per group was used for some schemes. Parameters were estimated using restricted maximum likelihood (REML). Bias and precision of estimates were used to assess their statistical quality. RESULTS: The dilution parameter of IGE can be estimated for simulated data with variation in group size. For all schemes, the length of confidence intervals ranged from 0.114 to 0.927 for d, from 0.149 to 0.198 for variance of DGE, from 0.011 to 0.086 for variance of IGE, and from 0.310 to 0.557 for genetic correlation between DGE and IGE. To estimate d, schemes with groups composed of two families performed slightly better than schemes with randomly composed groups. CONCLUSIONS: Dilution of IGE was estimable, and in general its estimation was more precise when CV of group size was larger. All estimated parameters were unbiased. Estimation of dilution of IGE allows the contribution of direct and indirect variance components to heritable variance to be quantified in relation to group size and, thus, it could improve prediction of the expected response to selection in environments with group sizes that differ from the average size.