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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 vitripennisoviposit 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. vitripennisHVRx-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.

Because of variation in linkage phase and heterozygosity among individuals, some individuals produce genetically more variable gametes than others. With the availability of genomic EBVs (GEBVs) or estimates of SNP-effects together with phased genotypes, differences in gametic variability can be quantified by simulating a set of virtual gametes of each selection candidate. Previous results in dairy cattle show that gametic variance can be large. Here, we show that breeders can increase the probability of breeding a top-ranking genotype and response to recurrent selection by selecting parents that produce more variable gametes, using the index I=GEBV+2xpSDgGEBV,where xpis the standardized normal truncation point belonging to selected proportion p, and SDgGEBVis the SD of the GEBV of an individual’s gametes. Benefits of the index were considerably larger in an ongoing selection program with equilibrium genetic parameters than in an initially unselected population. Superiority of the index over selection on GEBV increased strongly with the magnitude of the SDgGEBV,indicating that benefits of the index may vary considerably among populations. Compared to selection on ordinary GEBV, the probability of breeding a top-ranking individual can be increased by ∼36%, and response to selection by ∼3.6% when selection is strong (P= 0.001) based on values for the Holstein-Friesian dairy cattle population. Two-stage selection, with a preselection on GEBV and a final selection on the index, considerably reduced computational requirements with little loss of benefits. Response to multiple generations of selection and inheritance of the SDgEBVrequire further study.

Pooling semen of multiple boars is commonly used in swine production systems. Compared with single boar systems, this technique changes family structure creating maternal half-sib families. The aim of this simulation study was to investigate how pooling semen affects the accuracy of estimating direct and maternal effects for individual piglet birth weight, in purebred pigs. Different scenarios of pooling semen were simulated by allowing the same female to mate from 1 to 6 boars, per insemination, whereas litter size was kept constant (N = 12). In each pooled boar scenario, genomic information was used to construct either the genomic relationship matrix (G) or to reconstruct pedigree in addition to G. Genotypes were generated for 60,000 SNPs evenly distributed across 18 autosomes. From the 5 simulated generations, only animals from generations 3 to 5 were genotyped (N = 36,000). Direct and maternal true breeding values (TBV) were computed as the sum of the effects of the 1,080 QTLs. Phenotypes were constructed as the sum of direct TBV, maternal TBV, an overall mean of 1.25 kg, and a residual effect. The simulated heritabilities for direct and maternal effects were 0.056 and 0.19, respectively, and the genetic correlation between both effects was -0.25. All simulations were replicated 5 times. Variance components and direct and maternal heritability were estimated using average information REML. Predictions were computed via pedigree-based BLUP and single-step genomic BLUP (ssGBLUP). Genotyped littermates in the last generation were used for validation. Prediction accuracies were calculated as correlations between EBV and TBV for direct (accdirect) and maternal (accmat) effects. When boars were known, accdirect were 0.21 (1 boar) and 0.26 (6 boars) for BLUP, whereas for ssGBLUP, they were 0.38 (1 boar) and 0.43 (6 boars). When boars were unknown, accdirect was lower in BLUP but similar in ssGBLUP. For the scenario with known boars, accmat was 0.58 and 0.63 for 1 and 6 boars, respectively, under ssGBLUP. For unknown boars, accmat was 0.63 for 2 boars and 0.62 for 6 boars in ssGBLUP. In general, accdirect and accmat were lower in the single-boar scenario compared with pooled semen scenarios, indicating that a half-sib structure is more adequate to estimate direct and maternal effects. Using pooled semen from multiple boars can help us to improve accuracy of predicting maternal and direct effects when maternal half-sib families are larger than 2.

When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs.

Genetic selection has been applied for many generations in animal, plant, and experimental populations. Selection changes the allelic architecture of traits to create genetic gain. It remains unknown whether the changes in allelic architecture are different for the recently introduced technique of genomic selection compared to traditional selection methods and whether they depend on the genetic architectures of traits. Here, we investigate the allele frequency changes of old and new causal loci under 50 generations of phenotypic, pedigree, and genomic selection, for a trait controlled by either additive, additive and dominance, or additive, dominance, and epistatic effects. Genomic selection resulted in slightly larger and faster changes in allele frequencies of causal loci than pedigree selection. For each locus, allele frequency change per generation was not only influenced by its statistical additive effect but also to a large extent by the linkage phase with other loci and its allele frequency. Selection fixed a large number of loci, and 5 times more unfavorable alleles became fixed with genomic and pedigree selection than with phenotypic selection. For pedigree selection, this was mainly a result of increased genetic drift, while genetic hitchhiking had a larger effect on genomic selection. When epistasis was present, the average allele frequency change was smaller (∼15% lower), and a lower number of loci became fixed for all selection methods. We conclude that for long-term genetic improvement using genomic selection, it is important to consider hitchhiking and to limit the loss of favorable alleles.Genomic selection has revolutionized genetic improvement in animals and plants. Here, Wientjes et al. investigate the long-term effects of genomic selection on allele frequency changes of causal loci using stochastic simulations. Genomic selection rapidly changed allele frequencies, and the allele frequency change per locus was highly influenced by its effect and linkage with other loci. Moreover, selection fixed many favorable and unfavorable loci. For long-term genetic improvement using genomic selection, minimizing the loss of favorable alleles is important.

Pathogens have profound effects on livestock. The low heritabilities of individual binary disease status suggest limited prospects for genetic improvement. However, a proper quantitative genetic theory for infectious diseases, including transmission dynamics, is currently lacking. Here we present a quantitative genetic theory for endemic infectious diseases, focussing on the genetic factors that determine the prevalence (P; the mean fraction of the population that is infected). We present simple expressions for breeding values and genetic parameters for the prevalence. Without genetic variation in infectiousness, breeding values for prevalence are a factor 1/P greater than the ordinary breeding values for individual binary disease status (0/1). Hence, even though prevalence is the simple average of individual binary disease status, breeding values for prevalence show much greater variation than our ordinary breeding values. This implies that the genetic variance that determines the potential response of prevalence to selection is largely due to indirect genetic effects (IGE), and thus hidden to ordinary genetic analysis and selection. Hence, the genetic variance that determines the potential of livestock populations to respond to selection must be much greater than currently believed, particularly at low prevalence. We evaluated this implication using simulation of endemics following standard methods in epidemiology. Results show that response of prevalence to selection increases very strongly when prevalence decreases, and is much greater than predicted by our ordinary breeding values. These results supports our theoretical findings, and show that selection against infectious diseases is much more promising than currently believed.

Infectious diseases have profound effects on life, both in nature and agriculture. However, a quantitative genetic theory of the host population for the endemic prevalence of infectious diseases is almost entirely lacking. While several studies have demonstrated the relevance of transmission of infections for heritable variation and response to selection, current quantitative genetics ignores transmission. Thus, we lack concepts of breeding value and heritable variation for endemic prevalence, and poorly understand response of endemic prevalence to selection. Here, we integrate quantitative genetics and epidemiology, and propose a quantitative genetic theory for the basic reproduction number R0and for the endemic prevalence of an infection. We first identify the genetic factors that determine the prevalence. Subsequently, we investigate the population-level consequences of individual genetic variation, for both R0and the endemic prevalence. Next, we present expressions for the breeding value and heritable variation, for endemic prevalence and individual binary disease status, and show that these depend strongly on the prevalence. Results show that heritable variation for endemic prevalence is substantially greater than currently believed, and increases strongly when prevalence decreases, while heritability of disease status approaches zero. As a consequence, response of the endemic prevalence to selection for lower disease status accelerates considerably when prevalence decreases, in contrast to classical predictions. Finally, we show that most heritable variation for the endemic prevalence is hidden in indirect genetic effects, suggesting a key role for kin-group selection in the evolutionary history of current populations and for genetic improvement in animals and plants.Bijma, Hulst, and De Jong develop a quantitative genetic theory of the host population for both R0 and the prevalence of infectious diseases, showing that most of the heritable variation for endemic prevalence is hidden due to Indirect Genetic Effects resulting from transmission dynamics of the infection. Consequently, genetic variation in the host population and response to selection for the prevalence are large and increase strongly when prevalence decreases. In contrast to classical theory, genetic selection can eradicate infectious diseases.

Selection programmes are mainly concerned with increasing genetic gain. However, short-term progress should not be obtained at the expense of the within-population genetic variability. Different prediction models for the evolution within a small population of the genetic mean of a selected trait, its genetic variance and its inbreeding have been developed but have mainly been validated through Monte Carlo simulation studies. The purpose of this study was to compare theoretical predictions to experimental results. Two deterministic methods were considered, both grounded on a polygenic additive model. Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods. Two sets of experimental lines of chickens were used in this study: the Dutch lines undergoing true truncation mass selection, the other lines (French) undergoing mass selection with a restriction on the representation of the different families. This study confirmed, on an experimental basis, that modelling is an efficient approach to make useful predictions of the evolution of selected populations although the basic assumptions considered in the models (polygenic additive model, normality of the distribution, base population at the equilibrium, etc.) are not met in reality. The two deterministic methods compared yielded results that were close to those observed in real data, especially when the selection scheme followed the rules of strict mass selection: for instance, both predictions overestimated the genetic gain in the French experiment, whereas both predictions were close to the observed values in the Dutch experiment.

Covariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the data.

A breeding goal accounting for the effects of genotype by environment interaction ($\rm G\times E$) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where $\rm G\times E$ is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of $\rm G\times E$ (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait.

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress ($\Delta G$ ) are combined with expected rates of inbreeding ($\Delta F$ ) in a linear objective function ( $\Phi = \Delta G - ambda \Delta F$ ) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.

In conventional gene flow theory the rate of genetic gain is calculated as the summed products of genetic selection differential and asymptotic proportion of genes deriving from sex-age groups. Recent studies have shown that asymptotic proportions of genes predicted from conventional gene flow theory may deviate considerably from true proportions. However, the rate of genetic gain predicted from conventional gene flow theory was accurate. The current note shows that the connection between asymptotic proportions of genes and rate of genetic gain that is embodied in conventional gene flow theory is invalid, even though genetic gain may be predicted correctly from it.

Breeding programs aiming to improve the performance of crossbreds may benefit from genomic prediction of crossbred (CB) performance for purebred (PB) selection candidates. In this review, we compared genomic prediction strategies that differed in 1) the genomic prediction model used or 2) the data used in the reference population. We found 27 unique studies, two of which used deterministic simulation, 11 used stochastic simulation, and 14 real data. Differences in accuracy and response to selection between strategies depended on i) the value of the purebred crossbred genetic correlation (rpc), ii) the genetic distance between the parental lines, iii) the size of PB and CB reference populations, and iv) the relatedness of these reference populations to the selection candidates. In studies where a PB reference population was used, the use of a dominance model yielded accuracies that were equal to or higher than those of additive models. When rpcwas lower than ~0.8, and was caused mainly by G × E, it was beneficial to create a reference population of PB animals that are tested in a CB environment. In general, the benefit of collecting CB information increased with decreasing rpc. For a given rpc, the benefit of collecting CB information increased with increasing size of the reference populations. Collecting CB information was not beneficial when rpcwas higher than ~0.9, especially when the reference populations were small. Collecting only phenotypes of CB animals may slightly improve accuracy and response to selection, but requires that the pedigree is known. It is, therefore, advisable to genotype these CB animals as well. Finally, considering the breed-origin of alleles allows for modeling breed-specific effects in the CB, but this did not always lead to higher accuracies. Our review shows that the differences in accuracy and response to selection between strategies depend on several factors. One of the most important factors is rpc, and we, therefore, recommend to obtain accurate estimates of rpcof all breeding goal traits. Furthermore, knowledge about the importance of components of rpc(i.e., dominance, epistasis, and G × E) can help breeders to decide which model to use, and whether to collect data on animals in a CB environment. Future research should focus on the development of a tool that predicts accuracy and response to selection from scenario specific parameters.

Genetic selection for improved disease resistance is an important part of strategies to combat infectious diseases in agriculture. Quantitative genetic analyses of binary disease status, however, indicate low heritability for most diseases, which restricts the rate of genetic reduction in disease prevalence. Moreover, the common liability threshold model suggests that eradication of an infectious disease via genetic selection is impossible because the observed-scale heritability goes to zero when the prevalence approaches zero. From infectious disease epidemiology, however, we know that eradication of infectious diseases is possible, both in theory and practice, because of positive feedback mechanisms leading to the phenomenon known as herd immunity. The common quantitative genetic models, however, ignore these feedback mechanisms. Here, we integrate quantitative genetic analysis of binary disease status with epidemiological models of transmission, aiming to identify the potential response to selection for reducing the prevalence of endemic infectious diseases. The results show that typical heritability values of binary disease status correspond to a very substantial genetic variation in disease susceptibility among individuals. Moreover, our results show that eradication of infectious diseases by genetic selection is possible in principle. These findings strongly disagree with predictions based on common quantitative genetic models, which ignore the positive feedback effects that occur when reducing the transmission of infectious diseases. Those feedback effects are a specific kind of Indirect Genetic Effects; they contribute substantially to the response to selection and the development of herd immunity (i.e., an effective reproduction ratio less than one).

Selection programmes are mainly concerned with increasing genetic gain. However, short-term progress should not be obtained at the expense of the within-population genetic variability. Different prediction models for the evolution within a small population of the genetic mean of a selected trait, its genetic variance and its inbreeding have been developed but have mainly been validated through Monte Carlo simulation studies. The purpose of this study was to compare theoretical predictions to experimental results. Two deterministic methods were considered, both grounded on a polygenic additive model. Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods. Two sets of experimental lines of chickens were used in this study: the Dutch lines undergoing true truncation mass selection, the other lines (French) undergoing mass selection with a restriction on the representation of the different families. This study confirmed, on an experimental basis, that modelling is an efficient approach to make useful predictions of the evolution of selected populations although the basic assumptions considered in the models (polygenic additive model, normality of the distribution, base population at the equilibrium, etc.) are not met in reality. The two deterministic methods compared yielded results that were close to those observed in real data, especially when the selection scheme followed the rules of strict mass selection: for instance, both predictions overestimated the genetic gain in the French experiment, whereas both predictions were close to the observed values in the Dutch experiment.

Covariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the data.

A breeding goal accounting for the effects of genotype by environment interaction (G × E) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where G × E is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of G × E (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait.

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG- λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.

In conventional gene flow theory the rate of genetic gain is calculated as the summed products of genetic selection differential and asymptotic proportion of genes deriving from sex-age groups. Recent studies have shown that asymptotic proportions of genes predicted from conventional gene flow theory may deviate considerably from true proportions. However, the rate of genetic gain predicted from conventional gene flow theory was accurate. The current note shows that the connection between asymptotic proportions of genes and rate of genetic gain that is embodied in conventional gene flow theory is invalid, even though genetic gain may be predicted correctly from it.