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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. [ABSTRACT FROM AUTHOR]

Livestock populations are usually kept in groups. As a consequence, social interactions among individuals affect productivity, health, and welfare. Current selection methods (individual selection), however, ignore those interactions and yield suboptimal or in some cases even negative responses. In principle, selection between groups instead of individuals offers a solution, but has rarely been adopted in practice for two reasons. First, the relationship between group selection theory and common animal breeding concepts, such as the accuracy of selection, is unclear. Second, application of group selection requires keeping selection candidates in groups, which is often undesirable in practice. This work has two objectives. First, we derive expressions for the accuracy of individual and group selection, which provides a measurement of quality for those methods. Second, we investigate the opportunity to improve trails affected by interactions by using information on relatives kept in family groups, while keeping selection candidates individually. The accuracy of selection based on relatives is shown to be an analogy of the classical expression for traits not affected by interactions. Our results show that selection based on relatives offers good opportunities for effective genetic improvement of traits affected by interactions.

Interaction among individuals is universal, both in animals and in plants, and substantially affects evolution of natural populations and responses to artificial selection in agriculture. Although quantitative genetics has successfully been applied to many traits, it does not provide a general theory accounting for interaction among individuals and selection acting on multiple levels. Consequently, current quantitative genetic theory fails to explain why some traits do not respond to selection among individuals, but respond greatly to selection among groups. Understanding the full impacts of heritable interactions on the outcomes of selection requires a quantitative genetic framework including all levels of selection and relatedness. Here we present such a framework and provide expressions for the response to selection. Results show that interaction among individuals may create substantial heritable variation, which is hidden to classical analyses. Selection acting on higher levels of organization captures this hidden variation and therefore always yields positive response, whereas individual selection may yield response in the opposite direction. Our work provides testable predictions of response to multilevel selection and reduces to classical theory in the absence of interaction. Statistical methodology provided elsewhere enables empirical application of our work to both natural and domestic populations.

Interactions among individuals are universal, both in animals and in plants and in natural as well as domestic populations. Understanding the consequences of these interactions for the evolution of populations by either natural or artificial selection requires knowledge of the heritable components underlying them. Here we present statistical methodology to estimate the genetic parameters determining response to multilevel selection of traits affected by interactions among individuals in general populations. We apply these methods to obtain estimates of genetic parameters for survival days in a population of layer chickens with high mortality due to pecking behavior. We find that heritable variation is threefold greater than that obtained from classical analyses, meaning that two-thirds of the full heritable variation is hidden to classical analysis due to social interactions. As a consequence, predicted responses to multilevel selection applied to this population are threefold greater than classical predictions. This work, combined with the quantitative genetic theory for response to multilevel selection presented in an accompanying article in this issue, enables the design of selection programs to effectively reduce competitive interactions in livestock and plants and the prediction of the effects of social interactions on evolution in natural populations undergoing multilevel selection.

Relatedness estimators are widely used in genetic studies, but effects of population structure on performance of estimators, criteria to evaluate estimators, and benefits of using such estimators in conservation programs have to date received little attention. In this article we present new estimators, based on the relationship between coancestry and molecular similarity between individuals, and compare them with existing estimators using Monte Carlo simulation of populations, either panmictic or structured. Estimators were evaluated using statistical criteria and a diversity criterion that minimized relatedness. Results show that ranking of estimators depends on the population structure. An existing estimator based on two-gene and four-gene coefficients of identity performs best in panmictic populations, whereas a new estimator based on coancestry performs best in structured populations. The number of marker alleles and loci did not affect ranking of estimators. Statistical criteria were insufficient to evaluate estimators for their use in conservation programs. The regression coefficient of pedigree relatedness on estimated relatedness ([beta]2) was substantially lower than unity for all estimators, causing overestimation of the diversity constowed. A simple correction to achieve [beta]2 = 1 improves both existing and new estimators. Using relatedness estimates with correction considerably increased diversity in structured populations, but did not do so or even decreased diversity in panmictic populations.

Here we present the strategy that achieves the lowest possible rate of inbreeding ([DELTA]F) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a [DELTA]F as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and consequently [DELTA]F is minimized. Using the concept of long-term genetic contributions, the asymptotic [DELTA]F of the new strategy for random mating, M sires and d dams per sire, is [phi]/(12M), where [phi] = [1 + 2[(1/4).sup.d]]. Predictions were validated using Monte Carlo simulations. The scheme was shown to achieve the lowest possible [DELTA]F using pedigree alone and showed that further reductions in [DELTA]F below that obtained from random mating arise from preferential mating of relatives and not from their avoidance.

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 R0 and 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 R0 and 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. [ABSTRACT FROM AUTHOR]

Under gynogenetic reproduction, offspring receive genes only from their dams and completely homozygous offspring are produced within one generation. When gynogenetic reproduction is applied to fully inbred individuals, homozygous clone lines are produced. A mixed model method was developed for breeding value and variance component estimation in gynogenetic families, which requires the inverse of the numerator relationship matrix. A general method for creating the inverse for a population with unusual relationships between animals is presented, which reduces to simple rules as is illustrated for gynogenetic populations. The presence of clones in gynogenetic populations causes singularity of the numerator relationship matrix. However, clones can be regarded as repeated observations of the same genotype, which can be accommodated by modifying the incidence matrix, and by considering only unique genotypes in the estimation procedure. Optimum gynogenetic sib family sizes for estimating heritabilities and estimates of their accuracy were derived and compared to those for conventional full-sib designs. This was done by means of a deterministic derivation and by stochastic simulation using Gibbs sampling. Optimum family sizes were smallest for gynogenetic families. Only for low heritabilities, there was a small advantage in accuracy under the gynogenetic design.

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 xp is the standardized normal truncation point belonging to selected proportion p, and SDgGEBV is 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 SDgEBV require further study. [ABSTRACT FROM AUTHOR]

Predictions for the rate of inbreeding ([Delta]F) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expected contributions. Expected contributions of individuals were predicted using a linear model, [u.sub.i(x)] = [Alpha] + [Beta][s.sub.i], where [s.sub.i] denotes the selective advantage as a deviation from the contemporaries, which was the sum of the breeding values of the individual and the breeding values of its mates. The accuracy of predictions was evaluated for a wide range of population and genetic parameters. Accurate predictions were obtained for populations of 5-20 sires. For 20-80 sires, systematic underprediction of on average 11% was found, which was shown to be related to the goodness of fit of the linear model. Using simulation, it was shown that a quadratic model would give accurate predictions for those schemes. Furthermore, it was shown that, contrary, to random selection, [Delta] Fless than halved when the number of parents was doubled and that in specific cases [Delta]F may increase with the number of dams.

Predictions of rates of inbreeding ([Delta]F), based on the concept of long-term genetic contributions assuming the infinitesimal model, are developed for populations with discrete or overlapping generations undergoing mass selection. Phenotypes of individuals are assumed to be recorded prior to reproductive age and to remain constant over time. The prediction method accounts for inheritance of selective advantage both within and between age classes and for changing selection intensities with age. Terms corresponding to previous methods that assume constant selection intensity with age are identified. Predictions are accurate (relative errors [is less than or equal to] 8%), except for cases with extreme selection intensities in females in combination with high heritability. With overlapping generations [Delta]F reaches a maximum when parents are equally distributed over age classes, which is mainly due to selection of the same individuals in consecutive years. [Delta]F/year decreases much more slowly compared to [Delta]F/generation as the number of younger individuals increases, whereas the decrease is more similar as the number of older individuals increases. The minimum [Delta]F (per year or per generation) is obtained when most parents were in the later age classes, which is mainly due to an increased number of parents per generation. With overlapping generations, the relationship between heritability and [Delta]F is dependent on the age structure of the population.

Tractable forms of predicting rates of inbreeding ([Delta]F) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. [Delta]F was shown to be ~1/4(1 - [Omega]) times the expected sum of squared lifetime contributions, where [Omega] is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express [Delta]F in terms of expected long-term contributions that are conditional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. With random mating, if selected family sizes are assumed to be independent Poisson variables then the expected long-term contribution could be substituted for the observed, providing 1/4 (since [Omega] = 0) was increased to 1/2. Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting [Delta]F with sib indices in discrete generations since previously published solutions had proved complex.

Different methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate genomic relationships affects the estimate of genetic variances, covariances, and correlations. The aim of this article is to define the multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that by using current allele frequencies to calculate genomic relationships within a population, current genetic variances are estimated. In this article, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations between populations and validated it using simulations. When the scaling factor of across-population genomic relationships is equal to the product of the square roots of the scaling factors for within-population genomic relationships, the genetic correlation is estimated unbiasedly even though estimated genetic variances do not necessarily refer to the current population. When this property is not met, the correlation based on estimated variances should be multiplied by a correction factor based on the scaling factors. In this study, we present a genomic relationship matrix which directly estimates current genetic variances as well as genetic correlations between populations. [ABSTRACT FROM AUTHOR]

Predicting the accuracy of estimated genomic values using genome-wide marker information is an important step in designing training populations. Currently, different deterministic equations are available to predict accuracy within populations, but not for multipopulation scenarios where data from multiple breeds, lines or environments are combined. Therefore, our objective was to develop and validate a deterministic equation to predict the accuracy of genomic values when different populations are combined in one training population. The input parameters of the derived prediction equation are the number of individuals and the heritability from each of the populations in the training population; the genetic correlations between the populations, i.e., the correlation between allele substitution effects of quantitative trait loci; the effective number of chromosome segments across predicted and training populations; and the proportion of the genetic variance in the predicted population captured by the markers in each of the training populations. Validation was performed based on real genotype information of 1033 Holstein-Friesian cows that were divided into three different populations by combining half-sib families in the same population. Phenotypes were simulated for multiple scenarios, differing in heritability within populations and in genetic correlations between the populations. Results showed that the derived equation can accurately predict the accuracy of estimating genomic values for different scenarios of multipopulation genomic prediction. Therefore, the derived equation can be used to investigate the potential accuracy of different multipopulation genomic prediction scenarios and to decide on the most optimal design of training populations. [ABSTRACT FROM AUTHOR]

A method to predict long-term genetic contributions of ancestors to future generations is studied in detail for a population with overlapping generations under mass or sib index selection. An existing method provides insight into the mechanisms determining the flow of genes through selected populations, and takes account of selection by modeling the long-term genetic contribution as a linear regression on breeding value. Total genetic contributions of age classes are modeled using a modified gene flow approach and long-term predictions are obtained assuming equilibrium genetic parameters. Generation interval was defined as the time in which genetic contributions sum to unity, which is equal to the turnover time of genes. Accurate predictions of long-term genetic contributions of individual animals, as well as total contributions of age classes were obtained. Due to selection, offspring of young parents bad an above-average breeding value. Long-term genetic contributions of youngest age classes were therefore higher than expected from the age class distribution of parents, and generation interval was shorter than the average age of parents at birth of their offspring. Due to an increased selective advantage of offspring of young parents, generation interval decreased with increasing heritability and selection intensity. The method was compared to conventional gene flow and showed more accurate predictions of long-term genetic contributions.

Genetic selection is a major force shaping life on earth. In classical genetic theory, response to selection is the product of the strength of selection and the additive genetic variance in a trait. The additive genetic variance reflects a population's intrinsic potential to respond to selection. The ordinary additive genetic variance, however, ignores the social organization of life. With social interactions among individuals, individual trait values may depend on genes in others, a phenomenon known as indirect genetic effects. Models accounting for indirect genetic effects, however, lack a general definition of heritable variation. Here I propose a general definition of the heritable variation that determines the potential of a population to respond to selection. This generalizes the concept of heritable variance to any inheritance model and level of organization. The result shows that heritable variance determining potential response to selection is the variance among individuals in the heritable quantity that determines the population mean trait value, rather than the usual additive genetic component of phenotypic variance. It follows, therefore, that heritable variance may exceed phenotypic variance among individuals, which is impossible in classical theory. This work also provides a measure of the utilization of heritable variation for response to selection and integrates two well-known models of maternal genetic effects. The result shows that relatedness between the focal individual and the individuals affecting its fitness is a key determinant of the utilization of heritable variance for response to selection. [ABSTRACT FROM AUTHOR]