Are economic selection indices always superior to a desired gains index?

Conclusions The comparison of different selection indices is justified only if the indices are constrated to achieve the same profit function, even when each index is not optimized with respect to that profit function.When a profit function is known and is non-linear, the desired gains index may be more efficient than the economic index. The optimum desired gains index should be determined by iterative techniques over several generations to compare the genetic progress with the economic index, because gains by the economic index are not linear and the changes observed in the initial generations of selection are not the same rates in future generations, although those changes are linear in the case of the desired gains index.     

Selection index updating

Summary When traits become evident at different ages or there are large differences in the costs of measuring various traits, selection by independent culling levels may give a higher aggregate economic return than index selection because not all traits need to be measured on all individuals. The problems with optimum independent culling selection is that general solutions are not possible and numerical integration is needed for specific cases. Recently, Xu and Muir (1991) developed a new independent culling level procedure by use of orthogonal transformation of the original characters. With their procedure, explicit solutions for optimum truncation points are possible without numerical integration. As such, the procedure is proficient for any number of stages, and generalized theoretical comparisons of alternative breeding strategies are possible. However, their procedure was limited to the case where selection is for one character at each stage. In this paper, our previous results are extended to the general case of multi-stage index selection, called selection index updating. This procedure is called selection index updating because as traits become available in latter stages, each subsequent index contains all of the traits available up to that stage.The procedure is to develop sequential indices for each stage such that correlations among indices at different stages are zero. Optimum culling points are obtained for the updating procedure by using Xu and Muir's (1991) iterative equations. Due to the property of orthogonality of the updated indices, aggregate gain can be partitioned into gains due to various stages of selection. Partitioning of aggregate economic gain is useful to breeders who desire to adjust individual trait selection intensity based on facilities available at that stage. Methods are discussed to modify the procedure to obtain maximum aggregate economic return per unit of cost associated with obtaining measures on each trait. An application of multi-stage selection is demonstrated using a set of data for Rhode Island Red layer type chickens. A second example demonstrates the use of multi-stage selection optimized with respect to aggregate economic gain and costs associated with obtaining measurements.Journal Paper No. 12813 of the Purdue University Agricultural Experiment Station     

Multiple-trait breeding values for parental selection in self-pollinating crops

Using breeding values in parental selection of self-pollinating crops seems to be superior to conventional selection strategies, where selection is often based on several traits which are correlated among each other. However, analysing each trait separately can bias estimates of breeding values. This study examined responses to selection for total merit indices based on breeding values resulting from single- and multiple-trait best linear unbiased prediction (BLUP). We generated data for a multi-environment trial of a “virtual” parental population in which the phenotypic value of inbred lines was influenced by additive, additive-by-additive epistatic, year, location, block and genotype-by-environment interaction effects. Two traits with heritabilities of 0.7 and 0.3 and nine different correlation scenarios between traits (estimated phenotypic correlation ranging from −0.39 to +0.36) were simulated. Gain in selection response was greater for multiple-trait than for single-trait breeding values, especially if traits were negatively correlated. For all correlation scenarios, the overall standard errors of difference of multiple-trait predictors were lower than those of single-trait analysis.     

Predicted accuracy of and response to genomic selection for new traits in dairy cattle

Genomic selection relaxes the requirement of traditional selection tools to have phenotypic measurements on close relatives of all selection candidates. This opens up possibilities to select for traits that are difficult or expensive to measure. The objectives of this paper were to predict accuracy of and response to genomic selection for a new trait, considering that only a cow reference population of moderate size was available for the new trait, and that selection simultaneously targeted an index and this new trait. Accuracy for and response to selection were deterministically evaluated for three different breeding goals. Single trait selection for the new trait based only on a limited cow reference population of up to 10 000 cows, showed that maximum genetic responses of 0.20 and 0.28 genetic standard deviation (s.d.) per year can be achieved for traits with a heritability of 0.05 and 0.30, respectively. Adding information from the index based on a reference population of 5000 bulls, and assuming a genetic correlation of 0.5, increased genetic response for both heritability levels by up to 0.14 genetic s.d. per year. The scenario with simultaneous selection for the new trait and the index, yielded a substantially lower response for the new trait, especially when the genetic correlation with the index was negative. Despite the lower response for the index, whenever the new trait had considerable economic value, including the cow reference population considerably improved the genetic response for the new trait. For scenarios with a zero or negative genetic correlation with the index and equal economic value for the index and the new trait, a reference population of 2000 cows increased genetic response for the new trait with at least 0.10 and 0.20 genetic s.d. per year, for heritability levels of 0.05 and 0.30, respectively. We conclude that for new traits with a very small or positive genetic correlation with the index, and a high positive economic value, considerable genetic response can already be achieved based on a cow reference population with only 2000 records, even when the reliability of individual genomic breeding values is much lower than currently accepted in dairy cattle breeding programs. New traits may generally have a negative genetic correlation with the index and a small positive economic value. For such new traits, cow reference populations of at least 10 000 cows may be required to achieve acceptable levels of genetic response for the new trait and for the whole breeding goal.     

Response to mass selection when the genotype by environment interaction is modelled as a linear reaction norm

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.     

Index versus tandem selection after repeated generations of selection

Summary A theoretical comparison between two multiple-trait selection methods, index and tandem selection, after several generations of selection was carried out. An infinite number of loci determining the traits, directional and truncation selection, discrete generations and infinite population size were assumed. Under these assumptions, changes in genetic parameters over generations are due to linkage disequilibrium generated by selection. Changes continue for several generations until equilibrium is approached. Algebraic expressions for asymptotic responses from index selection can be derived if index weights are maintained constant across generations. Expressions at equilibrium for genetic parameters and responses are given for the index and its component traits. The loss in response by using initial index weights throughout all generations, instead of updating them to account for changes in genetic parameters, was analyzed. The benefit of using optimum weights was very small ranging from 0% to about 1.5% for all cases studied. Recurrence formulae to predict genetic parameters and responses at each generation of selection are given for both index and tandem selection. A comparison between expected response in the aggregate genotype at equilibrium from index and tandem selection is made considering two traits of economic importance. The results indicate that although index selection is more efficient for improving the aggregate breeding value, its relative efficiency with respect to tandem selection decreases after repeated cycles of selection. The reduction in relative efficiency is highest with the highest selection intensity and heritabilities and with negative correlations between the two traits. The advantage of index over tandem selection might be further reduced if changes in genetic parameters due to gene frequency changes produced by selection, random fluctuations due to the finite size of the population, and errors in estimation of parameters, were also considered.     

Genetic differences based on a beef terminal index are reflected in future phenotypic performance differences in commercial beef cattle

The increased demand for animal-derived protein and energy for human consumption will have to be achieved through a combination of improved animal genetic merit and better management strategies. The objective of the present study was to quantify whether differences in genetic merit among animals materialised into phenotypic differences in commercial herds. Carcass phenotypes on 156 864 animals from 7301 finishing herds were used, which included carcass weight (kg), carcass conformation score (scale 1 to 15), carcass fat score (scale 1 to 15) at slaughter as well as carcass price. The price per kilogram and the total carcass value that the producer received for the animal at slaughter was also used. A terminal index, calculated in the national genetic evaluations, was obtained for each animal. The index was based on pedigree index for calving performance, feed intake and carcass traits from the national genetic evaluations. Animals were categorised into four terminal index groups on the basis of genetic merit estimates that were derived before the expression of the phenotypic information by the validation animals. The association between terminal index and phenotypic performance at slaughter was undertaken using mixed models; whether the association differed by gender (i.e. young bulls, steers and heifers) or by early life experiences (animals born in a dairy herd or beef herd) was also investigated. The regression coefficient of phenotypic carcass weight, carcass conformation and carcass fat on their respective estimated breeding values (EBVs) was 0.92 kg, 1.08 units and 0.79 units, respectively, which is close to the expectation of one. Relative to animals in the lowest genetic merit group, animals in the highest genetic merit group had, on average, a 38.7 kg heavier carcass, with 2.21 units greater carcass conformation, and 0.82 units less fat. The superior genetic merit animals were, on average, slaughtered 6 days younger than their inferior genetic merit contemporaries. The superior carcass characteristics of the genetically elite animals materialised in carcasses worth €187 more than those of the lowest genetic merit animals. Although the phenotypic difference in carcass traits of animals divergent in terminal index differed statistically by animal gender and early life experience, the detected interactions were generally biologically small. This study clearly indicates that selection on an appropriate terminal index will produce higher performing animals and this was consistent across all production systems investigated.     

The use of constrained selection indexes in breeding for economic merit

Summary Various methods exist for the derivation of restricted and/or desired gains selection indexes, and their use in applied breeding has been advocated. It is shown that there exists a set of implied linear economic weights for all constrained indexes and their derivation is given. Where economic weights are linear and known, a standard selection index is, by definition, optimal and thus a constrained index will usually be suboptimal. It is argued that economic weights can always be estimated and that the effects of uncertain weights can be examined by sensitivity analysis. If economic weights are nonlinear, use of the first order (linear) economic weights or a derived linear index, using previously described methods, will give very close to optimum economic selection responses. Examples from the literature indicate that severe losses of potential economic gain can possibly occur through use of a constrained index. It is concluded that constrained indexes should be avoided for economic genetic selection.     

Genomic selection: prediction of accuracy and maximisation of long term response

Genomic selection refers to the use of dense markers covering the whole genome to estimate the breeding value of selection candidates for a quantitative trait. This paper considers prediction of breeding value based on a linear combination of the markers. In this case the best estimate of each marker’s effect is the expectation of the effect conditional on the data. To calculate this requires a prior distribution of marker effects. If the marker effects are normally distributed with constant variance, BLUP can be used to calculate the estimated effects of the markers and hence the estimated breeding value (EBV). In this case the model is equivalent to a conventional animal model in which the relationship matrix among the animals is estimated from the markers instead of the pedigree. The accuracy of the EBV can approach 1.0 but a very large amount of data is required. An alternative model was investigated in which only some markers have non-zero effects and these effects follow a reflected exponential distribution. In this case the expected effect of a marker is a non-linear function of the data such that apparently small effects are regressed back almost to zero and consequently these markers can be deleted from the model. The accuracy in this case is considerably higher than when marker effects are normally distributed. If genomic selection is practiced for several generations the response declines in a manner that can be predicted from the marker allele frequencies. Genomic selection is likely to lead to a more rapid decline in the selection response than phenotypic selection unless new markers are continually added to the prediction of breeding value. A method to find the optimum index to maximise long term selection response is derived. This index varies the weight given to a marker according to its frequency such that markers where the favourable allele has low frequency receive more weight in the index.     

Selection Indices and Multivariate Analysis Show Similar Results in the Evaluation of Growth and Carcass Traits in Beef Cattle

This research evaluated a multivariate approach as an alternative tool for the purpose of selection regarding expected progeny differences (EPDs). Data were fitted using a multi-trait model and consisted of growth traits (birth weight and weights at 120, 210, 365 and 450 days of age) and carcass traits (longissimus muscle area (LMA), back-fat thickness (BF), and rump fat thickness (RF)), registered over 21 years in extensive breeding systems of Polled Nellore cattle in Brazil. Multivariate analyses were performed using standardized (zero mean and unit variance) EPDs. The k mean method revealed that the best fit of data occurred using three clusters (k = 3) (P < 0.001). Estimates of genetic correlation among growth and carcass traits and the estimates of heritability were moderate to high, suggesting that a correlated response approach is suitable for practical decision making. Estimates of correlation between selection indices and the multivariate index (LD1) were moderate to high, ranging from 0.48 to 0.97. This reveals that both types of indices give similar results and that the multivariate approach is reliable for the purpose of selection. The alternative tool seems very handy when economic weights are not available or in cases where more rapid identification of the best animals is desired. Interestingly, multivariate analysis allowed forecasting information based on the relationships among breeding values (EPDs). Also, it enabled fine discrimination, rapid data summarization after genetic evaluation, and permitted accounting for maternal ability and the genetic direct potential of the animals. In addition, we recommend the use of longissimus muscle area and subcutaneous fat thickness as selection criteria, to allow estimation of breeding values before the first mating season in order to accelerate the response to individual selection.     

Optimal properties of the conditional mean as a selection criterion

Summary Rules for selection that maximize the expected merit of selected candidates are discussed. When the proportion selected is constant, selection based on conditional means of merit given the observations is optimum in the above sense, regardless of the distribution. This does not hold if the proportion selected is random. When the expected value of the observations is a linear function of a set of unknown parameters, selection can be based on a vector of corrected records, w. It is shown that under normality, the conditional mean of merit given w is the best linear unbiased predictor (BLUP), provided that the expected value of the merit function is the same in all candidates. A Bayesian argument is given to justify the use of BLUP as a selection rule when the expected merit differs from candidate to candidate.     

Index selection with nonlinear profit function as a tool to achieve simultaneous genetic gain

Summary Simultaneous improvement of several, and often negatively correlated, traits is frequently a desired objective in forest tree breeding. A profit function that includes a combination of both linear weights and weights for the cross-products of trait combinations facilitates the construction of a linear index, with an attractive response in all traits. A detailed algorithm for finding the index coefficients is provided, along with three examples of applications in tree breeding. The index is also a powerful tool in optimizing the selection for a ratio of two traits. It is argued that a more equal progress in several traits provides a safetey net when faced with economic uncertainties. The provided algorithm eliminates the need for direct search techniques. Existence of a dual set of linear weights means that the statistical properties of the index based on nonlinear profit functions are identical to those of the classical Smith-Hazel type of index.     

Selection response in traits with maternal inheritance

Maternal inheritance is the non-Mendelian transmission of traits from mothers to their offspring. Despite its presence in virtually all organisms, acting through a variety of mechanisms, the evolutionary consequences of maternal inheritance are not well understood. Here we review and extend a model of the inheritance and evolution of multiple quantitative characters with complex pathways of maternal effects. Extensions of the earlier model include common family environmental effects not associated with maternal phenotype, sexual dimorphism, and paternal effects (non-Mendelian influence of the father on offspring traits). We find that, in contrast to simple Mendelian inheritance, maternal inheritance produces qualitatively different evolutionary dynamics for two reasons: (1) the response to selection on a set of characters depends not only on their additive genetic variances and covariances, but also on maternal characters that influence them, and (2) time lags in the response to selection create a form of evolutionary momentum. These results have important implications for evolution in natural populations and practical applications in the economic improvement of domesticated species. We derive selection indices that maximize either the economic improvement in a single generation of artificial selection or the asymptotic rate of improvement in long-term selection programmes, based on individual merit or a combination of individual and family merit. Numerical examples show that accounting for maternal inheritance can lead to considerable increases in the efficiency of artificial selection.     

The effects of selection indices for sustainable hill sheep production on carcass composition and muscularity of lambs, measured using X-ray computed tomography

A multi-trait selection index designed to improve the overall economic performance of hill sheep, including both maternal and lamb traits, has been developed and tested in a selection experiment over 7 years. Two versions of the index were tested, with different economic weights applied to the traits, on two different hill farms: one version including maternal and growth traits; the other version with additional breeding goals of carcass weight, fatness and conformation scores. Responses to selection, using both versions of the index, suggest that improvements are being made in overall index score and lamb growth. This study investigated the indirect effects of these selection indices on lamb carcass composition and muscularity traits, as measured using X-ray computed tomography (CT) scanning. A total of 499 lambs from the two hill farms were CT scanned at weaning (approximately 120 days of age). Approximately half of the lambs from each farm were from the selection line (S, animals with highest index scores selected for breeding), while the other half were from a control line (C, animals with average index scores selected). Composition and muscularity traits were estimated on each lamb from CT data and differences between genetic lines investigated, within farm, using restricted maximum likelihood analyses, adjusting for either live weight or age. Results showed that the selection index without carcass traits produced lambs with carcass composition that was not significantly different to control lambs at a given live weight or age. Including carcass traits in the index resulted in lambs with no compositional differences (except for a slight increase in bone) at a set age compared with controls. At a given live weight however, selection lambs had less fat and lower carcass weights and killing-out percentage. Muscularity (3-D muscle shape) and muscle area shape (2-D) were not improved as a result of selection on either version of the index (including carcass weight and grades in the breeding goals or not) and, at a fixed live weight, muscularity in hind leg and lumbar regions tended to be higher in the C line. To accelerate changes in carcass composition and muscularity within the context of a multi-trait selection index for hill sheep, consideration should therefore be given to including objective CT-derived carcass traits in the index in addition to the Meat and Livestock Commission (MLC) carcass grades or ultrasound measurements.     

An empirical comparison of selection methods for the improvement of biomass

Summary A single generation of upward truncation selection on families with 20% selected was carried out in each of five replicates using Tribolium castaneum as the test organism. The experiment involved eight lines: N — selected for offspring number; W — selected for pupal weight; B — selected for biomass; Q — quadratic index selected; L₂₁ — linear index selected with relative economic weights of 21 offspring number to pupal weight; L₁₁ — linear index selected with relative economic weights of 11 offspring number to pupal weight; L₁₂ — linear index selected with relative economic weights of 12 offspring number to pupal weight; C — an unselected control.Biomass (weight of offspring per family), offspring number, and pupal weight were measured. No differences in response to selection were found among the linear index lines and the pupal weight line with regard to any trait analysed. Generally, response to selection in the linear index lines and pupal weight line was small for offspring number and high for pupal weight. Selection pressure on offspring number in these lines seemed to be dependent on the correlation between offspring number and pupal weight. As a result, response to selection for biomass was poor in the linear index and pupal weight selected lines. In the case of the linear indices, poor response to selection for biomass appeared to be due to the violation of the assumption of additivity of the traits included in the definition of aggregate genotype.The responses in the quadratic index, biomass, and offspring number selected lines were equal with respect to selection for biomass. The response of the quadratic index selected line was less than the responses of the biomass and offspring number selected lines for offspring number, but the response in the quadratic index line was as large as that of any other line included in the experiment and greater than the biomass and offspring number selected lines where pupal weight was the criterion.Highly significant amounts of variation were found for all traits indicating that more replicates are needed for precise evaluation of selection systems.     

Incorporation of competitive effects in forest tree or animal breeding programs

Competition among domesticated plants or animals can have a dramatic negative impact on yield of a stand or farm. The usual quantitative genetic model ignores these competitive interactions and could result in seriously incorrect breeding decisions and acerbate animal well-being. A general solution to this problem is given, for either forest tree breeding or penned animals, with mixed-model methodology (BLUP) utilized to separate effects on the phenotype due to the individuals' own genes (direct effects) and those from competing individuals (associative effects) and thereby to allow an optimum index selection on those effects. Biological verification was based on two lines of Japanese quail selected for 6-week weight; one line was selected only for direct effects (D-BLUP) while the other was selected on an optimal index for both direct and associative effects (C-BLUP). Results over 23 cycles of selection showed that C-BLUP produced a significant positive response to selection (b=0.52+/-0.25 g/hatch) whereas D-BLUP resulted in a nonsignificant negative response (b=-0.10+/-0.25 g/hatch). The regression of percentage of mortality on hatch number was significantly different between methods, decreasing with C-BLUP (b=-0.06+/-0.15 deaths/hatch) and increasing with D-BLUP (b=0.32+/-0.15 deaths/hatch). These results demonstrate that the traditional D-BLUP approach without associative effects not only is detrimental to response to selection but also compromises the well-being of animals. The differences in response show that competitive effects can be included in breeding programs, without measuring new traits, so that costs of the breeding program need not increase.     

Selection for uniformity in livestock by exploiting genetic heterogeneity of residual variance

In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in residual variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of variance was in most situations negative, indicating that selection for reduced variance increases profit. Predicted responses in residual variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current residual variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing residual variance. With optimum traits, selection pressure shifts gradually from the mean to the variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.     

多个连锁数量性状位点的多性状最优化选择

一种扩展的方法能够在多个世代对具有多个数量性状位点的多性状选择进行最优化。这种方法的基础是在目标雨数中用综合遗传值替代单个性状遗传值,并在整个规划期内最大化所有世代选择反应的加权和。利用多阶段系统优化控制理论,整个最优化问题通过一个向前和向后的迭代循环解决。用一个实际育种猪群的育种参数来评价该方法的选择效果,并和标准QTL选择和常规BLUP选择进行比较。结果表明,优化选择要优于标准QTL选择和常规BLUP选择。经济权重对优化选择的影响较明显,随着达100kg日龄赋予的经济权重的增加,优化选择的优势越明显。优化选择通过两种方式增加总选择反应：1）选择早期减少一部分QTL选择反应;2）对达100kgH龄给予更大的权重。选择后期优化累积贴现选择比优化终端选择给予达100kgH龄更大的权重。     

Characterization of DGAT1 Allelic Effects in a Sample of North American Holstein Cattle

A putative causative mutation underlying a QTL was identified as a lysine to alanine non-conservative substitution at amino acid 232 of the gene encoding the acylCoA:diacylglycerol acyltransferase (DGAT1) protein. Our goal was to characterize the allelic substitution effects of this DGAT1 mutation in a large sample of Holstein bulls from North America. Statistically significant effects were identified for all of the milk production traits and somatic cell scores. Estimated average effects of substituting the lysine allele for the alanine variant on Holstein bull daughter yield deviations were ?81 kg, 3.7 kg, ?1.1 kg, 0.063%, 0.012%, and ?0.023 units for milk yield, fat yield, protein yield, fat component, protein component, and SCS, respectively. These estimates were largely in agreement with previous studies; however, the magnitudes of the estimates were much smaller in this study. Impacts on economic indices for net merit, cheese merit, and fluid merit were modest. Because of the strong antagonism between fat and protein yield and how those traits influence economic indices, selection for DGAT1 genotypes will likely not find widespread application in the U.S.     

The evolution of trade-offs under directional and correlational selection

Using quantitative genetic theory, we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sibling experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.