An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

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     

Optimising two-stage independent culling selection in tree and animal breeding

Summary Theory is given for a simple practical method of predicting gain from two-stage independent culling, where stage 1 of selection is for individual performance and stage 2 is for either progeny performance only, or an index combining individual and progeny performance. Expected gain is determined as a direct function of heritabilities, genetic correlations, selection intensities and progeny-testing capacity. Results show the effect these parameters can have on proportions selected at each stage and, if multiple selection criteria are used, traits selected for first. Methods are discussed in the context of tree and animal breeding, with an example taken from forestry.     

Reproductive fitness and artificial selection in animal breeding: culling on fitness prevents a decline in reproductive fitness in lines of Drosophila melanogaster selected for increased inebriation time

Summary The maintenance of reproductive fitness in lines subjected to artificial selection is one of the major problems in animal breeding. The decline in reproductive performance has neither been predictable from heritabilities and genetic correlations, nor have conventional selection indices been adequate to avoid the problem. Gowe (1983) has suggested that the heritabilities of reproductive traits are non-linear, with heritabilities being higher on the lower fitness side. Consequently, he has predicted that culling on reproductive fitness in artificial selection lines will be effective in preventing the usual declines in fitness. An experimental evaluation of Gowe's prediction has been carried out by comparing fitnesses of replicated lines of three treatments: selection for increased inebriation time without culling on fitness (HO), selection for inebriation time with culling of 20% (4/20) of selected females on reproductive fitness (HS), and unselected controls (C). Response to selection for inebriation time in the two selection treatments was similar. After 25 generations, the competitive index, a measure of reproductive fitness, was significantly lower in the HO treatment than the HS treatment, while the HS treatment did not differ from the control lines or the base population. These results demonstrate for the first time that culling on reproductive fitness in selection lines can be used to prevent the usual decline in reproductive performance.     

Converting multi-trait breeding objectives into operative selection indexes to ensure genetic gains in low-input sheep and goat breeding programmes

Small ruminant breeding programmes in low-input production systems are best organised at the community level. Participant farmers have to agree on goal traits and their relative importance. When BLUP breeding values of goal traits are not available in time, appropriate selection indexes can be used to aid visual selection. Taking Ethiopian Abergelle goat and Bonga sheep community-based breeding programmes (CBBPs) as an example, breeding objective functions were defined and selection indexes were constructed and evaluated. Breeding goals for Abergelle goats included early sale weight, survival and milk production. Breeding goals for Bonga included the number of offspring born, sale weight and survival. Economic weights of objective traits can be used in several ways depending on measured traits and the reliability of their genetic parameters. Selection indexes included combinations of objective traits measured on candidates and their dams and situations when Abergelle communities prefer to restrict genetic changes in number of offspring born or adult weight and when Bonga communities prefer to restrict changes in adult weight. Genetic and economic gains were evaluated as well as sensitivity to feed cost assumptions and to repeated dam records. After independent culling on preponderant traits such as coat colour and horn/tail type, sires in Abergelle goat community breeding programmes should be selected on indexes including at least own early live weight and their dams average milk production records. Sires for Bonga sheep programmes should be selected on own early live weight and desirably also on their dam’s number of offspring born. Sensitivity to feed cost assumptions was negligible but repeated measurements of dam records improved index accuracies considerably. Restricting genetic changes in number of offspring born or adult weight is not recommended.     

Accuracy of marker-assisted selection with auxiliary traits

Genetic information on molecular markers is increasingly being used in plant and animal improvement programmes particularly as indirect means to improve a metric trait by selection either on an individual basis or on the basis of an index incorporating such information. This paper examines the utility of an index of selection that not only combines phenotypic and molecular information on the trait under improvement but also combines similar information on one or more auxiliary traits. The accuracy of such a selection procedure has been theoretically studied for sufficiently large populations so that the effects of detected quantitative trait loci can be perfectly estimated. The theory is illustrated numerically by considering one auxiliary trait. It is shown that the use of an auxiliary trait improves the selection accuracy; and, hence, the relative efficiency of index selection compared to individual selection which is based on the same intensity of selection. This is particularly so for higher magnitudes of residual genetic correlation and environmental correlation having opposite signs, lower values of the proportion of genetic variation in the main trait associated with the markers, negligible proportion of genetic variation in the auxiliary trait associated with the markers, and lower values of the heritability of the main trait but higher values of the heritability of the auxiliary trait.     

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.     

Improving grain yield in backcross populations from Avena sativa × A. sterilis matings by using independent culling for harvest index and vegetative growth index or unit straw weight

Summary Grain yield was selected in Avena sativa X A. sterilis populations of segregates by applying independent culling for harvest index and either vegetative growth index or unit straw weight. Samples of lines intensively selected for harvest index had high harvest index but low grain yield because they had low vigor. Populations intensively selected for growth rate index or unit straw weight had high biological yield but low harvest index. Intensive selection for grain yield per se resulted in samples with high grain yield, but they were late and tall. Samples selected for harvest index at a 25% selection intensity first and subsequently selected for vegetative growth index or unit straw weight had grain yield as high as the samples selected for grain yield per se and vegetative growth index, and they had acceptable heading date and plant height. Backcrosses three and four were best, among the various BC generations, for selecting oat lines with high grain yield and suitable agronomic traits. CI 7463 was superior to CI 8044 as a recurrent parent, and B 445 was inferior to other A. sterilis accessions as a donor parent.Journal Paper No. J-12287 of the Iowa Agric, and Home Econ. Exp. Stn., Ames, IA 50011. Project 2447. This research was supported in part by a grant from the World Food Institute, Iowa State University, Ames, IA, USA     

Genetic improvement of production while maintaining fitness

Selection for production tends to decrease fitness, in particular, major components such as reproductive performance. Under an infinitesimal genetic model restricted index selection can maintain reproductive performance while improving production. However, reproductive traits are thought to be controlled by a finite number of recessive alleles at low frequency. Culling for low reproduction may weed out the negative homozygous genotypes for reproduction in any generation, thus controlling the frequencies of alleles negative for reproduction. Restricted index selection, culling for low reproduction and a new method called empirical restricted index selection were compared for their efficiency in improving production while maintaining reproduction. Empirical restricted index selection selects animals that have on average the highest estimated breeding values for production and on average the same estimated breeding values for reproduction as the base population. An infinitesimal genetic model and models with a finite number of loci for reproduction with rare deleterious recessive alleles, which have additive, dominant or no pleiotropic effects on production, were considered. When reproduction was controlled by a finite number of loci with rare recessive alleles, restricted index selection could not maintain reproduction. The culling of 20% of the animals on reproduction maintained reproduction with all genetic models, except for the model where loci for reproduction had additive effects on production. Empirical restricted selection maintained reproduction with all models and yielded higher production responses than culling on reproduction, except when there were dominant pleiotropic effects on production.     

Genetic Variance and Correlation after Selection for Two Traits by Index, Independent Culling Levels and Extreme Selection

Three two-trait selection methods were analyzed for their effects on genetic variance and correlation by multivariate methods, two-locus methods and computer simulation. The two-trait selection methods studied were independent culling levels (ICL), index (IND) and extreme (EXT) selection. The effects of the selection methods on genetic variance and correlation were partitioned into permanent effects due to changes in gene frequencies and temporary effects due to nonrandom association of alleles at different loci. Multivariate methods were used to predict temporary effects from a single generation of selection by each method and from several generations of index selection. Two-locus theory was used to determine the stability and rank of temporary effects on genetic correlation for all three methods. Predictions were compared to computer simulation results. When selection increased the means of both traits, EXT had the lowest (closest to -1.0) genetic correlation and highest variances, while ICL tended to have the highest (closest to 1.0) genetic correlation. When selection increased the mean of one trait and decreased the mean of the other, EXT had the highest genetic variances and correlation, while ICL had the lowest genetic variances and correlation.     

Economic weights of somatic cell score in dairy sheep

The economic weights for somatic cell score (SCS) have been calculated using profit functions. Economic data were collected in the Latxa breed. Three aspects have been considered: bulk tank milk payment, veterinary treatments due to high SCS, and culling. All of them are non-linear profit functions. Milk payment is based on the sum of the log-normal distributions of somatic cell count, and veterinary treatments on the probability of subclinical mastitis, which is inferred when individual SCS surpass some threshold. Both functions lead to non-standard distributions. The derivatives of the profit function were computed numerically. Culling was computed by assuming that a conceptual trait culled by mastitis (CBM) is genetically correlated to SCS. The economic weight considers the increase in the breeding value of CBM correlated to an increase in the breeding value of SCS, assuming genetic correlations ranging from 0 to 0.9. The relevance of the economic weights for selection purposes was checked by the estimation of genetic gains for milk yield and SCS under several scenarios of genetic parameters and economic weights. The overall economic weights for SCS range from − 2.6 to − 9.5 € per point of SCS, with an average of − 4 € per point of SCS, depending on the expected average SCS of the flock. The economic weight is higher around the thresholds for payment policies. Economic weights did not change greatly with other assumptions. The estimated genetic gains with economic weights of 0.83 € per l of milk yield and − 4 € per point of SCS, assuming a genetic correlation of − 0.30, were 3.85 l and − 0.031 SCS per year, with an associated increase in profit of 3.32 €. This represents a very small increase in profit (about 1%) relative to selecting only for milk yield. Other situations (increased economic weights, different genetic correlations) produced similar genetic gains and changes in profit. A desired-gains index reduced the increase in profit by 3%, although it could be greater depending on the genetic parameters. It is concluded that the inclusion of SCS in dairy sheep breeding programs is of low economic relevance and recommended only if recording is inexpensive or for animal welfare concerns.     

Multitrait index based on factor analysis and ideotype‐design: proposal and application on elephant grass breeding for bioenergy

This study proposes a new multitrait index based on factor analysis and ideotype‐design (FAI‐BLUP index), and validates its potential on the selection of elephant grass genotypes for energy cogeneration. Factor analysis was carried out, and afterwards, factorial scores of each ideotype were designed according to the desirable and undesirable factors, and the spatial probability was estimated based on genotype‐ideotype distance, enabling genotype ranking. In order to quantify the potential of the FAI‐BLUP index, genetic gains were predicted and compared with the Smith‐Hazel classical index. The FAI‐BLUP index allows ranking the genotypes based on multitrait, free from multicollinearity, and it does not require assigning weights, as in the case of the Smith‐Hazel classical index and its derived indices. Furthermore, the genetic correlation ‐ positive or negative ‐ within each factor was taken into account, preserving their traits relationship, and giving biological meaning to the ideotypes. The FAI‐BLUP index indicated the 15 elephant grass with the highest performance for conversion to bioenergy via combustion, and predicted balanced and desirable genetic gains for all traits. In addition, the FAI‐BLUP index predicted gains of approximately 62% of direct selection, simultaneously for all traits that are desired to be increased, and approximately 33% for traits which are desired to be decreased. The genotypes selected by the FAI‐BLUP index have potential to improve all traits simultaneously, while the Smith‐Hazel classical index predicted gains of 66% for traits that are desired to be increased, and ?32% for traits that are desired to be decreased, and it does not have potential to improve all traits simultaneously. The FAI‐BLUP index provides an undoubtable selection process and can be used in any breeding programme aiming at selection based on multitrait.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

Optimum proportions selected with unequal sex numbers

Summary Optimum proportions selected for each sex, giving the maximum selection response up to some specified time, have been investigated. Selection was carried out from a constant number of individuals scored per generation. It has been shown that the maximum response after t generations of selection is obtained when the number of individuals scored and the proportion selected is the same for males and females every generation. Specific situations, where the sex-ratio among scored or breeding individuals or the selected proportion of males or females is taken as given throughout the whole selection process, have been studied, optimum strategies being described in each case. The procedures leading to maximum advance at the selection limit have also been considered in all these situations.     

An Experimental Evaluation of Genetic Correlation

Heritability and genetic correlations realized from both single-trait and antagonistic index selection were compared with paternal half-sib estimates. Primary attention was focused on the genetic correlation between six-week body weight and six-week tail length. Parameters realized from single-trait selection were in excellent agreement with paternal half-sib estimates. However, the realized genetic correlation between six-week body weight and six-week tail length obtained from index selection was significantly greater than the other estimates. Differential inbreeding levels and realized selection intensities were considered and rejected as being causative factors for these results. Linkage disequilibrium probably was not a factor either, as the base population had been randomly mated and randomly selected with a large effective population size for many generations. It was concluded that with antagonistic index selection, the pleiotropic effects of genes may be more powerful in retarding response in aggregate genotype than current theory would suggest. Replication of all selected and control lines allowed the use of between-line estimators of sampling variances of realized genetic parameters in the above comparisons. Generally, standard errors of realized genetic parameters were much smaller than corresponding paternal half-sib standard errors. Thus, selection was an efficient method of estimation.     

Selection indices for desired relative genetic gains with inequality constraints

Summary A selection index which maximizes genetic gains in a desired direction has been previously suggested. We extend this index to the case where desired relative genetic gains are constrained to be not less or not greater than pre-specified levels. Further, we suggest an index for desired relative genetic gains constrained to be between certain levels. All these indices are obtained using quadratic programming techniques.     

Prediction of response with overlapping generations accounting for multistage selection

Summary A generalization of Hill's equations predicting response to selection is developed that accounts for multiple stage selection in either or both sexes. The method accounts for the flow of genes for animals selected at later stages. This allows for the use of genetic gains from later stages, which explains the reduction in variance due to previous selection. Genetic gains from different selection differentials in each reproductive pathway are incorporated into the equations. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory.The method is applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. Two models were compared: (1) the first model accounted for two-stage selection of males, the first stage being based on pedigree information and the second stage on both pedigree and progeny test information; and (2) the second model assumed single-stage male selection. Selection was based on milk volume, milk fat, and milk protein yields. The predicted asymptotic rates for a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% by assuming singlestage male selection.Journal Paper No. J14146 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa; Project No. 1053     

Integrating genomic selection into dairy cattle breeding programmes: a review

Extensive genetic progress has been achieved in dairy cattle populations on many traits of economic importance because of efficient breeding programmes. Success of these programmes has relied on progeny testing of the best young males to accurately assess their genetic merit and hence their potential for breeding. Over the last few years, the integration of dense genomic information into statistical tools used to make selection decisions, commonly referred to as genomic selection, has enabled gains in predicting accuracy of breeding values for young animals without own performance. The possibility to select animals at an early stage allows defining new breeding strategies aimed at boosting genetic progress while reducing costs. The first objective of this article was to review methods used to model and optimize breeding schemes integrating genomic selection and to discuss their relative advantages and limitations. The second objective was to summarize the main results and perspectives on the use of genomic selection in practical breeding schemes, on the basis of the example of dairy cattle populations. Two main designs of breeding programmes integrating genomic selection were studied in dairy cattle. Genomic selection can be used either for pre-selecting males to be progeny tested or for selecting males to be used as active sires in the population. The first option produces moderate genetic gains without changing the structure of breeding programmes. The second option leads to large genetic gains, up to double those of conventional schemes because of a major reduction in the mean generation interval, but it requires greater changes in breeding programme structure. The literature suggests that genomic selection becomes more attractive when it is coupled with embryo transfer technologies to further increase selection intensity on the dam-to-sire pathway. The use of genomic information also offers new opportunities to improve preservation of genetic variation. However, recent simulation studies have shown that putting constraints on genomic inbreeding rates for defining optimal contributions of breeding animals could significantly reduce achievable genetic gain. Finally, the article summarizes the potential of genomic selection to include new traits in the breeding goal to meet societal demands regarding animal health and environmental efficiency in animal production.     

Gametic models for multitrait selection schemes to study variance of response and drift under adverse genetic correlations

A major issue faced by breeders is how to effectively manage adverse correlations in breeding programs. We present results of a Monte Carlo allele-based simulation of the changes in response and variance of response under adverse genetic correlations by using the examples of two contrasting selection methods: the ‘Smith-Hazel’ selection index (SH) and independent culling (IC). We assumed several gene models, which included linkage and antagonistic pleiotropy as the primary drivers of adverse genetic correlations. The different behaviors of these selection methods allowed us to identify the mechanism behind the generation of uncertainty under antagonistic trait selection: IC had the properties of stabilizing selection, while SH behaved more similar to disruptive selection. Although SH outperformed IC in terms of genetic gain, this advantage happened at the cost of higher variance of response and loss of heterozygosity. Using an optimum selection algorithm (OS) to prevent the loss of heterozygosity through a constraint on inbreeding in SH/OS increased marginally the reliability, remaining still below that of IC under equal conditions. However, SH/OS had lower inbreeding (ΔF) than IC for equivalent levels of genetic gain, so a compromise between high selection reliability, low ΔF, and gain must be made by a breeder under antagonistic trait selection even with the use of optimization tools.     

Evaluation of the Culling Variate Used by Breeders in Actual Selection

The theoretical basis and computational procedures for estimating the culling variate utilized by breeders in actual selection are presented. The essential part of this procedure is to derive the unknown culling variate in terms of a linear combination of traits based on realized indirect selection differentials of those traits and phenotypic variances and covariances among traits in the population. Special emphasis is placed on the distribution of the variables involved. The accuracy of the culling variate is estimated by use of the biserial correlation with some modifications. Numerical illustrations are given for different types of selection.