Aggregate Breeding Value Research Articles

Characteristics of restricted selection indices and geometrical interpretation of restricted breeding values.

Restricted selection is used to control genetic changes in one or more characters. Three main selection indices are adopted for this purpose. First, Kempthorne's index is used to maximize aggregate breeding value (BV) with changes in some traits restricted to zero; second, Harville's index is used to maximize aggregate BV with proportional changes for some traits; and third, Yamada's index is mathematically used to achieve the relative desired changes for all traits. Kempthorne's index is equivalent to Harville's index. However, the relationship between Kempthorne's and Yamada's indices has not been clarified. In addition, the characteristics of restricted selection indices and the relationship between BV and restricted BV (RBV) are also unknown. The aim of this study was to clarify the characteristics of restricted selection indices and describe the relationship between BV and RBV by using linear algebra and geometric techniques, respectively. First, I proved that Yamada's index is part of Kempthorne's index. Second, I investigated the relationship between BVs that were estimated using an ordinary selection index (EBVs) and RBVs estimated using a restricted selection index (ERBVs) and proved that the ERBVs of the restricted traits are proportional to the relative desired changes. Third, I proved that RBV is represented by a linear function of BV and geometrically represented the relationship between BV and RBV. In this study, new findings on restricted selection indices and RBV were obtained. This useful clarification of the relationship between BV and RBV will make it possible to evaluate the response to selection using not only a restricted selection index, but also a restricted BLUP in computer simulation studies.

Potential response from selection schemes based on progeny testing and genomic selection for the Chilean dairy cattle under pastoral systems: a deterministic simulation.

Recently, a selection index called Valor Económico Lechero (VEL) was developed for Chilean dairy cattle under pasture. However, a specific selection scheme has not yet been implemented. This study aimed to estimate genetic progress from selection on the VEL selection index based on selection schemes using progeny testing (PT) and genomic selection (GS). Under a PT-scheme, estimated genetic progress was 41.50, 3.44, and 2.33 kg/year for milk, fat, and protein yield, respectively. The realised genetic gain takes eight-year after the PT-scheme implementation, which may be a disincentive for implementing a PT-scheme, suggesting that importing frozen semen of proven bulls could be a preferred alternative. In this case, an option may be to conduct the genetic evaluation of those bulls using their progeny in Chile for the traits included in VEL selection index. In the case of implementing a specific selection scheme, compared to PT, a more profitable alternative might be the implementation of a GS-scheme, that would result in a faster genetic gain in the aggregate breeding value or merit for all the traits included in the selection objective (0.323-0.371 vs. 0.194 σg/year).

Selection scheme designs for dairy cattle milked once daily in New Zealand: a deterministic approach

ABSTRACT In New Zealand, a specific selection scheme for the dairy cattle population milked once-a-day (OAD) has not been implemented. This study aims to investigate estimated genetic progress for different selection objectives based on selection scheme designs using progeny testing (PT) and genomic selection (GS) in OAD herds. Under a PT-scheme, estimated genetic progress ranged from 7 to 45 kg/year (milk), 2.18–2.24 kg/year (fat), and 0.83–1.71 kg/year (protein). Conversely, genetic gains resulting from selecting bulls generated in twice-a-day (TAD) milking systems and used to inseminate cows in OAD herds, ranged between 12 and 52 kg/year (milk), 2.34 and 3.22 kg/year (fat) and 0.83 and 2.29 kg/year (protein). Correlated responses tend to be greater in the yield traits when the emphasis on fertility, residual survival and body condition score were reduced in the selection objective. Further correlated responses in yield traits were reduced when type-related traits were included in the selection objective, in particular when bulls were tested in TAD systems. A more immediate and profitable alternative might be the implementation of a GS-scheme, that would result in a faster genetic gain in the aggregate breeding value or merit for all the traits included in the selection objective (0.310–0.368 vs 0.191–0.196 σg/yr).

An alternative derivation method of mixed model equations from best linear unbiased prediction (BLUP) and restricted BLUP of breeding values not using maximum likelihood.

Two mixed model equations (MME) for best linear unbiased prediction (BLUP) of breeding values and for restricted BLUP of breeding values were derived by maximum likelihood from the joint normal probability distribution of the observations and breeding values. As a result, MME is actually more general than maximum likelihood because we can prove that each set of solutions of MME are identical to BLUP and restricted BLUP of breeding values and then it does not depend on normality. In the present study, the author shows deriving directly each MME from BLUP and restricted BLUP equations for breeding values without assuming the joint normal distribution of the data and random effects. However, if we cannot assume the multivariate normal density distribution of the estimated aggregate breeding value and each breeding value for selected traits, the response to selection by restricted BLUP may deviate from the expected values.

Multi-trait and multi-source selection indices for milk production and reproductive traits in a herd of Holstein cattle in Egypt

The main aim of this study was explore possibility to improve milk production and reproductive traits of Holstein cattle via selection index method which include general, reduced, sub and Multi-source of information indices (Own-Performance, Full-Sibs and Half-Sibs). D ata was obtained from a commercial farm (Safi Masr for Developing the Animal Resources), located in the Nile Delta, Dakahlia, Egypt. Data included 4791 records of 1797 cows, 794 dams and 67 sires that represented the period from 2002 to 2012. Estimates of genetic and phenotypic parameters for studied traits were computed and used to construct 18 selection indices to improve milk production and reproductive traits. F ull index incorporating milk yield at 305d (305-dMY), lactation period (LP), days open (DO) and age at first calving (AFC) had the highest correlation with aggregate breeding value (R ih = 0.518; RE=100%). The correlation fell to 0.455 when 305-dMY was omitted from the index. The general index has the maximum expected genetic gain in 305-dMY (132.6 kg) per generation were accompanied by decrease of LP (-4.679 day), DO (-3.449 day) and AFC (-1.41 month) when all four traits were included in the index (I 1 ). The expected genetic gain for 305-dMY decreased to 26.84 kg/generation when 305-dMY was excluded in index 5 (I 5 ). In addition, Using multi-source of information will enhance correlation with aggregate breeding value (R ih = 0.740; RE=142.91%) and raised the expected genetic gain per generation for 305-dMY (209 kg) and decreasing the expected genetic gain for LP (-6.37 day), DO (-4.244 day) and AFC (1.843 month) when all four traits were included in the index (I 16 ). It could be suggested using the higher indexes of Rih (I 1 (RE=100) ) to improve milk production and reproductive traits in Holstein cattle under own-performance strategy and using (I 16 (RE= 142.91 ) ) under multi-source strategy to get high accuracy and higher expected genetic changes per generation compare to general index.

A bioeconomic model of a genetic improvement program of abalone

This study predicts the long-term economic effects of a genetic improvement program of Australian abalone. A detailed bioeconomic model was constructed, which allows the combination of the biological, technological, and economic aspects of genetic improvement. This research focuses on analyzing various traits through an aggregate breeding value and selection index. In this study, the traditional formula of annual genetic gain is used to allow a detailed analysis of biomass future behavior in terms of the intertemporal evolution of the traits analyzed. The results showed that the production program of genetic management in Australian abalone is profitable but only in the very long term, and it is influenced mainly by the progressive increase in the biomass of each abalone and the survival rate. Sensitivity analysis showed that the weight at harvest is the most important trait, suggesting that it is more beneficial for a farmer to focus on genetically improving this trait. In addition, reproductive factors (especially survival from competent larvae until sexual maturity) had a particularly strong impact on the results, much more than the factors related to genetic improvement and economics, such as the discount rate and selling price.

Selection indexes for genetic improvement of yearling weight in Egyptian buffaloes

Abstract. Estimates of genetic and phenotypic parameters for body weight at birth, 3, 6, 9, and 12 months of age, and for preweaning and postweaning average daily gain were computed and used to construct 14 selection indexes to improve the 12-month weight in Egyptian buffaloes. The full index incorporating body weight at birth, 3, 6, 9 and 12 months of age had the highest correlation with aggregate breeding value (rTI=0.63). The correlation fell to 0.62 when body weight at birth and 3 months were omitted from the index. Selection for body weight at 12 months of age alone is expected to be 76.2 % as efficient as selection for the full index. The maximum expected genetic gain in 12-month body weight was 8.85 kg/generation when all five body weights were included in the index; this decreased to 8.09 kg/generation when body weights at birth, 3 and 6 months were excluded and further decreased to 6.94 kg/ generation when selection based on yearling weight only. From the practical standpoint, selection on I5 involving body weight at 9 month of age can be considered as the best for improving body weight at 12 month since its application is earlier, less expensive, higher accuracy than any index excluding body weight at 12 month and giving reasonable amount (+5.39 kg) improvement in yearling weight as compared to direct selection (+6.94 kg).

Response to selection from using identified genes and quadratic indices in two-traits breeding goals

Benefits from the use of optimised selection for maximising genetic gain while constraining the rate of inbreeding were evaluated through stochastic simulation for scenarios where the breeding goal includes two negatively correlated traits. One of the traits was controlled only by polygenes and had a heritability of 0.3 while the other trait was controlled by an identified additive biallelic QTL (with an initial allele frequency of 0.15) and by polygenes and had a polygenic heritability of 0.1. Optimised selection was compared to standard truncation selection both when the information on the QTL was used and when it was ignored. Extra gains in the breeding goal were observed throughout the 10 simulated generations from the combined use of optimised contributions and QTL information although, as expected, this scheme was not the most effective for improving individual traits. By generation ten, the gain in the aggregate breeding value with optimised selection was about 12% higher than with truncation selection. Optimised selection allowed extra polygenic responses in both traits but these extra responses were negative for the trait under mixed inheritance. The use of the QTL allowed not only positive gains in the trait with the lowest heritability, but also avoided the loss of the favourable allele. The effect of selecting for the QTL on each trait depended on its relative weight in the selection index and not exclusively on the inheritance model.

Konstruktion von Indizes mit Restriktionen in Random Regression Modellen zur Veränderung der Wachstumskurve

Abstract. Title of the paper: Index construction with restrictions in random regression models to change the pattern of the growth curve Random regression models provide estimated breeding values (EBV) for the complete growth curve for any target age. The animal-specific curves can be described as the weighted sum of continuous covariates with random regression coefficients. By using the covariance matrix K of the additive genetic regression coefficients the response to index selection can be calculated for any age or time of the test period. In this study selection indexes with equality restrictions based on the eigenvectors of matrix K were used to modify the growth curve of the population. In order to demonstrate the index construction a matrix K was used, estimated from repeated measurements for body weight of bulls by using Legendre polynomials as covariates. Indexes for high and low growth rate until age at the reflection point were derived subject to the restriction of zero gain for initial and final body weight. Selection strategies for improving body weight at the end of the test period while holding the daily gain in a certain time interval on a desired level were compared. By using so-called "restrictive economic values", an aggregate breeding value for body weight was derived from EBV for individual growth curve.

Estimates of genetic parameters and genetic trends for live weight and fleece traits in Menz sheep

Menz sheep are indigenous to the highlands of Ethiopia, and highly valued for their meat and wool production. The area is characterized as a low input mixed barley-sheep production system. In 1998, a selection experiment was set up to evaluate the response of Menz sheep to selection for yearling live weight (WT12) and greasy fleece weight (GFW) combined in an economic index. In this paper, we report the results of this breeding program obtained between 1998 and 2003. Average annual genetic selection responses for WT12 and GFW were 1.506 and 0.043 kg in the selected flock and 0.392 and −0.008 kg in the control flock. Annual genetic trends in the selected flock, estimated by regressing BLUP estimated breeding values on year of birth, were 0.495 ± 0.053 kg for WT12, 0.012 ± 0.002 kg for GFW, and Birr 5.53 ± 0.55 for the aggregate breeding value (1 Ethiopian Birr = 0.115 USD). Corresponding values for the control flock were 0.276 ± 0.065 kg, 0.003 ± 0.002 kg and Birr 2.93 ± 0.69. Correlated responses in birth weight (WT0), weaning weight (WT3), 6-month weight (WT6) and staple length (STPL) in the selected flock were 0.038 ± 0.005 kg, 0.271 ± 0.03 kg, 0.388 ± 0.039 kg and 0.011 ± 0.017 cm, respectively. Heritabilities, estimated by fitting a multitrait individual animal model were 0.464 ± 0.014, 0.477 ± 0.016, 0.514 ± 0.017, 0.559 ± 0.019, 0.393 ± 0.016 and 0.339 ± 0.014 for WT0, WT3, WT6, WT12, GFW and staple length (STPL), respectively. Phenotypic and genetic correlations between all traits were positive, except for STPL and WT12. Estimates of genetic parameters and observed genetic trends confirm that selective breeding can lead to significant genetic improvement in Menz sheep.

Correlated responses in tissue weights measured <i>in vivo</i> by computer tomography in Dorset Down sheep selected for lean tissue growth

The aim of this study was to estimate correlated responses in lean, fat and bone weights in vivo in Dorset Down sheep selected for lean tissue growth. Over the period 1986-1992 inclusive, the lean tissue growth line had been selected using two economic indices for an increased aggregate breeding value incorporating predicted lean and fat weights with positive and negative economic weightings, respectively. The control line was selected for no change in lean tissue growth each year. Animals were born and run on pasture all year round. X-ray computer tomography was used to estimate the weights of lean, fat and bone in vivo in the 1994-born sheep, aged 265-274 days and selected randomly into 12 rams and 12 ewes from the selected line and 10 rams and 9 ewes from the control line. The lean tissue growth line had significantly greater responses in lean weight (+0.65 + 0.10 kg) and lean percentage (+1.19 + 0.17%) and significantly lesser fat weight (-0.36 + 0.08 kg) and fat percentage (-1.88 + 0.20%) compared to the control line. There was a significant increase in bone weight (+0.27 + 0.03 kg) and bone percentage (+0.69 + 0.09%) in the lean tissue growth line compared to the control line. Responses differed significantly between sexes of the lean tissue growth line, rams having a greater response in weight of lean (+1.22 + 0.20 vs. +0.08 + 0.22 kg) and bone (+0.45 + 0.06 vs. +0.09 + 0.07 kg), and a lesser response in weight of fat (-0.03 + 0.15 vs. -0.70 + 0.16 kg) than the ewes. Selection led to significant changes in lean (increase) and fat weights (decrease), and bone weight increased. Although responses in the lean tissue growth line differed significantly between sexes, there were confounding factors due to differences in management and lack of comparison at equal stage of development. Therefore, to assess real genetic differences further studies should be conducted taking these factors into consideration. Keywords: Lean tissue growth, Computer tomography, Selection index, Responses, Sheep South African Journal of Animal Science Vol.33(3) 2003: 176-184

Genetic and phenotypic parameters and responses in index component traits for breeds of sheep selected for lean tissue growth

The aims of this experiment were to estimate genetic and phenotypic parameters, and responses in vivo for selection index component traits, i.e. live weight, fat depth and muscle depth. Performance data sets were available from lean tissue growth selection experiments for Border Leicester (n=613), Coopworth (n=1711) and Dorset Down (n=820) ram flocks and from a Corriedale progeny testing ram flock (n=722). Lean tissue growth flocks had been selected for an increased aggregate breeding value incorporating predicted lean and fat weights with positive and negative economic weightings, respectively, over the period 1986–1992 inclusive. Estimates of genetic and phenotypic parameters and responses in index component traits were derived from multivariate AIREML analyses, fitting an individual animal model including animal as a random variable, birth rank, year and age of dam fitted as fixed effects and age at measurement as a covariable. Rates of response for each index component were obtained by regressing best linear unbiased prediction (BLUP) breeding values (BV) on time. Index component traits had medium to high (0.20±0.04 to 0.45±0.08) heritability estimates. Estimates of genetic and phenotypic correlations were predominantly low to moderate (0.20–0.60), although a few were high (>0.60). Live weight (+0.24±0.09kg per year) and muscle depth (+0.05±0.02mm per year) increased and fat depth (−0.03±0.02mm per year) decreased under selection. Responses, adjusted for animal size were greatest in fat depth (−0.90±0.63% per year) and least in muscle depth (+0.18±0.06% per year) with live weight being intermediate (+0.45±0.12% per year). Although not significantly different (P>0.05), estimates of genetic and phenotypic parameters and responses to selection varied between breeds. Variation in genetic and phenotypic parameters led to variation in predicted responses for lean and fat weights between breeds, suggesting that in order to design more optimal breeding programmes breed specific parameters should be used.

Evaluation of the efficiency of alternative selection schemes and breeding objectives in dairy sheep of Greece

AbstractThe genetic and economic efficiency of alternative selection schemes and breeding objectives for the Karagouniki dairy sheep in Greece was investigated by model calculations. Criteria of efficiency were the annual genetic gain for the aggregate breeding value, the profit per ewe in the population and the annual selection responses for single traits. The introduction of a two-tier selection scheme, where the recorded ewes are separated into a nucleus and a pre-nucleus, was found superior in both genetic and economic terms for a breeding objective comprising the traits milk yield and number of lambs weaned per ewe per annum. Highest rates for annual genetic gain and selection responses were obtained when the nucleus size was proportionately 0·05 of the population (200 000 ewes), the size of the test matings 0·50 to 0·60 of the size of the pre-nucleus unit (0·10 of the population) and the number of daughters per test ram 40. Opening the nucleus to replacement ewes from the lower tier did not affect positively the annual genetic gain and the selection responses. Furthermore, a breeding objective comprising the traits fat yield and number of lambs weaned per ewe and per annum was found very efficient in both genetic and economic terms while selection on growth and carcass traits did not seem to be justified.

Benefit of multiple trait selection to increase reproductive traits: experimental evidence from golden hamsters.

Fifteen generations of selection were conducted to study responses for litter size at birth (LSB), weight at weaning of standardized litter (LWW), and individual body weight at 8 wk of age (BW8) using golden hamsters as an experimental model for pigs. The experiment involved three lines: selection on an aggregate breeding value of LSB, LWW, and BW8 (line W); selection on an aggregate breeding value of LSB and LWW (line R); and a randomly selected control (line C). Selection in W and R was based on breeding values from a multiple trait animal model. Restricted maximum likelihood with an animal model was used to estimate genetic parameters and genetic trends. Heritability estimates for LSB, LWW, and BW8 were .10, .47, and .52, respectively, and genetic correlations between traits were all positive. The mean estimated breeding value (EBV) for LSB in generation 15 was +2.2 pups in W and R. The mean EBV for LWW in generation 15 was +318 g for W and +174 g for R, and for BW8 means were +64 g and +24 g, respectively. Average inbreeding at generation 16 was 13.4, 19.5, and 8.0% for W, R, and C, respectively. Including BW8 in the selection criterion reduced inbreeding and had a beneficial effect on selection responses in LSB, LWW, and BW8.

The Selection Index—Then, Now, and for the Future

When improvement is desired for several traits that may differ in variability, heritability, economic importance, and in the correlation among their phenotypes and genotypes, simultaneous multiple-trait index selection was more effective than independent culling levels or sequential selection. Such comparisons required definition of aggregate breeding value determined jointly by breeding values and the economic importance of the component traits. The economic weight should approximate the partial regression of cost per unit of enterprise output value on breeding value for each trait. These can vary with production and marketing system, with performance of traits, and with breed role (i.e., paternal, maternal, or general) in crossbreeding systems. Genetic gains desired to maintain competitive ranking also may define the relative importance of traits. Because information available to estimate breeding values varies among the ages and categories of individuals under selection and because means are unknown, regressed (BLUP) predictions of trait breeding values are useful. They allow appropriate economic weights to be applied as the last step for predicting aggregate breeding values for individuals of different age classes, and they simplify choosing the proportions of selected breeders from each age class that maximize rate of change in aggregate breeding values. Inappropriate economic weights or errors in the parameters used to predict trait breeding values overestimate realized response in true aggregate breeding value.

Prediction of asymptotic rates of response from selection on multiple traits using univariate and multivariate best linear unbiased predictors

AbstractPredicted rate of genetic response for multiple trait breeding objectives from multivariate analyses is compared with that from univariate analyses for a range of breeding schemes, A selection index that approximates a multipl trait best linear unbiased prediction (BLUP) animal model is utilized. Changes in genetic parameters due to linkage disequilibrium generated by selection are accounted for. This study shows that asymptotic response in the aggregate breeding value, and its component traits, to selection on multivariate predictions, can easily be calculated from first generation responses, which use ancestral information. For two-path breeding schemes with equal accuracy for males and females, proportional reductions in responses depend only on selection intensity. In general, benefit from multivariate over univariate analyses is slightly smaller at the asymptote than in the first generation. Multivariate analyses give substantially more response than univariate analyses on untransformed data, when correlations between traits are high and when genetic and phenotypic correlations have opposite signs. The advantage of multivariate analyses decreases with increasing family size. When three random factors (additive genetic, common and individual environmental effects) are included in the model, the benefit of multivariate analysis is negligible if univariate analyses are performed on canonical traits. In this case, the advantage of multivariate analyses is never higher than 1% for all cases studied. These results are of particular relevance to the design of genetic evaluation programmes.

Index versus tandem selection after repeated generations of selection

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.

Multistage Selection for Genetic Gain by Orthogonal Transformation

An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.

Multistage selection for genetic gain by orthogonal transformation.

Abstract An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.

Estimates of genetic parameters and predicted selection responses for growth, fat and lean traits in mice.

Heritabilities (ĥ2) and genetic correlations (rG) were estimated by regression of offspring on sire in two replicate, unselected lines of mice. Traits were associated with growth, feed efficiency, fat deposition and lean tissue. The ĥ2 for growth traits ranged from .34 to .42, except for 3-wk body weight, which was only .05. The ĥ2 for feed efficiency was .28. Ranges in ĥ2 were .45 to .50 for fat deposition traits and .36 to .42 for lean tissue traits. The rG involving 3-wk to 6-wk feed efficiency with hind carcass and fat measurements at 12 wk were small. Antagonisms were found between the sign of rG and the direction of usual breeding goals for pairs of traits (e.g., rG greater than 0 between fat deposition and hind carcass weight and rG less than 0 between hind carcass as a percentage of body weight and body weight). Selection indexes were developed to counteract these antagonisms. Modified selection indexes were compared where responses in individual traits rather than the aggregate breeding value were of major importance. The aggregate breeding values and selection indexes included: 1) epididymal fat pad weight and body weight, 2) hind carcass weight and body weight, or 3) all three traits. Economic weights in retrospect were calculated for the modified selection indexes. In some cases, expected correlated responses in component traits were not influenced greatly over a wide range of ratios of economic weights, but in other cases the component traits changed sharply over a narrow range of ratios.