The purpose of this work was to quantify the additive genetic correlations between prevalent radiographic findings in the limbs of Warmblood riding horses and performance parameters. Data on 3725 Hanoverian Warmblood horses selected for sale at auctions in the period 1991 to 1998 were used. The numbers of annual entries (TE) and placings (TP) in tournament competitions in the period 1991 to 2002 served as measures of performance in riding sports. Multivariate genetic analyses were performed in linear animal models using restricted maximum likelihood (REML). The four most prevalent radiographic findings, i.e. osseous fragments in fetlock (OFF) and hock joints (OFH), deforming arthropathy in hock joints (DAH) and pathologic changes in navicular bones (PCN) were analysed jointly with the performance parameters, i.e. TE and TP. Additive genetic correlations between the radiographic findings and the performance in sports were in many cases close to zero. There were some indications for significantly negative, but few indications for significantly positive additive genetic correlations between radiological conditions in the equine limbs and the performance of Warmblood riding horses in dressage, show-jumping and basic build-up competitions. Breeding measures that allow for orthopaedic health traits could therefore contribute to maximize the breeding progress in terms of sport performance.

Five data sets with records of first, second and third lambings of the White Alpine sheep (WAS1, WAS2), the Brown-Headed Meat sheep (BFS), the Black-Brown Mountain sheep (SBS) and the Valais Black-Nose sheep (SNS) of Switzerland were used to estimate phenotypic and genetic parameters for litter size using a multitrait and a repeatability model by the REML method. The sets contained litter information from 26 274, 25 165, 18 913, 14 953 and 21 726 ewes, respectively. Average numbers of litters per ewe were between 2·09 and 2·31. Average litter sizes at birth were between 1·36 and 1·57 lambs in first, between 1·52 and 1·75 in second and, between 1·56 and 1·86 in third parities. Multitrait estimates of heritability for size of first litters were 0·164, 0·157, 0·117, 0·223 and 0·116 for the WAS1, WAS2, BFS, SBS and SNS data, respectively. The corresponding estimates were 0·176, 0·165, 0·140, 0·208 and 0·134 for second and, 0·141, 0·155, 0·121, 0·145 and 0·107 for third litters. The systematic increase in phenotypic variances from first to third litter within data sets favoured the multivariate over the repeatability approach. Genetic correlations between size of the first three litters were, with one exception, above 0·927. Random flock ✕ year and sire of litter effects contributed between 2·2% and 13·2% and between 0·7% and 4·7% to the phenotypic variance of the traits, respectively. Residuals contributed between 70·6% and 84·2% to this parameter, estimates for the third litter were always highest. Heritability estimates from the repeatability model were smaller than the smallest multivariate estimates. Expected genetic gain in litter size from selection on the multitrait model was equal to the achieved response from the repeatability approach.

This paper reports the selection responses achieved, and related results, following 9 years of index selection for lean growth in Suffolk sheep. The breeding goal of the index used comprised carcass lean weight and carcass fat weight at a constant age, with relative economic values of + 3 and –1 per kg. The selection criteria were live weight (LWT), ultrasonic fat depth (UFD) and ultrasonic muscle depth (UMD) adjusted to a constant age of 150 days. By year 9, responses in LWT, UFD and UMD in both sexes, as judged by the divergence between selection and control line performance, amounted to 4·88 kg, -1·1 mm and 2·8 mm respectively; these responses are between 7 and 15% of the overall means of the traits concerned. Although selection was originally on index scores based on phenotypic records, the retrospective analyses reported here used the mixed model applications of residual maximum likelihood to estimate parameters and best linear unbiased prediction to predict breeding values. The statistical model comprised fixed effects plus random effects accounting for direct additive, maternal additive and temporary environmental variation. Estimated genetic trends obtained by regressing estimated breeding values on year of birth were similar to annual responses estimated by comparing selection and control line means. Estimates of direct heritabilities were 0·054, 0·177, 0·286, 0·561 and 0·410 for birth weight (BWT), weaning weight (WWT), LWT, UFD and UMD respectively. Corresponding estimates of maternal heritabilities were 0·287, 0·205, 0·160, 0·083 and 0·164. Phenotypic correlations between all pairs of traits were positive and usually moderately high. There were low negative direct additive correlations between BWT and WWT, and between BWT and LWT, but higher positive maternal additive correlations between all other pairs of weight traits.

A selection index procedure which utilizes both, purebred and crossbred information was developed for the sire line of a three-path crossbreeding scheme in pigs, to predict response to best linear unbiased prediction (BLUP) selection with an animal model. Purebred and crossbred performance were treated as correlated traits. The breeding goal was crossbred performance but methods can be applied to other goals. A hierarchical mating structure was used. Sires were mated to purebred dams to generate replacements and to F^ from the dam line to generate fattening pigs. Generations were discrete, inbreeding was ignored. The selection index included purebred and crossbred phenotypic information of the current generation and estimated breeding values for purebred and crossbred performance of parents and mates of parents from the previous generation. Reduction of genetic variance due to linkage disequilibrium and reduction of selection intensity due to finite population size and due to correlated index values was accounted for. Selection was undertaken until asymptotic responses were reached. The index was used to optimize the number of selected parents per generation and the number of offspring tested per litter, and to make inferences on the value of crossbred information when the breeding goal was crossbred performance. It was optimal to test a maximum number of offspring per litter, mainly due to increased female selection intensities. Maximum response reductions due to linkage disequilibrium and correlated index values were 32% and 29% respectively. Correcting for correlated index values changed ranking of breeding schemes. Benefit of crossbred information was largest when the genetic correlation between purebred and crossbred performance was low. Due to high correlations between index values in that case, the optimum number of selected sires increased considerably when crossbred information was included.

Data from 4150 Landrace pigs tested during the period 1989-94 for backfat thickness and age at 100 kg in an open selection nucleus were analysed with the standard restricted maximum likelihood/best linear unbiased prediction method and with a Bayesian approach based on the marginal posterior distributions of parameters of interest achieved via Gibbs sampling. Breeding values and fixed effects were sampled from normal distributions and (co)variance components from inverted Wishart distributions. The Bayesian analysis indicated that the selection was effective for both traits. Assuming flat priors for the (co)variance components, the posterior means of the annual rates of response to selection for both traits were −0·473 days and −0·212 mm. The influence of informative priors constructed from (co)variances estimated in the French Landrace breed on inferences about genetic and common environmental parameters, genetic group effects and total and annual responses was also examined.

The value of using a marker for a quantitative trait locus (QTL) affecting a sex-limited trait in an outbred poultry breeding nucleus was studied. Marker and QTL were in linkage equilibrium in the base population. The recombination rate between marker and QTL was 0-05. A closed nucleus with 9000 chickens per generation was deterministically simulated. The genetic model contained polygenes and a QTL linked to a marker. Genetic effects explained proportionately 0·3 of the phenotypic variance before selection. Under selection, polygenic variance reached an equilibrium and QTL variance decreased continuously over time. Cocks were selected in two steps. First the best cocks of each full-sib family were selected (within-family selection) while final selection took place after information on fiill-sibs was available. Hens were selected after they had completed production. The effect of using marker information in estimating breeding values was studied in an ongoing breeding programme. Transmission of marker alleles was always traceable. Cumulative response over five generations increased proportionately by 0·06 to 0·13 if a marker linked to a QTL that explained 0·2 of the genetic variance was used. Cumulative response increased up to 0·28 if the QTL explained 0-8 of the genetic variance. Additional response due to the use of a marker increased with increasing intensity of within-family selection of cocks, increased with increasing variance explained by the QTL and was higher if within-family selection of cocks was carried out after rather than before their sibs had complete records.

Alternative closed breeding schemes for beef cattle are analysed using stochastic computer simulation. Multiple ovulation and embryo transfer (MOET) schemes are compared with conventional schemes (schemes without MOET) with an equal expected number of progeny born per year. Schemes are compared for genetic gain and inbreeding obtained after 25 years of selection. The trait considered, evaluated in both sexes, has an initial heritability of 0·35. Different population sizes and numbers of sires selected are evaluated. Current realistic parameters for embryo production are assumed in MOET schemes.

After 25 years of selection, and with no control on inbreeding, cumulative genetic gains are about 50% higher in MOET schemes compared with conventional schemes. The benefit from MOET is mostly due to increased selection intensities in females. The rate of inbreeding increases by up to nearly 300% when MOET is used. This maximum percentage increase in inbreeding following the use of MOET can be reduced to about 100% when selection and mating strategies for controlling inbreeding are used. The effect of the number of sires used on the inbreeding obtained is more important than the effect of the size of the herd. In MOET schemes, increasing the number of sires selected by a factor of three, leads to reductions in inbreeding rates of 40%. When schemes of the same size are compared at similar acceptable inbreeding levels, MOET schemes give around 30% higher genetic progress than conventional schemes.

Weaning weights (or weight nearest to 205 days of age) from 8086 Mashona calves were collected from seven herds covering the period 1976 to 1988. Estimates of (co)variance components were obtained by restricted maximum likelihood using a derivative free algorithm and fitting an individual animal model. Estimates of direct additive heritability, maternal additive heritability, their correlation, total heritability and repeatability, obtained under two models were 0·243 and 0·281, 0·113 and 0·392, –0·282 and –0·269, 0·252 and 0·298, and 0·409 and 0·573, respectively. Trends within herd were estimated from the mean value of progeny born within a particular year. There were no significant trends in direct additive breeding values. A general decline in maternal breeding values was observed. Only one herd (herd 1) had a significant eroiyonmeYital freni (0·385 kg/year). It IMS emphftsilfiti that any future revision of the method used to improve the weaning weights of beef cattle should also improve their maternal breeding values.

Predicted 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.

Formulas were derived to predict asymptotic response to selection on best linear unbiased predictors (BLUP) of breeding values that account for selection-induced gametic phase disequilibrium, also known as the ‘Bulmer’ effect. Breeding programmes in populations of infinite size and with discrete generations were considered. For two-path breeding programmes with equal male and female accuracy of selection, relative reductions in response due to gametic phase disequilibrium were independent of heritability. Reductions in response depended only on intensities of selection and ranged from 0·22 to 0·27 when selected proportions were less than 04 for both males and females. With unequal accuracy of males and females, relative reductions in response depended on the ratio of accuracies, in addition to selection intensities. For given selection intensities, reductions were up to proportionately 0·08 larger with unequal accuracies than reductions obtained for equal accuracies. Relative reductions in response for breeding programmes with four paths of selection depended on intensity and accuracy of selection in each path, but were within a range similar to that observed for two-path programmes. Gametic phase disequilibrium will, therefore, not greatly affect ranking and relative differences among alternative breeding programmes.

Gametic phase disequilibrium had a larger effect on response with selection on BLUP than on phenotype, which is largely due to larger relative reductions in accuracy of selection with BLUP. Despite larger relative reductions, asymptotic response to selection on BLUP is expected to be larger than selection on phenotype.

The effect of increased female reproductive rates on selection response, on efficiency of progeny testing and on the openness of the nucleus was investigated in open nucleus breeding plans. Conventional progeny testing plans and closed nucleus plans are special classes of open nucleus plans. In the open nucleus plans, generation intervals and selection across tiers were optimized. The number of offspring per elite dam was varied from 1 to 41, progeny testing of young bulls in the female base population was varied from 0 to 100 test records and the size of the nucleus was varied from 250 to 2000 young bulls born per year. Also efficiency of selection was varied: efficient selection in T(heoretical)-schemes and less efficient selection in P(ractical)-schemes. Especially, selection of base parents was less efficient i n P-schemes.

The deterministic prediction model took account of variance reduction due to selection and reduction of selection differentials due to correlations between estimated breeding values of relatives (order statistics). For closed nucleus plans, the results of the model were verified with Monte Carlo simulation results.

By increasing female reproductive rates, genetic gain increased by a factor 0·08 and 0·16 for the T- and P-schemes respectively. The nuclei in P-schemes were less open, due to the less efficient selection in the female base population. Schemes that were less open benefited more from increased female reproductive rates because selection differentials in small nuclei increased more than those in large base populations. The optimal open nucleus plan became less open with increasing female reproduction. Generally, progeny testing of bulls reduced genetic gain (by up to a factor 0·1) but it also reduced inbreeding rates. Progeny testing was more efficient in schemes that were less open: in P-schemes with 41 offspring per dam, progeny testing increased genetic gain. With many offspring per dam there were fewer full-sib families, causing lower selection differentials due to order statistics effects. This effect could be prevented by increasing the size of the nucleus.

The published theoretical estimates of equilibrium genetic change possible by progeny testing in dairy cattle are too high. Much of the overestimation is because no account has been taken of the temporary reduction in genetic variation due to selection of parents and ancestors. A particular efficient progeny testing scheme was modelled theoretically and simulated on computer using a continuous infinitesimal additive model. To make the simulation feasible an elite breeding herd of females was used, and progeny testing was done outside the herd. The proportional reduction in genetic variance due to previous selection was 0·25, 0·27 and 0·29 for original heritabilities of 0·05, 0·25 and 0·50, with the theoretical and simulated results being very similar. The theoretical and simulated proportional losses in equilibrium selection responses were 0·22 and 0·26, 0·21 and 0·22 and 0·21 and 0·25, respectively, for the three levels of heritability. Thus, most of the loss in response in the simulation results came from the reduction in genetic variance due to selection.