Durum wheat (Triticum turgidum L. subsp. durum) is a major crop in the Mediterranean region, widely grown for its nutritional value and economic importance. Durum wheat breeding can contribute to global food security through the introduction of new cultivars exhibiting drought tolerance and higher yield potential in the Mediterranean environments. In this study, 25 durum wheat genotypes (23 elite breeding lines and two national checks) were evaluated for five drought-adaptive traits (days to heading, days to maturity, plant height, 1000-kernel weight and grain yield) and eight drought tolerance indices including stress tolerance index (STI), geometric mean productivity (GMP), mean productivity (MP), stress susceptibility index, tolerance index, yield index, yield stability index and drought response index under rainfed and irrigated conditions during three cropping seasons (2019–2022). Multi-trait stability index (MTSI) technique was applied to select genotypes with higher grain yield, 1000-kernel weight, plant stature and early flowering and maturity simultaneously; as well as for higher drought tolerance in each and across years. A heat map correlation analysis and principal component analysis were applied to study the relationships among drought tolerance indices and the pattern of variation among genotypes studied. Factor analysis was applied for identification of traits that contributed most in stability analyses. Significant and positive correlations were observed among the three drought tolerance indices of STI, GMP and MP with mean yields under both rainfed and irrigated conditions in each and across years, suggest the efficiency of these indices as selection criteria for improved drought tolerance and yield performance in durum wheat. The genotypes ranked based on MTSI varied from environment to environment, showing the impact of environment on genotypes performance, but several of the best performing lines were common across environments. According to MTSI for agronomic traits, the breeding lines G20, G6, G25 and G18 exhibited highest performance and trait stability across environmental conditions, and the selected genotypes had strength towards grain yield, 1000-kernel weight and earliness. Using the MTSI, breeding lines G20, G5, G16 and G7 were selected as drought tolerant genotypes with high mean performance. Breeding line G20 from ICARDA germplasm showed highest trait stability performance and drought tolerance across environments. The MTSI was a useful tool for selecting genotypes based on their agronomic performance and drought tolerance that could be exploited for identification and selection of elite genotypes with desired multi-traits. Based on the results, breeding lines G20 and G6 should be recommended for short-term release programme and/ or utilized in durum wheat population improvement programme for agronomic performance and drought tolerance traits that tolerate climate variations.

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).

Maize (Zea mays L.) grain yield is severely constrained by drought and this study was conducted to assess gains in grain yield and other traits of released maize cultivars. Twenty-three maize cultivars plus a check were evaluated under drought and well-watered conditions at Zaria and Kadawa during 2015/2016 and 2016/2017 dry seasons. The 24 cultivars were evaluated using 6 x 4 lattice design with three replications. Genotypes differed significantly for all measured traits except anthesis-silking interval (ASI), husk cover, and number of ears per plant under drought, and ASI, husk cover, and ear aspect under well-watered conditions. Under drought, grain yield ranged from 2251 kg ha−1 for SAMMAZ 31 to 4938 kg ha−1 for SAMMAZ 19, with a genetic gain of 1.93% yr−1. Under well-watered conditions, grain yield varied from 3082 kg ha−1 for SAMMAZ 37 to 5689 kg ha−1 for SAMMAZ 51, with the same genetic gain found under drought conditions. Grain yield reduction as a result of drought was 28.4% and performance under drought predicted performance under well-watered conditions better than vice versa with regression coefficient value of 0.8. Grain yield had significant correlations with all measured traits under both water conditions, except for husk cover, plant and ear heights under drought. Our data revealed that substantial genetic gains have been made in breeding for high grain yield cultivars under drought and well-watered conditions over a period of 16 years in Nigeria.

The objective of this study was to establish different single or multiple trait selection indices to calculate genetic and economic gains by combining some production, reproduction and udder health traits in a population similar to the overall practical situation in Iran, with and without imposing restrictions on genetic change for some traits. The SelAction software was used to perform the analyses based on selection index theory through a deterministic model. Results indicated that among established indices, the index that showed the highest genetic gain for milk yield did not maximize the total genetic and economic gains. Rather, the index that included all production, reproduction and udder health traits yielded the highest genetic and economic gains. When we placed restriction on the selection indices, the economic gain decreased and the amount of reduction depended on the heritability and the correlation of restricted trait(s) with other traits. Generally, regarding the economic genetic gain per generation, the indices based on records of 200 offspring were 4.819% more efficient than those that used information of 100 offspring.

The use of sexed semen in dairy and beef cattle production provides a number of benefits at both farm and industry levels. There is an increasing demand for dairy and beef products across the globe, which will necessitate a greater focus on improving production efficiency. In dairy farming, there is surplus production of unwanted male calves. Male dairy calves increase the risk of dystocia compared with heifer calves, and as an unwanted by-product of breeding with conventional semen, they have a low economic value. Incorporating sexed semen into the breeding programme can minimise the number of unwanted male dairy calves and reduce dystocia. Sexed semen can be used to generate herd replacements and additional heifers for herd expansion at a faster rate from within the herd, thereby minimising biosecurity risks associated with bringing in animals from different herds. Furthermore, the use of sexed semen can increase herd genetic gain compared with use of non-sorted semen. In dairy herds, a sustainable breeding strategy could combine usage of sexed semen to generate replacements only, and usage of beef semen on all dams that are not suitable for generating replacements. This results in increased genetic gain in dairy herd, increased value of beef output from the dairy herd, and reduced greenhouse gas emissions from beef. It is important to note, however, that even a small decrease in fertility of sexed semen relative to conventional semen can negate much of the economic benefit. A high fertility sexed semen product has the potential to accelerate herd expansion, minimise waste production, improve animal welfare and increase profitability compared with non-sorted conventional semen.

Soybean yield gain over the last century has been attributed to both genetic and agronomic improvements. Recent research has characterized how breeding efforts to improve yield gain have also secondarily impacted agronomic practices such as seeding rate, planting date, and fungicide use. To our knowledge, no research has characterized the relationship between weed–soybean interference and genetic yield gain. Therefore, the objectives of this research were to determine whether newer cultivars would consistently yield higher than older cultivars under increasingly competitive environments, and whether soybean breeding efforts over time have indirectly increased soybean competitiveness. Field research was conducted in 2014, 2015, and 2016 in which 40 maturity group (MG) II soybean cultivars released between 1928 and 2013 were grown season-long with three different densities of volunteer corn (0, 2.8, and 11.2 plants m−2). Soybean seed yield of newer cultivars was higher than older cultivars at each volunteer corn density (P<0.0001). Soybean seed yield was also higher in the weed-free treatment than at low or high volunteer corn seeding rates. However, soybean cultivar release year did not affect late-season volunteer corn shoot dry biomass at either seeding rate of 2.8 or 11.2 seeds m−2. The results indicate that while soybean breeding efforts have increased yield potential over time, they have not increased soybean competitiveness with volunteer corn. These results highlight the importance of other cultural practices such as planting date and crop row spacing for weed suppression in modern soybean production systems.

We tested the hypothesis that mating strategies with genomic information realise lower rates of inbreeding (∆F) than with pedigree information without compromising rates of genetic gain (∆G). We used stochastic simulation to compare ∆F and ∆G realised by two mating strategies with pedigree and genomic information in five breeding schemes. The two mating strategies were minimum-coancestry mating (MC) and minimising the covariance between ancestral genetic contributions (MCAC). We also simulated random mating (RAND) as a reference point. Generations were discrete. Animals were truncation-selected for a single trait that was controlled by 2000 quantitative trait loci, and the trait was observed for all selection candidates before selection. The criterion for selection was genomic-breeding values predicted by a ridge-regression model. Our results showed that MC and MCAC with genomic information realised 6% to 22% less ∆F than MC and MCAC with pedigree information without compromising ∆G across breeding schemes. MC and MCAC realised similar ∆F and ∆G. In turn, MC and MCAC with genomic information realised 28% to 44% less ∆F and up to 14% higher ∆G than RAND. These results indicated that MC and MCAC with genomic information are more effective than with pedigree information in controlling rates of inbreeding. This implies that genomic information should be applied to more than just prediction of breeding values in breeding schemes with truncation selection.

Researches on local breeds have mainly focused on the scientific and technical activities of genetic gain production and/or maintain genetic variability. The diffusion of the genetic gain used to be taken for granted, or considered as of little importance as the State was subsidizing official breeding schemes. However, diffusion and sustainability of small local-breeding schemes are threatened by current changes in breeding activities and organizations. Diversification of farming and breeding objectives, liberalization of public policies on breeding activities, decrease in public support change the business model of breeding organizations. Local breeds are particularly concerned, as they may be threatened by more competitive and widespread ones. Indeed, the management of the diffusion dimension of breeding activities gets a greater importance. Thus, there is a need for a better understanding of the market of genetic gain and the strategies of its participants. To investigate this issue, we study with quantitative and qualitative data, the way the genetic market works in the case of local dairy sheep breeds in the Western Pyrenees. In this area, the use of artificial insemination (AI) outside nucleus flocks is weak. The diffusion is mainly based on the exchanges of live breeding animals, but the number and substance of the exchanges are unknown. We analyse two types of markets, which are set up: the official sale of breeding animals, organized by the breeding centre; the parallel market of rams' exchanges by mutual agreement between farmers. We find several paradoxical results: the more expensive animals are sold outside of the breeding schemes, while the genetic value is more uncertain; the breeding centre does not find enough buyers for its rams, while there is a shortage of rams in the region; outside the breeding schemes, the parallel market of rams is dominant. We also identify that there is a diversity of prices on the market, which cannot be explained based on the scientific evaluation of animals. We show the existence of a second-hand market of rams. In conclusion, we argue that there are various ways of managing the diffusion of genetic gain, and that the market is only one of this.

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.

Alternative Norwegian sheep breeding schemes were evaluated by stochastic simulation of a breeding population with about 120 000 ewes, considering the gain for an aggregate genotype including nine traits and also the rate of inbreeding. The schemes were: a scheme where both young unproven rams (test rams) and proven rams (elite rams) are used in artificial insemination (AI scheme), a scheme with test rams in natural mating in ram circles and elite rams (from one and a half years of age) in AI across all flocks in the country (NMAI2 scheme), a scheme where, in addition to testing rams, the youngest elite rams (one and a half years of age) are also used in natural mating in ram circles, while older elite rams are used in AI (NMAI1 scheme), and a scheme, acting as a control, where both test and elite rams are used in natural mating (NM scheme). Within the NMAI- and AI-schemes, experimentation was performed for percent ewes inseminated to elite rams v. test rams (EM%), numbers of ewes inseminated per elite ram (EAIn), and numbers of ewes mated per test ram by natural service (TNMn) or by AI (TAIn), respectively. With a restriction on the rate of inbreeding (⩽0.8% per generation), the AI scheme gave similar gain to the NMAI2 scheme (and about 40% more than did the NM scheme). Less gain was generated by the NMAI1 scheme, but it was still considerably more than for the NM scheme (about 25%). In the AI scheme, relatively few ewes (200/300) should be inseminated to each test/elite ram, and a low EM% should be chosen (10%). In the NMAI schemes, TNMn should be relatively high (40 to 50), combined with average and somewhat larger than average EAIn (NMAI2: 700 ewes, NMAI1: 900 ewes), and EM% medium (30%).

We reasoned that mating animals by minimising the covariance between ancestral contributions (MCAC mating) will generate less inbreeding and at least as much genetic gain as minimum-coancestry mating in breeding schemes where the animals are truncation-selected. We tested this hypothesis by stochastic simulation and compared the mating criteria in hierarchical and factorial breeding schemes, where the animals were selected based on breeding values predicted by animal-model BLUP. Random mating was included as a reference-mating criterion. We found that MCAC mating generated 4% to 8% less inbreeding than minimum-coancestry mating in the hierarchical and factorial breeding schemes without any loss in genetic gain. Moreover, it generated upto 28% less inbreeding and about 3% more genetic gain than random mating. The benefits of MCAC mating over minimum-coancestry mating are worthwhile because they can be achieved without extra costs or practical constraints. MCAC mating merely uses pedigree information to pair the animals more appropriately and is clearly a worthy alternative to minimum-coancestry mating and probably any other mating criterion. We believe, therefore, that MCAC mating should be used in breeding schemes where pedigree information is available.

The objective of the study was to evaluate the effect on reproductive performance of varying level of concentrate supplementation with both high and medium genetic merit cows in a spring calving grass-based system of milk production. The effect of year, cow genetic merit for milk production and concentrate feeding level on milk production, body condition score, live weight, blood metabolites and dry-matter (DM) intake were studied. A repeated measures model with a factorial arrangement of genetic merit and concentrate feeding level was used to do this. Associations between these variables and pregnancy to first service (PREG1), pregnancy to first and second service (PREG12) and overall pregnancy (PREG) rates were assessed using logistic regressions for year 2.

Cows were grouped into high (HM) and medium (MM) genetic merit based on their pedigree indices for milk production (PD milk). The HM cows had a PD milk of + 276 (s.d. 100) kg, while the MM cows had mean PD milk of + 81 (s.d. 95) kg. Within genetic merit groupings, cows were assigned to one of three concentrate feeding levels; low (LC), 376 kg; medium (MC), 810 kg; and high (HC), 1540 kg of concentrate per cow per lactation. In year 1, all 78 cows were second lactation animals, while in year 2, 71 cows (previously in year 1) were third lactation and 12 second lactation. All cows calved between February and April, and were presented for rebreeding from late April until late July each year.

When treatment means were compared, genotype and concentrate feeding levels had no significant effects on reproductive performance while year was significant for most parameters. Comparing year 2 to year 1 pregnancy rate to first service (P 0•001; 37 v. 64%), pregnancy rate to first and second service (P < 0•05; 64 v. 81%), overall pregnancy rate (P < 0•05; 78 v. 92%) were lower. Also in year 2, cows had significantly higher milk yields at first insemination (36•9 v. 32•3 kg per cow per day), greater live-weight losses from calving to first insemination (-86 v. –53 kg per cow), lower live-weight gain in the 90 days after their first insemination (+ 24•6 v. + 34•2 kg per cow), higher DM intake (20•6 v. 17•3 kg DM per cow per day) and lower plasma glucose concentrations (3•18 v. 3•61 mmol/l) than in year 1.

In year 2, there were significant negative associations between the likelihood of PREG12 and both PD milk and live-weight gain in the 90 days after first insemination. The results of this study indicate that continued selection for increased milk production, resulting in greater partitioning of energy to milk production rather than body reserves will reduce reproductive performance and offering higher levels of concentrate supplementation may not alleviate this problem.

The Sahiwal cattle, one of the best dairy breeds of Zebu cattle in India and Pakistan, originate from the Montgomery district of Pakistan and is distributed on farmer herds in certain pockets of the bordering districts of Punjab and Rajsthan in India. The animals of this breed are also available in Kenya and are used for crossing with local East African Zebu types to improve milk production. Sahiwal cattle have deep body, loose skin, short legs, stumpy horns and a broad head with pale red to dark brown body colour. The average body weight in adult females and males is around 350 and 500 kg, respectively. The animals of this breed are maintained on various State and Central Government farms, privately owned farms, charitable trusts and a small proportion of animals are also available with the farmers. More than 1 200 breedable females are available at various farms in the country. The average lactation milk yield of Sahiwal cattle on organized farms ranges between 1 500 to 2 500 kg. However, in well-managed herds, the highest lactation milk production in certain cows is more than 4 500 kg. The overall weighted average milk yield, age at first calving, lactation length and calving interval based on the performance at various herds is around 1 900 kg, 36 months, 315 days and 420 days, respectively. The fat and Solid Non Fat (SNF) percent ranges from 4.6 to 5.2 percent and 8.9 to 9.3 percent, respectively. Quite a large proportion of pure-bred Sahiwal cattle maintained on organized breeding farms has been used for the production of cross-bred cattle. As a result, different cross-bred strains of dairy cattle viz Karan Swiss, Karan Fries and Frieswal have evolved at the National Dairy Research Institute, Karnal and Military Dairy Farms. The breed has also been utilized for the production of synthetic strains like Jamaica Hope (JH), Australian Milking Zebu (AMZ) and Australian Friesian Sahiwal (AFS) in other countries. Currently, efforts are being made to characterize, evaluate and conserve the breed in field conditions. More than 0.10 million doses of frozen semen of this breed are cryopreserved at various semen banks in the country. The frozen semen is being utilized for strengthening and genetically improving the existing herds of the breed through progeny testing programmes of sires associating various herds of Sahiwal in the country.

Using deterministic methods, rates of genetic gain (Δ G) and inbreeding (Δ F) were compared between pure line selection (PLS) and combined crossbred purebred selection (CCPS), for the sire line of a three-way crossbreeding scheme. Purebred performance and crossbred performance were treated as genetically correlated traits assuming the infinitesimal model. Breeding schemes were compared at a fixed total number of purebred selection candidates, i.e. including crossbred information did not affect the size of the purebred nucleus. Selection was by truncation on estimated breeding values for crossbred performance. Rates of genetic gain were predicted using a pseudo-BLUP selection index. Rates of inbreeding were predicted using recently developed methods based on long-term genetic contributions. Results showed that changing from PLS to CCPS may increase ΔF by a factor of 2·14. In particular with high heritabilities and low purebred-crossbred genetic correlations, CCPS requires a larger number of parents than PLS, to avoid excessive ΔF. The superiority of CCPS over PLS was judged by comparing ΔG from both selection strategies at the same ΔF. At the same ΔF, CCPS was superior to PLS and the superiority of CCPS was only moderately reduced compared with the situation without a restriction on ΔF. This paper shows that the longterm genetic contribution theory can be used to balance ΔF and ΔG in animal breeding schemes within very limited computing time.

Methods that maximize genetic response in populations with overlapping generations while controlling rate of inbreeding by constraining the average relationship among selection candidates were compared. Firstly, computer simulations of closed nucleus selection schemes showed that a two-stage optimization algorithm approach, where the distribution of parents within and thereafter over age classes was optimized resulted in different breeding schemes than an approach that performed an iteration on this distribution. It yielded significantly lower annual genetic gain (0·194 v. 0·223 σp units), fewer animals selected (21·9 v. 26·4) and longer generation intervals (2·38 v. 1·68 years) but maintained the rate of inbreeding closer to its constraint. In large schemes, iteration may be computationally the only feasible method for the optimization of parents across age classes. Secondly, the use of conventional relationships for constraining inbreeding was compared with that of augmented relationships, which do not depend on the level of inbreeding. Both relationships resulted in very similar breeding schemes, but the use of augmented relationships avoids correction of the current level of inbreeding. Thirdly, a constraint of the rate of inbreeding on a per year basis was compared with a constraint on a per generation basis. When optimizing per generation, the generation interval was shorter compared with a scheme where an analogous annual restriction was in place (2·01 v. 2·38 years) and the annual rate of genetic gain was higher (0·214 v. 0·194 σp units).

Weaning weight in a single flock of 600 ewes and 40 rams was simulated through 30 consecutive lambings. The objective was to compare the simple breeding value model with the maternal effects model for lamb evaluation under the Segureña selection scheme. Three selection strategies were tested: selection on breeding values estimated by a simple breeding value model that ignores maternal effects (method 1), selection on direct additive values only (method 2) or on the sum of direct and maternal additive values (method 3), both latter methods utilizing a maternal effects model. Average values obtained in the last lamb crop were about 18 kg for the phenotypic mean, about 5 kg for direct additive values and about -1 kg for maternal additive values, for all three methods. Average inbreeding coefficient of the last crop was more than 0·13 in method 1 but was less than 0·12 in the others. All differences were not statistically significant (P > 0·05). Consequently, the simple breeding value model can be used for the genetic evaluation of weaning weight of candidates for selection in the Segureña scheme. The effect of variation in the magnitude of parameters was evaluated through four sets of parameters. Results showed that with a higher additive maternal component, method (3) would become increasingly necessary. The need for method (3) is accentuated with more negative additive covariance between direct and maternal effects. Thus, for higher maternal effects or more negative additive correlation, the use of the complete model (with maternal effects) becomes unavoidable. Varying population size, however, affects only the inbreeding accumulated, as long as the same methods of selection are used.

A genetic algorithm (GA) was used to find optimal male and female age distributions in a natural mating system that maximizes cumulative response to mass selection over a 20-year time horizon for the case where inbreeding affects reproduction at 0·0 (F-0) and 0·1 (F-10) per 0·1 inbreeding coefficient. Twenty breeding female population sizes were considered ranging from 25 to 500 breeding females distributed across five age groups. Loss of response due to inbreeding effects on reproduction ranged from 19.4% and 15.5% in small breeding female populations to 2.5% and 5.2% in large breeding female populations when number of males was fixed (FX) or optimized (OP), respectively. OP resulted in an increase in response over FX ranging from 0·0 % to 69.3% for F-0 and 0·0 % to 77.6% for F-10. The potential loss of genetic gain that resulted from ignoring the inbreeding effects upon reproduction when they really existed ranged from 0·1 % to 44.6%. The potential loss of genetic gain that resulted from including inbreeding effects upon reproduction when they did not exist ranged from 0·1% to 3.9%. Optimal male and female age structures depended upon breeding female population size, the number of breeding males and inbreeding effects. Ignoring inbreeding effects upon reproduction may result in over estimation of response to selection. Use of a GA allowed accounting for complex relationships in the optimization.

A procedure for maximizing genetic gain (after a number of generations of selection) for a given rate of inbreeding or for a given coefficient of variation of response is presented. An infinitesimal genetic model is assumed. Mass selection is practised for a number of discrete generations. With constraints on inbreeding, expected rates of genetic progress (ΔG) are combined with expeced rates of inbreeding (ΔF) in a linear objective function (Ω = ΔG - μΔF). In addition, an expression to approximate the rate of gain at any generation accounting for changes in genetic parameters due to linkage disequilibrium and due to inbreeding is derived. Predicted gain is in general within 5% of that obtained from simulation. Thus, both ΔG and ΔF are obtained from simple analytical formulae. An equivalent function is used when the coefficient of variation of response (CV) is the parameter restricted (Ω = ΔG -μCV). Maximization of the objective function Ω for appropriate values of μ gives the optimum number of sires and dams selected when specific constraints on the level of inbreeding or the coefficient of variation of response are imposed. The method is applied to a practical situation in fish breeding. Optimum mating ratios and optimum numbers of sires selected are obtained for different scored population sizes and heritabilities. Results obtained with this procedure agree very well with results from simulation studies. The optimum number of sires increases with the size of the scheme and with more severe restrictions on risk. In the schemes considered, the optimum mating ratio is equal to 2 unless the constraint on the rate of inbreeding is severe, the size of the scheme is small and the heritability is low. In these situations the optimum mating ratio is equal to 1. The procedure is general in terms of generations of selection considered and in terms of parameters to be constrained. A large amount of computer processor unit time is saved with this method in comparison with simulation procedures.

Open and closed nucleus and conventional and modern progeny testing schemes were compared for expectation and variance of genetic gain. Generation intervals were optimized, with minimum values of 2 and 6 years (progeny test results available) for males in nucleus and progeny testing schemes, respectively. Females had a minimum generation interval of 2 years, except in the conventional progeny testing schemes, which had a minimum of 4 years (one individual record available). Apart from the generation intervals and the progeny test, open nucleus and progeny testing schemes were identical, since ‘nucleus females’ are also born in progeny testing schemes, being full-sibs of the young bulls and dispersed over commercial herds. The number of nucleus sires (bull sires) selected was varied between four and 32. Selection was for milk production.

A deterministic model was used, that accounted for variance reduction due to selection and the effects of finite size and family structure on the selection differentials. Prediction of the variance of the selection response accounted for selection of full- and paternal half-sibs.

Closed nucleus schemes gave a factor 0·03, 0·13 and 0·19 larger response rates than open nucleus and modern and conventional progeny testing schemes, respectively. Reduction of genetic variance of open nucleus schemes was larger than that of closed nucleus schemes, which caused the slightly higher response rates of closed nucleus schemes. Standard deviations of selection responses of closed nucleus schemes were a factor 0·46, 0·79 and 0·86 larger, respectively.

Preference for the schemes was assessed using a quadratic utility function expressing risk and inbreeding aversion. The increase in genetic gain due to shortening of generation intervals more than compensated for its increased variance. Whether the increased genetic gain due to closing the nucleus compensated for its increased variance depended on the amount of risk aversion. Selection of four sires and eight to 16 sires had the highest utility in progeny testing and nucleus schemes, respectively.

An analysis of cow reproductive traits was carried out on 2057 lactation records of Egyptian buffaloes. A total of 651 daughters (paternal half-sisters) of 82 sires were available for the analysis. Reproductive traits analysed were age at first, second and third calving (AC), number of services per conception (NSC), gestation length (GL) and calving interval (CI). Year of calving affected most reproductive traits (P < 0·001) while no important differences were detected among months of calving. Means of NSC, GL and CI decreased linearly (P < 0·01) as parity advanced. Age of cow at calving exerted a pronounced effect (P < 0·001) on NSC and CI. There was no systematic change in the estimates of heritability and sire components of variance for reproductive measures over the first three lactations. Heritability estimates for NSC and GL in the different parities were generally low, ranging between 0·04 and 0·18, while moderate estimates for AC and CI were obtained. Phenotypic correlations between reproductive traits were positive and relatively moderate or low. For most traits, positive and relatively high or moderate estimates of genetic correlations were observed. Mating bull was found to be an important source of variation for reproductive performance of Egyptian buffaloes. The highly significant effect of mating bull on reproductive traits could be considered as evidence for the importance of evaluating bull semen quality before the mating of cows