Developing flexible models for genetic evaluations in smallholder crossbred dairy farms

The productivity of smallholder dairy farms is very low in developing countries. Important genetic gains could be realized using genomic selection, but genetic evaluations need to be tailored for lack of pedigree information and very small farm sizes. To accommodate this situation, we propose a flexible Bayesian model for the genetic evaluation of milk yield, which allows us to simultaneously account for nongenetic random effects for farms and varying SNP variance (BayesR model). First, we used simulations based on real genotype data from Indian crossbred dairy cattle to demonstrate that the proposed model can separate the true genetic and nongenetic parameters even for small farm sizes (2 cows on average) although with high standard errors in scenarios with low heritability. The accuracy of genomic genetic evaluation increased until farm size was approximately 5. We then applied the model to real data from 4,655 crossbred cows with 106,109 monthly test day milk records and 689,750 autosomal SNPs. We estimated a heritability of 0.16 (0.04) for milk yield and using cross-validation, a genomic estimated breeding value (GEBV) accuracy of 0.45 and bias (regression of phenotype on GEBV) of 1.04 (0.26). Estimated genetic parameters were very similar using BayesR, BayesC, and genomic BLUP approaches. Candidate genes near the top variants, IMMP2L and ARHGEF2, have been previously associated with milk protein composition, mastitis resistance, and milk cholesterol content. The estimated heritability and GEBV accuracy for milk yield are much lower than those from intensive or pasture-based systems in many countries. Further increases in the number of phenotyped and genotyped animals in farms with at least 2 cows (preferably 3-5, to allow for dropout of cows) are needed to improve the estimation of genetic effects in these smallholder dairy farms.

Genetic relationships between weight loss in early lactation and daily milk production throughout the lactation in Holstein cows

After calving, high-yielding dairy cows mobilize body reserves for energy, sometimes to the detriment of health and fertility. This study aimed to estimate the genetic correlation between body weight loss until nadir and daily milk production (MY24) in first- (L1) and second-lactation (L2) Holstein cows. The data set included 859,020 MY24 records and 570,651 daily raw body weight (BWr) phenotypes from 3,989 L1 cows, and 665,361 MY24 records and 449,449 BWr phenotypes from 3,060 L2 cows, recorded on 36 French commercial farms equipped with milking robots that included an automatic weighing platform. To avoid any bias due to change in digestive content, BWr was adjusted for variations in feed intake, estimated from milk production and BWr. Adjusted body weight was denoted BW. The genetic parameters of BW and MY24 in L1 and L2 cows were estimated using a 4-trait random regression model. In this model, the random effects were fitted by second-order Legendre polynomials on a weekly basis from wk 1 to 44. Nadir of BW was found to be earlier than reported in the literature, at 29 d in milk, and BW loss from calving to nadir was also lower than generally assumed, close to 29 kg. To estimate genetic correlations between body weight loss and production, we defined BWL5 as the loss of weight between wk 1 and 5 after calving. Genetic correlations between BWL5 and MY24 ranged from -0.26 to 0.05 in L1 and from -0.11 to 0.10 in L2, according to days in milk. These moderate to low values suggest that it may be possible to select for milk production without increasing early body mobilization.

Validation of single-step genomic BLUP random regression test-day models and SNP effects analysis on milk yield in French Saanen goats

The shape of the lactation curve is linked to an animal's health, feed requirements, and milk production throughout the year. Random regression models (RRM) are widely used for genetic evaluation of total milk production throughout the lactation and for milk yield persistency. Genomic information used with the single-step genomic BLUP method (ssGBLUP) substantially improves the accuracy of genomic prediction of breeding values in the main dairy cattle breeds. The aim of this study was to implement an RRM using ssGBLUP for milk yield in Saanen dairy goats in France. The data set consisted of 7,904,246 test-day records from 1,308,307 lactations of Saanen goats collected in France between 2000 and 2017. The performance of this type of evaluation was assessed by applying a validation step with data targeting candidate bucks. The model was compared with a nongenomic evaluation and a traditional evaluation that use cumulated performance throughout the lactation model (LM). The incorporation of genomic information increased correlations between daughter yield deviations (DYD) and estimated breeding values (EBV) obtained with a partial data set for candidate bucks. The LM and the RRM had similar correlation between DYD and EBV. However, the RRM reduced overestimation of EBV and improved the slope of the regression of DYD on EBV obtained at birth. This study shows that a genomic evaluation from a ssGBLUP RRM is possible in dairy goats in France and that RRM performance is comparable to a LM but with the additional benefit of a genomic evaluation of persistency. Variance of adjacent SNPs was studied with LM and RRM following the ssGBLUP. Both approaches converged on approximately the same regions explaining more than 1% of total variance. Regions associated with persistency were also found.

Combining datasets in a dynamic residual feed intake model and comparison with linear model results in lactating Holstein cattle

A new method to estimate residual feed intake (RFI) was recently developed based on a multi-trait random regression model. This approach deals with the dynamic nature of the lactation, which is in contrast with classical linear approaches. However, an issue remains: pooling data across sites and years, which implies dealing with different (and sometimes unknown) diet energy contents. This will be needed for genomic evaluation. In this study, we tested whether merging two individual datasets into a larger one can lead to valuable results in comparison to analysing them on their own with the multi-trait random regression model. Three datasets were defined: the first one with 1 063 lactations, the second one with 205 lactations from a second farm and the third one combining the data of the two first datasets (1 268 lactations). The model was applied to the three datasets to estimate individual RFI as well as variance components and correlations between the four traits included in the model (fat and protein corrected milk production, BW, feed intake and body condition score), and a fixed month-year-farm effect was used to define the contemporary group. The variance components and correlations between animal effects of the four traits were very similar irrespective of the dataset used with correlations higher than 0.94 between the different datasets. The RFI estimates for animals from their single farm only were also very similar (r > 0.95) to the ones computed from the merged dataset (Dataset 3). This highlights that the contemporary group correction in the model adequately accounts for differences between the two feeding environments. The dynamic model can thus be used to produce RFI estimates from merged datasets, at least when animals are raised in similar systems. In addition, the 205 lactations from the second farm were also used to estimate the RFI with a linear approach. The RFI estimated by the two approaches were similar when the considered period was rather short (r = 0.85 for RFI for the first 84 days of lactation) but this correlation weakened as the period length grew (r = 0.77 for RFI for the first 168 days of lactation). This weakening in correlations between the two approaches when increasing the used time-period reflects that only the dynamic model permits the regression coefficients to evolve in line with the physiological changes through the lactation. The results of this study enlarge the possibilities of use for the dynamic RFI model.

Influence of production, reproduction, morphology, and health traits on true and functional longevity in French Holstein cows

In the long term, resilient animals are able to maintain their normal biological processes when confronted with environmental perturbations, reducing their risk of being culled. Therefore, longevity can be proposed as an indicator of long-term resilience. Decisions to remove a given dairy cow from the herd are mainly related to low milk production (i.e., voluntary culling) or to reasons other than production (i.e., involuntary culling). The aptitude of animals to delay any culling is defined as true longevity (TL), whereas functional longevity (FL) is the ability to avoid involuntary culling. The aim of the study was to investigate the influence of production, reproduction, morphology, and health traits on TL and FL, to identify risk factors for culling. Data included 278,217 lactations from 122,461 Holstein Friesian cows reared in 640 herds. The length of productive life, calculated as the time between first calving and culling, or censoring, was used as the measure of longevity. Survival analysis was performed using proportional hazards models assuming a piecewise Weibull distribution of the baseline hazard function, with or without adjustment for milk production to evaluate FL and TL. Insemination status, calving ease, mastitis, somatic cell count, displaced abomasum, and udder depth had significant relationships with TL and FL. Differences in estimates of relative risk between TL and FL showed that milk production often influenced culling decisions: farmers are more prone to cull animals with low production even when they had good other characteristics. The culling risk factors identified in the present study can be used to study resilience in dairy cattle and to improve genetic evaluations of functional or total longevity.

Improved dairy cattle mating plans at herd level using genomic information

From 2012 to 2018, 223 180 Montbéliarde females were genotyped in France and the number of newly genotyped females increased at a rate of about 33% each year. With female genotyping information, farmers have access to the genomic estimated breeding values of the females in their herd and to their carrier status for genetic defects or major genes segregating in the breed. This information, combined with genomic coancestry, can be used when planning matings in order to maximize the expected on-farm profit of future female offspring. We compared different mating allocation approaches for their capacity to maximize the expected genetic gain while limiting expected progeny inbreeding and the probability to conceive an offspring homozygous for a lethal recessive allele. Three mate allocation strategies (random mating (RAND), sequential mating (gSEQ€) and linear programing mating (gLP€)) were compared on 160 actual Montbéliarde herds using male and female genomic information. Then, we assessed the benefit of using female genomic information by comparing matings planned using only female pedigree information with the equivalent strategy using genomic information. We measured the benefit of adding genomic expected inbreeding and risk of conception of an offspring homozygous for a lethal recessive allele to Net merit in mating plans. The influence of three constraints was tested: by relaxing the constraint on availability of a particular semen type (sexed or conventional) for bulls, by adding an upper limit of 8.5% coancestry between mate pairs or by using a more stringent maximum use of a bull in a herd (5% vs 10%). The use of genomic information instead of pedigree information improved the mate allocation method in terms of progeny expected genetic merit, genetic diversity and risk to conceive an offspring homozygous for a lethal recessive allele. Optimizing mate allocation using linear programming and constraining coancestry to a maximum of 8.5% per mate pair reduced the average coancestry with a small impact on expected Net Merit. In summary, for male and female selection pathways, using genomic information is more efficient than using pedigree information to maximize genetic gain while constraining the expected inbreeding of the progeny and the risk to conceive an offspring homozygous for a lethal recessive allele. This study also underlines the key role of semen type (sexed vs conventional) and the associated constraints on the mate allocation algorithm to maximize genetic gain while maintaining genetic diversity and limiting the risk to conceive an offspring homozygous for a lethal recessive allele.

A new method to estimate residual feed intake in dairy cattle using time series data

In dairy, the usual way to measure feed efficiency is through the residual feed intake (RFI) method. However, this method is, in its classical form, a linear regression, which, by construction, does not take into account the evolution of the RFI components across time, inducing approximations in the results. We present here a new approach that incorporates the dynamic dimension of the data. Using a multitrait random regression model, the correlations between milk, live weight, DM intake (DMI) and body condition score (BCS) were investigated across the lactation. In addition, at each time point, by a matrix regression on the variance-covariance matrix and on the animal effects from the three predictor traits, a predicted animal effect for intake was estimated, which, by difference with the actual animal effect for intake, gave a RFI estimation. This model was tested on historical data from the Aarhus University experimental farm (1 469 lactations out of 740 cows). Correlations between animal effects were positive and high for milk and DMI and for weight and DMI, with a maximum mid-lactation, stable across time at around 0.4 for weight and BCS, and slowly decreasing along the lactation for milk and weight, DMI and BCS, and milk and BCS. At the Legendre polynomial coefficient scale, the correlations were estimated with a high accuracy (averaged SE of 0.04, min = 0.02, max = 0.05). The predicted animal effect for intake was always extremely highly correlated with the milk production and highly correlated with BW for the most part of the lactation, but only slightly correlated with BCS, with the correlation becoming negative in the second half of the lactation. The estimated RFI possessed all the characteristics of a classical RFI, with a mean at zero at each time point and a phenotypic independence from its predictors. The correlation between the averaged RFI over the lactation and RFI at each time point was always positive and above 0.5, and maximum mid-lactation (>0.9). The model performed reasonably well in the presence of missing data. This approach allows a dynamic estimation of the traits, free from all time-related issues inherent to the traditional RFI methodology, and can easily be adapted and used in a genetic or genomic selection context.

Exploring simultaneous perturbation profiles in milk yield and body weight reveals a diversity of animal responses and new opportunities to identify resilience proxies

Livestock husbandry aims to manage the environment in which animals are reared to enable them to express their production potential. However, animals are often confronted with perturbations that affect their performance. Evaluating effects of these perturbations on animal performance could provide metrics to quantify and understand how animals cope with their environment, and therefore to better manage them. Body weight (BW) and milk yield (MY) dynamics over lactation may be used for this purpose. The goal of this study was to estimate an unperturbed performance trajectory using a differential smoothing approach on both MY and BW time series, and then to identify the perturbations and extract their phenotypic features. Daily MY and BW records from 490 primiparous Holstein cows from 33 commercial French herds were used. From the fitting procedure, estimated unperturbed performance trajectories of BW and MY were clustered into 3 groups. After the fitting procedure, 1,754 deviations were detected in the MY time series and 964 were detected in the BW time series across all cows. Overall, 425 of these deviations were detected during the same period (±10 d) in both MY and BW time series, 76 of which started at the same time. Results suggest that combining various individual dynamic measures and revealing the relationship that exists between them could be of great value in obtaining reliable estimates of resilience components in large populations.

Estimation of genetic parameters for dairy traits and somatic cell score in the first 3 parities using a random regression test-day model in French Alpine goats

Lactation curve shape can affect an animal's health, feed requirements, and milk production throughout the year. We implemented a random regression model for the genetic evaluation of lactation curve shapes of dairy traits in French Alpine goats for their first 3 parities. Milk, fat, and protein yields, fat and protein contents, somatic cell score, and fat/protein ratio were considered. The data consisted of test-day records from 49,849 first lactation Alpine goats during their first 3 lactations. The reference model used a Legendre polynomial of order 2 for each parity to describe the genetic and permanent environmental effects, and was compared with a model that combined the second and third parities. A rank reduction of the variance-covariance matrix was also performed using an eigenvalue decomposition for each parity from the 2 models. Genetic parameters were consistent between the models tested. With a reduction to rank 2 and combining the second and third parities, the first 2 principal components correctly summarized the genetic variability of milk yield level and persistency, with a near-nil correlation between the 2, and with a much shorter computation time than the reference model. A favorable correlation of +0.43 between milk yield persistency and fat/protein ratio persistency at the beginning of the lactation was found from buck estimated breeding values.

Impact of conformation traits on functional longevity in South African Holstein cattle

A proportional hazards model with a piecewise Weibull baseline hazard was used to determine the impact of observed scores for rump, udder, feet and leg traits on longevity. Conformation data of a total of 15 704 cows with either of or all 13 type traits for the period 1995–2013 were obtained from the Holstein Society of South Africa. Functional longevity was defined as the number of days from first calving to culling or censoring, adjusted for production. Type traits were fitted to the reference model one at a time. The model included the fixed time-dependent effect of region by year of calving, within-herd milk production class by year-season, number of lactations by stage of lactation by within-herd milk production class, protein and fat percent production class by year of calving, herd size by annual herd size change, fixed time-independent effect of age at first calving and presence of type record. Cows without type scores were 7–26% more likely to be culled than those with scores. Udder traits had the greatest impact on functional longevity. Fore teat placement had the strongest influence on functional longevity followed by udder depth, fore udder attachment, median ligament and rear treat placement. Rump and udder width had the least Chi-square contributions. Risk of culling was significantly higher for cows with very narrow chest, weak median ligament, extremely towed out teats and short rump height. There is potential for indirectly selecting animals for longevity based on udder type trait information.

Energy balance and body reserves in rabbit females selected for longevity

<p>The aim of this study was to compare the energy balance and dynamic of body reserves in rabbit females divergently selected for longevity. One hundred and twenty-nine females from a high longevity line (HL) and 131 females of a low longevity line (LL) were studied from the 1^st to the 3^rd kindling. Litter size and weight and female body weight were measured at kindling (1^st, 2^nd and 3^rd), insemination (2^nd and 3^rd) and at weaning (1^st and 2^nd). The total body electric conductivity (TOBEC) method was used to estimate the body reserves in all females at artificial insemination and at weaning, and at kindling in females that achieved parturition. Energy balance between the 11^th and the 21^th d of lactation was also calculated for these females. No significant difference was found for fertility or for the number of offspring born alive and weaned. However, the total number of offspring born was higher in the LL line than in the HL line at the 2^nd parturition (+1.12±0.46 g; P&lt;0.05). Consequently, the number of stillborn offspring was higher in the LL line. LL females were 4% heavier than HL females at the first parturition (P&lt;0.05), but then HL females had a higher live weight gain than LL females from the 1st parturition to the 2^nd artificial insemination (+107.0±29 g; P=0.049), leading to a similar weight between the lines at the 2^nd artificial insemination. There was no significant difference between lines for estimated energy used for growth between the 11^th and the 21^th d of lactation, or for estimated milk production (2365±30 g in HL line vs. 2398±30 g in LL line), estimated using the weight gain of the kits between the 11^th and 21^st d of lactation, for feed intake measured during this period (351±5 g/d in HL line vs. 359±5 g/d in LL line) or for energy balance (–6.11±0.3 MJ in HL line vs. –6.30±0.3 MJ in LL line). However, body energy content was higher in HL females than in LL (+2.72±0.64 MJ; P=0.001). In conclusion, selection for higher functional longevity results in a better ability of females to use body reserves in their early reproductive life.</p>

Estimation of genetic parameters for functional longevity in the South African Holstein cattle using a piecewise Weibull proportional hazards model

Non-genetic factors influencing functional longevity and the heritability of the trait were estimated in South African Holsteins using a piecewise Weibull proportional hazards model. Data consisted of records of 161,222 of daughters of 2,051 sires calving between 1995 and 2013. The reference model included fixed time-independent age at first calving and time-dependent interactions involving lactation number, region, season and age of calving, within-herd class of milk production, fat and protein content, class of annual variation in herd size and the random herd-year effect. Random sire and maternal grandsire effects were added to the model to estimate genetic parameters. The within-lactation Weibull baseline hazards were assumed to change at 0, 270, 380 days and at drying date. Within-herd milk production class had the largest contribution to the relative risk of culling. Relative culling risk increased with lower protein and fat per cent production classes and late age at first calving. Cows in large shrinking herds also had high relative risk of culling. The estimate of the sire genetic variance was 0.0472 ± 0.0017 giving a theoretical heritability estimate of 0.11 in the complete absence of censoring. Genetic trends indicated an overall decrease in functional longevity of 0.014 standard deviation from 1995 to 2007. There are opportunities for including the trait in the breeding objective for South African Holstein cattle.

Genomic and single-step evaluations of carcass traits of young bulls in dual-purpose cattle

Genetic evaluations for carcass traits of young bulls in Normande and Montbeliarde breeds are currently being developed in France. In order to determine a suitable genomic evaluation for three carcass traits of young bulls, genomic breeding values were estimated for young candidates to selection using different approaches. Records of 111,789 Normande and 118,183 Montbeliarde were used. Average progeny pre-adjusted performances (DYD) were calculated for sires. Evaluation approaches were compared based on an assessment of their accuracy (correlation between DYD and estimated breeding values [EBVs]) and bias (regression coefficient of DYD on EBVs) on the 20% youngest AI sires. All genomic approaches were generally more accurate than BLUP (+.045 to +.116 correlation points), except for age at slaughter where single-step GBLUP (SSGBLUP) was the only genomic method leading to a greater accuracy (+.038 to +.126 points). The best setting of the SSGBLUP relationship matrix was characterized by a weight of 30% for pedigree information in the genomic relationship matrix. SSGBLUP was the most valuable evaluation approach for the evaluation of carcass traits of Normande and Montbeliarde young bulls.

Genomic evaluation of regional dairy cattle breeds in single-breed and multibreed contexts

An important prerequisite for high prediction accuracy in genomic prediction is the availability of a large training population, which allows accurate marker effect estimation. This requirement is not fulfilled in case of regional breeds with a limited number of breeding animals. We assessed the efficiency of the current French routine genomic evaluation procedure in four regional breeds (Abondance, Tarentaise, French Simmental and Vosgienne) as well as the potential benefits when the training populations consisting of males and females of these breeds are merged to form a multibreed training population. Genomic evaluation was 5-11% more accurate than a pedigree-based BLUP in three of the four breeds, while the numerically smallest breed showed a < 1% increase in accuracy. Multibreed genomic evaluation was beneficial for two breeds (Abondance and French Simmental) with maximum gains of 5 and 8% in correlation coefficients between yield deviations and genomic estimated breeding values, when compared to the single-breed genomic evaluation results. Inflation of genomic evaluation of young candidates was also reduced. Our results indicate that genomic selection can be effective in regional breeds as well. Here, we provide empirical evidence proving that genetic distance between breeds is only one of the factors affecting the efficiency of multibreed genomic evaluation.

Short communication: Improving accuracy of predicting breeding values in Brazilian Holstein population by adding data from Nordic and French Holstein populations

The present study investigated the improvement of prediction reliabilities for 3 production traits in Brazilian Holsteins that had no genotype information by adding information from Nordic and French Holstein bulls that had genotypes. The estimated across-country genetic correlations (ranging from 0.604 to 0.726) indicated that an important genotype by environment interaction exists between Brazilian and Nordic (or Nordic and French) populations. Prediction reliabilities for Brazilian genotyped bulls were greatly increased by including data of Nordic and French bulls, and a 2-trait single-step genomic BLUP performed much better than the corresponding pedigree-based BLUP. However, only a minor improvement in prediction reliabilities was observed in nongenotyped Brazilian cows. The results indicate that although there is a large genotype by environment interaction, inclusion of a foreign reference population can improve accuracy of genetic evaluation for the Brazilian Holstein population. However, a Brazilian reference population is necessary to obtain a more accurate genomic evaluation.

A preliminary investigation into genotype x environment interaction in South African Holstein cattle for reproduction and production traits

The purpose of the study was to investigate a possible genotype by environment interaction in first calf South African Holstein cows for both production and reproduction traits. Data from 100 975 cows on a total mixed ration (TMR) and 22 083 pasture based cows were used. These cows were the progeny of 4 391 sires and 84 935 dams produced over a period of 11 generations. Traits analysed were milk production (corrected to a 305-day equivalent) and age at first calving (AFC). Both were recorded over a period of 30 years from 1980 - 2010. Production or AFC in each environment (TMR vs. pasture) was treated as a separate trait. Bivariate analyses, fitting an animal model using the ASREML software, were used to obtain genetic correlations between the traits measured in each environment. The fixed factors included were a concatenation of breeder-keeper-year for both milk production and AFC and age at first calving which was fitted as a linear regression for milk production. The random part consisted of the direct additive effects only. The genetic correlation for milk production measured in the two different environments was 0.90 (0.027) and that of age at first calving 0.28 (0.12). The heritability estimates for milk production were 0.23 (0.008) under the TMR system and 0.32 (0.015) for the pasture based system, while the estimates for AFC were 0.063 (0.005) and 0.055 (0.009), respectively. The rather large-scale effect in the heritability (0.23 → 0.32), as well as the correlation of less than one for milk production between the two environments, indicates that a G x E may exist. However, the low genetic correlation between the two environments for AFC is much more real and indicates that G x E should be taken into account when sire selection is performed.Keywords: Age at first calving, milk production, total mixed ration, pasture

Efficiency of multi-breed genomic selection for dairy cattle breeds with different sizes of reference population

Single-breed genomic selection (GS) based on medium single nucleotide polymorphism (SNP) density (~50,000; 50K) is now routinely implemented in several large cattle breeds. However, building large enough reference populations remains a challenge for many medium or small breeds. The high-density BovineHD BeadChip (HD chip; Illumina Inc., San Diego, CA) containing 777,609 SNP developed in 2010 is characterized by short-distance linkage disequilibrium expected to be maintained across breeds. Therefore, combining reference populations can be envisioned. A population of 1,869 influential ancestors from 3 dairy breeds (Holstein, Montbéliarde, and Normande) was genotyped with the HD chip. Using this sample, 50K genotypes were imputed within breed to high-density genotypes, leading to a large HD reference population. This population was used to develop a multi-breed genomic evaluation. The goal of this paper was to investigate the gain of multi-breed genomic evaluation for a small breed. The advantage of using a large breed (Normande in the present study) to mimic a small breed is the large potential validation population to compare alternative genomic selection approaches more reliably. In the Normande breed, 3 training sets were defined with 1,597, 404, and 198 bulls, and a unique validation set included the 394 youngest bulls. For each training set, estimated breeding values (EBV) were computed using pedigree-based BLUP, single-breed BayesC, or multi-breed BayesC for which the reference population was formed by any of the Normande training data sets and 4,989 Holstein and 1,788 Montbéliarde bulls. Phenotypes were standardized by within-breed genetic standard deviation, the proportion of polygenic variance was set to 30%, and the estimated number of SNP with a nonzero effect was about 7,000. The 2 genomic selection (GS) approaches were performed using either the 50K or HD genotypes. The correlations between EBV and observed daughter yield deviations (DYD) were computed for 6 traits and using the different prediction approaches. Compared with pedigree-based BLUP, the average gain in accuracy with GS in small populations was 0.057 for the single-breed and 0.086 for multi-breed approach. This gain was up to 0.193 and 0.209, respectively, with the large reference population. Improvement of EBV prediction due to the multi-breed evaluation was higher for animals not closely related to the reference population. In the case of a breed with a small reference population size, the increase in correlation due to multi-breed GS was 0.141 for bulls without their sire in reference population compared with 0.016 for bulls with their sire in reference population. These results demonstrate that multi-breed GS can contribute to increase genomic evaluation accuracy in small breeds.

Comparison between sire-maternal grandsire and animal models for genetic evaluation of longevity in a dairy cattle population with small herds

Survival analysis techniques for sire-maternal grandsire (MGS) and animal models were used to test the genetic evaluation of longevity in a Slovenian Brown cattle population characterized by small herds. Three genetic models were compared: a sire-MGS model for bulls and an approximate animal model based on estimated breeding values (EBV) from the sire-MGS model for cows, an animal model, and an animal model based on the estimated variance components from the sire-MGS model. In addition, modeling the contemporary group effect was defined as either a herd or a herd-year (HY) effect. With various restrictions on the minimum HY group size (from 1 to 10 cows per HY), changes in estimates of variance components, and consequently also in EBV, were observed for the sire-MGS and animal models. Variance of contemporary group effects decreased when an HY effect was fitted instead of a herd effect. In the case of a sire-MGS model, estimates of additive genetic variance were mostly robust to changes in minimum HY group size or fitting herd or HY effect, whereas they increased in the animal model when HY instead of herd effects was fitted, possibly revealing some confounding between cow EBV and contemporary group effect. Estimated heritabilities from sire-MGS models were between 0.091 and 0.119 and were mainly influenced by the restriction on the HY group size. Estimated heritabilities from animal models were higher: between 0.125 and 0.160 when herd effect was fitted and between 0.171 and 0.210 when HY effect was fitted. Rank correlations between the animal model and the approximate animal model based on EBV from the sire-MGS model were high: 0.94 for cows and 0.93 for sires when a herd effect was fitted and 0.90 for cows and 0.93 for sires when an HY effect was fitted. Validation performed on the independent validation data set revealed that the correlation between sire EBV and daughter survival were slightly higher with the approximate animal model based on EBV from the sire-MGS model compared with the animal model. The correlations between the sire EBV and daughter survival were higher when the model included an HY effect instead of a herd effect. To avoid confounding and reduce computational requirements, it is suggested that the approximate animal model based on EBV from the sire-MGS model and HY as a contemporary group effect is an interesting compromise for practical applications of genetic evaluation of longevity in cattle populations.

The Survival Kit: software to analyze survival data including possibly correlated random effects

The Survival Kit is a Fortran 90 Software intended for survival analysis using proportional hazards models and their extension to frailty models with a single response time. The hazard function is described as the product of a baseline hazard function and a positive (exponential) function of possibly time-dependent fixed and random covariates. Stratified Cox, grouped data and Weibull models can be used. Random effects can be either log-gamma or normally distributed and can account for a pedigree structure. Variance parameters are estimated in a Bayesian context. It is possible to account for the correlated nature of two random effects either by specifying a known correlation coefficient or estimating it from the data. An R interface of the Survival Kit provides a user friendly way to run the software.

Computational strategies for national integration of phenotypic, genomic, and pedigree data in a single-step best linear unbiased prediction

The single-step genomic BLUP (SSGBLUP) is a method that can integrate pedigree and genotypes at molecular markers in an optimal way. However, its present form (regular SSGBLUP) has a high computational cost (cubic in the number of genotyped animals) and may need extensive rewriting of genetic evaluation software. In this work, we propose several strategies to implement the single step in a simpler manner. The first one expands the single-step mixed-model equations to obtain equivalent equations from which the regular (including pedigree and records only) mixed-model equations are a subset. These new equations (unsymmetric extended SSGBLUP) have low computational cost, but require a nonsymmetric solver such as the biconjugate gradient stabilized method or successive underrelaxation, which is a variant of successive overrelaxation, with a relaxation factor lower than 1. In addition, we show a new derivation of the single-step method, which includes, as an extra effect, deviations from strictly polygenic breeding values. As a result, the same set of equations as above is obtained. We show that, whereas the new derivation shows apparent problems of nonpositive definiteness for certain covariance matrices, a proper equivalent model including imaginary effects always exists, leading always to the regular SSGBLUP mixed model equations. The system of equations can be solved (iterative SSGBLUP) by iterating between a pedigree and records evaluation and a genomic evaluation (each one solved by any iterative or direct method), whereas global iteration can use a block version of successive underrelaxation, which ensures convergence. The genomic evaluation can explicitly include marker or haplotype effects and possibly involve nonlinear (e.g., Bayesian by Markov chain Monte Carlo) methods. In a simulated example with 28,800 individuals and 1,800 genotyped individuals, all methods converged quickly to the same solutions. Using existing efficient methods with limited memory requirements to compute the products Gt and A(22)t for any t (where G and A(22) are genomic and pedigree relationships for genotyped animals, and t is a vector), all strategies can be converted to iteration on data procedures for which the total number of operations is linear in the number of animals + number of genotyped animals × number of markers.

Short communication: Imputation performances of 3 low-density marker panels in beef and dairy cattle

Low-density chips are appealing alternative tools contributing to the reduction of genotyping costs. Imputation enables researchers to predict missing genotypes to recreate the denser coverage of the standard 50K (∼50,000) genotype. Two alternative in silico chips were defined in this study that included markers selected to optimize minor allele frequency and spacing. The objective of this study was to compare the imputation accuracy of these custom low-density chips with a commercially available 3K chip. Data consisted of genotypes of 4,037 Holstein bulls, 1,219 Montbéliarde bulls, and 991 Blonde d'Aquitaine bulls. Criteria to select markers to include in low-density marker panels are described. To mimic a low-density genotype, all markers except the markers present on the low-density panel were masked in the validation population. Imputation was performed using the Beagle software. Combining the directed acyclic graph obtained with Beagle with the PHASEBOOK algorithm provides fast and accurate imputation that is suitable for routine genomic evaluations based on imputed genotypes. Overall, 95 to 99% of alleles were correctly imputed depending on the breed and the low-density chip used. The alternative low-density chips gave better results than the commercially available 3K chip. A low-density chip with 6,000 markers is a valuable genotyping tool suitable for both dairy and beef breeds. Such a tool could be used for preselection of young animals or large-scale screening of the female population.

Application of Bayesian least absolute shrinkage and selection operator (LASSO) and BayesCπ methods for genomic selection in French Holstein and Montbéliarde breeds

Recently, the amount of available single nucleotide polymorphism (SNP) marker data has considerably increased in dairy cattle breeds, both for research purposes and for application in commercial breeding and selection programs. Bayesian methods are currently used in the genomic evaluation of dairy cattle to handle very large sets of explanatory variables with a limited number of observations. In this study, we applied 2 bayesian methods, BayesCπ and bayesian least absolute shrinkage and selection operator (LASSO), to 2 genotyped and phenotyped reference populations consisting of 3,940 Holstein bulls and 1,172 Montbéliarde bulls with approximately 40,000 polymorphic SNP. We compared the accuracy of the bayesian methods for the prediction of 3 traits (milk yield, fat content, and conception rate) with pedigree-based BLUP, genomic BLUP, partial least squares (PLS) regression, and sparse PLS regression, a variable selection PLS variant. The results showed that the correlations between observed and predicted phenotypes were similar in BayesCπ (including or not pedigree information) and bayesian LASSO for most of the traits and whatever the breed. In the Holstein breed, bayesian methods led to higher correlations than other approaches for fat content and were similar to genomic BLUP for milk yield and to genomic BLUP and PLS regression for the conception rate. In the Montbéliarde breed, no method dominated the others, except BayesCπ for fat content. The better performances of the bayesian methods for fat content in Holstein and Montbéliarde breeds are probably due to the effect of the DGAT1 gene. The SNP identified by the BayesCπ, bayesian LASSO, and sparse PLS regression methods, based on their effect on the different traits of interest, were located at almost the same position on the genome. As the bayesian methods resulted in regressions of direct genomic values on daughter trait deviations closer to 1 than for the other methods tested in this study, bayesian methods are suggested for genomic evaluations of French dairy cattle.

Solution of multiple trait animal models with missing data on some traits

SUMMARY

In multiple trait animal model evaluations, several transformations (canonical, triangular, combined) can be used to decrease the size of the mixed model equations or to increase their sparsity. A simple method based on an EM argument and replacing missing records by their expectation given the current parameters allows the use of the canonical transformation in situations where data are missing and selection is ignorable. The convergence behavior of these different approaches were compared on real data sets simulating different missing patterns. The combined transformation is always better than the triangular transformation. The extended version of the canonical transformation clearly leads to the fastest convergence, in terms of overall CPU time, especially when a reduced animal model is used (2 to 3 times faster than the triangular transformation) and when more traits are considered simultaneously. RÉSUMÉ: Solution des modèles animales multicaractères avec fichiérs manquantes Dans les évaluations multicaractères de type modèle animal, diverses transformations (canonique, triangulaire, combinée) peuvent être utilisées pour diminuer la taille du système d'équations du modèle mixte ou pour en accroître le nombre d'éléments nuls. Une méthode simple basée sur un raisonnement de type EM et remplaçant les données manquantes par leur espérance sachant la valeur courante des paramètres permet l'utilisation de la transformation canonique dans des situations avec données manquantes et où le processus de sélection peut être ignoré. Les vitesses de convergence de ces différentes approches ont été comparées ` partir de fichiers réels simulant différent types de données manquantes. La transformation combinée s'est revelée toujours meilleure que la transformation triangulaire. La version étendue de la transformation canonique conduit clairement ` la convergence la plus rapide, tout spécialement quand un modèle animal réduit est utilisé (2 ` 3 fois plus rapide que la transformation triangulaire) et quand un grand nombre de caractères sont considérés simultanément. ZUSAMMENFASSUNG: Lósung bei Mehrmerkmalsmodellen und teilweise fehlenden Daten bei einzelnen Merkmalen Beim Mehrmerkmal-Tiermodell können mehrere Transformationen (kanonisch, Winkel, kombiniert) zur Reduktion der Gleichungszahl oder zur Steigerung der null Elemente verwendet werden. Eine einfache Methode, die auf EM-Schlußfolgerungen beruht und fehlende Beobachtungen mit ihren Erwartungswerten (aufgrund gegebener Parameter) ersetzt, gestattet Verwendung kanonischer Transformation bei teilweise fehlenden Daten und vernachlässigbarer Selektion. Das Konvergenzverhalten verschiedener Ansätze wurde an realem Datenmaterial mit simulierten Fehlmustern verglichen. Die erweiterte Transformation ist immer besser als die Winkeltransformation, und diese kanonische Transformation führt hinsichtlich CPU-Zeit zur schnellsten Konvergenz, besonders wenn ein reduziertes Tiermodell mit mehreren Merkmalen verwendet wurde (2- bis 3 mal schneller als Winkeltransformation).

A comparison of partial least squares (PLS) and sparse PLS regressions in genomic selection in French dairy cattle

Genomic selection involves computing a prediction equation from the estimated effects of a large number of DNA markers based on a limited number of genotyped animals with phenotypes. The number of observations is much smaller than the number of independent variables, and the challenge is to find methods that perform well in this context. Partial least squares regression (PLS) and sparse PLS were used with a reference population of 3,940 genotyped and phenotyped French Holstein bulls and 39,738 polymorphic single nucleotide polymorphism markers. Partial least squares regression reduces the number of variables by projecting independent variables onto latent structures. Sparse PLS combines variable selection and modeling in a one-step procedure. Correlations between observed phenotypes and phenotypes predicted by PLS and sparse PLS were similar, but sparse PLS highlighted some genome regions more clearly. Both PLS and sparse PLS were more accurate than pedigree-based BLUP and generally provided lower correlations between observed and predicted phenotypes than did genomic BLUP. Furthermore, PLS and sparse PLS required similar computing time to genomic BLUP for the study of 6 traits.

Genomic selection in French dairy cattle

Genomic selection is implemented in French Holstein, Montbéliarde, and Normande breeds (70%, 16% and 12% of French dairy cows). A characteristic of the model for genomic evaluation is the use of haplotypes instead of single-nucleotide polymorphisms (SNPs), so as to maximise linkage disequilibrium between markers and quantitative trait loci (QTLs). For each trait, a QTL-BLUP model (i.e. a best linear unbiased prediction model including QTL random effects) includes 300–700 trait-dependent chromosomal regions selected either by linkage disequilibrium and linkage analysis or by elastic net. This model requires an important effort to phase genotypes, detect QTLs, select SNPs, but was found to be the most efficient one among all tested ones. QTLs are defined within breed and many of them were found to be breed specific. Reference populations include 1800 and 1400 bulls in Montbéliarde and Normande breeds. In Holstein, the very large reference population of 18 300 bulls originates from the EuroGenomics consortium. Since 2008, ~65 000 animals have been genotyped for selection by Labogena with the 50k chip. Bulls genomic estimated breeding values (GEBVs) were made official in June 2009. In 2010, the market share of the young bulls reached 30% and is expected to increase rapidly. Advertising actions have been undertaken to recommend a time-restricted use of young bulls with a limited number of doses. In January 2011, genomic selection was opened to all farmers for females. Current developments focus on the extension of the method to a multi-breed context, to use all reference populations simultaneously in genomic evaluation.

Effect of imputing markers from a low-density chip on the reliability of genomic breeding values in Holstein populations

The purpose of this study was to investigate the imputation error and loss of reliability of direct genomic values (DGV) or genomically enhanced breeding values (GEBV) when using genotypes imputed from a 3,000-marker single nucleotide polymorphism (SNP) panel to a 50,000-marker SNP panel. Data consisted of genotypes of 15,966 European Holstein bulls from the combined EuroGenomics reference population. Genotypes with the low-density chip were created by erasing markers from 50,000-marker data. The studies were performed in the Nordic countries (Denmark, Finland, and Sweden) using a BLUP model for prediction of DGV and in France using a genomic marker-assisted selection approach for prediction of GEBV. Imputation in both studies was done using a combination of the DAGPHASE 1.1 and Beagle 2.1.3 software. Traits considered were protein yield, fertility, somatic cell count, and udder depth. Imputation of missing markers and prediction of breeding values were performed using 2 different reference populations in each country: either a national reference population or a combined EuroGenomics reference population. Validation for accuracy of imputation and genomic prediction was done based on national test data. Mean imputation error rates when using national reference animals was 5.5 and 3.9% in the Nordic countries and France, respectively, whereas imputation based on the EuroGenomics reference data set gave mean error rates of 4.0 and 2.1%, respectively. Prediction of GEBV based on genotypes imputed with a national reference data set gave an absolute loss of 0.05 in mean reliability of GEBV in the French study, whereas a loss of 0.03 was obtained for reliability of DGV in the Nordic study. When genotypes were imputed using the EuroGenomics reference, a loss of 0.02 in mean reliability of GEBV was detected in the French study, and a loss of 0.06 was observed for the mean reliability of DGV in the Nordic study. Consequently, the reliability of DGV using the imputed SNP data was 0.38 based on national reference data, and 0.48 based on EuroGenomics reference data in the Nordic validation, and the reliability of GEBV using the imputed SNP data was 0.41 based on national reference data, and 0.44 based on EuroGenomics reference data in the French validation.

Nongenetic effects and genetic parameters for length of productive life of Holstein cows in Hokkaido, Japan

Records of Holstein dairy cows in Hokkaido, Japan, were used to study the effects of environmental factors on length of productive life and to estimate genetic parameters for length of productive life. Each record was assigned to 1 of 3 data sets depending on the percentage of type-scored cows in the herd. This percentage was considered to partly reflect the management policy in each herd, in particular regarding culling. The A, B, and C data sets consisted of herds with none, less than 60%, and more than 60% of type-scored cows, respectively, and included 158,719, 787,598, and 131,499 records, respectively. Analyses of length of productive life were separately carried out on each data set using the Survival Kit software (Version 5.0). Nonparametric hazards estimates and the shape parameters of the baseline Weibull distribution differed between the 3 data sets. A cow having a sire originating from the United States or Canada had a relatively lower risk of being culled than a cow having Japanese sire in data set C. However, in data set A, a cow having a Canadian sire had a higher relative risk than a cow having a Japanese sire. The herd-year variance for data set A was about twice as large as for data set C. In contrast, the sire variance for data set A was about 40% of the one for data set C. As a result, heritability varied across data sets from 0.046 to 0.134. The results of this study suggest that it is important to consider factors related to herd management policy, such as the percentage of type-scored cows, in genetic analyses on length of productive life of Holstein cows in Hokkaido, Japan.

Validation of prognostic indices using the frailty model

A major issue when proposing a new prognostic index is its generalisibility to daily clinical practice. Validation is therefore required. Most validation techniques assess whether "on average" the results obtained by the prognostic index in classifying patients in a new sample of patients are similar to the results obtained in the construction set. We introduce a new important aspect of the generalisibility of a prognostic index: the heterogeneity of the prognostic index risk group hazard ratios over different centers. If substantial variability between centers exists, the prognostic index may have no discriminatory capability in some of the centers. To model such heterogeneity, we use a frailty model including a random center effect and a random prognostic index by center interaction. Statistical inference is based on a Bayesian approach using a Laplacian approximation for the marginal posterior distribution of the variances of the random effects. We investigate different ways to summarize the information available from this marginal posterior distribution. Our approach is applied to a real bladder cancer database for which we demonstrate how to investigate and interpret heterogeneity in prognostic index effect over centers.

Rainbow trout resistance to bacterial cold-water disease is moderately heritable and is not adversely correlated with growth

The objectives of this study were to estimate the heritabilities for and genetic correlations among resistance to bacterial cold-water disease and growth traits in a population of rainbow trout (Oncorhynchus mykiss). Bacterial cold-water disease, a chronic disease of rainbow trout, is caused by Flavobacterium psychrophilum. This bacterium also causes acute losses in young fish, known as rainbow trout fry syndrome. Selective breeding for increased disease resistance is a promising strategy that has not been widely used in aquaculture. At the same time, improving growth performance is critical for efficient production. At the National Center for Cool and Cold Water Aquaculture, reducing the negative impact of diseases on rainbow trout culture and improving growth performance are primary objectives. In 2005, when fish averaged 2.4 g, 71 full-sib families were challenged with F. psychrophilum and evaluated for 21 d. Overall survival was 29.3% and family rates of survival varied from 1.5 to 72.5%. Heritability of postchallenge survival, an indicator of disease resistance, was estimated to be 0.35 +/- 0.09. Body weights at 9 and 12 mo posthatch and growth rate from 9 to 12 mo were evaluated on siblings of the fish in the disease challenge study. Growth traits were moderately heritable, from 0.32 for growth rate to 0.61 for 12-mo BW. Genetic and phenotypic correlations between growth traits and resistance to bacterial cold-water disease were not different from zero. These results suggest that genetic improvement can be made simultaneously for growth and bacterial cold-water disease resistance in rainbow trout by using selective breeding.

Validation of an Approximate REML Algorithm for Parameter Estimation in a Multitrait, Multiple Across-Country Evaluation Model: A Simulation Study

A multitrait, multiple across-country evaluation (MT-MACE) model permitting a variable number of correlated traits per country allows international genetic evaluation models to more closely match national models. Before the MT-MACE evaluation can be applied, genetic (co)variance components within and across country must be estimated. An approximate REML algorithm for parameter estimation was developed and was validated via simulation. This method is based on the expectation maximization REML (EM-REML) algorithm. Because obtaining the inverse of co-efficient matrix is not usually feasible for large amounts of data, an algorithm using the multiple-trait effective daughter contribution (EDC) is proposed to provide approximate diagonal elements of the inverse matrix. The accuracy of the approximate EM-REML was tested with simulated data and compared with an average information REML (AI-REML) from available software. Two simulation studies were performed. First, data of 2 countries were simulated using a single-trait model. Estimates of across-country genetic correlations with the developed algorithm were unbiased and very precise. The precision, however, depended on the percentage of bulls with data in both countries. The results obtained with the approximate EM-REML software were very close to those obtained with the AI-REML software regarding estimated genetic correlations and bulls' estimated breeding values. The second simulation assumed a multiple trait model and the same number of traits, pedigree structure, EDC, and pattern of missing records as for actual observations for milk yield obtained from French and German national Holstein evaluations. As with the single-trait scenarios, the approximate EM-REML gave nearly unbiased and very precise estimates of within- and across-country genetic correlations. The results obtained in both simulation studies confirmed the suitability of the MT-MACE model and approximate EM-REML software in a wide range of situations. Even when the genetic trend was incorrectly estimated by the national evaluations, a joint analysis including a time effect in the MT-MACE model adequately corrected for this bias.

A stochastic simulation study on validation of an approximate multitrait model using preadjusted data for prediction of breeding values

Three different models for prediction of breeding values were compared in a stochastic simulation study of a dairy cattle population of 100,000 cows. The simulation was done in 2 steps. The first step involved 15 yr of selection using breeding values obtained in a univariate model for production and a trivariate model for mastitis occurrence, udder depth, and somatic cell score, in which production and mastitis occurrence were included in the breeding goal. This was done to create an initial population that had already been under selection. The second step consisted of 20 replicates of 4 different scenarios set up to make it possible to compare the different models. Two scenarios were based on univariate evaluations and one for udder health traits on trivariate evaluations, with 2 different breeding goals. In another scenario, an approximate multitrait model using preadjusted data in a 2-step procedure was used and in the last scenario, a complete linear multitrait model was carried out. Differences in genetic response in total merit over the last 15 yr of selection were compared and used to rank the models. The linear multitrait model gave the highest regression coefficient of true genetic values on year (3.073 +/- 0.069 in economic units), and this was significantly better than for the approximate multitrait model (2.819 +/- 0.047), which again was significantly better than for the univariate approach (2.672 +/- 0.060). The linear multitrait model cannot be applied to nearly the same number of traits as the approximate model. Therefore, the approximate model with developments handling breeding values from more complex models than presented in this paper is an option of choice in countries providing total merit indices that combine many traits because it does not neglect correlations between these traits.

An improved model for the French genetic evaluation of dairy bulls on length of productive life of their daughters

Functional longevity of dairy cows has been routinely evaluated in France since 1997 using a survival analysis model. Recently, we proposed a genetic trend validation test that could be used before including national data in an international evaluation of bulls on longevity of their daughters. Its application to the French Holstein data revealed a large overestimation of the genetic trend. It was found that the bias is the result of a change in the baseline hazard rate over time. A new proportional hazards model is proposed which accounts for this change. In the new model, the baseline is described as a stratified, piecewise Weibull hazard function within lactation, i.e. a function of the number of days since the most recent calving. Stratification is within year and parity. Different Weibull hazard functions are used over four periods: 0 to 270 days, 271 to 380 days, 381 days to day when dried, dry period until the next calving. The non-genetic effects included in the model were slightly different from the previous one. In particular the interaction effects between the within herd-year class of production and lactation number × stage of lactation on the one hand and year-season were accounted for. The estimated genetic variance was smaller than with the old model. The new genetic trend is almost flat. An illustration of the efficiency of selection on the estimated breeding values for longevity is presented.

Trends in milk production, calving rate and survival of cows in 14 Irish dairy herds as a result of the introgression of Holstein-Friesian genes

Trends in milk production, calving rates, and survival were monitored on a potential 5580 primiparous and multiparous Holstein-Friesian dairy cows across 14 Irish seasonal spring-calving dairy farms between the years 1990 and 2001. Over this period calving rate to first service (CALV1) reduced by 0·96% per year (55 to 44%;P< 0·001), calving rate to first and second service (CALV12) reduced by 0·84% per year ( 77 to 70%;P< 0·001) and herd average parity number reduced by 0·10 lactation per year (4·3 to 3·5;P<0·001). The proportion of North American Holstein Friesian (NAHF) genes in the cows increased by 5·5% per year (8 to 63%;P<0·001), while pedigree index for milk yield (PIMILK) of the cows increased by 25 kg per year (P<0·001). The predicted difference of the sires of the cows for calving interval and survival increased by 0·5 days (P<0·001) and reduced by 0·12% (P<0·001) per year, respectively. A negative association was found between increased phenotypic milk yield, NAHF and PIMILKand reduced calving rates as assessed by CALV1 and CALV12. Increased proportion of NAHF genes exhibited a negative effect on survival (P<0·001) whereas increased levels of heterosis had a positive impact on survival (P<0·001). The results of the present study indicate that in seasonal calving herds in Ireland a need for direct selection on traits related to fertility and survival is required to arrest and reverse the declining trends in calving rates and survival.

Short communication: genetic evaluation of the interval from first to last insemination with survival analysis and linear models

Sire breeding values for the interval between the first and last insemination were predicted using 4 proportional hazards models (survival analyses) and 2 linear mixed models to determine which would result in a more accurate genetic evaluation. A stochastic simulation describing the reproductive cycle of first-parity cows was conducted, in which true breeding values for conception rate were created. The model included the effects of sire and herd. The highest correlations between true breeding values for conception rate and breeding values for the interval between first and last insemination predicted by the survival analysis model and the linear model were 0.803 and 0.744, respectively. The results showed that when pregnancy status was known, survival models were more accurate than linear models to predict breeding values for conception rate when using observations on the interval between first and last insemination.