R. Rekaya

Use of test day yields for the genetic evaluation of production traits in Holstein-Friesian cattle

Abstract Bayesian methods and Gibbs sampling techniques have been applied to estimate genetic parameters for test-day (TD) yields in the Spanish Holstein-Friesian population. Three models were analyzed: (a) multitrait model on successive TD yields within the first lactation; (b) multitrait model on the first three lactations considering TD yields as repeated measures within lactations; (c) random regression model (RRM) on first lactation TD yield. Two alternative RRM were adjusted, RRM1 considered random regression on the genetic effects only, RRM2 included random regressions for the genetic and permanent environmental effects and allowed for heterogeneous residual variances. In model (a), heritabilities tended to be larger in middle lactation and genetic correlations among TD measures were large (>0.80). Large genetic correlations among lactations (>0.89) and heterogeneous variances for first vs. other lactations were found for model (b). RRM1 was found to be superior to the simple repeatability model (b) in terms of reducing residual variance. However, RRM1 produced very large estimates of the genetic variance at the beginning and end of the lactation. Genetic and environmental variances estimated under RRM2 tended to be close to the multitrait model (a). Large discrepancies in the genetic correlations among daily yields with respect to the one observed from the multitrait approach were found for RRM1 and, to a lesser extent, for RRM2.

Bayesian analysis of lifetime performance and prolificacy in Landrace sows using a linear mixed model with censoring

Abstract Factors affecting variation of length of productive life (LPL) and lifetime prolificacy (LTP) in Landrace sows were investigated. Herd life and prolificacy records were from 2616 daughters of 301 sires born in a nucleus herd between 1990 and 1996. Records from sows sold to other farms for production purposes were treated as randomly censored. Factors studied were year–season of herd entry, age at herd entry, litter size at first parity (for LPL) and sire of the sow. Additional censoring rates of 25 and 35% were created to assess influence of censoring on inferences. LPL, log(LPL) and LTP were analyzed using a linear mixed model with censoring. Age at herd entry did not affect the traits studied. Sows with smaller litters at first parity had a higher risk of being culled. Posterior means of heritability of LTP, LPL and log-LPL were 0.22–0.25. Intra-trait correlations between sire evaluations at the three censoring rates ranged between 0.69 and 0.96. Estimates of sire transmitting abilities obtained with censored records removed from the analysis were in less agreement with evaluations obtained with the actual data set than those found with the artificial censoring rates.

Assessment of environmental descriptors for studying genotype by environment interaction

Abstract Access to individual performance records opens up possibilities for treatment of genotype by environment interaction in international genetic evaluations. The ability to distinguish similar from dissimilar environments is thus important. Reaction norms were used in this study to evaluate several variables for their suitability to classify production environments for studies on genotype by environment interaction. Reaction norms describe the phenotypic expression of a genotype as a function of the environment, and can be modelled by random regression on environmental descriptors. Fifteen variables that measure aspects of management, genetic composition and climate were computed on herd level. Suitability of each variable to detect genotype by environment interaction was assessed through likelihood ratio tests for significant linear or quadratic random regression terms. First lactation records from approximately 40u2008000 Guernsey cows in four countries (Australia, Canada, USA and Republic of South Africa) were used. Variables with significant effect were: herd size, within-herd standard deviation of lactation yield, peak milk yield, persistency, days to peak production, calving pattern, age at first calving, rate of maturity, and annual rainfall. Genetic correlation between extreme environments for milk peak yield, within-herd standard deviation and annual rainfall were lower than 0.91, indicating that re-ranking of animals may occur.

Genetic variation of lactation curves in dairy sheep: a Bayesian analysis of Wood’s function

Abstract Test-day milk yield records (1752) of 451 first-lactation ewes in four flocks from Nebraska and Wisconsin were analyzed. Breeds included crosses among Dorset, Romanov, Targhee, Rideau Arcott, Polypay, Booroola Merino, Suffolk, Rambouillet, Finnsheep and East Friesian. The objective was to investigate genetic variation of features of lactation curves using a three-stage Bayesian hierarchy. Wood’s model, E ( y | a , b , c , t )= at b exp(− ct ), was used as first-stage; a indicates level of starting yield, and parameters b and c describe ascending and descending phases of the lactation curve; t is time. The second-stage model described variation between ewes. It had a linear structure including flock-year, age at lambing, type of lambing, length of suckling period and the expected percentage of genes of East Friesian origin as fixed effects, plus random additive genetic effects. The third stage included prior distributions for all unknown parameters. Gibbs sampling and the Metropolis–Hastings (MH) algorithm were employed for drawing samples from posterior distributions of parameters. A chain of 60u2008000 iterations (burn-in of 11u2008000) was used. Acceptance rate with MH was 24%. Residual variance (posterior mean) was 0.042 kg 2 . Posterior means of heritability of a , b and c were 0.35, 0.35 and 0.27, respectively. Estimates indicate that part of the variation in lactation curves between ewes is heritable. Genetic correlations were negligible, suggesting flexible scope for modifying lactation curves via genetic selection

Hierarchical nonlinear model for persistency of milk yield in the first three lactations of Holsteins

Abstract A nonlinear model, Wood’s function, was used to describe the shape of the lactation curve in the first three lactations of Holstein cows. Wood’s function was reparameterized to include the logarithm of persistency as a parameter. The data consisted of 65u2008677 test-day records of 2875 cows. All cows were required to have first lactation test-day milk yield records. A three-stage Bayesian hierarchical nonlinear model was implemented. The first stage described within-cow variation and the second stage accounted for between-animal variation. The third stage consisted of the priors used. Negative genetic correlations between the first (measure of yield) and second (related to the increasing yield phase of lactation) parameters of Wood’s function were found for all three lactations: −0.59, −0.55 and −0.39 for first, second and third lactations, respectively. The genetic correlation between the first parameter of Wood’s function and log-persistency was negative in each of the three lactations (−0.20, −0.31 and −0.31). The genetic correlation between the second parameter and log-persistency was low (0.06, 0.09, 0.03 for each of the lactation). Heritabilities of all parameters tended to decrease with parity, mainly due to an increase in residual variance. Heritabilities of persistency were 0.17, 0.16 and 0.14 for first, second and third lactations, respectively. The genetic correlation between persistency in the three lactations was 0.26 (first and second), 0.32 (second and third) and 0.23 (first and third). Residual correlations followed a similar pattern, but tended to be larger in absolute value than genetic correlations.

Assessment of heterogeneity of residual variances using changepoint techniques

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100 744 test-day records of 10 869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T1 and T2, (0 <T1 <T2 <tmax), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t() in the lactation phase i was modeled as: for (i = 1, 2, 3), where λιis a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20 000 iterations, 40 000 samples were drawn to estimate posterior features. The posterior modes of T1, T2, λ1, λ2, λ3, , , were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg2, respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg2 at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.

Comparison of restricted selection strategies: an application to selection of cashmere goats

Abstract The problem of restricted selection was investigated. The objective was to compare several strategies to change one trait whilst attempting to restrict changes in a correlated trait. To do so, seven selection strategies to impose a restriction on fibre quality while maximising fibre quantity were studied. A closed nucleus scheme for Cashmere goats was generated using stochastic computer simulation. The nucleus consisted of 200 breeding females. Number of males (ten) and mating ratio were constant except for those strategies in which linear programming and mate selection were applied. Unrestricted or restricted best lineal unbiased prediction (BLUP) were used for evaluation purposes. Selection was carried out during seven years. Comparisons were made in terms of achieved genetic response, variances of response and cumulative level of inbreeding. Most strategies successfully restricted fibre diameter; however, the achieved responses for quantity of fibre and variance of responses associated with restricted trait varied greatly among strategies. Restricted BLUP in two steps resulted in a similar response for fibre quantity and a better tool to restrict fibre diameter than regular Restricted BLUP. The use of linear programming techniques for male selection and Restricted BLUP for females selection appeared to be the most appealing strategy. This strategy was a good compromise between maintenance of the restriction and achieved genetic response for fibre quantity. Resulting cumulative level of inbreeding varied from 0.045 to 0.101 among strategies. There was no clear pattern of the relationship between level of inbreeding and variance of response.

Model comparison for genetic evaluation of milk yield in Uruguayan Holsteins

Three models for genetic evaluation of milk yield of Uruguayan Holstein cattle were compared using 159 169 lactation records from 81 928 cows calving between 1989 and 1998. Model I included the effects of herd-year-season, parity by age group, additive genetic merit, permanent environment, and residual. Model II included all effects in Model I, as well as number of days open and length of the dry period. Model III included all factors in Model II, and it accommodated heterogeneity of variance within contemporary groups (CG) through a pre-adjustment of the data based on empirical Bayes estimates of the CG variance. Estimates of heritability for milk yield were 0.23, 0.24 and 0.25, and estimates of repeatability were 0.55, 0.56 and 0.57 for Models I, II and III, respectively. Models were contrasted by examining changes in sire ranking and by a cross-validation procedure, based on the ability of the models to predict first, second and later lactations. Data were divided into two subsets, and records from one subset were predicted using location parameters estimated from the other subset. A resampling procedure was used to minimise the dependency on the sample structure. Correspondence between observed and predicted values was assessed in terms of square root of empirical mean square errors of prediction, percentage squared bias and the coefficient of determination ‘R2’. Adjustment for heterogeneous CG variance had a marked effect on rankings of animals, especially elite cows, where correlations between solutions from Models I and II versus Model III ranged from 0.53 to 0.80. The percentage of animals selected in common by each pair of models decreased when selection intensity increased. Cross-validation analyses suggested that an assumption of heterogeneity of CG variance is tenable, especially in later lactations, whereas some doubts arise in first lactations, most probably due to the data structure used in the analyses.