Comparison of random regression test-day models for Polish Black and White cattle

Test-day milk yields of first-lactation Black and White cows were used to select the model for routine genetic evaluation of dairy cattle in Poland. The population of Polish Black and White cows is characterized by small herd size, low level of production, and relatively early peak of lactation. Several random regression models for first-lactation milk yield were initially compared using the “percentage of squared bias” criterion and the correlations between true and predicted breeding values. Models with random herd-test-date effects, fixed age-season and herd-year curves, and random additive genetic and permanent environmental curves (Legendre polynomials of different orders were used for all regressions) were chosen for further studies. Additional comparisons included analyses of the residuals and shapes of variance curves in days in milk. The low production level and early peak of lactation of the breed required the use of Legendre polynomials of order 5 to describe age-season lactation curves. For the other curves, Legendre polynomials of order 3 satisfactorily described daily milk yield variation. Fitting third-order polynomials for the permanent environmental effect made it possible to adequately account for heterogeneous residual variance at different stages of lactation.     

Genetic parameters for a multiple-trait multiple-lactation random regression test-day model in Italian Holsteins

The objectives of this study were to estimate variance components for test-day milk, fat, and protein yields and average daily SCS in 3 subsets of Italian Holsteins using a multiple-trait, multiple-lactation random regression test-day animal model and to determine whether a genetic heterogeneous variance adjustment was necessary. Data were test-day yields of milk, fat, and protein and SCS (on a log₂ scale) from the first 3 lactations of Italian Holsteins collected from 1992 to 2002. The 3 subsets of data included 1) a random sample of Holsteins from all herds in Italy, 2) a random sample of Holsteins from herds using a minimum of 75% foreign sires, and 3) a random sample of Holsteins from herds using a maximum of 25% foreign sires. Estimations of variances and covariances for this model were achieved by Bayesian methods using the Gibbs sampler. Estimated 305-d genetic, permanent environmental, and residual variance was higher in herds using a minimum of 75% foreign sires compared with herds using a maximum of 25% foreign sires. Estimated average daily heritability of milk, fat, and protein yields did not differ among subsets. Heritability of SCS in the first lactation differed slightly among subsets and was estimated to be the highest in herds with a maximum of 25% foreign sire use (0.19 ± 0.01). Genetic correlations across lactations for milk, fat, and protein yields were similar among subsets. Genetic correlations across lactations for SCS were 0.03 to 0.08 higher in herds using a minimum of 75% or a maximum of 25% foreign sires, compared with herds randomly sampled from the entire population. Results indicate that adjustment for heterogeneous variance at the genetic level based on the percentage of foreign sire use should not be necessary with a multiple-trait random regression test-day animal model in Italy.     

Genetic parameters for tunisian holsteins using a test-day random regression model

Genetic parameters of milk, fat, and protein yields were estimated in the first 3 lactations for registered Tunisian Holsteins. Data included 140,187; 97,404; and 62,221 test-day production records collected on 22,538; 15,257; and 9,722 first-, second-, and third-parity cows, respectively. Records were of cows calving from 1992 to 2004 in 96 herds. (Co)variance components were estimated by Bayesian methods and a 3-trait-3-lactation random regression model. Gibbs sampling was used to obtain posterior distributions. The model included herd × test date, age × season of calving × stage of lactation [classes of 25 days in milk (DIM)], production sector × stage of lactation (classes of 5 DIM) as fixed effects, and random regression coefficients for additive genetic, permanent environmental, and herd-year of calving effects, which were defined as modified constant, linear, and quadratic Legendre coefficients. Heritability estimates for 305-d milk, fat and protein yields were moderate (0.12 to 0.18) and in the same range of parameters estimated in management systems with low to medium production levels. Heritabilities of test-day milk and protein yields for selected DIM were higher in the middle than at the beginning or the end of lactation. Inversely, heritabilities of fat yield were high at the peripheries of lactation. Genetic correlations among 305-d yield traits ranged from 0.50 to 0.86. The largest genetic correlation was observed between the first and second lactation, potentially due to the limited expression of genetic potential of superior cows in later lactations. Results suggested a lack of adaptation under the local management and climatic conditions. Results should be useful to implement a BLUP evaluation for the Tunisian cow population; however, results also indicated that further research focused on data quality might be needed.     

Genetic analysis of milk production traits of polish black and white cattle using large-scale random regression test-day models

Genetic parameters for milk, fat, and protein yield and persistency in the first 3 lactations of Polish Black and White cattle were estimated. A multiple-lactation model was applied with random herd-test-day effect, fixed regressions for herd-year and age-season of calving, and random regressions for the additive genetic and permanent environmental effects. Three data sets with slightly different edits on minimal number of days in milk and the size of herd-year class were used. Each subset included more than 0.5 million test-day records and more than 58,000 cows. Estimates of covariance components and genetic parameters for each trait were obtained by Bayesian methods using the Gibbs sampler. Due to the large size and a good structure of the data, no differences in estimates were found when additional criteria for record selection were applied. More than 95% of the genetic variance for all traits and lactations was explained by the first 2 principal components, which were associated with the mean yield and lactation persistency. Heritabilities of 305-d milk yield in the first 3 lactations (0.18, 0.16, 0.17) were lower than those for fat (0.12, 0.11, 0.12) and protein (0.13, 0.14, 0.15). Estimates of daily heritabilities increased in general with days in milk for all traits and lactations, with no apparent abnormalities at the beginning or end of lactation. Genetic correlations between yields in different lactations ranged from 0.74 (fat yield in lactations 1 and 3) to 0.89 (milk yield in lactations 2 and 3). Persistency of lactation was defined as the linear regression coefficient of the lactation curve. Heritability of persistency increased with lactation number for all traits and genetic correlations between persistency in different lactations were smaller than those for 305d yield. Persistency was not genetically correlated with the total yield in lactation.     

Prediction of daily milk, fat, and protein production by a random regression test-day model

Test-day genetic evaluation models have many advantages compared with those based on 305-d lactations; however, the possible use of test-day model (TDM) results for herd management purposes has not been emphasized. The aim of this paper was to study the ability of a TDM to predict production for the next test day and for the entire lactation. Predictions of future production and detection of outliers are important factors for herd management (e.g., detection of health and management problems and compliance with quota). Because it is not possible to predict the herd-test-day (HTD) effect per se, the fixed HTD effect was split into 3 new effects: a fixed herd-test month-period effect, a fixed herd-year effect, and a random HTD effect. These new effects allow the prediction of future production for improvement of herd management. Predicted test-day yields were compared with observed yields, and the mean prediction error computed across herds was found to be close to zero. Predictions of performance records at the herd level were even more precise. Discarding herds enrolled in milk recording for <1 yr and animals with very few tests in the evaluation file improved correlations between predicted and observed yields at the next test day (correlation of 0.864 for milk in first-lactation cows as compared with a correlation of 0.821 with no records eliminated). Correlations with the observed 305-d production ranged from 0.575 to 1 for predictions based on 0 to 10 test-day records, respectively. Similar results were found for second and third lactation records for milk and milk components. These findings demonstrate the predictive ability of a TDM.     

Assessment of homogeneity vs. heterogeneity of residual variance in random regression test-day models in a Bayesian analysis

Test-day first-lactation milk yields from Holstein cows were analyzed with a set of random regression models based on Legendre polynomials of varying order on additive genetic and permanent environmental effects. Homogeneity and heterogeneity of residual variance, assuming three and 30 arbitrary measurement error classes of different length were considered. Unknown parameters were estimated within a Bayesian framework. Bayes factors and a checking function for the cross-validation predictive densities of the data were the tools chosen for selecting among competing models. Residual variances obtained from 30 arbitrary intervals were nearly constant between d 70 and 300 and tended to increase towards the extremes of the lactation, especially at the onset. In early lactation, the temporary measurement errors were found to be larger and highly variable. A high order of the regression submodels employed for modeling the permanent environmental deviations tended to strongly correct the heterogeneity of the residual variance. Accordingly, the assumption of homogeneity of residual variance was the most plausible specification under both comparison criteria when the number of random regression coefficients was set to five. Otherwise, the heterogeneity assumption, using three or 30 error classes, was better supported, depending on the criterion and on the order of the submodel fitted for the permanent environmental effect.     

Random regression analysis of milk yield and milk composition in the first and second lactations of Murciano-Granadina goats

Records from the milk recording scheme of Spanish Murciano-Granadina goats were studied to estimate genetic (co)variance components and breeding values throughout the first and second lactations. The data used consisted of 49,696 monthly test-day records of milk (MY), protein (PY), fat (FY), and dry matter (DMY) yields from 5,163 goats, distributed in 20 herds, offspring of 2,086 does and 206 bucks. These records were analyzed by 2-trait random regression models (RRM) and a repeatability test-day model (RTDM). At the middle of lactation, heritability estimates for MY, DMY, and FY obtained with RTDM were larger than those estimated with RRM, and the opposite was true for PY. The RRM estimates of heritability for MY, FY, and PY were very similar throughout the trajectories of both lactations. Heritability estimates for DMY decreased through the lactation period. The genetic correlations between the first and second lactation records estimated for all traits by RRM were positive and ranged from 0.43 to 0.80 throughout the lactation curves. The correlation between BV estimated with RTDM and RRM was 0.742 for MY and 0.664 for DMY. The RRM could be a useful alternative to RTDM for the prediction of BV in this breed.     

Derivation and calculation of approximate reliabilities and daughter yield-deviations of a random regression test-day model for genetic evaluation of dairy cattle

Test-day milk, fat, protein yield, and somatic cell score (SCS) were analyzed separately using data from the first 3 lactations and a random regression model. Data used in the model were from Austria, Germany, and Luxembourg and from Holstein, Red, and Jersey dairy cattle. For reliability approximation, a multiple-trait effective daughter contribution (MTEDC) method was developed under general multiple trait models, including random regression test-day models, by extending the single-trait daughter equivalents concept. The MTEDC was applied to the very large dairy population, with about 15.5 million animals. The calculation of reliabilities required less computer memory than the corresponding iteration program and a significantly lower computing time equivalent to 24 rounds of iteration. A formula for daughter-yield deviations was derived for bulls under multiple-trait models. Reliability associated with daughter-yield deviations was approximated using the MTEDC method. Both the daughter-yield deviation formula and associated reliability method were verified in a simulation study using the random regression test-day model. Correlations of lactation daughter-yield deviations with estimated breeding values calculated from a routine genetic evaluation were 0.996 for all bulls and 0.95 for young bulls having only daughters with short lactations.     

Random regression test-day model for clinical mastitis: Genetic parameters,model comparison,and correlations with indicator traits

The objective was to study genetic (co)variance components for binary clinical mastitis (CM), test-day protein yield, and udder health indicator traits [test-day somatic cell score (SCS) and type traits of the udder composite] in the course of lactation with random regression models (RRM). The study used a data set from selected 15 large-scale contract herds including 26,651 Holstein cows. Test-day production and CM data were recorded from 2007 to 2012 and comprised parities 1 to 3. A longitudinal CM data structure was generated by assigning CM records to adjacent official test dates. Bivariate threshold-linear RRM were applied to estimate genetic (co)variance components between longitudinal binary CM (0 = healthy; 1 = diseased) and longitudinal Gaussian distributed protein yield and SCS test-day data. Heritabilities for liability to CM (heritability ~0.15 from 0 to 305 d after calving) were slightly higher than for SCS for corresponding days in milk (DIM) in the course of lactation. Daily genetic correlations between CM and SCS were moderate to high (genetic correlation ~0.70), but substantially decreased at the very end of lactation. Genetic correlations between CM at different test days were close to 1 for adjacent test days, but were close to zero for test days far apart. Daily genetic correlations between CM and protein yield were low to moderate. For identical DIM (e.g., DIM 20, 160, and 300), genetic correlations were −0.03, 0.11, and 0.18, respectively, and disproved pronounced genetic antagonisms between udder health and productivity. Correlations between estimated breeding values (EBV) for CM from the RRM and official EBV for linear type traits of the udder composite, including EBV from 74 influential sires (sires with >60 daughters), were −0.31 for front teat placement, −0.01 for rear teat placement, −0.31 for fore udder attachment, −0.32 for udder depth, and −0.08 for teat length. Estimated breeding values for CM from the RRM were compared with EBV from a multiple-trait model and with EBV from a repeatability model. For test days covering an identical time span and on a lactation level, correlations between EBV from RRM, multiple-trait model, and repeatability model were close to 1. Most relevant results suggest the routine application of threshold RRM to binary CM to (1) allow selection of genetically superior sires for distinct stages of lactation and (2) achieve higher selection response in CM compared with selection strategies based on indicator type traits or based on the indicator-trait SCS.     

Genetic parameters for milk production and persistency for Danish Holsteins estimated in random regression models using REML

(Co)variance components for milk, fat, and protein yield of 8075 first-parity Danish Holsteins (DH) were estimated in random regression models by REML. For all analyses, the fixed part of the model was held constant, whereas four different functions were applied to model the additive genetic effect and the permanent environment effect. Homogeneous residual variance was assumed throughout lactation. Univariate models were compared using a minimum of -2 ln(restricted likelihood) as the criterion for best fit. Heritabilities as a function of time were calculated from the estimated curve parameters from univariate analyses. Independent of the function applied and the trait in question, heritabilities were lowest in the beginning of the lactation. Heritabilities for persistency of fat yield were slightly higher than heritabilities for persistency of milk and protein yield. Genetic correlations between persistency and 305-d production were higher for protein and milk yield than for fat yield. Bivariate analyses between the production traits were carried out in sire models using the models with the best 3-parameter curve fit in the univariate analyses. Correlations between traits were calculated from covariance components for curve parameters estimated in bivariate analyses. Genetic correlations between milk and protein yield were higher than between milk and fat yield.     

Genetic analysis of somatic cell score in Norwegian cattle using random regression test-day models

The dataset used in this analysis contained a total of 341,736 test-day observations of somatic cell scores from 77,110 primiparous daughters of 1965 Norwegian Cattle sires. Initial analyses, using simple random regression models without genetic effects, indicated that use of homogeneous residual variance was appropriate. Further analyses were carried out by use of a repeatability model and 12 random regression sire models. Legendre polynomials of varying order were used to model both permanent environmental and sire effects, as did the Wilmink function, the Lidauer-M?ntysaari function, and the Ali-Schaeffer function. For all these models, heritability estimates were lowest at the beginning (0.05 to 0.07) and higher at the end (0.09 to 0.12) of lactation. Genetic correlations between somatic cell scores early and late in lactation were moderate to high (0.38 to 0.71), whereas genetic correlations for adjacent DIM were near unity. Models were compared based on likelihood ratio tests, Bayesian information criterion, Akaike information criterion, residual variance, and predictive ability. Based on prediction of randomly excluded observations, models with 4 coefficients for permanent environmental effect were preferred over simpler models. More highly parameterized models did not substantially increase predictive ability. Evaluation of the different model selection criteria indicated that a reduced order of fit for sire effects was desireable. Models with zeroth- or first-order of fit for sire effects and higher order of fit for permanent environmental effects probably underestimated sire variance. The chosen model had Legendre polynomials with 3 coefficients for sire, and 4 coefficients for permanent environmental effects. For this model, trajectories of sire variance and heritability were similar assuming either homogeneous or heterogeneous residual variance structure.     

Use of herd solutions from a random regression test-day model for diagnostic dairy herd management

In a random regression test-day model, environmental effects in addition to individual animal factors can be included and analyzed. Moreover, instead of herd-year classification of the management groups, the herd-test-day classification within the model better accounts for month-to-month short-term environmental variation in production and somatic cell count (SCC) traits. The herd management levels of milk yield (milk deviation from whole-country mean, kilograms/day), protein and fat concentration (protein and fat deviation, %), and SCC (SCC deviation, 1,000 cells/mL) are used in the dairy herd management Web application “Maitoisa” (in English, “Milky”). This management tool helps to recognize several management problems. For recognition of systematic patterns and single unusual test-days, a monthly time-trend analysis was developed to smooth the random fluctuations and display the yearly production pattern. In addition to analyzing single test-day deviations from the mean, modeled herd solutions assist users in identifying repeated phenomena and enable the forecasting of the management pattern for the subsequent year. The solutions are displayed either as tables or graphs plotted by calendar months. In addition to management effects of the farmer's own herd, he or she can request country or region percentiles to be displayed in the graphs. The Web service has been offered to farmers and dairy advisors since 2001, and it has proved to be a powerful tool for herd monitoring and planning.     

Genetic parameters for test-day electrical conductivity of milk for first-lactation cows from random regression models

Electrical conductivity (EC) of milk has been introduced as an indicator trait for mastitis during the last few decades. The correlation of EC to mastitis, easy access to EC data, and the low cost of recording are properties that make EC a good indicator trait for mastitis. In this study, EC was measured daily during the lactation and available from 2101 first-lactation Holstein cows in 8 herds in the United States. Data were analyzed with an animal model that included herd-test-day, age at calving and days in milk (DIM) as fixed effects, and random additive genetic and permanent environmental effects. A repeatability model and 5 random regression (RR) models with increasing order of Legendre polynomials were used. The goodness of fit for the different models was evaluated based on several tests. Our results indicate that the best model was a RR model with a fourth-order Legendre polynomial for both additive genetic and permanent environmental effects. Heritability estimates obtained with this model were from 0.26 to 0.36. Due to the relatively high heritability obtained for EC of milk, EC might be a potential indicator trait to use in a breeding program designed to reduce the incidence of mastitis.     

Use of test-day records beyond three hundred five days for estimation of three hundred five-day breeding values for production traits and somatic cell score of Canadian Holsteins

The Canadian Test-Day Model includes test-day (TD) records from 5 to 305 d in milk (DIM). Because 60% of Canadian Holstein cows have at least one lactation longer than 305 d, a significant number of TD records beyond 305 DIM could be included in the genetic evaluation. The aim of this study was to investigate whether TD records beyond 305 DIM could be useful for estimation of 305-d estimated breeding value (EBV) for milk, fat, and protein yields and somatic cell score. Data were 48,638,184 TD milk, fat, and protein yields and somatic cell scores from the first 3 lactations of 2,826,456 Canadian Holstein cows. All production traits were preadjusted for the effect of pregnancy. Subsets of data were created for variance-component estimation by random sampling of 50 herds. Variance components were estimated using Gibbs sampling. Full data sets were used for estimation of breeding values. Three multiple-trait, multiple-lactation random regression models with TD records up to 305 DIM (M305), 335 DIM (M335), and 365 DIM (M365) were fitted. Two additional models (M305a and M305b) used TD records up to 305 DIM and variance components previously estimated by M335 and M365, respectively. The effects common to all models were fixed effects of herd × test-date and DIM class, fixed regression on DIM nested within region × age × season class, and random regressions for additive genetic and permanent environmental effects. Legendre polynomials of order 6 and 4 were fitted for fixed and random regressions, respectively. Rapid increase of additive genetic and permanent environmental variances at extremes of lactations was observed with all 3 models. The increase of additive genetic and permanent environmental variances was at earlier DIM with M305, resulting in greater variances at 305 DIM with M305 than with M335 and M365. Model M305 had the best ability to predict TD yields from 5 through 305 DIM and less error of prediction of 305-d EBV than M335 and M365. Model M335 had smaller change of 305-d EBV of bulls over the period of 7 yr than did M305 and M365. Model M305a had the least error of prediction and change of 305-d EBV from all models. Therefore, the use of TD records of Holstein cows from 5 through 305 DIM and variance components estimated using records up to 335 DIM is recommended for the Canadian Test-Day Model.     

Genetic line comparisons and genetic parameters for endoparasite infections and test-day milk production traits

Keeping dairy cows in grassland systems relies on detailed analyses of genetic resistance against endoparasite infections, including between- and within-breed genetic evaluations. The objectives of this study were (1) to compare different Black and White dairy cattle selection lines for endoparasite infections and (2) the estimation of genetic (co)variance components for endoparasite and test-day milk production traits within the Black and White cattle population. A total of 2,006 fecal samples were taken during 2 farm visits in summer and autumn 2015 from 1,166 cows kept in 17 small- and medium-scale organic and conventional German grassland farms. Fecal egg counts were determined for gastrointestinal nematodes (FEC-GIN) and flukes (FEC-FLU), and fecal larvae counts for the bovine lungworm Dictyocaulus viviparus (FLC-DV). The lowest values for gastrointestinal nematode infections were identified for genetic lines adopted to pasture-based production systems, especially selection lines from New Zealand. Heritabilities were low for FEC-GIN (0.05–0.06 ± 0.04) and FLC-DV (0.05 ± 0.04), but moderate for FEC-FLU (0.33 ± 0.06). Almost identical heritabilities were estimated for different endoparasite trait transformations (log-transformation, square root). The genetic correlation between FEC-GIN and FLC-DV was 1.00 ± 0.60, slightly negative between FEC-GIN and FEC-FLU (?0.10 ± 0.27), and close to zero between FLC-DV and FEC-FLU (0.03 ± 0.30). Random regression test-day models on a continuous time scale [days in milk (DIM)] were applied to estimate genetic relationships between endoparasite and longitudinal test-day production traits. Genetic correlations were negative between FEC-GIN and milk yield (MY) until DIM 85, and between FEC-FLU and MY until DIM 215. Genetic correlations between FLC-DV and MY were negative throughout lactation, indicating improved disease resistance for high-productivity cows. Genetic relationships between FEC-GIN and FEC-FLU with milk protein content were negative for all DIM. Apart from the very early and very late lactation stage, genetic correlations between FEC-GIN and milk fat content were negative, whereas they were positive for FEC-FLU. Genetic correlations between FEC-GIN and somatic cell score were positive, indicating similar genetic mechanisms for susceptibility to udder and endoparasite infections. The moderate heritabilities for FEC-FLU suggest inclusion of FEC-FLU into overall organic dairy cattle breeding goals to achieve long-term selection response for disease resistance.     

Genetic evaluation of bulls and cows with single- and multiple-country test-day models

First-lactation milk yield test-day records on cows from Australia, Canada, Italy, and New Zealand were analyzed by single- and multiple-country random regression models. Models included fixed effects of herd-test day and breed composition-age at calving-season of calving by days in milk, and random regressions with Legendre polynomials of order four for animal genetic and permanent environmental effects. Milk yields in different countries were defined as genetically different traits for the purpose of multiple-trait model. Estimated breeding values of bulls and cows from single- and multiple-trait models were compared within and across countries for two traits: total milk yield in lactation and lactation persistency, defined as the linear coefficient of animal genetic curve. Correlations between single- and multiple-trait evaluations within country for total yield were higher than 0.95 for bulls and close to 1 for cows. Correlations for lactation persistency were lower than respective correlations for total yield. Between country correlations for lactation yield ranged from 0.93 to 0.96, indicating different ranking of bulls on different country scales under multiple-trait model. Lactation persistency had in general lower between-country correlations, with the highest values for Canada-Italy and Australia-New Zealand pairs, for both single- and multiple-country models. Although multiple-country random regression test-day model was computationally feasible for four countries, the same would not be true for routine international genetic evaluation in the near future.     

Associations of breed and feeding management with milk production curves at herd level using a random regression test-day model

Earlier studies identified large between-herd variation in estimated lactation curve parameters from test-day milk yield and milk composition records collected in Ragusa province, Italy. The objective of this study was to identify sources of variation able to explain these between-herd differences in milk production curves, by estimating associations of animal breed (Holstein Friesian vs. Brown Swiss), feeding system [separate feeding (SF) vs. total mixed ration (TMR)], and TMR chemical composition on milk and milk components herd curves. Data recorded from 1992 through 2007 for test-day (TD) milk, fat, and protein yields from 1,287,019 records of 148,951 lactations of 51,489 cows in 427 herds were processed using a random regression TD model. Random herd curves (HCUR) for milk, fat, and protein yields were estimated from the model per herd, year, and parity (1, 2, and 3+) using 4-order Legendre polynomials. From March 2006 through December 2007, samples of TMR were collected every 3 mo from 37 farms in Ragusa province. Samples were analyzed for dry matter, ash, crude protein, soluble nitrogen, acid detergent lignin, neutral detergent fiber, acid detergent fiber, and starch. Traits used to describe milk production curves were peak, days in milk at peak, persistency, and mean. Association of feeding system and animal breed with HCUR traits was investigated using a general mixed model procedure. Association of TMR chemical composition with HCUR traits was investigated using multivariate analysis with regression and stepwise model selection. Results were consistent for all traits and parities. Feeding system was significantly associated with HCUR peak and mean, with higher values for TMR. Animal breed was significantly associated with HCUR persistency, with higher values for Brown Swiss herds. Furthermore, animal breed influenced HCUR peak and mean, with higher values for Holstein Friesian herds. Crude protein had the largest effect on HCUR peak and mean, whereas the interaction between crude protein and dry matter mainly affected persistency. When provided by a national evaluation system, HCUR can be used as an indicator of herd feeding management.     

Inferring genetic parameters of lactation in Tropical Milking Criollo cattle with random regression test-day models

This study inferred genetic and permanent environmental variation of milk yield in Tropical Milking Criollo cattle and compared 5 random regression test-day models using Wilmink's function and Legendre polynomials. Data consisted of 15,377 test-day records from 467 Tropical Milking Criollo cows that calved between 1974 and 2006 in the tropical lowlands of the Gulf Coast of Mexico and in southern Nicaragua. Estimated heritabilities of test-day milk yields ranged from 0.18 to 0.45, and repeatabilities ranged from 0.35 to 0.68 for the period spanning from 6 to 400 d in milk. Genetic correlation between days in milk 10 and 400 was around 0.50 but greater than 0.90 for most pairs of test days. The model that used first-order Legendre polynomials for additive genetic effects and second-order Legendre polynomials for permanent environmental effects gave the smallest residual variance and was also favored by the Akaike information criterion and likelihood ratio tests.     

Random regression models for male and female fertility evaluation using longitudinal binary data

A longitudinal Bayesian threshold analysis of insemination outcomes was carried out using 2 random regression models with 3 (Model 1) and 5 (Model 2) parameters to model the additive genetic values at the liability scale. All insemination events of first-parity Holstein cows were used. The outcome of an insemination event was treated as a binary response of either a success (1) or a failure (0). Thus, all breeding information for a cow, including all service sires, was included, thereby allowing for a joint evaluation of male and female fertility. An edited data set of 369,353 insemination records from 210,373 first-lactation cows was used. On the liability scale, both models included the systematic effects of herd-year, month of insemination, technician, and regressions on age of service sire and milk yield during the first 100 d of lactation. The random effects in the model were the 3 or 5 random regression coefficients specific to each cow, the permanent effect of the cow, and the service sire effect. Using Model 1, the estimated heritability of an insemination outcome decreased from 0.035 at d 50 to 0.032 at d 140 and then increased continuously with DIM. The genetic correlations for insemination success at different time points ranged from 0.83 to 0.99, and their magnitude decreased with an increase in the interval between inseminations. A similar trend was observed for heritability and genetic correlations using Model 2. However, the average estimate of heritability was much higher (0.058) than those obtained using Model 1 or a repeatability model. In addition, the estimated genetic correlations followed the same trend as Model 1, but were lower and with a higher rate of decrease when the interval between inseminations increased. The posterior mean of service sire variance was 0.01 for both models, and permanent environmental variance was 0.05 and 0.02 for Models 1 and 2, respectively. Model comparison based on the Bayes factor indicated that Model 1 was more plausible, given the data.     

Validation of test-day models for genetic evaluation of dairy goats in Norway

Test-day data for daily milk yield and fat, protein, and lactose content were sampled from the years 1988 to 2003 in 17 flocks belonging to 2 genetically well-tied buck circles. In total, records from 2,111 to 2,215 goats for content traits and 2,371 goats for daily milk yield were included in the analysis, averaging 2.6 and 4.8 observations per goat for the 2 groups of traits, respectively. The data were analyzed by using 4 test-day models with different modeling of fixed effects. Model [0] (the reference model) contained a fixed effect of year-season of kidding with regression on Ali-Schaeffer polynomials nested within the year-season classes, and a random effect of flock test-day. In model [1], the lactation curve effect from model [0] was replaced by a fixed effect of days in milk (in 3-d periods), the same for all year-seasons of kidding. Models [2] and [3] were obtained from model [1] by removing the fixed year-season of kidding effect and considering the flock test-day effect as either fixed or random, respectively. The models were compared by using 2 criteria: mean-squared error of prediction and a test of bias affecting the genetic trend. The first criterion indicated a preference for model [3], whereas the second criterion preferred model [1]. Mean-squared error of prediction is based on model fit, whereas the second criterion tests the ability of the model to produce unbiased genetic evaluation (i.e., its capability of separating environmental and genetic time trends). Thus, a fixed structure with year (year, year-season, or possibly flock-year) was indicated to appropriately separate time trends. Heritability estimates for daily milk yield and milk content were 0.26 and 0.24 to 0.27, respectively.