Autoregressive and random regression test‐day models for multiple lactations in genetic evaluation of Brazilian Holstein cattle

Seasonal autoregressive integrated moving average (SARIMA) time-series model for milk production forecasting in pasture-based dairy cows in the Andean highlands

Milk production in the Andean highlands is variable over space and time. This variability is related to fluctuating environmental factors such as rainfall season which directly influence the availability of livestock feeding resources. The main aim of this study was to develop a time-series model to forecast milk production in a mountainous geographical area by analysing the dynamics of milk records thorough the year. The study was carried out in the Andean highlands, using time-series models of monthly milk records collected routinely from dairy cows maintained in a controlled experimental farm over a 9-year period (2008-2016). Several statistical forecasting models were compared. The Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percent Error (MAPE) were used as selection criteria to compare models. A relation between monthly milk records and the season of the year was modelled using seasonal autoregressive integrated moving average (SARIMA) methods to explore temporal redundancy (trends and periodicity). According to white noise residual test (Q = 13.951 and p = 0.052), Akaike Information Criterion and MAE, MAPE, and RMSE values, the SARIMA (1, 0, 0) x (2, 0, 0)12 time-series model resulted slightly better forecasting model compared to others. In conclusion, time-series models were promising, simple and useful tools for producing reasonably reliable forecasts of milk production thorough the year in the Andean highlands. The forecasting potential of the different models were similar and they could be used indistinctly to forecast the milk production seasonal fluctuations. However, the SARIMA model performed the best good predictive capacity minimizing the prediction interval error. Thus, a useful effective strategy has been developed by using time-series models to monitor milk production and alleviate production drops due to seasonal factors in the Andean highlands.

Random regression models using B-splines functions provide more accurate genomic breeding values for milk yield and lactation persistence in Murrah buffaloes

There is a great worldwide demand for cheese made with buffalo milk, due to its flavour and nutritional properties. In this context, there is a need for increasing the efficiency of buffalo milk production (including lactation persistence), which can be achieved through genomic selection. The most used methods for the genetic evaluation of longitudinal data, such as milk-related traits, are based on random regression models (RRM). The choice of the best covariance functions and polynomial order for modelling the random effects is an important step to properly fit RRM. To our best knowledge, there are no studies evaluating the impact of the order and covariance function (Legendre polynomials-LEG and B-splines-BSP) used to fit RRM for genomic prediction of breeding values in dairy buffaloes. Therefore, the main objectives of this study were to estimate variance components and evaluate the performance of LEG and BSP functions of different orders on the predictive ability of genomic breeding values for the first three lactations of milk yield (MY1, MY2, and MY3) and lactation persistence (LP1, LP2, and LP3) of Brazilian Murrah. Twenty-two models for each lactation were contrasted based on goodness of fit, genetic parameter estimates, and predictive ability. Overall, the models of higher orders of LEG or BSP had a better performance based on the deviance information criterion (DIC). The daily heritability estimates ranged from 0.01 to 0.30 for MY1, 0.08 to 0.42 for MY2, and from 0.05 to 0.47 for MY3. For lactation persistence (LP), the heritability estimates ranged from 0.09 to 0.32 for LP1, from 0.15 to 0.33 for LP2, and from 0.06 to 0.32 for LP3. In general, the curves plotted for variance components and heritability estimates based on BSP models presented lower oscillation along the lactation trajectory. Similar predictive ability was observed among the models. Considering a balance between the complexity of the model, goodness of fit, and credibility of the results, RRM using quadratic B-splines functions based on four or five segments to model the systematic, additive genetic, and permanent environment curves provide better fit with no significant differences between genetic variances estimates, heritabilities, and predictive ability for the genomic evaluation of dairy buffaloes.

Genetic parameters and genome-wide association for milk production traits and somatic cell score in different lactation stages of Shanghai Holstein population

The aim of this study was to investigate the genetic parameters and genetic architectures of six milk production traits in the Shanghai Holstein population. The data used to estimate the genetic parameters consisted of 1,968,589 test-day records for 305,031 primiparous cows. Among the cows with phenotypes, 3,016 cows were genotyped with Illumina Bovine SNP50K BeadChip, GeneSeek Bovine 50K BeadChip, GeneSeek Bovine LD BeadChip v4, GeneSeek Bovine 150K BeadChip, or low-depth whole-genome sequencing. A genome-wide association study was performed to identify quantitative trait loci and genes associated with milk production traits in the Shanghai Holstein population using genotypes imputed to whole-genome sequences and both fixed and random model circulating probability unification and a mixed linear model with rMVP software. Estimated heritabilities (h2) varied from 0.04 to 0.14 for somatic cell score (SCS), 0.07 to 0.22 for fat percentage (FP), 0.09 to 0.27 for milk yield (MY), 0.06 to 0.23 for fat yield (FY), 0.09 to 0.26 for protein yield (PY), and 0.07 to 0.35 for protein percentage (PP), respectively. Within lactation, genetic correlations for SCS, FP, MY, FY, PY, and PP at different stages of lactation estimated in random regression model were ranged from -0.02 to 0.99, 0.18 to 0.99, 0.04 to 0.99, 0.04 to 0.99, 0.01 to 0.99, and 0.33 to 0.99, respectively. The genetic correlations were highest between adjacent DIM but decreased as DIM got further apart. Candidate genes included those related to production traits (DGAT1, MGST1, PTK2, and SCRIB), disease-related (LY6K, COL22A1, TECPR2, and PLCB1), heat stress-related (ITGA9, NDST4, TECPR2, and HSF1), and reproduction-related (7SK and DOCK2) genes. This study has shown that there are differences in the genetic mechanisms of milk production traits at different stages of lactation. Therefore, it is necessary to conduct research on milk production traits at different stages of lactation as different traits. Our results can also provide a theoretical basis for subsequent molecular breeding, especially for the novel genetic loci.

Genotype by environment interaction for Holstein cattle populations using autoregressive and within- and across-country multi-trait reaction norms test-day models

The progenies of international bulls in diverse climatic conditions and management levels may lead to different expressions of their genetic potential resulting in a re-ranking of these bulls. Therefore, evaluate the presence of genotype by environment interaction (G×E) within and across countries is important to guide the decision-making on alternative selection strategies. Thus, a two-step reaction norm (RN) approach was used to investigate the presence of G×E in Portuguese and Brazilian Holstein cattle. In step 1, we performed a within-country genetic evaluation using an autoregressive model to obtain precorrected phenotypes and environmental gradients (herd test-day solutions, HTD levels). In step 2, the precorrected phenotypes were considered as two distinct traits in a bi-trait RN model to estimate variance components across HTD levels, genetic correlation between HTD levels in Portugal and Brazil, and RN of the estimated breeding values. Additionally, the genetic correlation between countries using a bi-trait random regression (RR) sire model was obtained. In step 1, genetic additive variance for milk yield (MY) in Portugal was 14.1% higher than in Brazil. For somatic cell score (SCS), the genetic additive variance in Portugal was 12.7% lower than in Brazil. Although similar heritability estimates for SCS were observed in both countries, MY heritabilities were 0.31 for Portugal and 0.23 for Brazil. Genetic correlations (SD) between both countries obtained using RR sire model were 0.78 (0.051) for MY and 0.75 (0.062) for SCS. In step 2, MY genetic correlations among HTD levels within countries were higher than 0.94 for Portugal and 0.98 for Brazil. Somatic cell score genetic correlations among HTD levels ranged from 0.70 to 0.99 for Portugal and from 0.84 to 0.99 for Brazil. The average (SD) of genetic correlation estimates between Portuguese and Brazilian HTD levels were 0.74 (0.009) for MY and 0.57 (0.060) for SCS. These results suggest the presence of G×E for MY and SCS of Holstein cattle between both countries. Although there was no indication of G×E between Brazilian herd environments, the low genetic correlation for SCS indicates potential re-ranking of bulls between extreme environmental gradient in Portugal. Overall, the results of this study evidence the importance of national and international genetic evaluation systems to assist dairy farmers in the selection of the best genotypes to obtain the expected returns from investments in imported semen and to realize genetic progress in dairy populations under local environmental conditions.

Autoregressive model for genetic evaluation of longitudinal reproductive traits in Brazilian Holstein cattle

Reproductive efficiency is major determinant of the dairy herd profitability. Thus, reproductive traits have been widely used as selection objectives in the current dairy cattle breeding programs. We aimed to evaluate strategies to model days open (DO), calving interval (CI) and daughter pregnancy rate (DPR) in Brazilian Holstein cattle. These reproductive traits were analysed by the autoregressive (AR) model and compared with classical repeatability (REP) model using 127,280, 173,092 and 127,280 phenotypic records, respectively. The first three calving orders of cows from 1,469 Holstein herds were used here. The AR model reported lower values for Akaike Information Criteria and Mean Square Errors, as well as larger model probabilities, for all evaluated traits. Similarly, larger additive genetic and lower residual variances were estimated from AR model. Heritability and repeatability estimates were similar for both models. Heritabilities for DO, CI and DPR were 0.04, 0.07 and 0.04; and 0.05, 0.06 and 0.04 for AR and REP models, respectively. Individual EBV reliabilities estimated from AR for DO, CI and DPR were, in average, 0.29, 0.30 and 0.29 units higher than those obtained from REP model. Rank correlation between EBVs obtained from AR and REP models considering the top 10 bulls ranged from 0.72 to 0.76; and increased from 0.98 to 0.99 for the top 100 bulls. The percentage of coincidence between selected bulls from both methods increased over the number of bulls included in the top groups. Overall, the results of model-fitting criteria, genetic parameters estimates and EBV predictions were favourable to the AR model, indicating that it may be applied for genetic evaluation of longitudinal reproductive traits in Brazilian Holstein cattle.