Phenotypic and genomic modeling of lactation curves: A longitudinal perspective.

Lactation curves, which describe the production pattern of milk-related traits over time, provide insightful information about individual cow health, resilience, and milk production efficiency. Key functional traits can be derived through lactation curve modeling, such as lactation peak and persistency. Furthermore, novel traits such as resilience indicators can be derived based on the variability of the deviations of observed milk yield from the expected lactation curve fitted for each animal. Lactation curve parameters are heritable, indicating that one can modify the average lactation curve of a population through selective breeding. Various statistical methods can be used for modeling longitudinal traits. Among them, the use of random regression models enables a more flexible and robust modeling of lactation curves compared with traditional models used to evaluate accumulated milk 305-d yield, as they enable the estimation of both genetic and environmental effects affecting milk production traits over time. In this symposium review, we discuss the importance of evaluating lactation curves from a longitudinal perspective and various statistical and mathematical models used to analyze longitudinal data. We also highlighted the key factors that influence milk production over time, and the potential applications of longitudinal analyses of lactation curves in improving animal health, resilience, and milk production efficiency. Overall, analyzing the longitudinal nature of milk yield will continue to play a crucial role in improving the production efficiency and sustainability of the dairy industry, and the methods and models developed can be easily translated to other longitudinal traits.

Genetic parameters and genome-wide association studies for mozzarella and milk production traits, lactation length, and lactation persistency in Murrah buffaloes.

Genetic and genomic analyses of longitudinal traits related to milk production efficiency are paramount for optimizing water buffaloes breeding schemes. Therefore, this study aimed to (1) compare single-trait random regression models under a single-step genomic BLUP setting based on alternative covariance functions (i.e., Wood, Wilmink, and Ali and Schaeffer) to describe milk (MY), fat (FY), protein (PY), and mozzarella (MZY) yields, fat-to-protein ratio (FPR), somatic cell score (SCS), lactation length (LL), and lactation persistency (LP) in Murrah dairy buffaloes (Bubalus bubalis); (2) combine the best functions for each trait under a multiple-trait framework; (3) estimate time-dependent SNP effects for all the studied longitudinal traits; and (4) identify the most likely candidate genes associated with the traits. A total of 323,140 test-day records from the first lactation of 4,588 Murrah buffaloes were made available for the study. The model included the average curve of the population nested within herd-year-season of calving, systematic effects of number of milkings per day, and age at first calving as linear and quadratic covariates, and additive genetic, permanent environment, and residual as random effects. The Wood model had the best goodness of fit based on the deviance information criterion and posterior model probabilities for all traits. Moderate heritabilities were estimated over time for most traits (0.30 ± 0.02 for MY; 0.26 ± 0.03 for FY; 0.45 ± 0.04 for PY; 0.28 ± 0.05 for MZY; 0.13 ± 0.02 for FPR; and 0.15 ± 0.03 for SCS). The heritability estimates for LP ranged from 0.38 ± 0.02 to 0.65 ± 0.03 depending on the trait definition used. Similarly, heritabilities estimated for LL ranged from 0.10 ± 0.01 to 0.14 ± 0.03. The genetic correlation estimates across days in milk (DIM) for all traits ranged from -0.06 (186-215 DIM for MY-SCS) to 0.78 (66-95 DIM for PY-MZY). The SNP effects calculated for the random regression model coefficients were used to estimate the SNP effects throughout the lactation curve (from 5 to 305 d). Numerous relevant genomic regions and candidate genes were identified for all traits, confirming their polygenic nature. The candidate genes identified contribute to a better understanding of the genetic background of milk-related traits in Murrah buffaloes and reinforce the value of incorporating genomic information in their breeding programs.

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.

Genotype-by-environment interactions for reproduction, body composition, and growth traits in maternal-line pigs based on single-step genomic reaction norms.

BACKGROUND: There is an increasing need to account for genotype-by-environment (G × E) interactions in livestock breeding programs to improve productivity and animal welfare across environmental and management conditions. This is even more relevant for pigs because selection occurs in high-health nucleus farms, while commercial pigs are raised in more challenging environments. In this study, we used single-step homoscedastic and heteroscedastic genomic reaction norm models (RNM) to evaluate G × E interactions in Large White pigs, including 8686 genotyped animals, for reproduction (total number of piglets born, TNB; total number of piglets born alive, NBA; total number of piglets weaned, NW), growth (weaning weight, WW; off-test weight, OW), and body composition (ultrasound muscle depth, MD; ultrasound backfat thickness, BF) traits. Genetic parameter estimation and single-step genome-wide association studies (ssGWAS) were performed for each trait. RESULTS: The average performance of contemporary groups (CG) was estimated and used as environmental gradient in the reaction norm analyses. We found that the need to consider heterogeneous residual variance in RNM models was trait dependent. Based on estimates of variance components of the RNM slope and of genetic correlations across environmental gradients, G × E interactions clearly existed for TNB and NBA, existed for WW but were of smaller magnitude, and were not detected for NW, OW, MD, and BF. Based on estimates of the genetic variance explained by the markers in sliding genomic windows in ssGWAS, several genomic regions were associated with the RNM slope for TNB, NBA, and WW, indicating specific biological mechanisms underlying environmental sensitivity, and dozens of novel candidate genes were identified. Our results also provided strong evidence that the X chromosome contributed to the intercept and slope of RNM for litter size traits in pigs. CONCLUSIONS: We provide a comprehensive description of G × E interactions in Large White pigs for economically-relevant traits and identified important genomic regions and candidate genes associated with GxE interactions on several autosomes and the X chromosome. Implementation of these findings will contribute to more accurate genomic estimates of breeding values by considering G × E interactions, in order to genetically improve the environmental robustness of maternal-line pigs.

Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models.

Genomic selection has been widely implemented in many livestock breeding programs, but it remains incipient in buffalo. Therefore, this study aimed to (1) estimate variance components incorporating genomic information in Murrah buffalo; (2) evaluate the performance of genomic prediction for milk-related traits using single- and multitrait random regression models (RRM) and the single-step genomic best linear unbiased prediction approach; and (3) estimate longitudinal SNP effects and candidate genes potentially associated with time-dependent variation in milk, fat, and protein yields, as well as somatic cell score (SCS) in multiple parities. The data used to estimate the genetic parameters consisted of a total of 323,140 test-day records. The average daily heritability estimates were moderate (0.35 ± 0.02 for milk yield, 0.22 ± 0.03 for fat yield, 0.42 ± 0.03 for protein yield, and 0.16 ± 0.03 for SCS). The highest heritability estimates, considering all traits studied, were observed between 20 and 280 d in milk (DIM). The genetic correlation estimates at different DIM among the evaluated traits ranged from -0.10 (156 to 185 DIM for SCS) to 0.61 (36 to 65 DIM for fat yield). In general, direct selection for any of the traits evaluated is expected to result in indirect genetic gains for milk yield, fat yield, and protein yield but also increase SCS at certain lactation stages, which is undesirable. The predicted RRM coefficients were used to derive the genomic estimated breeding values (GEBV) for each time point (from 5 to 305 DIM). In general, the tuning parameters evaluated when constructing the hybrid genomic relationship matrices had a small effect on the GEBV accuracy and a greater effect on the bias estimates. The SNP solutions were back-solved from the GEBV predicted from the Legendre random regression coefficients, which were then used to estimate the longitudinal SNP effects (from 5 to 305 DIM). The daily SNP effect for 3 different lactation stages were performed considering 3 different lactation stages for each trait and parity: from 5 to 70, from 71 to 150, and from 151 to 305 DIM. Important genomic regions related to the analyzed traits and parities that explain more than 0.50% of the total additive genetic variance were selected for further analyses of candidate genes. In general, similar potential candidate genes were found between traits, but our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the traits across parities. These results contribute to a better understanding of the genetic architecture of milk production traits in dairy buffalo and reinforce the relevance of incorporating genomic information to genetically evaluate longitudinal traits in dairy buffalo. Furthermore, the candidate genes identified can be used as target genes in future functional genomics studies.

Genetic evaluation of age at first calving for Guzerá beef cattle using linear, threshold, and survival Bayesian models.

Age at first calving (AFC) is characterized as a censored trait due to missing values provided by recording mistakes and nonoccurrence or delay in calving communication. In this context, we aimed to compare several statistical methods for genetic evaluation of AFC in Guzerá beef cattle under a Bayesian approach. Seven different methods were used for this purpose. The traditional linear mixed model (LM), which considers only uncensored records; the LM with simulated records (SM), which is based on data augmentation framework; the penalty method, in which a constant of 21 d was added to censored records; the bivariate threshold-linear method considering (TLcens) or not (TLmiss) censored information; and the piecewise Weibull proportional hazards model considering (PWPHcens) or not (PWPH) censored records. Heritability estimates ranged from 0.19 (TLcens) to 0.28 (SM) in nonsurvival approaches; and 0.40 and 0.46 to PWPH and PWPHcens methods, respectively. In general, breeding values correlations between different methods and the percentage of selected bulls in common indicated reranking, with these correlation ranging from -0.28 (between SM and PWPH) to 0.99 (between TLmiss and LM). The traditional LM, which considers only uncensored records, should be preferred due to its robustness and simplicity. Based on cross-validation analyses, we conclude that the TLmiss could be also a suitable alternative for breeding value prediction, and censored methods did not improve the analysis.