Fitting milk production curves through nonlinear mixed models

Fitting mathematical functions to extended lactation curves and forecasting late-lactation milk yields of dairy cows

A 305-d lactation followed by a 60-d dry period has traditionally been considered economically optimal, yet dairy cows in modern intensive dairy systems are frequently dried off while still producing significant quantities of milk. Managing cows for an extended lactation has reported production, welfare, and economic benefits, but not all cows are suitable for an extended lactation. Implementation of an extended lactation strategy on-farm could benefit from use of a decision support system, based on a mathematical lactation model, that can identify suitable cows during early lactation that have a high likelihood of producing above a target milk yield (MY) at 305 d in milk (DIM). Therefore, our objectives were (1) to compare the suitability of 3 commonly used lactation models for modeling extended lactations (Dijkstra, Wood, and Wilmink) in primiparous and multiparous cows under a variety of lactation lengths, and (2) to determine the amount of early-lactation daily MY data needed to accurately forecast MY at d 305 by using the most suitable model and determine whether this is sufficient for identifying cows suitable for an extended lactation before the end of a typical voluntary waiting period (50-90 d). Daily MY data from 467 individual Holstein-Friesian lactations (DIM >305 d; 379 ± 65-d lactation length [mean ± SD]) were fitted by the 3 lactation models using a nonlinear regression procedure. The parameter estimates of these models, lactation characteristics (peak yield, time to peak yield, and persistency), and goodness-of-fit were compared between parity and different lactation lengths. The models had similar performance, and differences between parity groups were consistent with previous literature. Then, data from only the first i DIM for each individual lactation, where i was incremented by 30 d from 30 to 150 DIM and by 50 d from 150 to 300 DIM, were fitted by each model to forecast MY at d 305. The Dijkstra model was selected for further analysis, as it had superior goodness-of-fit statistics for i= 30 and 60. The data set was fit twice by the Dijkstra model, with parameter bounds either unconstrained or constrained. The quality of predictions of MY at d 305 improved with increasing data availability for both models and assisting the model fitting procedure with more biologically relevant constraints on parameters improved the predictions, but neither was reliable enough for practical use on-farm due to the high uncertainty of forecasted predictions. Using 90 d of data, the constrained model correctly classified 66% of lactations as being above or below a target MY at d 305 of 25 kg/d, with a probability threshold of 0.95. The proportion of correct classifications became smaller at lower targets of MY at d 305 and became greater when using more lactation days. Overall, further work is required to develop a model that can forecast late-lactation MY with sufficient accuracy for practical use. We envisage that a hybridized machine learning and mechanistic model that incorporates additional historical and genetic information with early-lactation MY could produce meaningful lactation curve forecasts.

Genomic-based genetic parameters for resilience across lactations in North American Holstein cattle based on variability in daily milk yield records

Considering the increasing challenges imposed by climate change and the need to improve animal welfare, breeding more resilient animals capable of better coping with environmental disturbances is of paramount importance. In dairy cattle, resilience can be evaluated by measuring the longitudinal occurrences of abnormal daily milk yield throughout lactation. Aiming to estimate genetic parameters for dairy cattle resilience, we collected 5,643,193 daily milk yield records on automatic milking systems (milking robots) and milking parlors across 21,350 lactations 1 to 3 of 11,787 North American Holstein cows. All cows were genotyped with 62,029 SNPs. After determining the best fitting models for each of the 3 lactations, daily milk yield residuals were used to derive 4 resilience indicators: weighted occurrence frequency of yield perturbations (wfPert), accumulated milk losses of yield perturbations (dPert), and log-transformed variance (LnVar) and lag-1 autocorrelation (r_auto) of daily yield residuals. The indicator LnVar presented the highest heritability estimates (±standard error), ranging from 0.13 ± 0.01 in lactation 1 to 0.15 ± 0.02 in lactation 2; the other 3 indicators had relatively lower heritabilities across the 3 lactations (0.01-0.06). Based on bivariate analyses of each resilience indicator across lactations, stronger genetic correlations were observed between lactations 2 and 3 (0.88-0.96) than between lactations 1 and 2 or 3 (0.34-0.88) for dPert, LnVar, and r_auto. For the pairwise comparisons of different resilience indicators within each lactation, dPert had the strongest genetic correlations with wfPert (0.64) and r_auto (0.53) in lactation 1, whereas the correlations in lactations 2 and 3 were more variable and showed relatively high standard errors. The genetic correlation results indicated that different resilience indicators across lactations might capture additional biological mechanisms and should be considered as different traits in genetic evaluations. We also observed favorable genetic correlations of these resilience indicators with longevity and Net Merit index, but further biological validation of these resilience indicators is needed. In conclusion, this study provided genetic parameter estimates for different resilience indicators derived from daily milk yields across the first 3 lactations in Holstein cattle, which will be useful when potentially incorporating these traits in dairy cattle breeding schemes.

Investigating the effect of temporal, geographic, and management factors on US Holstein lactation curve parameters

We fit the Wood's lactation model to an extensive database of test-day milk production records of US Holstein cows to obtain lactation-specific parameter estimates and investigated the effects of temporal, spatial, and management factors on lactation curve parameters and 305-d milk yield. Our approach included 2 steps as follows: (1) individual animal-parity parameter estimation with nonlinear least-squares optimization of the Wood's lactation curve parameters, and (2) mixed-effects model analysis of 8,595,413 sets of parameter estimates from individual lactation curves. Further, we conducted an analysis that included all parities and a separate analysis for first lactation heifers. Results showed that parity had the most significant effect on the scale (parameter a), the rate of decay (parameter c), and the 305-d milk yield. The month of calving had the largest effect on the rate of increase (parameter b) for models fit with data from all lactations. The calving month had the most significant effect on all lactation curve parameters for first lactation models. However, age at first calving, year, and milking frequency accounted for a higher proportion of the variance than month for first lactation 305-d milk yield. All parameter estimates and 305-d milk yield increased as parity increased; parameter a and 305-d milk yield rose, and parameters b and c decreased as year and milking frequency increased. Calving month estimates parameters a, b, c, and 305-d milk yield were the lowest values for September, May, June, and July, respectively. The results also indicated the random effects of herd and cow improved model fit. Lactation curve parameter estimates from the mixed-model analysis of individual lactation curve fits describe well US Holstein lactation curves according to temporal, spatial, and management factors.

Does the Acknowledgement of αS1-Casein Genotype Affect the Estimation of Genetic Parameters and Prediction of Breeding Values for Milk Yield and Composition Quality-Related Traits in Murciano-Granadina?

Simple Summary

Genetic evaluations and the selection of breeding animals require the accurate estimation of genetic parameters for economically important traits. As a result, dairy livestock has evolved in response to the needs of producers and consumers. Genetic selection in goats has been mostly based on quantitative traits such as milk yield, fat, protein, and dry matter. However, as reported by the increased heritability values of these parameters after the inclusion of the different allelic variants of αS1 casein in evaluation models, the selection of animals carrying this gene could result in a more efficient genetic selection. High levels of genetic polymorphism (89.58% of polymorphic SNP—as only five out of the 48 SNPs assessed were monomorphic) that are related to greater production of coagulable proteins in milk, a fact that could be associated with a higher yield and improved curd firmness properties.

Abstract

A total of 2090 lactation records for 710 Murciano-Granadina goats were collected during the years 2005–2016 and analyzed to investigate the influence of the αS1-CN genotype on milk yield and components (protein, fat, and dry matter). Goats were genetically evaluated, including and excluding the αS1-CN genotype, in order to assess its repercussion on the efficiency of breeding models. Despite no significant differences being found for milk yield, fat and dry matter heritabilities, protein production heritability considerably increased after aS1-CN genotype was included in the breeding model (+0.23). Standard errors suggest that the consideration of genotype may improve the model’s efficiency, translating into more accurate genetic parameters and breeding values (PBV). Genetic correlations ranged from −0.15 to −0.01 between protein/dry matter and milk yield/protein and fat content, while phenotypic correlations were −0.02 for milk/protein and −0.01 for milk/fat or protein content. For males, the broadest range for reliability (R_AP) (0.45–0.71) was similar to that of females (0.37–0.86) when the genotype was included. PBV ranges broadened while the maximum remained similar (0.61–0.77) for males and females (0.62–0.81) when the genotype was excluded, respectively. Including the αS1-CN genotype can increase production efficiency, milk profitability, milk yield, fat, protein and dry matter contents in Murciano-Granadina dairy breeding programs.