Nitrogen excretion in dairy manure is a precursor for N2O and NH3 formation in livestock housing, manure storage facilities, and after manure is applied to land. Nitrous oxide is a major contributor to greenhouse gas emissions, and reducing N output from dairy production facilities can reduce the amount of anthropogenic N2O entering the atmosphere. The objective of the study was to conduct a comprehensive evaluation of extant prediction models for N excretion in feces and urine using extensive literature data. A total of 45 N excretion equations were evaluated for lactating cows, heifers, and nonlactating cows and steers. These equations were evaluated with 215 treatment means from 69 published studies collected over 20 yr from 1995 to 2015. Two evaluation methods were used: the root mean square prediction error and the concordance correlation coefficient. Equations constructed using a more rigorous development process fared better than older extant equations. Equations for heifers and nonlactating cows had greater error of prediction compared with equations used for lactating cows. This could be due to limited amount of data available for construction and evaluation of the equations. Urinary N equations had greater prediction errors than other forms of excretion, possibly due to high variability in urinary N excretion and challenges in urine collection. Fecal N equations had low error bias and reached an acceptable level of precision and accuracy.

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.

Dairy production is an important source of nutrients in the global food supply, but environmental impacts are increasingly a concern of consumers, scientists, and policy-makers. Many decisions must be integrated to support sustainable production—which can be achieved using a simulation model. We provide an example of the Ruminant Farm Systems (RuFaS) model to assess changes in the dairy system related to altered animal feed efficiency. RuFaS is a whole-system farm simulation model that simulates the individual animal life cycle, production, and environmental impacts. We added a stochastic animal-level parameter to represent individual animal feed efficiency as a result of reduced residual feed intake and compared High (intake = 94% of expected) and Very High (intake = 88% of expected) efficiency levels with a Baseline scenario (intake = 100% of expected). As expected, the simulated total feed intake was reduced by 6 and 12% for the High and Very High efficiency scenarios, and the expected impact of these improved efficiencies on the greenhouse gas emissions from enteric methane and manure storage was a decrease of 4.6 and 9.3%, respectively.

This analysis introduces a stochastic herd simulation model and evaluates the estimated reproductive and economic performance of combinations of reproductive management programs for both heifers and lactating cows. The model simulates the growth, reproductive performance, production, and culling for individual animals and integrates individual animal outcomes to represent herd dynamics daily. The model has an extensible structure, allowing for future modification and expansion, and has been integrated into the Ruminant Farm Systems model, a holistic dairy farm simulation model. The herd simulation model was used to compare outcomes of 10 reproductive management scenarios based on common practices on US farms with combinations of estrous detection (ED) and artificial insemination (AI), synchronized estrous detection (synch-ED) and AI, timed AI (TAI, 5-d CIDR-Synch) programs for heifers; and ED, a combination of ED and TAI (ED-TAI, Presynch-Ovsynch), and TAI (Double-Ovsynch) with or without ED during the reinsemination period for lactating cows. The simulation was run for a 1,000-cow (milking and dry) herd for 7 yr, and we used the outcomes from the final year to evaluate results. The model accounted for incomes from milk, sold calves, and culled heifers and cows, as well as costs from breeding, AI, semen, pregnancy diagnosis, and calf, heifer, and cow feed. We found that the interaction between heifer and lactating dairy cow reproductive management programs influences herd economic performance primarily due to heifer rearing costs and replacement heifer supply. The greatest net return (NR) was achieved when combining heifer TAI and cow TAI without ED during the reinsemination period, whereas the lowest NR was obtained when combining heifer synch-ED with cow ED.

The objective of this study was to compare the application of iterative linear programming (iteLP), sequential quadratic programming (SQP), and mixed-integer nonlinear programming-based deterministic global optimization (MINLP_DGO) on ration formulation for dairy cattle based on Nutrient Requirements of Dairy Cattle (NRC, 2001). Least-cost diets were formulated for lactating cows, dry cows, and heifers. Nutrient requirements including energy, protein, and minerals, along with other limitations on dry matter intake, neutral detergent fiber, and fat were considered as constraints. Five hundred simulations were conducted, with each simulation randomly selecting 3 roughages and 5 concentrates from the feed table in NRC (2001) as the feed resource for each of 3 animal groups. Among the 500 simulations for lactating cows, 57, 45, and 21 simulations did not yield a feasible solution when using iteLP, SQP, and MINLP_DGO, respectively. All the simulations for dry cows and heifers were feasible when using SQP and MINLP_DGO, but 49 and 11 infeasible simulations occurred when using iteLP for dry cows and heifers, respectively. The average ration costs per animal per day of the feasible solutions obtained by iteLP, SQP, and MINLP_DGO were $4.78 (±0.71), $4.45 (±0.65), and $4.44 (±0.65) for lactating cows; $2.39 (±0.52), $1.48 (±0.26), and $1.48 (±0.26) for dry cows; and $0.98 (±0.72), $0.97 (±0.15), and $0.91 (±0.14) for heifers, respectively. The average computation time of iteLP, SQP, and MINLP_DGO were 0.59 (±1.87) s, 1.15 (±0.62) s, and 58.69 (±68.45) s for lactating cows; 0.041 (±0.070) s, 0.76 (±0.37) s, and 14.84 (±39.09) s for dry cows; and 1.60 (±2.90) s, 0.51 (±0.19) s, and 16.45 (±45.56) s for heifers, respectively. In conclusion, iteLP had limited capability of formulating least-cost diets when nonlinearity existed in the constraints. Both SQP and MINLP_DGO handled the nonlinear constraints well, with SQP being faster, whereas MINLP_DGO was able to return a feasible solution under some situations where SQP could not.

In this study, we developed a machine learning framework to detect clinical mastitis (CM) at the current milking (i.e., the same milking) and predict CM at the next milking (i.e., one milking before CM occurrence) at the quarter level. Time series quarter-level milking data were extracted from an automated milking system (AMS). For both CM detection and prediction, the best classification performance was obtained from the decision tree-based ensemble models. Moreover, applying models on a data set containing data from the current milking and past 9 milkings before the current milking showed the best accuracy for detecting CM; modeling with a data set containing data from the current milking and past 7 milkings before the current milking yielded the best results for predicting CM. The models combined with oversampling methods resulted in specificity of 95 and 93% for CM detection and prediction, respectively, with the same sensitivity (82%) for both scenarios; when lowering specificity to 80 to 83%, undersampling techniques facilitated models to increase sensitivity to 95%. We propose a feasible machine learning framework to identify CM in a timely manner using imbalanced data from an AMS, which could provide useful information for farmers to manage the negative effects of CM.