The objectives of the study were to develop a multivariate framework for analyzing energy balance data from lactating cows and investigate potential changes in maintenance requirements and partial efficiencies of energy utilization by lactating cows over the years. The proposed model accounted for the fact that metabolizable energy intake, milk energy output, and tissue energy balance are random variables that interact mutually. The model was specified through structural equations implemented in a Bayesian framework. The structural equations, along with a model traditionally used to estimate energetic parameters, were fitted to a large database of indirect calorimetry records from lactating cows. Maintenance requirements and partial efficiencies for both models were similar to values reported in the literature. In particular, the estimated parameters (with 95% credible interval in parentheses) for the proposed model were: net energy requirement for maintenance equal to 0.36 (0.34, 0.38) MJ/kg of metabolic body weight·day; the efficiency of utilizing dietary energy for milk production and tissue gain were 0.63 (0.61, 0.64) and 0.70 (0.68, 0.72), respectively; the efficiency of utilizing body stores for milk production was 0.89 (0.87, 0.91). Furthermore, additional analyses were conducted for which energetic parameters were allowed to depend on the decade in which studies were conducted. These models investigated potential changes in maintenance requirements and partial efficiencies over the years. Canonical correlation analysis was used to investigate the association between changes in energetic parameters with additional dietary and animal characteristics available in the database. For both models, net energy requirement for maintenance and the efficiency of utilizing dietary energy for milk production and tissue gain increased in the more recent decades, whereas the efficiency of utilizing body stores for milk production remained unchanged. The increase in maintenance requirements in modern milk production systems is consistent with the literature that describes increased fasting heat production in cows of higher genetic merit. The increase in utilization of dietary energy for milk production and tissue gain was partially attributed to the changes in dietary composition, in particular to the increase in dietary ether extract to levels closer to currently observed in modern milk production systems. Therefore, the estimated energetic parameters from this study can be used to update maintenance requirements and partial efficiencies of energy utilization in North American feeding systems for lactating cows.

The idea of managing cows for extended lactations rather than lactations of the traditional length of 1 yr primarily arose from observations of increasing problems with infertility and cows being dried off with high milk yields. However, it is vital for the success of extended lactation practices that cows are able to maintain milk yield per feeding day when the length of the calving interval (CInt) is increased. Milk yield per feeding day is defined as the cumulated lactation milk yield divided by the sum of days between 2 consecutive calvings. The main objective of this study was to investigate the milk production of cows managed for lactations of different lengths, and the primary aim was to investigate the relationship between CInt, parity, and milk yield. Five measurements of milk yield were used: energy-corrected milk (ECM) yield per feeding day, ECM yield per lactating day, cumulative ECM yield during the first 305 d of lactation, as well as ECM yield per day during early and late lactation. The analyses were based on a total of 1,379 completed lactations from cows calving between January 2007 and May 2013 in 4 Danish commercial dairy herds managed for extended lactation for several years. Herd-average CInt length ranged from 414 to 521 d. The herds had Holstein, Jersey, or crosses between Holstein, Jersey, and Red Danish cows with average milk yields ranging from 7,644 to 11,286 kg of ECM per cow per year. A significant effect of the CInt was noted on all 5 measurements of milk yield, and this effect interacted with parity for ECM per feeding day, ECM per lactating day and ECM per day during late lactation. The results showed that cows were at least able to produce equivalent ECM per feeding day with increasing CInt, and that first- and second-parity cows maintained ECM per lactating day. Cows with a CInt between 17 and 19 mo produced 476 kg of ECM more during the first 305 d compared with cows with a CInt of less than 13 mo. Furthermore, early-lactation ECM yield was greater for all cows and late-lactation ECM yield was less for second-parity and older cows when undergoing an extended compared with a shorter lactation. Increasing CInt increased the dry period length with 3 to 5d. In conclusion, the group of cows with longer CInt were able to produce at least equivalent amounts of ECM per feeding day when the CInt was up to 17 to 19 mo on these 4 commercial dairy farms.

Linear and non-linear models have been extensively utilised for the estimation of net and metabolisable energy requirements and for the estimation of the efficiencies of utilising dietary energy for maintenance and tissue gain. In growing animals, biological principles imply that energy retention rate is non-linearly related to the energy intake level because successive increments in energy intake above maintenance result in diminishing returns for tissue energy accretion. Heat production in growing cattle has been traditionally described by logarithmic regression and exponential models. The objective of the present study was to develop Bayesian models of energy retention and heat production in growing cattle using parametric and non-parametric techniques. Parametric models were used to represent models traditionally employed to describe energy use in growing steers and heifers whereas the non-parametric approach was introduced to describe energy utilisation while accounting for non-linearities without specifying a particular functional form. The Bayesian framework was used to incorporate prior knowledge of bioenergetics on tissue retention and heat production and to estimate net and metabolisable energy requirements (NEM and MEM, respectively), and the partial efficiencies of utilising dietary metabolisable energy for maintenance (km) and tissue energy gain (kg). The database used for the study consisted of 719 records of indirect calorimetry on steers and non-pregnant, non-lactating heifers. The NEM was substantially larger in energy retention models (ranged from 0.40 to 0.50 MJ/kg BW0.75.day) than were NEM estimates from heat-production models (ranged from 0.29 to 0.49 MJ/kg BW0.75.day). Similarly, km was also larger in energy retention models than in heat production models. These differences are explained by the nature of y-intercepts (NEM) in these two models. Energy retention models estimate fasting catabolism as the y-intercept, while heat production models estimate fasting heat production. Conversely, MEM was virtually identical in all models and approximately equal to 0.53 MJ/kg BW0.75.day in this database.

The idea of managing cows for extended lactations rather than lactations of the traditional length of 1 yr primarily arose from observations of increasing problems with infertility and cows being dried off with high milk yields. However, it is vital for the success of extended lactation practices that cows are able to maintain milk yield per feeding day when the length of the calving interval (CInt) is increased. Milk yield per feeding day is defined as the cumulated lactation milk yield divided by the sum of days between 2 consecutive calvings. The main objective of this study was to investigate the milk production of cows managed for lactations of different lengths, and the primary aim was to investigate the relationship between CInt, parity, and milk yield. Five measurements of milk yield were used: energy-corrected milk (ECM) yield per feeding day, ECM yield per lactating day, cumulative ECM yield during the first 305 d of lactation, as well as ECM yield per day during early and late lactation. The analyses were based on a total of 1,379 completed lactations from cows calving between January 2007 and May 2013 in 4 Danish commercial dairy herds managed for extended lactation for several years. Herd-average CInt length ranged from 414 to 521 d. The herds had Holstein, Jersey, or crosses between Holstein, Jersey, and Red Danish cows with average milk yields ranging from 7,644 to 11,286. kg of ECM per cow per year. A significant effect of the CInt was noted on all 5 measurements of milk yield, and this effect interacted with parity for ECM per feeding day, ECM per lactating day and ECM per day during late lactation. The results showed that cows were at least able to produce equivalent ECM per feeding day with increasing CInt, and that first- and second-parity cows maintained ECM per lactating day. Cows with a CInt between 17 and 19. mo produced 476 kg of ECM more during the first 305 d compared with cows with a CInt of less than 13 mo. Furthermore, early-lactation ECM yield was greater for all cows and late-lactation ECM yield was less for second-parity and older cows when undergoing an extended compared with a shorter lactation. Increasing CInt increased the dry period length with 3 to 5. d. In conclusion, the group of cows with longer CInt were able to produce at least equivalent amounts of ECM per feeding day when the CInt was up to 17 to 19 mo on these 4 commercial dairy farms.

Enteric methane emission is a major greenhouse gas from livestock production systems worldwide. Dietary manipulation may be an effective emission-reduction tool; however, the associated costs may preclude its use as a mitigation strategy. Several studies have identified dietary manipulation strategies for the mitigation of emissions, but studies examining the costs of reducing methane by manipulating diets are scarce. Furthermore, the trade-off between increase in dietary costs and reduction in methane emissions has only been determined for a limited number of production scenarios. The objective of this study was to develop an optimization framework for the joint minimization of dietary costs and methane emissions based on the identification of a set of feasible solutions for various levels of trade-off between emissions and costs. Such a set of solutions was created by the specification of a systematic grid of goal programming weights, enabling the decision maker to choose the solution that achieves the desired trade-off level. Moreover, the model enables the calculation of emission-mitigation costs imputing a trading value for methane emissions. Emission imputed costs can be used in emission-unit trading schemes, such as cap-and-trade policy designs. An application of the model using data from lactating cows from dairies in the California Central Valley is presented to illustrate the use of model-generated results in the identification of optimal diets when reducing emissions. The optimization framework is flexible and can be adapted to jointly minimize diet costs and other potential environmental impacts (e.g., nitrogen excretion). It is also flexible so that dietary costs, feed nutrient composition, and animal nutrient requirements can be altered to accommodate various production systems.

Water is essential in livestock production systems. In typical dairy production systems, 90% of the total water used by a dairy farm is attributed to feed production. Theoretically, ration manipulation is a method to potentially reduce the irrigation water needed for feed crops without dramatically increasing diet costs. However, published quantitative studies on the relationship between feed production and water use that are integrated with linear programming models are scarce. The overall objective of this study was to develop an optimization framework that could achieve a balance between minimization of dietary costs and dietary irrigation water usage, and that could be used as a framework for future research and models for various livestock production systems. Weighted goal programming models were developed to minimize the dietary costs and irrigation water usage for a hypothetical cow under 8 different environmental scenarios. The environmental conditions used a 2 × 2 × 2 factorial design, including 2 atmospheric CO₂ concentrations (400 and 550 ppm), 2 water years (dry and wet), and 2 irrigation methods (furrow and drip). A systematic weighting scheme was used to model the trade-off between minimizing diet cost and minimizing irrigation water use for feedstuffs. Each environmental condition generated a set of distinct diets, which each met the same nutrient requirements of the hypothetical cow but had a different water usage when the weighting scheme was changed from weighting minimum diet costs to minimum irrigation water usage. For water resource planning in areas of dairy production, this set of unique solutions provides the decision maker with different feeding options according to diet cost, water usage, and available feeds. As water was more constrained, dietary dry matter intake increased, concentrations of neutral detergent fiber, ether extract, and energy decreased, and the concentration of lignin increased because less nutritive but more water-saving feedstuffs were included in the diet. Mitigation costs of water usage were calculated from goal programming results and indicated that the potential value of water under water-limited conditions (e.g., in a drought region) was higher than that under water-sufficient conditions. However, a smaller increase in feed costs can initially significantly reduce water usage compared with that of a least-cost diet, which implies that the reduction of water usage through ration manipulation might be possible. This model serves as a framework for the study of irrigation water usage in dairy production and other livestock production systems and for decision-making processes involved in water resources planning in the broader area of animal production.

Quantification of dairy cattle nitrogen (N) excretion and secretion is necessary to improve the efficiency with which feed N is converted to milk N (ENU). Faecal and urinary N excretion and milk N secretion are correlated with each other and thus are more accurately described by a multivariate model that can accommodate the covariance between the three observations than by three separate univariate models. Further, by simultaneously predicting the three routes of excretion and taking advantage of the mass balance relationships between them, covariate effects on N partitioning from feed to faeces and absorbed N and from absorbed N to milk and urine N and animal ENU can be estimated. A database containing 1094 lactating dairy cow observations collated from indirect calorimetry experiments was used for model development. Dietary metabolisable energy content (ME, MJ/kg DM) increased ENU at a decreasing rate, increased the efficiency with which feed N was converted to absorbed N and decreased the efficiency with which absorbed N was converted to milk N. However, the parameter estimate of the effect of ME on post-absorption efficiency was not different from zero when the model was fitted to a data subset in which net energy and metabolisable protein were at or above requirement. This suggests the effect of ME on post-absorption N use is dependent on the energy status of the animal.