Metabolism of the lactating cow. I. Animal elements of a mechanistic model

Predicting fat cover in beef cattle to make on-farm management decisions: a review of assessing fat and of modeling fat deposition

Demands of domestic and foreign market specifications of carcass weight and fat cover, of beef cattle, have led to the development of cattle growth models that predict fat cover to assist on-farm managers make management decisions. The objectives of this paper are 4-fold: 1) conduct a brief review of the biological basis of adipose tissue accretion, 2) briefly review live and carcass assessments of beef cattle, and carcass grading systems used to develop quantitative compositional and quality indices, 3) review fat deposition models: Davis growth model (DGM), French National Institute for Agricultural Research growth model (IGM), Cornell Value Discovery System (CVDS), and BeefSpecs drafting tool (BeefSpecsDT), and 4) appraise the process of translating science and practical skills into research/decision support tools that assist the Beef industry improve profitability. The r2 for live and carcass animal assessments, using several techniques across a range of species and traits, ranged from 0.61 to 0.99 and from 0.52 to 0.99, respectively. Model evaluations of DGM and IGM were conducted using Salers heifers (n = 24) and Angus-Hereford steers (n = 15) from an existing publication and model evaluations of CVDS and BeefSpecsDT were conducted using Angus steers (n = 33) from a research trial where steers were grain finished for 101 d in a commercial feedlot. Evaluating the observed and predicted fat mass (FM) is the focus of this review. The FM mean bias for Salers heifers were 7.5 and 1.3 kg and the root mean square error of prediction (RMSEP) were 31.2 and 27.8 kg and for Angus-Hereford steers the mean bias were -4.0 and -10.5 kg and the RMSEP were 9.14 and 21.5 kg for DGM and IGM, respectively. The FM mean bias for Angus steers were -5.61 and -2.93 kg and the RMSEP were 12.3 and 13.4 kg for CVDS and BeefSpecsDT, respectively. The decomposition for bias, slope, and deviance were 21%, 12%, and 68% and 5%, 4%, and 91% for CVDS and BeefSpecsDT, respectively. The modeling efficiencies were 0.38 and 0.27 and the models were within a 20 kg level of tolerance 91% and 88% for CVDS and BeefSpecsDT, respectively. Fat deposition models reported in this review have the potential to assist the beef industry make on-farm management decisions on live cattle before slaughter and improve profitability. Modelers need to continually assess and improve their models but with a caveat of 1) striving to minimize inputs, and 2) choosing on-farm inputs that are readily available.

Quantification of methane emitted by ruminants: a review of methods

The contribution of greenhouse gas (GHG) emissions from ruminant production systems varies between countries and between regions within individual countries. The appropriate quantification of GHG emissions, specifically methane (CH4), has raised questions about the correct reporting of GHG inventories and, perhaps more importantly, how best to mitigate CH4 emissions. This review documents existing methods and methodologies to measure and estimate CH4 emissions from ruminant animals and the manure produced therein over various scales and conditions. Measurements of CH4 have frequently been conducted in research settings using classical methodologies developed for bioenergetic purposes, such as gas exchange techniques (respiration chambers, headboxes). While very precise, these techniques are limited to research settings as they are expensive, labor-intensive, and applicable only to a few animals. Head-stalls, such as the GreenFeed system, have been used to measure expired CH4 for individual animals housed alone or in groups in confinement or grazing. This technique requires frequent animal visitation over the diurnal measurement period and an adequate number of collection days. The tracer gas technique can be used to measure CH4 from individual animals housed outdoors, as there is a need to ensure low background concentrations. Micrometeorological techniques (e.g., open-path lasers) can measure CH4 emissions over larger areas and many animals, but limitations exist, including the need to measure over more extended periods. Measurement of CH4 emissions from manure depends on the type of storage, animal housing, CH4 concentration inside and outside the boundaries of the area of interest, and ventilation rate, which is likely the variable that contributes the greatest to measurement uncertainty. For large-scale areas, aircraft, drones, and satellites have been used in association with the tracer flux method, inverse modeling, imagery, and LiDAR (Light Detection and Ranging), but research is lagging in validating these methods. Bottom-up approaches to estimating CH4 emissions rely on empirical or mechanistic modeling to quantify the contribution of individual sources (enteric and manure). In contrast, top-down approaches estimate the amount of CH4 in the atmosphere using spatial and temporal models to account for transportation from an emitter to an observation point. While these two estimation approaches rarely agree, they help identify knowledge gaps and research requirements in practice.

Evaluation of Molly model predictions of ruminal fermentation, nutrient digestion, and performance by dairy cows consuming ryegrass-based diets

Several studies have been conducted to improve grazing management and supplementation in pasture-based systems. However, it is necessary to develop tools that integrate the available information linking the representation of biological processes with animal performance for use in decision making. The objective of this study was to evaluate the precision and accuracy of the Molly cow model predictions of ruminal fermentation, nutrient digestion, and animal performance by cows consuming pasture-based diets to identify model strengths and weaknesses, and to derive new digestive parameters when relevant. Model modifications for adipose tissue, protein synthesis in lean body mass and viscera representation were included. Data used for model evaluations were collected from 25 publications containing 115 treatment means sourced from studies conducted with lactating dairy cattle. The inclusion criteria were that diets contained ≥45% perennial ryegrass (Lolium perenne L.), and that dry matter intake, dietary ingredient composition, and nutrient digestion observations were reported. Animal performance and N excretion variables were also included if they were reported. Model performance was assessed before and after model reparameterization of selected digestive parameters, global sensitivity analysis was conducted after reparameterization, and a 5-fold cross evaluation was performed. Although rumen fermentation predictions were not significantly improved, rumen volatile fatty acids absorption rates were recalculated, which improved the concordance correlation coefficient (CCC) for rumen propionate and ammonia concentration predictions but decreased CCC for acetate predictions. Similar degradation rates of crude protein were observed for grass and total mixed ration diets, but rumen-undegradable protein predictions seemed to be affected by the solubility of the protein source as was the intestinal digestibility coefficient. Ruminal fiber degradation was greater after reparameterization, driven primarily by hemicellulose degradation. Predictions of ruminal and fecal outflow of neutral detergent fiber and acid detergent fiber, as well as total fecal output predictions, improved significantly after reparameterization. Blood urea N and urinary N excretion predictions resulted in similar accuracy using both sets of model parameters, whereas fecal N excretion predictions were significantly improved after reparameterization. Body weight and body condition score predictions were greatly improved after model modifications and reparameterization. Before reparameterization, yield predictions for daily milk, milk fat, milk protein, and milk lactose were greatly overestimated (mean bias of 61.0, 58.7, 73.7, and 64.6% of mean squared error, respectively). Although this problem was partially addressed by model modifications and reparameterization (mean bias of 3.2, 1.1, 1.7, and 0.4% of mean squared error, respectively), CCC values were still small. The ability of the model to predict grass digestion and animal performance in dairy cows consuming pasture-based diets was improved, demonstrating the applicability of this model to these productive systems. However, the failure to predict grass digestion based on standard model inputs without reparameterization indicates there are still fundamental challenges in characterizing feeds for this model.

Estimating in vitro ruminal ammonia-N using multiple linear models and artificial neural networks based on the CNCPS nitrogenous fractions of cattle rations with low concentrate/roughage ratios

The objectives of this study were to investigate the relationship between the in vitro ruminal ammonia nitrogen (NH₃ -N) concentration and the Cornell Net Carbohydrate and Protein System (CNCPS) N-fractions of feeds for cattle and further compare the performance of developing multiple linear regression (MLR) and artificial neural network (ANN) models in estimating the NH₃ -N concentration in rumen fermentation. Two data sets were established, of which the training data set containing forty-five rations for cattle with concentrate/roughage ratios of 50:50, 40:60, 30:70, 20:80 and 10:90 used for developing models and the test data set containing ten other rations with the same concentrate/roughage ratios with the training data set were used for validating of models. The NH₃ -N concentrations of feed samples were measured using an in vitro incubation technique. The CNCPS N-fractions (g), for example PB₁ (rapidly degraded true protein), PB₂ (neutral detergent soluble nitrogen), PB₃ (acid detergent soluble nitrogen) of rations, were calculated based on chemical analysis. Statistical analysis indicated that the NH₃ -N concentration (mg) was significantly correlated with the CNCPS N-fractions (g) PB₁ , PB₂ and PB₃ in a multiple linear pattern: NH₃ -N = (130.70±33.80) PB₁  + (155.83±17.89) PB₂ - (85.44±37.69) PB₃  + (42.43±1.05), R²  = 0.77, p < 0.0001, n = 45. The results indicated that both MLR and ANN models were suitable for predicting in vitro NH₃ -N concentration of rations using CNCPS N-fractions PB₁ , PB₂ , and PB₃ as independent variables while the neural network model showed better performance in terms of greater r² , CCC and lower RMSPE between the observed and predicted values.

A revised representation of ruminal pH and digestive reparameterization of the Molly cow model

Ruminal pH is a critical factor to regulate nutrient degradation and fermentation. However, it has been poorly predicted in the Molly cow model, and recent improvements in the representation of nitrogen cycling across the rumen wall altered some of the modeled responses to feed nutrients, resulting in some model bias. The objectives of this study were to further improve the representation of pH and to refit parameters related to ruminal metabolism and nutrient digestion in the model to resolve this bias, and to use the improved model to estimate nitrogen and energy fluxes with varying rumen-degradable protein (RDP; 40 vs. 60%) and ruminally degraded starch (RDSt; 50 vs. 75%). A meta data set containing 284 peer reviewed studies with 1,223 treatment means was used to derive parameter estimates for ruminal metabolism and nutrient digestions. Refitting the parameters significantly improved the accuracy and precision of the model predictions for ruminal nutrient outflow [acid detergent fiber (ADF), neutral detergent fiber (NDF), total N, microbial N, nonammonia N, and nonammonia nonmicrobial N], ammonia and blood urea concentrations, and fecal nutrient outflow (protein, ADF, and NDF). The prediction error for body weight was decreased from 19.3 to 6.2% with decreased mean bias (from 76.0 to 11.5%) and slope bias (from 17.2 to 7.7%), primarily due to improved representations of ruminal dry matter and liquid pool size. Adding ammonia concentration as a driver to the pH equation increased the precision of predicted ruminal pH and, thereby, the precision of predicted volatile fatty acid (VFA) concentrations, due to improved representation of pH regulation of VFA production rates. Although minor mean and slope bias were observed for ruminal pH and VFA concentrations, the concordance correlation coefficients indicated that much of the observed variation in these variables remains unexplained. Overall, the biological functions of nutrient degradation and digestion appear to be represented without bias. Simulated results indicated that decreasing RDP and RDSt proportions in an isonitrogenous and isocaloric diet can slightly improve N efficiency, and increasing RDSt proportions can increase energy efficiency.

Molly reborn in C++ and R

The dairy cow model 'Molly' is a mixed discrete event-continuous system model that simulates feeding, metabolism and lactation of dairy cows. Decades of model development have resulted in a valuable tool in dairy science. Due to the deprecation of the ACSL (Advanced Continuous Simulation Language) programming language, Molly has been translated into C++. This paper describes the translation process and discusses the advantages of the new implementation, one of which is the ability to run Molly within RStudio, a popular integrated development environment (IDE) for data science.

Use of Mechanistic Nutrition Models to Identify Sustainable Food Animal Production

To feed people in the coming decades, an increase in sustainable animal food production is required. The efficiency of the global food production system is dependent on the knowledge and improvement of its submodels, such as food animal production. Scientists use statistical models to interpret their data, but models are also used to understand systems and to integrate their components. However, empirical models cannot explain systems. Mechanistic models yield insight into the mechanism and provide guidance regarding the exploration of the system. This review offers an overview of models, from simple empirical to more mechanistic models. We demonstrate their applications to amino acid transport, mass balance, whole-tissue metabolism, digestion and absorption, growth curves, lactation, and nutrient excretion. These mechanistic models need to be integrated into a full model using big data from sensors, which represents a new challenge. Soon, training in quantitative and computer science skills will be required to develop, test, and maintain advanced food system models.

Effect of stearic or oleic acid on milk performance and energy partitioning when fed in diets with low and high rumen-active unsaturated fatty acids in early lactation

This experiment was conducted to determine the effects of stearic acid (SA; C18:0) or rumen-protected oleic acid (OA; C18:1 cis-9) on milk performance and energy partitioning of early lactation cows when supplemented in diets with low and high level of rumen unsaturated fatty acids (RUFA). In low RUFA experiment (LRUFA), FA supplement rich in either SA or calcium salts OA was added to a basal diet with a low concentration of RUFA (0.75% vs. 1.4%, LRUFA-SA vs. LRUFA-OA). In high RUFA experiment (HRUFA), 2% soybean oil was added to the diet fed in the LRUFA experiment. In each experiment, 30 multiparous cows were blocked by parity and predicted transmitting ability for milk yield and were randomly fed 1 of 2 treatment diets from 2 to 13 wk postpartum. In the LRUFA experiment, LRUFA-SA had 2.4 kg/d more dry matter intake (DMI) (P < 0.01), 3.8 kg/d more energy-corrected milk (P < 0.01), and 0.3% units more milk fat percentage (P < 0.01) and 0.2 kg/d more milk fat yield (P < 0.01). Dietary treatments did not affect body weight, energy balance, and energy intake partitioning into milk, maintenance, and body tissues (P > 0.1). In the HRUFA experiment, HRUFA-SA had 1.4 kg/d more DMI (P = 0.03) but similar milk and milk components yields (P > 0.1). HRUFA-SA had a tendency to gain more body weight (P = 0.07) and had more positive energy balance (P = 0.01) and decreased gross feed efficiency (milk yield/DMI) (P = 0.01). Consistently, HRUFA-SA increased intake energy partitioning into body tissues (P = 0.02) and decreased energy partitioning into milk (P = 0.01). In summary, SA supplementation had more DMI relative to OA, but the effects on milk and milk fat production were different and affected by the level of RUFA in the basal diet. In application, SA supplementation was more effective to improve milk production when included in the basal diet with the low RUFA.

ASN-ASAS SYMPOSIUM: FUTURE OF DATA ANALYTICS IN NUTRITION: Mathematical modeling in ruminant nutrition: approaches and paradigms, extant models, and thoughts for upcoming predictive analytics1,2

This paper outlines typical terminology for modeling and highlights key historical and forthcoming aspects of mathematical modeling. Mathematical models (MM) are mental conceptualizations, enclosed in a virtual domain, whose purpose is to translate real-life situations into mathematical formulations to describe existing patterns or forecast future behaviors in real-life situations. The appropriateness of the virtual representation of real-life situations through MM depends on the modeler's ability to synthesize essential concepts and associate their interrelationships with measured data. The development of MM paralleled the evolution of digital computing. The scientific community has only slightly accepted and used MM, in part because scientists are trained in experimental research and not systems thinking. The scientific advancements in ruminant production have been tangible but incipient because we are still learning how to connect experimental research data and concepts through MM, a process that is still obscure to many scientists. Our inability to ask the right questions and to define the boundaries of our problem when developing models might have limited the breadth and depth of MM in agriculture. Artificial intelligence (AI) has been developed in tandem with the need to analyze big data using high-performance computing. However, the emergence of AI, a computational technology that is data-intensive and requires less systems thinking of how things are interrelated, may further reduce the interest in mechanistic, conceptual MM. Artificial intelligence might provide, however, a paradigm shift in MM, including nutrition modeling, by creating novel opportunities to understand the underlying mechanisms when integrating large amounts of quantifiable data. Associating AI with mechanistic models may eventually lead to the development of hybrid mechanistic machine-learning modeling. Modelers must learn how to integrate powerful data-driven tools and knowledge-driven approaches into functional models that are sustainable and resilient. The successful future of MM might rely on the development of redesigned models that can integrate existing technological advancements in data analytics to take advantage of accumulated scientific knowledge. However, the next evolution may require the creation of novel technologies for data gathering and analyses and the rethinking of innovative MM concepts rather than spending resources in collecting futile data or amending old technologies.

A revised representation of urea and ammonia nitrogen recycling and use in the Molly cow model

Accurately predicting nitrogen (N) digestion, absorption, and metabolism will allow formulation of diets that more closely match true animal needs from a broad range of feeds, thereby allowing efficiency of N utilization and profit to be maximized. The objectives of this study were to advance representations of N recycling between blood and the gut and urinary N excretion in the Molly cow model. The current work includes enhancements (1) representing ammonia passage to the small intestine; (2) deriving parameters defining urea synthesis and ruminal urea entry rates; (3) adding representations of intestinal urea entry, microbial protein synthesis in the hindgut, and fecal urea-N excretion; and (4) altering existing urinary N excretion equations to scale with body weight and adding purine derivatives as a component of urinary N excretion. After the modifications, prediction errors for ruminal outflows of total N, microbial N, and nonammonia, nonmicrobial N were 29.8, 32.3, and 26.2% of the respective observed mean values. Prediction errors of each were approximately 7 percentage units lower than the corresponding values before model modifications and fitting due primarily to decreased slope bias. The revised model predicted ruminal ammonia and blood urea concentrations with substantially decreased overall error and reductions in slope and mean bias. Prediction errors for gut urea-N entry were decreased from 70.5 to 26.7%, which was also a substantial improvement. Adding purine derivatives to urinary N predictions improved the accuracy of predictions of urinary N output. However, urinary urea-N excretion remains poorly predicted with 69.0% prediction errors, due mostly to overestimated urea-N entry rates. Adding representations of undigested microbial nucleic acids, microbial protein synthesized in the hindgut, and urea-N excretion in feces decreased prediction errors for fecal N excretion from 21.1 to 17.1%. The revised model predicts that urea-N entry into blood accounts for approximately 64% of dietary N intake, of which 64% is recycled to the gut lumen. Between 48 and 67% of the urea recycled to the gut flows into the rumen largely depending on diet, which accounts for 29 to 54% of total ruminal ammonia production, and 65 to 76% of this ammonia-N is captured in microbial protein, which represents 17% of N intake. Based on model simulations, feeding a diet with moderately low crude protein and high rumen-undegradable protein could increase apparent ruminal N efficiency by 20%.

Standing on giant shoulders: a personal recollection of the lives and achievements of eminent animal scientists 1965–2015

This article is a compilation of pieces that are part biographical sketches and part personal recollections of 18 scientists with whom the author was acquainted in three continents over almost 50 years. The subjects, from Australia, the United States and the United Kingdom, will be recognisable to many in the field, especially more experienced scientists. For younger scientists, the article also is intended to put a human face on a generation of famous researchers who otherwise would be familiar only as somewhat anonymous authors of classic papers and reviews.

Evaluating the ability of a lifetime nutrient-partitioning model for simulating the performance of Australian Holstein dairy cows

The present study determined the ability of a lifetime nutrient-partitioning model to simulate individual genetic potentials of Australian Holstein cows. The model was initially developed in France and has been shown to be able to accurately simulate performance of individual cows from various breeds. Generally, it assumes that the curves of cow performance differ only in terms of scaling, but the dynamic shape is universal. In other words, simulations of genetic variability in performance between cow genotypes can be performed using scaling parameters to simply scale the performance curves up or down. Validation of the model used performance data from 63 lactations of Australian Holstein cows offered lucerne cubes plus grain-based supplement. Individual cow records were used to derive genetic scaling parameters for each animal by calibrating the model to minimise root mean-square errors between observed and fitted values, cow by cow. The model was able to accurately fit the curves of bodyweight, milk fat concentration, milk protein concentration and milk lactose concentration with a high degree of accuracy (relative prediction errors <5%). Daily milk yield and weekly body condition score were satisfactorily predicted, although slight under-predictions of milk yield were identified during the last stage of lactation (relative prediction errors ≈11.1–15.6%). The prediction of feed intake was promising, with the value of relative prediction error of 18.1%. The results also suggest that the current recommendation of energy required for maintenance of pasture-based cows might be under-estimated. In conclusion, this model can be used to simulate genetic variability in the production potential of Australian cows. Thus, it can be used for simulation of consequences of future genetic-selection strategies on lifetime performance and efficiency of individual cows.

A dynamic, mechanistic model of metabolism in adipose tissue of lactating dairy cattle

Research in dairy cattle biology has resulted in a large body of knowledge on nutrition and metabolism in support of milk production and efficiency. This quantitative knowledge has been compiled in several model systems to balance and evaluate rations and predict requirements. There are also systems models for metabolism and reproduction in the cow that can be used to support research programs. Adipose tissue plays a significant role in the success and efficiency of lactation, and recent research has resulted in several data sets on genomic differences and changes in gene transcription of adipose tissue in dairy cattle. To fully use this knowledge, we need to build and expand mechanistic, dynamic models that integrate control of metabolism and production. Therefore, we constructed a second-generation dynamic, mechanistic model of adipose tissue metabolism of dairy cattle. The model describes the biochemical interconversions of glucose, acetate, β-hydroxybutyrate (BHB), glycerol, C16 fatty acids, and triacylglycerols. Data gathered from our own research and published references were used to set equation forms and parameter values. Acetate, glucose, BHB, and fatty acids are taken up from blood. The fatty acids are activated to the acyl coenzyme A moieties. Enzymatically catalyzed reactions are explicitly described with parameters including maximal velocity and substrate sensitivity. The control of enzyme activity is partially carried out by insulin and norepinephrine, portraying control in the cow. Model behavior was adequate, with sensitive responses to changing substrates and hormones. Increased nutrient uptake and increased insulin stimulate triacylglycerol synthesis, whereas a reduction in nutrient availability or increase in norepinephrine increases triacylglycerol hydrolysis and free fatty acid release to blood. This model can form a basis for more sophisticated integration of existing knowledge and future studies on metabolic efficiency of dairy cattle.

Ruminal pH predictions for beef cattle: Comparative evaluation of current models

This study evaluated 8 empirical models for their ability to accurately predict mean ruminal pH in beef cattle fed a wide range of diets. Models tested that use physically effective fiber (peNDF) as a dependent variable were Pitt et al. (1996, PIT), Mertens (1997, MER), Fox et al. (2004, FOX), Zebeli et al. (2006, ZB6), and Zebeli et al. (2008, ZB8), and those that use rumen VFA were Tamminga and Van Vuuren (1988, TAM), Lescoat and Sauvant (1995, LES), and Allen (1997, ALL). A data set of 65 published papers (231 treatment means) for beef cattle was assembled that included information on animal characteristics, diet composition, and ruminal fermentation and mean pH. Model evaluations were based on mean square prediction error (MSPE), concordance correlation coefficient (CCC), and regression analysis. The prediction potential of the models varied with low root MSPE (RMSPE) values of 4.94% and 5.37% for PIT and FOX, RMSPE values of 9.66% and 12.55% for ZB6 and MER, and intermediate RMSPE values of 5.66% to 6.26% for the other models. For PIT and FOX, with the lowest RMSPE, approximately 96% of MSPE was due to random error, whereas for ZB6 and MER, with the highest RMSPE, 15.85% and 23.42% of MSPE, respectively, was due to linear bias, and 37.19% and 60.12% of the error, respectively, was due to deviation of the regression slope from unity. The CCC was greatest for PIT (0.67) and FOX (0.62), followed by 0.60 for LES and TAM, 0.52 for ZB8, 0.39 for MER, 0.34 for ALL, and 0.22 for ZB6. Residuals plotted against model-predicted values showed linear bias (P < 0.001) for all models except PIT (P = 0.976) and FOX (P = 0.054) and mean bias (P < 0.001) except for FOX (P = 0.293), LES (P = 0.215), and TAM (P = 0.119). The study showed that the empirical models PIT and FOX, based on peNDF, and LES and TAM, based on VFA, are preferred over the others for prediction of mean ruminal pH in beef cattle fed a wide range of diets. Several animal (BW and intake), diet (forage and OM contents), and ruminal (ammonia and acetate concentrations) factors were (P < 0.001) related to the residuals for each model. We conclude that the accuracy of prediction of mean ruminal pH was relatively low for all extant models. Consideration of factors in addition to peNDF and total VFA, as well as the use of data from studies with continuous measurement of ruminal pH over 24 h or more, would be useful in the development of improved models for predicting ruminal pH in beef cattle.

Prediction of enteric methane emissions from cattle

Agriculture has a key role in food production worldwide and it is a major component of the gross domestic product of several countries. Livestock production is essential for the generation of high quality protein foods and the delivery of foods in regions where animal products are the main food source. Environmental impacts of livestock production have been examined for decades, but recently emission of methane from enteric fermentation has been targeted as a substantial greenhouse gas source. The quantification of methane emissions from livestock on a global scale relies on prediction models because measurements require specialized equipment and may be expensive. The predictive ability of current methane emission models remains poor. Moreover, the availability of information on livestock production systems has increased substantially over the years enabling the development of more detailed methane prediction models. In this study, we have developed and evaluated prediction models based on a large database of enteric methane emissions from North American dairy and beef cattle. Most probable models of various complexity levels were identified using a Bayesian model selection procedure and were fitted under a hierarchical setting. Energy intake, dietary fiber and lipid proportions, animal body weight and milk fat proportion were identified as key explanatory variables for predicting emissions. Models here developed substantially outperformed models currently used in national greenhouse gas inventories. Additionally, estimates of repeatability of methane emissions were lower than the ones from the literature and multicollinearity diagnostics suggested that prediction models are stable. In this context, we propose various enteric methane prediction models which require different levels of information availability and can be readily implemented in national greenhouse gas inventories of different complexity levels. The utilization of such models may reduce errors associated with prediction of methane and allow a better examination and representation of policies regulating emissions from cattle.

Revised digestive parameter estimates for the Molly cow model

The Molly cow model represents nutrient digestion and metabolism based on a mechanistic representation of the key biological elements. Digestive parameters were derived ad hoc from literature observations or were assumed. Preliminary work determined that several of these parameters did not represent the true relationships. The current work was undertaken to derive ruminal and postruminal digestive parameters and to use a meta-approach to assess the effects of interactions among nutrients and identify areas of model weakness. Model predictions were compared with a database of literature observations containing 233 treatment means. Mean square prediction errors were assessed to characterize model performance. Ruminal pH prediction equations had substantial mean bias, which caused problems in fiber digestion and microbial growth predictions. The pH prediction equation was reparameterized simultaneously with the several ruminal and postruminal digestion parameters, resulting in more realistic parameter estimates for ruminal fiber digestion, and moderate reductions in prediction errors for pH, neutral detergent fiber, acid detergent fiber, and microbial N outflow from the rumen; and postruminal digestion of neutral detergent fiber, acid detergent fiber, and protein. Prediction errors are still large for ruminal ammonia and outflow of starch from the rumen. The gain in microbial efficiency associated with fat feeding was found to be more than twice the original estimate, but in contrast to prior assumptions, fat feeding did not exert negative effects on fiber and protein degradation in the rumen. Microbial responses to ruminal ammonia concentrations were half saturated at 0.2mM versus the original estimate of 1.2mM. Residuals analyses indicated that additional progress could be made in predicting microbial N outflow, volatile fatty acid production and concentrations, and cycling of N between blood and the rumen. These additional corrections should lead to an even more robust representation of the effects of dietary nutrients on ruminal metabolism and nutrient absorption, of animal performance, and the environmental impact of dairy production.

Application of Top-Down and Bottom-up Systems Approaches in Ruminant Physiology and Metabolism

Systems biology is a computational field that has been used for several years across different scientific areas of biological research to uncover the complex interactions occurring in living organisms. Applications of systems concepts at the mammalian genome level are quite challenging, and new complimentary computational/experimental techniques are being introduced. Most recent work applying modern systems biology techniques has been conducted on bacteria, yeast, mouse, and human genomes. However, these concepts and tools are equally applicable to other species including ruminants (e.g., livestock). In systems biology, both bottom-up and top-down approaches are central to assemble information from all levels of biological pathways that must coordinate physiological processes. A bottom-up approach encompasses draft reconstruction, manual curation, network reconstruction through mathematical methods, and validation of these models through literature analysis (i.e., bibliomics). Whereas top-down approach encompasses metabolic network reconstructions using ‘omics’ data (e.g., transcriptomics, proteomics) generated through DNA microarrays, RNA-Seq or other modern high-throughput genomic techniques using appropriate statistical and bioinformatics methodologies. In this review we focus on top-down approach as a means to improve our knowledge of underlying metabolic processes in ruminants in the context of nutrition. We also explore the usefulness of tissue specific reconstructions (e.g., liver and adipose tissue) in cattle as a means to enhance productive efficiency.

A teleonomic model describing performance (body, milk and intake) during growth and over repeated reproductive cycles throughout the lifespan of dairy cattle. 1. Trajectories of life function priorities and genetic scaling

The prediction of the control of nutrient partitioning, particularly energy, is a major issue in modelling dairy cattle performance. The proportions of energy channelled to physiological functions (growth, maintenance, gestation and lactation) change as the animal ages and reproduces, and according to its genotype and nutritional environment. This is the first of two papers describing a teleonomic model of individual performance during growth and over repeated reproductive cycles throughout the lifespan of dairy cattle. The conceptual framework is based on the coupling of a regulating sub-model providing teleonomic drives to govern the work of an operating sub-model scaled with genetic parameters. The regulating sub-model describes the dynamic partitioning of a mammal female's priority between life functions targeted to growth (G), ageing (A), balance of body reserves (R) and nutrient supply of the unborn (U), newborn (N) and suckling (S) calf. The so-called GARUNS dynamic pattern defines a trajectory of relative priorities, goal directed towards the survival of the individual for the continuation of the specie. The operating sub-model describes changes in body weight (BW) and composition, foetal growth, milk yield and composition and food intake in dairy cows throughout their lifespan, that is, during growth, over successive reproductive cycles and through ageing. This dynamic pattern of performance defines a reference trajectory of a cow under normal husbandry conditions and feed regimen. Genetic parameters are incorporated in the model to scale individual performance and simulate differences within and between breeds. The model was calibrated for dairy cows with literature data. The model was evaluated by comparison with simulations of previously published empirical equations of BW, body condition score, milk yield and composition and feed intake. This evaluation showed that the model adequately simulates these production variables throughout the lifespan, and across a range of dairy cattle genotypes.

Effect of high-sugar grasses on methane emissions simulated using a dynamic model

High-sugar grass varieties have received considerable attention for their potential ability to decrease N excretion in cattle. However, feeding high-sugar grasses alters the pattern of rumen fermentation, and no in vivo studies to date have examined this strategy with respect to another environmental pollutant: methane (CH(4)). Modeling allows us to examine potential outcomes of feeding strategies under controlled conditions, and can provide a useful framework for the development of future experiments. The purpose of the present study was to use a modeling approach to evaluate the effect of high-sugar grasses on simulated CH(4) emissions in dairy cattle. An extant dynamic, mechanistic model of enteric fermentation and intestinal digestion was used for this evaluation. A simulation database was constructed and analysis of model behavior was undertaken to simulate the effect of (1) level of water-soluble carbohydrate (WSC) increase in dietary dry matter, (2) change in crude protein (CP) and neutral detergent fiber (NDF) content of the plant with an increased WSC content, (3) level of N fertilization, and (4) presence or absence of grain feeding. Simulated CH(4) emissions tended to increase with increased WSC content when CH(4) was expressed as megajoules per day or percent of gross energy intake, but when CH(4) was expressed in terms of grams per kilogram of milk, results were much more variable due to the potential increase in milk yield. As a result, under certain conditions, CH(4) (g/kg of milk) decreased. The largest increases in CH(4) emissions (MJ/d or % gross energy intake) were generally seen when WSC increased at the expense of CP in the diet and this can largely be explained by the representation in the model of the type of volatile fatty acid produced. Effects were lower when WSC increased at the expense of NDF, and intermediary when WSC increased at the expense of a mixture of CP and NDF. When WSC increased at the expense of NDF, simulated milk yield increased and, therefore, CH(4) (g/kg of milk) tended to decrease. Diminished increases of CH(4) (% gross energy intake or g/kg of milk) were simulated when DMI was increased with elevated WSC content. Simulation results suggest that high WSC grass, as a strategy to mitigate N emission, may increase CH(4) emissions, but that results depend on the grass composition, DMI, and the units chosen to express CH(4). Overall, this project demonstrates the usefulness of modeling for hypothesis testing in the absence of observed experimental results.

Development of a dynamic, mechanistic model of lamb metabolism and growth

A dynamic, mechanistic model of lamb metabolism and growth was developed for the purpose of evaluating hypotheses regarding the mechanisms of action of growth promotants. The model relates tissue growth to DNA accretion and protein turn-over. State variables include circulating amino acids, glucose, lipids and acetate; four protein pools (carcass, viscera, other tissues and wool) and storage triacylglycerol are also included. Equations are mainly of the Michaelis-Menten form, allowing for nutrient utilization patterns to be determined by relative tissue affinities for substrates (ko.5), enzymatic capacities (Vmax) and substrate concentrations ([S]). Protein degradation rates are defined as first-order with respect to protein. The model adequately simulated growth from 20 to 40 kg empty body weight. Simulated changes in nutrient input yielded reasonable energy balance response patterns, although theoretical growth efficiencies were greater than those observed in practice. Variations in volatile fatty acid absorption patterns were accommodated well, with predicted nitrogen retention closely approximating experimental observations. The model also responded appropriately to changes in dietary protein level, with body fat varying inversely with amino acid absorption. In summary, the model was found to perform adequately for the purpose of examining mechanisms responsible for alteration of growth and body composition.

DairyMod and EcoMod: biophysical pasture-simulation models for Australia and New Zealand

DairyMod and EcoMod, which are biophysical pasture-simulation models for Australian and New Zealand grazing systems, are described. Each model has a common underlying biophysical structure, with the main differences being in their available management options. The third model in this group is the SGS Pasture Model, which has been previously described, and these models are referred to collectively as ‘the model’. The model includes modules for pasture growth and utilisation by grazing animals, water and nutrient dynamics, animal physiology and production and a range of options for pasture management, irrigation and fertiliser application. Up to 100 independent paddocks can be defined to represent spatial variation within a notional farm. Paddocks can have different soil types, nutrient status, pasture species, fertiliser and irrigation management, but are subject to the same weather. Management options include commonly used rotational grazing management strategies and continuous grazing with fixed or variable stock numbers. A cutting regime simulates calculation of seasonal pasture growth rates. The focus of the present paper is on recent developments to the management routines and nutrient dynamics, including organic matter, inorganic nutrients, leaching and gaseous nitrogen losses, and greenhouse gases. Some model applications are presented and the role of the model in research projects is discussed.

A Redefinition of the Representation of Mammary Cells and Enzyme Activities in a Lactating Dairy Cow Model

The Molly model predicts various aspects of digestion and metabolism in the cow, including nutrient partitioning between milk and body stores. It has been observed previously that the model underpredicts milk component yield responses to nutrition and consequently overpredicts body energy store responses. In Molly, mammary enzyme activity is represented as an aggregate of mammary cell numbers and activity per cell with minimal endocrine regulation. Work by others suggests that mammary cells can cycle between active and quiescent states in response to various stimuli. Simple models of milk production have demonstrated the utility of this representation when using the model to simulate variable milking and nutrient restriction. It was hypothesized that replacing the current representation of mammary cells and enzyme activity in Molly with a representation of active and quiescent cells and improving the representation of endocrine control of cell activity would improve predictions of milk component yield. The static representation of cell numbers was replaced with a representation of cell growth during gestation and early lactation periods and first-order cell death. Enzyme capacity for fat and protein synthesis was assumed to be proportional to cell numbers. Enzyme capacity for lactose synthesis was represented with the same equation form as for cell numbers. Data used for parameter estimation were collected as part of an extended lactation trial. Cows with North American or New Zealand genotypes were fed 0, 3, or 6 kg of concentrate dry matter daily during a 600-d lactation. The original model had root mean square prediction errors of 17.7, 22.3, and 19.8% for lactose, protein, and fat yield, respectively, as compared with values of 8.3, 9.4, and 11.7% for the revised model, respectively. The original model predicted body weight with an error of 19.7% vs. 5.7% for the revised model. Based on these observations, it was concluded that representing mammary synthetic capacity as a function of active cell numbers and revisions to endocrine control of cell activity was meritorious.

Modelling of nutrient partitioning in growing pigs to predict their anatomical body composition. 1. Model description

A dynamic mechanistic model was developed for growing and fattening pigs. The aim of the model was to predict growth rate and the chemical and anatomical body compositions from the digestible nutrient intake of gilts (20–105 kg live weight). The model represents the partitioning of digestible nutrients from intake through intermediary metabolism to body protein and body fat. State variables of the model were lysine, acetyl-CoA equivalents, glucose, volatile fatty acids and fatty acids as metabolite pools, and protein in muscle, hide–backfat, bone and viscera and body fat as body constituent pools. It was assumed that fluxes of metabolites follow saturation kinetics depending on metabolite concentrations. In the model, protein deposition rate depended on the availability of lysine and of acetyl-CoA. The anatomical body composition in terms of muscle, organs, hide–backfat and bone was predicted from the chemical body composition and accretion using allometric relationships. Partitioning of protein, fat, water and ash in muscle, organs, hide–backfat and bone fractions were driven by the rates of muscle protein and body fat deposition. Model parameters were adjusted to obtain a good fit of the experimental data from literature. Differential equations were solved numerically for a given set of initial conditions and parameter values. In the present paper, the model is presented, including its parameterisation. The evaluation of the model is described in a companion paper.

Quantitative aspects of ruminant predicting animal performance

Rations for dairy cattle are currently balanced to meet needs for energy, protein, vitamins, and minerals. While individual vitamins and minerals are considered, energy and protein are generally treated in aggregate even though entities within those aggregates can affect milk yield and composition. Significant efforts have been undertaken to describe ruminal metabolism in detail, but descriptions of post-absorptive metabolism assume constant fractional conversions of energy and protein to milk. A quantitative understanding of nutrient metabolism by the post-absorptive tissues is required, and the splanchnic tissues are critical components of the post-absorptive system as they mediate absorption of nutrients and play a rôle in regulation of metabolite availability.

Glucogenic precursor supply can significantly affect endocrine status as well as splanchnic release of glucose, acetate, lactate, ketones, and the non-essential amino acids. Although the relative affinities of the splanchnic tissues for the essential amino acids (AA) are low as compared with the udder, net clearance on a daily basis represents approximately 2/3 of the net supply to the animal due largely to recycling of AA back to the tissue bed. This could be significantly reduced by stimulating removal and use by the udder as splanchnic affinities are much lower than mammary affinities. Additionally, the essential AA composition of absorbed protein is significantly modified by these tissues due to differing affinities for each of the AA. The extent of that modification is not a fixed constant but rather a function of several factors including milk yield. The accuracy of our current feeding systems could be improved if such variable rates of substrate removal replaced current static estimates.

Accounting for Energy and Protein Reserve Changes in Predicting Diet-Allowable Milk Production in Cattle

Current ration formulation systems used to formulate diets on farms and to evaluate experimental data estimate metabolizable energy (ME)-allowable and metabolizable protein (MP)-allowable milk production from the intake above animal requirements for maintenance, pregnancy, and growth. The changes in body reserves, measured via the body condition score (BCS), are not accounted for in predicting ME and MP balances. This paper presents 2 empirical models developed to adjust predicted diet-allowable milk production based on changes in BCS. Empirical reserves model 1 was based on the reserves model described by the 2001 National Research Council (NRC) Nutrient Requirements of Dairy Cattle, whereas empirical reserves model 2 was developed based on published data of body weight and composition changes in lactating dairy cows. A database containing 134 individually fed lactating dairy cows from 3 trials was used to evaluate these adjustments in milk prediction based on predicted first-limiting ME or MP by the 2001 Dairy NRC and Cornell Net Carbohydrate and Protein System models. The analysis of first-limiting ME or MP milk production without adjustments for BCS changes indicated that the predictions of both models were consistent (r(2) of the regression between observed and model-predicted values of 0.90 and 0.85), had mean biases different from zero (12.3 and 5.34%), and had moderate but different roots of mean square errors of prediction (5.42 and 4.77 kg/d) for the 2001 NRC model and the Cornell Net Carbohydrate and Protein System model, respectively. The adjustment of first-limiting ME- or MP-allowable milk to BCS changes improved the precision and accuracy of both models. We further investigated 2 methods of adjustment; the first method used only the first and last BCS values, whereas the second method used the mean of weekly BCS values to adjust ME- and MP-allowable milk production. The adjustment to BCS changes based on first and last BCS values was more accurate than the adjustment to BCS based on the mean of all BCS values, suggesting that adjusting milk production for mean weekly variations in BCS added more variability to model-predicted milk production. We concluded that both models adequately predicted the first-limiting ME- or MP-allowable milk after adjusting for changes in BCS.

Metabolic Models of Ruminant Metabolism: Recent Improvements and Current Status

The NC-1009 regional research project has two broad goals of quantifying the properties of feeds and the metabolic interactions among nutrients that influence nutrient availability for milk production and that alter synthesis of milk, and using those quantitative relationships to challenge and refine computer-based nutrition systems for dairy cattle. The objective of this paper was to review progress in modeling. Significant progress has been made in model refinements over the past 10 yr as exemplified by the most recent NRC model (2001) and work on the Molly model of Baldwin and colleagues (1987). These models have different objectives but share many properties. The level of aggregation of the NRC model (2001) does not allow detailed analyses of specific metabolic reactions that affect nutritional efficiency. The Baldwin model is aggregated at the pathway level and is therefore amenable to assessment with a broad range of biological measurements. Recent improvements to that model include the addition of an ingredient based input scheme, use of in situ data to set ruminal protein degradation rates, and refinement of the representation of mammary cell numbers and activity. Although the Baldwin model appears to be appropriate structurally, several parameters are known to be inadequate. Predictions of ruminal N metabolism and total-tract starch digestions have similar accuracy as the NRC model. However, the NRC more accurately predicts total-tract fiber digestion and both models significantly overpredict total-tract lipid digestion. These errors contribute to overpredictions of weight retention when simulating full lactations with the Baldwin model and may result in performance prediction errors with the NRC model. Limitations remain in the descriptions of metabolism and metabolic regulation of the splanchnic, viscera, adipose tissue, body muscle, and mammary tissue. Integration of genetic control mechanisms can expand these efforts to assist genetic selection as well as feeding management decisions.

Modeling the effects of stressors on the performance of populations of pigs

A simulation model that predicts the effect of the social, physical, and nutritional environments on pig food intake and performance was extended to deal with individual variation. The aim was to investigate the effect of between-animal variation on the performance of a population of growing pigs. Variation was generated in initial state, growth potential, and ability to cope when exposed to social "stressors" (EX). Variation in initial state is described by initial body weight (BW0), from which the chemical composition of the pig is calculated. Variation in growth potential is described by creating variation in the genetic growth descriptors. Variation in EX exists between genotypes, where it has been suggested that leaner, more modern genotype pigs tend to be less able to cope. It is expected that within a population or group that the social environment (i.e., position within the social hierarchy) also affects an individual's ability to cope. In the model, it is assumed that the larger, more dominant individuals are better able to cope when exposed to social stressors. Consequently, within a population, EX is correlated with body weight around the genotype mean. Model predictions showed that increasing the variation in BW0 and EX increased the variation in pig performance. This is an important practical consideration in commercial pig production, where the heterogeneity of the population at slaughter may affect the profitability of an enterprise. The way a stressor constrains performance determines whether the mean population response to a given stressor is the same as the average individual response. If all pigs in a group are affected at the same stressor intensity (e.g., all are either mixed or not), then the predicted average individual and mean population responses will be the same. If, however, the intensity of stressor at which performance becomes limiting differs between individuals (such as space allowance or temperature), differences between the individual and mean population responses will be predicted. Variation in the growth response of a population was determined to a greater extent by variation in EX and BW0 than by variation in growth potential, when pigs were housed in simulated conditions likely to be encountered in commercial environments. Consequently, decreasing the variation in initial body weight and improving ability of pigs to cope may be a better way of improving pig performance than selecting only for increased growth potential.

Limitations of conventional models and a conceptual framework for a nutrient flow representation of energy utilization by animals

Conventional models of energy utilization by animals, based on partitioning metabolizable energy (ME) intake or net energy (NE), are reviewed. The limitations of these methods are discussed, including various experimental, analytical and conceptual problems. Variation in the marginal efficiency of utilizing energy can be attributed to various factors: diet nutrient composition; animal effects on diet ME content; diet and animal effects on ME for maintenance (MEm); experimental methodology; and important statistical issues. ME partitioning can account for some of the variation due to animal factors, but not that related to nutrient source. In addition to many of the problems associated with ME, problems with NE pertain to: estimation of NE for maintenance (NEm); experimental and analytical methodology; and an inability to reflect variation in the metabolic use of NE. A conceptual framework is described for a new model of energy utilization by animals, based on representing explicit flows of the main nutrients and the important biochemical and biological transformations associated with their utilization. Differences in energetic efficiency from either dietary or animal factors can be predicted with this model.