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Methane (CH4) is one of the major greenhouse gases being targeted for reduction by the Kyoto protocol. The focus of recent research in animal science has thus been to develop or improve existing CH4 prediction models to evaluate mitigation strategies to reduce overall CH4 emissions. Eighty-three beef and 89 dairy data sets were collected and used to develop statistical models of CH4 production using dietary variables. Dry matter intake (DMI), metabolizable energy intake, neutral detergent fiber, acid detergent fiber, ether extract, lignin, and forage proportion were considered in the development of models to predict CH4 emissions. Extant models relevant to the study were also evaluated. For the beef database, the equation CH4 (MJ/d)=2.94 (± 1.16) + 0.059 (± 0.0201)×metabolizable energy intake (MJ/d) + 1.44 (± 0.331)×acid detergent fiber (kg/d)-4.16 (± 1.93)×lignin (kg/d) resulted in the lowest root mean square prediction error (RMSPE) value (14.4%), 88% of which was random error. For the dairy database, the equation CH4 (MJ/d)=8.56 (± 2.63) + 0.14 (± 0.056)×forage (%) resulted in the lowest RMSPE value (20.6%) and 57% of error from random sources. An equation based on DMI also performed well for the dairy database: CH4 (MJ/d)=3.23 (± 1.12) + 0.81 (± 0.086)×DMI (kg/d), with a RMSPE of 25.6% and 91% of error from random sources. When the dairy and beef databases were combined, the equation CH4 (MJ/d)=3.27 (± 0.79) + 0.74 (± 0.074)×DMI (kg/d) resulted in the lowest RMSPE value (28.2%) and 83% of error from random sources. Two of the 9 extant equations evaluated predicted CH4 production adequately. However, the new models based on more commonly determined values showed an improvement in predictions over extant equations.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the liver of the lactating dairy cow is constructed and solved in the steady state. An original ten-pool model is adopted and solved by cleaving it into two five-pool sub-models, one representing phenylalanine and the other tyrosine. If assumptions are made, model solution permits calculation of the rate of phenylalanine and tyrosine uptake from portal vein and hepatic arterial blood supply, hydroxylation, and synthesis and degradation of constitutive protein. The model requires the measurement of plasma flow rate through the liver in combination with amino acid concentrations and plateau isotopic enrichments in arterial and portal and hepatic vein plasma during a constant infusion of [1-13C]phenylalanine and [2,3,5,6-2H]tyrosine tracers. It also requires estimates of the rate of oxidation and protein export secretion. Analysis of measurement errors in experimental enrichments and infusion rates on model solutions indicated that accurate values of the intracellular and extracellular enrichments are central to minimising errors in the calculated flows. Solving the model by cleaving into two five-pool schemes rather than solving the ten-pool scheme directly is preferred as there appears to be less compounding of errors and the results consistently appear to be more biologically feasible. The model provides a means for assessing the impact of hepatic metabolism on amino acid availability to peripheral tissues such as the mammary gland.

Phenylalanine (PHE) and to a lesser extent TYR are two commonly used amino acid tracers for measuring protein metabolism in a variety of species and tissues. The model examined in this paper was developed to resolve trans-organ and stable isotope dilution data collected from experiments with lactating dairy cows using these tracers. Two methods of solving the model, i.e. as two four-pool submodels, one representing PHE and the other TYR, or as an integrated eight-pool model, are investigated and the alternative solutions are contrasted. Solving the model as the two four-pool submodels rather than the integrated 8-pool model is preferred as the equations are slightly simpler and their application less susceptible to any compounding of measurement errors. The data used to illustrate the model were taken from experiments conducted to investigate the effects of high and low protein diets on the partitioning of PHE and TYR between milk protein synthesis and other metabolic fates by the mammary gland.

Methane, in addition to being a significant source of energy loss to the animal that can range from 0·02 to 0·12 of gross energy intake, is one of the major greenhouse gases being targeted for reduction by the Kyoto protocol. Thus, one of the focuses of recent research in animal science has been to develop or improve existing methane prediction models in order to increase overall understanding of the system and to evaluate mitigation strategies for methane reduction. Several dynamic mechanistic models of rumen function have been developed which contain hydrogen gas balance sub-models from which methane production can be predicted. These models predict methane production with varying levels of success and in many cases could benefit from further development. Central to methane prediction is accurate volatile fatty acid prediction, representation of the competition for substrate usage within the rumen, as well as descriptions of protozoal dynamics and pH. Most methane models could also largely benefit from an expanded description of lipid metabolism and hindgut fermentation. The purpose of the current review is to identify key aspects of rumen microbiology that could be incorporated into, or have improved representation within, a model of ruminant digestion and environmental emissions.

Canada is committed to reducing its greenhouse gas emissions to 6% below 1990 amounts between 2008 and 2012, and methane is one of several greenhouse gases being targeted for reduction. Methane production from ruminants is one area in which the agriculture sector can contribute to reducing our global impact. Through mathematical modeling, we can further our understanding of factors that control methane production, improve national or global greenhouse gas inventories, and investigate mitigation strategies to reduce overall emissions. The purpose of this study was to compile an extensive database of methane production values measured on beef cattle, and to generate linear and nonlinear equations to predict methane production from variables that describe the diet. Extant methane prediction equations were also evaluated. The linear equation developed with the smallest root mean square prediction error (RMSPE, % observed mean) and residual variance (RV) was Eq. I: CH₄, MJ/d = 2.72 (±0.543) + [0.0937 (±0.0117) x ME intake, MJ/d] + [4.31 (±0.215) x Cellulose, kg/d] - [6.49 (±0.800) x Hemicellulose, kg/d] - [7.44 (±0.521) x Fat, kg/d] [RMSPE = 26.9%, with 94% of mean square prediction error (MSPE) being random error; RV = 1.13]. Equations based on ratios of one diet variable to another were also generated, and Eq. P, CH₄, MJ/d = 2.50 (±0.649) - [0.367 (±0.0191) x (Starch:ADF)] + [0.766 (±0.116) x DMI, kg/d], resulted in the smallest RMSPE values among these equations (RMSPE = 28.6%, with 93.6% of MSPE from random error; RV = 1.35). Among the nonlinear equations developed, Eq. W, CH₄, MJ/d = 10.8 (±1.45) x (1 - e[⁻⁰.¹⁴¹ ⁽±⁰.⁰³⁸¹⁾ x DMI, kg/d]), performed well (RMSPE = 29.0%, with 93.6% of MSPE from random error; RV = 3.06), as did Eq. W₃, CH₄, MJ/d = 10.8 (±1.45) x [1 - e{⁻ [⁻⁰.⁰³⁴ x ⁽NFC/NDF⁾ ⁺ ⁰.²²⁸] x DMI, kg/d}] (RMSPE = 28.0%, with 95% of MSPE from random error). Extant equations from a previous publication by the authors performed comparably with, if not better than in some cases, the newly developed equations. Equation selection by users should be based on RV and RMSPE analysis, input variables available to the user, and the diet fed, because the equation selected must account for divergence from a \"normal\" diet (e.g., high-concentrate diets, high-fat diets).

Mechanistic models (MMs) have served as causal pathway analysis and ‘decision-support’ tools within animal production systems for decades. Such models quantitatively define how a biological system works based on causal relationships and use that cumulative biological knowledge to generate predictions and recommendations (in practice) and generate/evaluate hypotheses (in research). Their limitations revolve around obtaining sufficiently accurate inputs, user training and accuracy/precision of predictions on-farm. The new wave in digitalization technologies may negate some of these challenges. New data-driven (DD) modelling methods such as machine learning (ML) and deep learning (DL) examine patterns in data to produce accurate predictions (forecasting, classification of animals, etc.). The deluge of sensor data and new self-learning modelling techniques may address some of the limitations of traditional MM approaches – access to input data (e.g. sensors) and on-farm calibration. However, most of these new methods lack transparency in the reasoning behind predictions, in contrast to MM that have historically been used to translate knowledge into wisdom. The objective of this paper is to propose means to hybridize these two seemingly divergent methodologies to advance the models we use in animal production systems and support movement towards truly knowledge-based precision agriculture. In order to identify potential niches for models in animal production of the future, a cross-species (dairy, swine and poultry) examination of the current state of the art in MM and new DD methodologies (ML, DL analytics) is undertaken. We hypothesize that there are several ways via which synergy may be achieved to advance both our predictive capabilities and system understanding, being: (1) building and utilizing data streams (e.g. intake, rumination behaviour, rumen sensors, activity sensors, environmental sensors, cameras and near IR) to apply MM in real-time and/or with new resolution and capabilities; (2) hybridization of MM and DD approaches where, for example, a ML framework is augmented by MM-generated parameters or predicted outcomes and (3) hybridization of the MM and DD approaches, where biological bounds are placed on parameters within a MM framework, and the DD system parameterizes the MM for individual animals, farms or other such clusters of data. As animal systems modellers, we should expand our toolbox to explore new DD approaches and big data to find opportunities to increase understanding of biological systems, find new patterns in data and move the field towards intelligent, knowledge-based precision agriculture systems.

In view of environmental concerns with regard to phosphorus (P) pollution and the expected global P scarcity, there is increasing interest in improving P utilization in dairy cattle. In high-producing dairy cows, P requirements for milk production comprise a significant fraction of total dietary P requirements. Although variation in P content of milk can affect the efficiency of P utilization for milk production (i.e. the fraction of ingested P that is incorporated in milk), this variation is poorly understood. It was hypothesized that the P content of milk is related to both milk protein and milk lactose content, but not necessarily to milk fat content. Three existing experiments comprising individual animal data on milk yield and fat, protein, lactose and P content of milk (in total 278 observations from 121 cows) were analysed to evaluate this hypothesis using a mixed model analysis. The models including the effects of both protein and lactose content of milk yielded better prediction of milk P content in terms of root-mean-square prediction error (RMSPE) and concordance correlation coefficient (CCC) statistics than models with only protein included as prediction variable; however, estimates of effect sizes varied between studies. The inclusion of milk fat content in equations already including protein and lactose did not further improve prediction of milk P content. Equations developed to describe the relationship between milk protein and lactose contents (g/kg) and milk P content (g/kg) were: (Expt 1) P in milk=−0·44(±0·179)+0·0253(±0·00300)×milk protein+0·0133(±0·00382)×milk lactose (RMSPE: 5·2%; CCC: 0·71); (Expt 2) P in milk=−0·26 (±0·347)+0·0174(±0·00328)×milk protein+0·0143 (±0·00611)×milk lactose (RMSPE: 6·3%; CCC: 0·40); and (Expt 3) P in milk=−0·36(±0·255)+0·0131(±0·00230)×milk protein+0·0193(±0·00490)×milk lactose (RMSPE: 6·5%; CCC: 0·55). Analysis of the three experiments combined, treating study as a random effect, resulted in the following equation to describe the same relationship as in the individual study equations: P in milk=−0·64(±0·168)+0·0223(±0·00236)×milk protein+0·0191(±0·00316)×milk lactose (RMSPE: 6·2%; CCC: 0·61). Although significant relationships between milk protein, milk lactose and milk P were found, a considerable portion of the observed variation remained unexplained, implying that factors other than milk composition may affect the P content of milk. The equations developed may be used to replace current fixed milk P contents assumed in P requirement systems for cattle.

A dynamic, mechanistic model of enteric fermentation was used to investigate the effect of type and quality of grass forage, dry matter intake (DMI) and proportion of concentrates in dietary dry matter (DM) on variation in methane (CH4) emission from enteric fermentation in dairy cows. The model represents substrate degradation and microbial fermentation processes in rumen and hindgut and, in particular, the effects of type of substrate fermented and of pH on the production of individual volatile fatty acids and CH4 as end-products of fermentation. Effects of type and quality of fresh and ensiled grass were evaluated by distinguishing two N fertilization rates of grassland and two stages of grass maturity. Simulation results indicated a strong impact of the amount and type of grass consumed on CH4 emission, with a maximum difference (across all forage types and all levels of DMI) of 49 and 77% in g CH4/kg fat and protein corrected milk (FCM) for diets with a proportion of concentrates in dietary DM of 0·1 and 0·4, respectively (values ranging from 10·2 to 19·5 g CH4/kg FCM). The lowest emission was established for early cut, high fertilized grass silage (GS) and high fertilized grass herbage (GH). The highest emission was found for late cut, low-fertilized GS. The N fertilization rate had the largest impact, followed by stage of grass maturity at harvesting and by the distinction between GH and GS. Emission expressed in g CH4/kg FCM declined on average 14% with an increase of DMI from 14 to 18 kg/day for grass forage diets with a proportion of concentrates of 0·1, and on average 29% with an increase of DMI from 14 to 23 kg/day for diets with a proportion of concentrates of 0·4. Simulation results indicated that a high proportion of concentrates in dietary DM may lead to a further reduction of CH4 emission per kg FCM mainly as a result of a higher DMI and milk yield, in comparison to low concentrate diets. Simulation results were evaluated against independent data obtained at three different laboratories in indirect calorimetry trials with cows consuming GH mainly. The model predicted the average of observed values reasonably, but systematic deviations remained between individual laboratories and root mean squared prediction error was a proportion of 0·12 of the observed mean. Both observed and predicted emission expressed in g CH4/kg DM intake decreased upon an increase in dietary N:organic matter (OM) ratio. The model reproduced reasonably well the variation in measured CH4 emission in cattle sheds on Dutch dairy farms and indicated that on average a fraction of 0·28 of the total emissions must have originated from manure under these circumstances.

The use of repeated measures analysis of variance (ANOVA) options for the analysis of in vitro ruminal fermentation gas production profiles is illustrated. Because of the different variances and covariance structures among profile observations, ordinary ANOVA for more than two-time points is not recommended. To mitigate this problem, the Greenhouse–Geisser epsilon correction can be applied to reduce the degrees of freedom, inflated by violation of the sphericity assumption, for F ratio probability calculations. After this correction, the Box–Greenhouse–Geisser ANOVA (modified ANOVA) layout appears similar to the layout of a split-plot design ANOVA with whole plots divided into subplots (incubation time). Any F tests in the main plot part are valid but F tests involving the time factor from the subplot part need modification because time factor, by its very nature, cannot be allocated at random. Application of multivariate ANOVA, distance multivariate ANOVA, ante-dependence and mixed model analysis are also considered. All these options lend themselves to wide application in the applied biological sciences.

Monensin is a common feed additive used in various countries, where 1 of the associated benefits for use in beef cattle is improved efficiency of energy metabolism by the rumen bacteria, the animal, or both. Modeling fermentation-altering supplements is of interest, and thus, it is the purpose of this paper to quantify the change in VFA profile caused by monensin dose in high-grain-fed beef cattle. The developmental database used for meta-analysis included 58 treatment means from 16 studies from the published literature, and the proportional change in molar acetate, propionate, and butyrate (mol/100 mol) as well as total VFA (mM) with monensin feeding dose (mg/kg DM, concentration in the feed) was evaluated using the MIXED procedure (SAS Inst. Inc., Cary, NC) with the study treated as a random effect. The mean monensin dose in the literature database was 30.9 ± 3.70 mg/kg DM and ranged from 0.0 to 88.0 mg/kg DM. Mean DMI was 7.8 ± 0.26 kg DM/d, mean concentrate proportion of the diet was 0.87 ± 0.01, and mean treatment period was 42 ± 5.6 d. Results produced the following equations: proportional change in acetate (mol/100 mol) = -0.0634 (± 0.0323) × monensin (mg/kg DM)/100 (P = 0.068), proportional change in propionate (mol/100 mol) = 0.260 (± 0.0735) × monensin (mg/kg DM)/100 (P = 0.003), and proportional change in butyrate (mol/100 mol) = -0.335 (± 0.0916) × monensin (mg/kg DM)/100 (P = 0.002). The change in total VFA was not significantly related to monensin dose (P = 0.93). The results presented here indicate that the shift in VFA profile may be dose dependent, with increasing propionate and decreasing acetate and butyrate proportions (mol/100 mol). These equations could be applied within mechanistic models of rumen fermentation to represent the effect of monensin dose on the VFA profile in high-grain-fed beef cattle.