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Department of Dairy Science, Virginia Polytechnic Institute and State University, Blacksburg 24061Animal Science Institute, Universidad Austral de Chile, Valdivia 5110566, Chile
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.
). The primary countries making extensive use of grazing systems for milk production include New Zealand and southern Australia (over 95% of farms use grassland), western Europe (varying from 30% in Denmark to 100% in Ireland), and some countries in South America (e.g., around 85% in Chile;
). Generally, the proportion of grazed herbage in the diet varies according to country, the type of system, and season, ranging from 50% of annual DMI in systems with grazing seasons shorter than 6 mo to 90% in countries with 12-mo growing seasons (
). Temperate grazing systems are generally characterized by the use of perennial ryegrass (Lolium perenne L.) as a predominant species due to its high forage production and nutritional quality for grazing ruminants (
Pasture-based milk production systems may have intrinsic advantages over confinement systems in terms of lower environmental impact, competitive production costs, superior product quality, and better animal welfare (
). However, systems making use of a high proportion of pasture have increased variability in animal production compared with those on TMR due to daily and seasonal variation in pasture composition, interactions with supplementary feeds, eating patterns, and management (
). The model was developed, tested, and enhanced mainly using data from mixed diets that included conserved forages (e.g., corn silage and alfalfa hay) fed as a TMR (
). Considering that a key aim of a mechanistic model is to capture mechanisms that allow simulations across the full range of inputs, Molly could be a useful tool for the study of the nutritional response to fresh grass-based diets (
suggested that the model could be applied to various grazing system interactions after improving its representation of fiber degradation. However, its ability to represent temperate pasture-based diet digestion after such changes has not been assessed.
We hypothesized that the latest version of the Molly cow model properly represents ruminal fermentation and digestion from ryegrass-based diets, and no additional modifications should be needed. The objectives of this study were (1) to evaluate the adequacy of the latest version of the Molly model (
) using data from cows consuming fresh ryegrass-based diets relative to ruminal fermentation, nutrient digestion, and animal performance; (2) if deficiencies were identified, to derive a model representative of ryegrass-based diets; and (3) to identify underlying mechanisms that could be used to direct further model improvements.
MATERIALS AND METHODS
Model Description
The model used was an updated version of the mechanistic and dynamic Molly cow model that was first described by
Metabolism of the lactating cow. III. Properties of mechanistic models suitable for evaluation of energetic relationships and factors involved in the partition of nutrients.
in: Kebreab E. Dijkstra J. Bannink A. Gerrits W.J.J. France J. Nutrient Digestion and Utilization in Farm Animals: Modelling Approaches. CAB International,
2006: 328-348
). Additionally, particle size characterization of diets (based on a particle separator with 3 sieves) was needed as an input to the large, medium, and small particle pools in the rumen. Large and medium particles are subject to reduction by mastication, whereas medium and small particles are subject to rumen fermentation (as a function of particle surface area) and passage. Water-soluble and insoluble pools of nutrients are represented in the model, which are dependent on the solubility of the nutrients in the particulate pools (
). Although pectin, VFA, lactic acid, glycerol, and organic acids can be separately specified in model inputs, they are all combined with feed sugars in the soluble carbohydrates pool for modeling fermentation purposes (
Soluble components can pass from the rumen or be fermented by rumen microbes and the products absorbed, while insoluble components are subject to degradation and entry into the soluble pool, or they can escape the ruminal degradation. Thus, ruminal particle passage (including undegraded feed particles, soluble nutrients, and microbes) is represented as a function of particle size, particle concentrations in the rumen, and liquid passage rate (
). Digesta outflow considers soluble (carbohydrates, amino acids, fats, and ash) and insoluble entities (starch, hemicellulose, cellulose, protein, lignin, and ash), and microbes. Entities passing from the rumen can be digested and absorbed in the postruminal gastrointestinal tract or be excreted in feces (
). Constant intestinal digestion coefficients are defined in the model for chemical entities (starch, holocellulose, fat, soluble and insoluble ash, and insoluble protein) and for microbial nutrient content (protein and lipids). Soluble carbohydrates and amino acids passing to the intestine are considered 100% absorbable. Fecal components are calculated from indigested starch, holocellulose, protein, fat, lignin, and ash from the diet, and also from indigested microbes.
In the model, tissue and organs are represented as pools for lean body mass (muscle and skin), viscera (liver, intestines, pancreas, and mammary glands), and adipose tissue. Metabolic transactions are aggregated at the pathway level representing protein synthesis and degradation, lipogenesis, esterification, lipolysis, and milk fat, protein, and lactose synthesis. Finally, oxidative metabolism is explicitly accounted in terms of ATP production and utilization (
). Continuous model modifications and updates have been undertaken to improve representations of mechanistic functions and improve the model predictions as listed by
To identify peer review articles pertinent to the aim of this study, an electronic search was performed using different web-based platforms: Web of Science (https://www.webofscience.com/wos/woscc/basic-search), CAB Abstracts (https://www.cabdirect.org/cabdirect/search/), and Google Scholar (https://scholar.google.com/). A list of keywords was used to account for animal species (cow, cattle, dairy cows); nutrient utilization (digestion, digestibility); pasture species (Lolium perenne L., ryegrass, perennial ryegrass); and productive system (pasture, pasture-based system, grazing). Boolean operators “AND” and “OR” were used for combine the different selected keywords. Searches included articles published in English and Spanish between 1970 and 2020.
Around 70 publications were originally identified. Later, selected publications were screened based on 2 inclusion criteria: (1) Pasture inclusion included studies in which pasture intake represented 45% or more of the total diet (mean 77%), and the botanical composition of the forage was at least 70% perennial ryegrass (Lolium perenne L.) were selected; and (2) diet composition and nutrient utilization data included studies that reported DMI, ingredient composition of the diets, and nutrient digestion variables (DM, OM, ADF, NDF, starch or protein digestibility, ruminal outflow, or fecal outflow), or those values could be calculated from the reported data. Additionally, ruminal fermentation variables (pH, ammonia, and VFA concentrations), milk production, milk composition, BW, BCS, BUN, and N excretion data reported in selected publications were also recorded when available for modeling purposes, but they were not used as selection criteria. Considering that only 3 of the 14 selected studies using the established criteria reported changes in BW and only one reported BCS, a set of 11 studies conducted by the authors with grazing cows that reported BW and BCS were also included in this work to account for tissue mobilization in the whole animal model. Articles selected met the criteria of pasture inclusion (with the exception of some specific treatments), reported diet composition, and reported DMI, but they did not report diet digestion measurements. A separate list of initially selected articles and the added studies is provided in Supplemental Tables S1 and S2 (http://hdl.handle.net/10919/103450). The final data set included data from 25 publications representing 115 treatment means, conducted with lactating dairy cows (primarily Holstein-Friesian) managed in pasture-based systems. A list of the references is provided in Table 1, and a descriptive summary of the data set is presented in Table 2.
Table 1A listing of references for the experimental data used for model evaluations and parameter estimation
A comparison of perennial ryegrass cultivars differing in heading date and grass ploidy with spring calving dairy cows grazed at two different stocking rates.
Effects of feeding perennial ryegrass with an elevated concentration of water-soluble carbohydrates on intake, rumen function and performance of dairy cows.
Quantifying the influence of sward height, concentrate level and initial milk yield on the milk production and grazing behaviour of continuously stocked dairy cows.
Effect of increasing pasture allowance and grass silage on animal performance, grazing behaviour and rumen fermentation parameters of dairy cows in early lactation during autumn.
These studies consider at least one treatment with less than 45% of pasture inclusion decreasing treatments mean. However, they were also included to consider variation in the diets.
These studies consider at least one treatment with less than 45% of pasture inclusion decreasing treatments mean. However, they were also included to consider variation in the diets.
These studies consider at least one treatment with less than 45% of pasture inclusion decreasing treatments mean. However, they were also included to consider variation in the diets.
These studies consider at least one treatment with less than 45% of pasture inclusion decreasing treatments mean. However, they were also included to consider variation in the diets.
2 Others treatments were not considered because they used different pasture species.
3 These studies consider at least one treatment with less than 45% of pasture inclusion decreasing treatments mean. However, they were also included to consider variation in the diets.
Initial BW and BCS were required as inputs to initialize the model, but only treatments that reported initial and final values for BW and BCS were used for model evaluation of respective variables predictions.
Initial BW and BCS were required as inputs to initialize the model, but only treatments that reported initial and final values for BW and BCS were used for model evaluation of respective variables predictions.
2 Initial BW and BCS were required as inputs to initialize the model, but only treatments that reported initial and final values for BW and BCS were used for model evaluation of respective variables predictions.
3 Forage represents percentage of fibrous feedstuffs intake as pasture, hay, silage, and supplementary crops.
The initial BCS (a required model initialization input) was assumed to be 3.0 (scale 1 to 5) when it was not reported, but the assumed values were excluded from evaluations of BCS predictions. Similarly, if initial BW was not reported (3 studies representing 7 treatments) an assumed value of 580 kg was used. Finally, in one of the studies DIM was not available and was assumed to 150 d.
Further details of nutrient inputs required by the model are described by
. The nutrient composition values of individual ingredients were used in calculating dietary nutrients when they were reported. Missing nutrients were obtained from tabular values in
values were used. Lignin and starch content of ryegrass were not commonly reported, therefore a value of 2% of DM was assumed for each one based on literature (
). Dietary pectin, VFA, lactic acid, glycerol, and organic acids were not generally reported and were assumed to be 5% of dietary DM based on other OM components plus ash summing to unity. Initial ruminally undegraded starch was assumed to be 25% of total starch for all the diet as reported by
for diets including up to 4 kg of starch (the highest value observed was 3.66 kg).
Duodenal flows of ADF and NDF were reported for 2 and 5 studies, respectively, and those values were used to estimate in situ-derived extent of ruminal fiber degradation, a required model input. Estimated extents of ADF and NDF degradation for the remaining studies were estimated using a fractional passage rate (Kp) of 5.5%/h for ryegrass, and a fractional degradation rate (Kd) of 13.9%/h, as reported for pasture diets (
Efecto del nivel de suplementación con concentrado sobre la respuesta productiva en vacas lecheras a pastoreo primaveral con alta disponibilidad de pradera.
Rumen degradation characteristics of ryegrass herbage and ryegrass silage are affected by interactions between stage of maturity and nitrogen fertilisation rate.
Particle breakdown and rumen digestion of fresh ryegrass (Lolium perenne L.) and lucerne (Medicago sativa L.) fed to cows during a restricted feeding period.
for total mixed rations (mean 51.8% of forage) were considered.
However, using those equations resulted in overestimation of ruminal VFA and microbial N, whereas pH was underestimated compared with observed values (123.92 vs. 115.49 mmol/L, 0.28 vs. 0.24 kg/d, and 5.71 vs. 6.13 for predicted and observed rumen VFA concentrations, microbial N, and rumen pH, respectively). Considering that the extent of fermentation is associated with the small and medium particle pools in the model, the small and medium particle feed fractions may have been overestimated. Conversely, an apparent underestimation of the diet large particle fraction was also suggested.
To address this data deficiency, representative feedstuffs from pasture-based systems were assessed for particle size and the results used as inputs for those ingredients. Ingredients that were assessed included ryegrass (diploid cultivar One50), ryegrass silage (stack and bale), corn silage (hybrid LG30211), ryegrass hay, concentrate mixture (60% grounded corn, 30% triticale, and 10% expeller-extracted canola meal), pelleted concentrate, and partial TMR of varying proportions of pasture silage, corn silage, grounded corn, triticale grain, and expeller-extracted canola meal, collected from 5 dairy farms in the southern area of Chile (Los Rios and Los Lagos regions) during July of 2019. Samples of ryegrass were taken above 4 cm using scissors, simulating the stubble remaining after grazing. Two ryegrass particle size profiles were selected, lower or upper 20 cm, to represent medium and high pasture allowances, respectively. Samples were taken from different random places across the paddocks. Silage samples were manually collected from different places and depths within the silos. Concentrate mixture and concentrate pellets were sampled from the feeders in the milking parlor when they were offered to the cows. Partial TMR samples were taken from the top, middle, and bottom levels of the TMR residing in the feed bunk at different locations immediately after feed was delivered. Particle size profiles of feedstuffs was determined using approximately 450 g of sample and a Penn State Particle Separator with 3 sieves (4, 8, and 19 mm). The sampling procedure and particle distribution determinations were repeated 3 times per feedstuff, and the mean values were used to represent the particle size profiles for the work herein (Table 3).
Table 3Particle size distribution (percent remaining on each screen) for ryegrass and different feeds used in dairy pasture-based systems collected from Chile
Pasture samples were collected by cutting 4 cm above ground level. Two particle size profiles were estimated for ryegrass according to the herbage height.
Pasture samples were collected by cutting 4 cm above ground level. Two particle size profiles were estimated for ryegrass according to the herbage height.
(≥20 cm)
Stack silage
Bale silage
Corn silage
Pasture hay
Grain mix
Pelleted concentrate
Partial TMR
Upper sieve
>19.0
91.80
94.59
38.57
69.23
14.49
85.71
0.56
0.00
21.03
Middle sieve
8.0–19.0
4.92
2.70
42.66
12.50
62.15
8.93
4.44
67.74
52.34
Lower sieve
4.0–8.0
1.64
1.35
10.23
9.62
15.89
3.57
14.44
30.91
17.76
Bottom pan
<4.0
1.64
1.35
8.54
8.65
7.48
1.79
80.56
1.34
8.88
1 Values correspond to the average of 3 samples.
2 Pasture samples were collected by cutting 4 cm above ground level. Two particle size profiles were estimated for ryegrass according to the herbage height.
Preliminary analysis of outliers in the compiled data was made assuming outliers occurred at more than 3 standard deviations from the mean. Two treatment means for milk fat percentage (
Nitrogen fertiliser effects on milk yield and composition, pasture intake, nitrogen and energy partitioning, and rumen fermentation parameters of dairy cows in early lactation.
Nitrogen fertiliser effects on milk yield and composition, pasture intake, nitrogen and energy partitioning, and rumen fermentation parameters of dairy cows in early lactation.
) indicated that BW change (kg/d) and milk yield (kg/d) predictions were overestimated by the model. To address the BW problem, the representation of lean body (QPOth, kg) and visceral protein mass (QPVis, kg) was altered following the approach of
with protein synthesis in the body (FAa, POth) and visceral compartments (FAa, PVis for viscera). That model is based on the concept of DNA accumulation from conception to maturity and protein synthesis are driven by the need to achieve a target ratio of protein to DNA, reflecting the concept of a fixed cell size. Hyperplastic growth reflects accumulation of DNA and protein in concert, and hypertrophy reflects protein accumulation exceeding rates of DNA accumulation (
). Based on that concept, model protein synthesis equations were redefined including a target protein to DNA ratio for each compartment (FPOth, DNA and FPVis, DNA, mol/mol):
[1]
[2]
where VmAa, POth and VmAa, PVis represented the maximal rates of protein synthesis for QPOth and QPVis (mol/d), OthDNA and VisDNA represented the mass of DNA in the Oth and Vis compartments (kg). The DNA mass is calculated from constants values, and DNA accretion is obtained from the difference of DNA mass of current to the mature BW (
). Both KAa, POth and KAa, PVis represented the affinity constants for CAa (mol/L), AHor represented anabolic hormone (unitless with a reference point of 1), and CAa the plasma amino acid concentrations (mol/L). The x was added to allow adjustments of sensitivity to CAa and AHor, but it was set to a value of 1 and not considered further in this work. Protein degradation in each compartment was by mass action as originally defined.
The original work indicated that the protein to DNA ratio increased until the animal reached approximately 300 kg (growing animals) and remained constant at weights above 300 kg. Although this ratio had been proposed for use in protein accretion modeling, it had not been included in the Molly model (
). Therefore, we took this approach to scale the ratio of mass of DNA in lean body or viscera to their respective protein mass to a target cell size (FPOth, DNA and FPVis, DNA) as described in Equations 1 and 2, to reduce the large deviations observed in the former ratio.
In the model, animal BW was used as an input to calculate initial tissue and organ weights, which dynamically changes during the simulation representing the balance of nutrient mobilization and deposition. Initial BCS was also a model input, which was used to calculate the initial adipose pool size based on the equations of
A target BCS was previously defined in the model to accommodate body nutrient status as a driver of lactation hormone metabolism (synthesis and catabolism;
). The target BCS was set to 3.0 in this work as in previous studies. However, we observed an overprediction of initial adipose tissue mass together with lower predictions of final BCS. To address this issue, we replaced the empirical estimation of target mass of adipose tissue (WtAdipT) described by
). Although this addressed the initialization problem, using a fixed WtAdipT for growing animals results in inappropriate body composition targets as the animal grows. We addressed this problem for lactation hormone synthesis (FLHor, Syn, a unitless generic representation of the somatotropin axis;
) by representing the effects of WtAdip as a ratio to fat-free, nonpregnant EBW for both the target ratio and the ratio at any time:
[3]
where VmLHor, Syn represented the maximal rate of lactation hormone synthesis (U/d); kAa and kGlc represented affinity constants for AA and glucose (mol/L); CGlc represented plasma glucose concentrations; CAa represented plasma AA concentrations; and χ and λ are sensitivity exponents described by
. The ratio WtAdipT/iEBWNonFatNonUter represented the target WtAdip over the initial, nonpregnant, empty BW; and WtAdip/EBWNonFatNonUter the ratio at any point in time. In this manner the target ratio (numerator) is a constant defined at model initialization, and the ratio WtAdip/EBWNonFatNonUter changes during the simulation reflecting the prevailing animal nutritional state.
Model Settings, Parameters Estimation, and Reparameterization
All simulations were conducted using acslX modeling software (version 3.1.4.2, Aegis Technologies Group Inc.). Differential equations were solved using a fourth order variable step Runge-Kutta integration algorithm with a maximum step size of 0.005 d. The model was set to simulate 14 d to ensure that steady state was achieved before comparison to the observed values. To account for some of the study effects during parameter estimations, the predicted dietary nutrients were compared with observed values and any bias within study was used to adjust ingredient nutrients for that study to align observed and predicted data (
An average mature BW of 600 kg was set to represent medium-sized animals typically used in pasture-based systems. Milk lactose yield is mechanistically predicted in the model from mammary biosynthetic capacity. However, milk volume is assumed to be solely driven by the osmotic pull of lactose resulting in a constant lactose content of 4.62%. The FORSET VFA stoichiometric matrix (representing diets with a forage inclusion greater than 60%) was selected to represent the high forage diets in the meta data (
). This set of stoichiometric coefficients was used to predict the ruminal fermentation pattern from different substrates (mol of individual VFA/mol of substrates fermented). Main differences from the MIXSET used for represent TMR diet are: 20% greater acetate production from soluble carbohydrates and starch, and 9% less from cellulose; lower propionate from soluble carbohydrate, starch and hemicellulose (7, 18, and 35%, respectively), and 47% lower butyrate from soluble carbohydrates, whereas butyrate is greater from hemicellulose and cellulose (21 and 41%, respectively).
Digestion parameters were initially set to reflect those reported by
. It is important to note that those updates were derived mainly from diets using preserved forages and grain mixes typical of North American diets fed to North American dairy cows.
Following initial model evaluations and identification of deficiencies, a new set of parameter values was derived by fitting 24 model parameters to the data (reparameterization). Those parameters were selected based on the observed prediction errors and model structure and sensitivity. These included parameters involved in predictions of rumen pH; VFA and ammonia metabolism; ruminal fiber, protein and starch degradation and digestion; and those affected by the model modifications. A full list is provided in Table 4. No information was available to evaluate fat digestion. Due to very limited starch digestion information (only one study reported fecal values), direct parameterization of ruminal and intestinal starch digestion was not possible. However, ruminal OM outflow was reported for a limited number of studies and fecal OM was reported for about half of studies, and thus starch digestibility could be deduced by difference from OM digestion where the other elements of OM were defined by respective observations of fecal output. Given the lack of FA data, this approach implicitly assumed that predicted FA digestion was unbiased, and thus any bias in that prediction would also be present in the starch digestion estimates.
Model reparameterization was performed using the Direction Set algorithm to maximize the log-likelihood to find the best combination of parameter values that explain the observed data (
). Due to acslX computational limitations a maximum of 19 parameters can be simultaneously estimated per solution. Parameters selected for each run were based on the flow of nutrient digestion and utilization with ruminal fermentation and digestive parameters derived first followed by those related to nutrient partitioning with the fermentation and digestive parameters fixed to the prior solution. In the course of this work, several parameters were found to be uninfluential and thus were fixed and removed from the parameter derivation set. Constrains were used to avoid nonbiological parameter values which can lead to unstable solutions. Intestinal digestion coefficients were bounded to a maximum of 1 and a minimum of 0.
Model Comparisons and Evaluation
The accuracy and precision of model predictions before and after reparameterization were assessed by calculation of root mean squared errors (RMSE), mean bias, slope bias (
). Significance of model changes was assessed by comparison of the squared residuals before and after model reparameterization using t-test for variables that were normally distributed (previous log-transformation if relevant) or using a Mann-Whitney test for nonparametric data (Table 5). The tests guided interpretation of differences in RMSE (expressed as % of the mean) for a given variable, however model adequacy was determined using the combination of all indicators previously mentioned. The overall effects of the changes on model performance were assessed using a log-likelihood ratio test and Bayesian Information Criterion values (BIC;
). For these tests, the difference in degrees of freedom before and after reparameterization was 0 and thus 1 degree of freedom difference was used to assign probability values.
Table 5Residual error analyses for Molly predictions of grazing dairy cow trials before (I) and after (F) model reparameterization
I (initial predictions) refers to the model predictions using the parameters derived by Li and Hanigan (2020); F (final predictions) refers to the model predictions after model reparameterization to pasture-based diets. RMSE and concordance correlation coefficient (CCC) values in parentheses are after removing Carruthers and Neil (1997) treatments for ruminal propionate predictions; after removing the treatment with the smaller value of NANMN (Rearte et al., 2003); after removing Miller et al. (2001) treatments for fecal DM, NDF, and ADF outflow; after removing the treatment with the greater value for fecal N excretion (Van Vuuren et al., 1992); or after removing the larger value of blood urea (Totty et al., 2013). Only RMSE value for fecal ADF was significant after treatment removal, and it is also presented in the table.
P-values were calculated to support the interpretation of RMSE; they were obtained from the comparison of the squared residuals before and after model reparameterization through t-test for variables normally distributed (previous log-transformation) or Mann-Whitney test for nonparametric data.
Milk lactose content is assumed as a fixed constant in the model (a value 4.62% was used) so slope bias and CCC values could be calculated. Dashes indicate slope bias and CCC values that were not possible to calculate.
%
42
4.61
4.62
4.62
3.2
3.2
2.7
2.7
—
—
—
—
—
Milk fat, kg/d
106
0.99
1.35
0.97
46.7
22.8
58.7
1.1
22.8
23.0
−0.05
0.18
<0.01
Milk protein, kg/d
106
0.80
1.10
0.82
43.4
20.7
73.7
1.7
7.8
18.3
0.01
0.12
<0.01
Milk lactose, kg/d
42
1.06
1.40
1.04
40.9
21.9
64.6
0.4
9.3
12.5
0.14
0.36
<0.01
BW, kg
65
567.08
521.66
561.27
8.5
3.2
89.6
10.2
0.5
9.5
0.59
0.91
<0.01
BCS, 1 to 5
48
2.69
2.17
2.31
19.0
14.1
94.4
88.6
0.5
1.4
0.31
0.45
<0.01
1 I (initial predictions) refers to the model predictions using the parameters derived by
; F (final predictions) refers to the model predictions after model reparameterization to pasture-based diets. RMSE and concordance correlation coefficient (CCC) values in parentheses are after removing
Increasing the water soluble carbohydrate/protein ratio of temperature pasture affects the ruminal digestion of energy and protein in dairy cows.
in: Proc. VI International Symposium on the Nutrition of Herbivores. Tropical and Subtropical Agroecosystems, Merida, Mexico. Autonomous University of Yucatan,
2003: 251-254
). Only RMSE value for fecal ADF was significant after treatment removal, and it is also presented in the table.
2 NANMN = nonammonia, nonmicrobial N.
3 Milk lactose content is assumed as a fixed constant in the model (a value 4.62% was used) so slope bias and CCC values could be calculated. Dashes indicate slope bias and CCC values that were not possible to calculate.
* P-values were calculated to support the interpretation of RMSE; they were obtained from the comparison of the squared residuals before and after model reparameterization through t-test for variables normally distributed (previous log-transformation) or Mann-Whitney test for nonparametric data.
Model sensitivity of 19 derived parameters (maximum of simultaneous parameters for model estimations), was assessed using a global approach for 27 variables representing ruminal fermentation, ruminal outflow, fecal output, nitrogen metabolism and excretion, and animal performance (Table 6, Table 7). Parameters were selected based on the magnitude of parameter discrepancies after reparameterization as it was not possible to include all of them due to algorithm constraints. For this analysis, the Fourier amplitude sensitivity test based on
was used. The parameters were randomly sampled from a flat distribution with boundaries of 70 and 130% of the final values (after reparameterization). Resampling was set to 3 and the interference factor was set to 4 (
). These settings resulted in a sampling population of 439,185 simulations from which the global sensitivity coefficients were derived, and the analysis was repeated for each output variable.
Table 6Global sensitivity of model digestive predictions to selected model parameters
19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. Parameter constrains were set to 70 and 130% of the final parameter estimates (Table 4). Data are expressed as a fraction of the total variance, explained by each model parameter selected, when predicting each specific variable; values larger than 3 decimals are presented.
Am = ammonia; Ac = ruminal acetate; Pr = ruminal propionate; Bu = ruminal butyrate; MiN = microbial nitrogen passage; NAN = nonammonia nitrogen passage; NANMN = nonammonia, nonmicrobial nitrogen passage.
Ruminal fermentation
Ruminal outflow
Fecal output
pH
Am
VFA
Ac
Pr
Bu
MiN
NAN
NANMN
NDF
ADF
DM
OM
NDF
ADF
Ruminal
KRUADF,Rum
0.001
KslpRUADF,Rum
KHcCs1,Rum
KRUP,Rum
0.017
0.002
0.833
0.389
KslpRUP,Rum
KAmMi,Rum
0.010
0.002
0.005
KYATP,Rum
0.168
0.034
0.088
KAmpH,Rum
0.003
0.001
0.002
0.001
0.001
0.002
0.055
0.001
0.002
0.002
0.001
0.001
0.002
0.002
KpH,Rum
0.862
0.110
0.879
0.841
0.794
0.803
0.355
0.013
0.210
0.354
0.359
0.171
0.161
0.301
0.311
KVFApH,Rum
0.086
0.002
0.050
0.069
0.034
0.095
0.058
0.111
0.112
0.052
0.051
0.095
0.097
KAm,RumBld
0.002
0.803
0.001
0.011
0.002
0.005
0.002
0.002
0.001
0.001
0.001
KAc,RumBld
0.007
0.001
0.003
0.027
0.003
0.004
0.006
0.001
0.003
0.008
0.008
0.004
0.004
0.007
0.007
KPr,RumBld
0.005
0.001
0.002
0.005
0.069
0.003
0.003
0.001
0.001
0.004
0.004
0.002
0.002
0.003
0.003
KBu,RumBld
0.001
0.001
0.007
0.001
0.001
0.001
0.001
0.001
Postruminal
KProtein,IntFec
0.001
0.362
0.394
KStarch,IntFec
0.008
0.076
KFiber,IntFec
0.088
0.085
0.149
0.103
Urea excretion
KUr, BldUrin
0.036
Body composition
FPOth,DNA
0.004
1 19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. Parameter constrains were set to 70 and 130% of the final parameter estimates (Table 4). Data are expressed as a fraction of the total variance, explained by each model parameter selected, when predicting each specific variable; values larger than 3 decimals are presented.
2 Definitions for each of the model parameters are given in Table 4.
3 Am = ammonia; Ac = ruminal acetate; Pr = ruminal propionate; Bu = ruminal butyrate; MiN = microbial nitrogen passage; NAN = nonammonia nitrogen passage; NANMN = nonammonia, nonmicrobial nitrogen passage.
19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. Parameter constrains were set to 70 and 130% of the final parameter estimates (Table 4). Data are expressed as a fraction of the total variance, explained by each model parameter selected, when predicting each specific variable. Values >3 decimals are presented.
NUR = urinary N; FEC N = fecal N; MY = milk yield; MF% = milk fat percentage; MP% = milk protein percentage; ML% = milk lactose percentage; MFY = milk fat yield; MPY = milk protein yield; MLY = milk lactose yield.
N metabolism and excretion
Animal performance
BUN
NUR
FEC N
MY
MF%
MP%
ML%
MFY
MPY
MLY
BW
BCS
Ruminal
KRUADF,Rum
0.001
KslpRUADF,Rum
0.001
KHcCs1,Rum
0.001
KRUP,Rum
0.004
0.028
0.002
0.005
0.001
0.009
0.001
0.005
0.005
0.007
KslpRUP,Rum
0.001
KAmMi,Rum
0.001
KYATP,Rum
0.001
0.001
KAmpH,Rum
0.001
0.001
0.001
0.001
0.001
KpH,Rum
0.059
0.242
0.001
0.002
0.794
0.331
0.001
0.873
0.002
0.584
0.685
KVFApH,Rum
0.002
0.045
0.001
0.001
0.051
0.019
0.012
KAm,RumBld
0.001
0.001
0.001
0.001
KAc,RumBld
0.003
0.001
0.004
0.001
0.009
KPr,RumBld
0.003
0.001
0.001
0.003
0.002
0.001
KBu,RumBld
0.001
0.001
0.001
Postruminal
KProtein,IntFec
0.025
0.371
0.995
0.364
0.048
0.283
0.001
0.371
0.364
0.119
0.008
KStarch,IntFec
0.002
0.007
0.003
0.005
0.007
0.001
0.004
0.002
0.003
0.011
0.082
KFiber,IntFec
0.001
0.001
0.001
0.002
0.019
Urea excretion
KUr, BldUrin
0.829
0.034
0.001
Body composition
FPOth,DNA
0.064
0.273
0.579
0.044
0.212
0.001
0.003
0.575
0.579
0.197
0.022
1 19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. Parameter constrains were set to 70 and 130% of the final parameter estimates (Table 4). Data are expressed as a fraction of the total variance, explained by each model parameter selected, when predicting each specific variable. Values >3 decimals are presented.
2 Definitions for each of the model parameters are given in Table 4.
3 NUR = urinary N; FEC N = fecal N; MY = milk yield; MF% = milk fat percentage; MP% = milk protein percentage; ML% = milk lactose percentage; MFY = milk fat yield; MPY = milk protein yield; MLY = milk lactose yield.
To further evaluate the veracity of parameter estimates, a 5-fold cross evaluation was performed. This approach was used rather than a semi-exhaustive method due to the computational requirements for the work. The data set (115 treatments means) was divided in 5 subsets of equal size (23 treatments). The same 19 model parameters used for global sensitive analyses were fitted to 4 of the 5 subsets (training data) and the derived parameter estimates were used with the model to predict the remaining subset (test data). Training data selection, parameter estimation, and model testing were conducted an additional 19 times and the overall results used to calculate variance and model performance estimates.
Mixed model, multiple regression was performed to identify additional model elements that require improvement. This was achieved by regressing residuals for ruminal fermentation and digestion predictions on observed DMI, BW, and dietary nutrient composition (CP, fat, NSC, starch, sugars, NDF, ADF, ash, lignin, soluble CP, RUP, soluble starch, rumen undegraded ADF, forage NDF, and roughage). Such regressions allow identification of potentially missing nutrient actions or interactions. Study effects were included as a random variable and regressions were conducted using a backward elimination approach with a significance level of 0.05. Multicollinearity was assessed by calculation of variance inflation factors with variables having variance inflation factors greater than 5 removed from the regression model (
). In these analyses, positive coefficients indicate the model under predicted responses to the independent variable, whereas negative coefficients imply overprediction of responses. Also, the presence of a significant relationship suggests that the model might not properly represent the effects or fate of that nutrient. A detailed residual analysis is provided in Supplemental Tables S3, S4, and S5 (http://hdl.handle.net/10919/103450). Part of the results are discussed in the manuscript when relevant; further association of residuals with model deficiencies has been previously discussed in similar work by
All statistical summaries of the data, data handling, residuals analyses, plots, RMSE, and CCC estimations were conducted with R Studio (version 1.2.1335, RStudio Inc.).
RESULTS AND DISCUSSION
As a mechanistic model, Molly can be expected to represent different feeding scenarios including those outside of the data used for derivation. However, at lower levels of integration the model uses empirical representation which may not capture the true relationship thereby affecting the ability to predict diets different than those used during model parameterization, i.e., pasture-based diets.
Model predictions using the initial set of parameters had a maximum log-likelihood value of −535, whereas after model reparameterization the maximum log-likelihood value was −99, which represents a substantial improvement. Additionally, BIC decreased after reparameterization from 1,160 to 287 indicating that the North American parameter set was not representative of ryegrass-based diets.
As shown in Table 5, some ruminal fermentation variables were minimally improved after model reparameterization, and some predictions degraded slightly, which could suggest accommodation of some nonrumen variables occurred at the cost of lost precision in other predictions. This is an indication that the available data were not completely adequate for the objective. Similarly, ruminal N outflow predictions were not significantly improved, although the data were too limited to provide concluding remarks. This was supported by the high standard deviation values obtained after the 5-fold cross evaluation. Ruminal fiber outflow, fecal output (DM, OM, and fiber), milk and fecal N excretion, and animal performance predictions were improved after model reparameterization. These improvements in model performance suggest that grass nutrient digestibility deviates from expected based on the relationships observed for digestion of North American diets, which are largely absent of ryegrass. Thus, either the characterization of the diets or the model representations of digestion are deficient, and the model cannot be universally applied across diet types as expected. The improvements in predictions of ryegrass diet digestibility partially explain the improvements in animal performance predictions.
Ruminal Metabolism
pH and VFA
Before model reparameterization, ruminal pH and VFA concentrations had RMSE values of 2.9 and 14.6%, and CCC values of 0.17 and 0.26, respectively (Table 5). After reparameterization, the CCC for ruminal pH remained the same, and the CCC value for VFA decreased to 0.17. The RMSE differences for individual VFA concentrations were not significant after reparameterization; CCC values for ruminal acetate predictions improved but CCC for propionate worsened (Table 5).
Although RMSE and slope bias were negligible for pH predictions, variation explained by the model was a small fraction of the total variation as indicated by a low CCC value. This indicates that that the model is not capturing much of the intrinsic variation in the data either because the model is missing one or more key mechanisms or because random measurement error is large relative to the range in predictions.
included ammonia effects on ruminal pH predictions to address this problem in a recent Molly update, but they found that pH predictions continued to lack precision. As pH affects fermentation and VFA absorption, a portion of the variation in VFA concentrations may be due to poor pH predictions. However, predictions of pH were only slightly sensitive to ruminal ammonia concentrations (Table 6). Volatile fatty acid concentrations had a stronger influence. This part of the model still requires additional work to improve pH predictions independently of the production system. A concerted effort using ruminal observations collected within day across varying diets is required to determine if the problem is due to unrepresentative sampling with respect to sampling location, sampling time relative to meals, eating patterns within the day, diet sorting, and feeding management. These problems can be exacerbated with pasture-based diets (
Concentrations of VFA in the rumen depend on the balance of VFA production and absorption where the latter is represented as a mass action function of each VFA (KAc, RumBld, KPr, RumBld, and KBu, RumBld). In turn, pH predictions are driven by VFA (KVFApH, Rum) and ammonia concentrations (KAmpH, Rum) with an intercept to center the equation (KpH, Rum; Table 4). The decrease in absorption rates of propionate and butyrate explained the reduced mean bias after reparameterization and resulted in increased ruminal propionate and butyrate concentrations compared with the values before reparameterization. On the other hand, the absorption rate of acetate increased after reparameterization. Interestingly, the CCC value for ruminal acetate concentration decreased from 0.25 to 0.00 after reparameterization, whereas CCC values for propionate concentration increased from 0.35 to 0.42, primarily due to a decrease in the mean bias of propionate from 42.6 to 1.4%. The lack of concordance of acetate predictions and the greater slope bias (38.3%) likely indicates that there are factors affecting ruminal fermentation that are not being considered or the approach to representing acetate production was biased.
Although modifications in VFA absorption rate constants resulted in a smaller molar proportion of acetate, acetate absorption rates and concentrations were increased relative to the prior model configuration reported by
. The changes may suggest inaccuracy in the predicted production rates or regulation of transport kinetics with the high forage diets that was not captured in the current equations.
Extant rumen models represent substrates that originate from forages and concentrates as a common pool, which is an oversimplification for pasture-based diets where fresh pasture and concentrates are generally fed separately (
). Although in most mechanistic rumen models, predictions of VFA are based on stoichiometric coefficients from chemical substrates, it has been reported that this approach is inaccurate for general application (i.e., coefficients derived for one forage type perform poorly when applied to another forage type; e.g.,
). Therefore, fresh ryegrass and cultivar variation within may have not been well represented when deriving digestion and fermentation coefficients for high forage diets, which were primarily composed of alfalfa, corn silage, and hay (
). If the composition of VFA produced from grass-based diets is different than for other diet and forage types, this likely reflects altered microbial population structure elicited by changes in diet composition, pH, and feeding patterns that are not currently captured in the model (
Before reparameterization, the RMSE for ruminal ammonia concentrations was 42.3%, and it remained largely unchanged (P = 0.9) at 37.8% after reparameterization. However, the mean bias decreased from 12.8 to 3.8%, the slope bias decreased from 14.2 to 6.3%, and the CCC increased from 0.51 to 0.62 after model reparameterization, indicating improved accuracy and precision (Figure 1A). This resulted from a decrease in the rate constant for ammonia absorption (KAm, RumBld) from 12.3 to 10.4 d−1 (Table 4). At a pH of 6.5 or lower, ammonia (NH3) will be almost entirely ionized (around 99%) and be absorbed as ammonium (NH4+) via a putative K channel (
). The reduction in the ammonia absorption rate constant, KAm, RumBld, could be due to the greater K concentration in ryegrass diets (3 to 6% depending on season) compared with typical TMR values of 1.0 to 1.2% (
). However, other factors could affect urea recycling and NH3 absorption via saliva production as bicarbonate flux is only empirically represented in the model.
Figure 1Observed (●, black) or residual (▲, red) versus predicted values after model reparameterization for: (A) ruminal ammonia concentrations (mmol/L); (B) ruminal NAN outflow (kg/d); (C) ruminal nonammonia, nonmicrobial N (NANMN) outflow (g/d); (D) ruminal microbial N outflow (kg/d); (E) fecal N excretion (kg/d); and (F) urinary N excretion (kg/d). The solid lines represent individual studies, and points represent the different treatments within each study. The dotted lines represent the line of unity. * indicates the smaller value of NANMN (
Increasing the water soluble carbohydrate/protein ratio of temperature pasture affects the ruminal digestion of energy and protein in dairy cows.
in: Proc. VI International Symposium on the Nutrition of Herbivores. Tropical and Subtropical Agroecosystems, Merida, Mexico. Autonomous University of Yucatan,
2003: 251-254
(0.1 to 15.9 mmol/L). However, the accuracy of ammonia predictions remained moderate (Table 8) and the difference in ammonia absorption rate remained after cross evaluation (Table 9), in support of the reparameterization.
Table 8Model parameters resulting from 5-fold cross evaluation using pasture-based diets
19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. A 5-fold cross evaluation was performed (group size used was 23 treatments and 20 repetitions were performed).
No SD was observed because the parameter reached the maximum biological value at each running.
0.00
0.00
KFiber,IntFec
0.13
0.04
30.77
7.37 × 10−6
Urea excretion
KUr, BldUrin
0.32
0.02
6.25
2.20 × 10−4
Body composition
FPOth,DNA
15,927.66
1,270.90
7.98
0.74
1 19 parameters were selected based on discrepancies after reparameterization, this amount is the maximum limit of simultaneous model estimation. A 5-fold cross evaluation was performed (group size used was 23 treatments and 20 repetitions were performed).
2 Coefficients of variation for parameter values after cross evaluation.
3 Correspond to the SE of SD obtained after each k-fold cross evaluation running.
4 No SD was observed because the parameter reached the maximum biological value at each running.
Milk lactose content is assumed as a fixed constant in the model (a value 4.62% was used) so slope bias and concordance correlation coefficient (CCC) values could be calculated.
%
8
4.61
0.04
4.63
0.00
2.92
0.92
14.90
23.46
—
—
—
—
Milk fat, kg/d
21
1.00
0.04
0.98
0.02
22.44
2.68
4.57
7.65
21.65
8.65
0.15
0.13
Milk protein, kg/d
21
0.81
0.03
0.82
0.02
20.38
2.02
3.81
4.56
22.83
12.59
0.06
0.13
Milk lactose, kg/d
8
1.08
0.10
1.05
0.04
21.64
4.35
17.04
20.25
23.45
26.22
0.30
0.28
BW, kg
13
565.79
8.11
553.75
9.83
3.56
0.68
37.51
19.57
13.06
13.71
0.87
0.06
BCS, 1 to 5
8
2.68
0.07
2.31
0.06
14.40
1.52
91.06
4.31
1.61
2.52
0.43
0.13
1 A 5-fold cross evaluation was performed (group size used was 23 treatments and 20 repetitions were performed). MSE = mean squared error.
2 Average number of observations used in the 5-fold cross evaluation.
3 NANMN = nonammonia, nonmicrobial N.
4 Milk lactose content is assumed as a fixed constant in the model (a value 4.62% was used) so slope bias and concordance correlation coefficient (CCC) values could be calculated.
Additional improvements in NH3 predictions are likely related to data quality (ammonia concentrations are subject to the same sampling issues discussed for VFA and pH), with important diurnal changes in rumen ammonia concentration in pasture-based diets, and thus, sampling at given times may not be a reflection of steady state (
Temporal fermentation and microbial community dynamics in rumens of sheep grazing a ryegrass-based pasture offered either in the morning or in the afternoon.
). Finally, the kinetic parameters used to reflect inherent differences among ingredients may not reflect the complete nature of protein degradability for fresh temperate grasses which would affect ammonia predictions (
Characterization of the nutritive value of perennial ryegrass (Lolium perenne L.) dominated pastures using updated chemical methods with application for the Cornell Net Carbohydrate and Protein System.
The RMSE for microbial nitrogen prediction decreased from 23.9 to 20.7% after reparameterization but it was not significant. However, the slope bias decreased from 21.4 to 3.5%, whereas the CCC value increased from 0.06 to 0.21 (Table 5). Microbial growth is represented in Molly as a function of fermentable substrate availability and subsequent conversion of ATP generated to microbial mass (YATP), a process affected by ruminal ammonia, dietary fat, and AA concentrations (
The efficiency constant for yield of microbial mass per mol of ATP from fermentation (KYATP, Rum, g of microbial DM/mol of ATP) was lower after reparameterization (Table 4). Similarly, the constant for the effect of ruminal concentrations of ammonia on microbial growth (KAmMi, Rum) decreased from 3.6 to 3.1 mmol/L (but SD of parameters overlap), and the sensitivity exponent to adjust the effect of ammonia on microbial growth (XEAm) decreased from 1.00 to 0.69 mol/mol. The combination of changes resulted in an efficiency of 70% of maximal microbial yield at the mean ammonia concentration of 10.5 mmol/L compared with 75% efficiency using the initial parameters. This suggests that microbial growth on high pasture diets is a less efficient process than in balanced mixed diets. The revised parameter value for KYATP, Rum was consistent during cross evaluations, however, the SD for KAmMi, Rum overlapped with the prior parameter suggesting that the revised estimate may not be a significant change (Table 8).
In fresh grass, ruminal degradation rates are higher for CP than OM or NDF (
Effects of synchronizing the rate of dietary energy and nitrogen release in diets with a similar carbohydrate composition on rumen fermentation and microbial protein synthesis in sheep.
). Such an asynchrony of rumen available N and carbohydrates in time may influence the efficiency of microbial protein synthesis. Although the potential problem is at least partially mitigated by recycling of N to the rumen from blood urea (
). If synchrony is important, it could explain a portion of the model imprecision herein because we were unable to consider within-day feeding effects due to lack of data.
The residual analysis (Supplemental Table S4, http://hdl.handle.net/10919/103450) showed that NSC was positively correlated with microbial N passage residual errors (P < 0.01), with microbial protein production underestimated when diets contained less than 15% NSC. Those diets represented mainly 100% pasture diets. Also, the NSC concentrations indicated lush grass growth with a high fraction of digestible fiber and an NSC fraction composed primarily of soluble sugars. Under those conditions, the microbial growth is stimulated as previously discussed.
reported that greater concentrations of ruminally fermentable fiber may enhance transformation of ruminal ammonia to microbial N compensating for the low NSC content. Our use of a single degradability to represent pasture fiber regardless of grass quality could be the source of the residual error relationship with NSC.
Starch and Fiber Degradation
Due to a lack of in situ-based, ruminal starch degradation data, requisite in situ predicted extent of ruminal starch degradations was set to 75% for all diets. After model reparameterization, the intercept (KRUSt, Rum) used to adjust the in situ-based degradation estimates was essentially 0, and the slope scalar (KslpRUSt, Rum) was 0.23 indicating that the initial rate of rumen degradation was greater than needed to achieve the predicted ruminal outflow which averaged 73.7% ± 8.0. However, as noted above, this derivation was by difference form OM outflow and thus subject to bias in predictions of degradation of any of the other components of OM. Ruminal starch degradation of 89.2% was reported by
Rumen metabolism, omasal flow of nutrients, and microbial dynamics in lactating dairy cows fed fresh perennial ryegrass (Lolium perenne L.) not supplemented or supplemented with rolled barley grain.
in cows consuming perennial ryegrass plus 3.5 kg DM of rolled barley grain, which is greater than our initial assumption (but inside our range of predictions) and was most likely influenced by the starch source and processing (
The intestinal starch digestion constant was found to be the maximum of 1.00 g of digested starch per gram of starch intake (Table 4) and was consistent in cross evaluations (Table 8). This implies complete starch digestion in the intestines which may be possible if amylase activity remains high and total ruminal outflow of starch is low, but this is not generally observed in practice (
reported values of 0.95 (g/g) and 0.93 (g/g) for intestinal starch digestibility in cows consuming 9.3 kg/d of ryegrass plus 7 kg/d of starchy or fibrous concentrate, whereas
Rumen metabolism, omasal flow of nutrients, and microbial dynamics in lactating dairy cows fed fresh perennial ryegrass (Lolium perenne L.) not supplemented or supplemented with rolled barley grain.
reported 98% apparent starch digestibility in the total tract. Although greater intestinal starch digestion seems to better represent pasture-based diets than the coefficient of 0.75 derived previously for TMR diets, 100% digestibility seems unlikely. It is likely the greater than expected value reflects bias in either measurement of fecal OM or prediction of the other components of fecal OM. Small and large intestinal starch digestibility values of 0.9 are used in the Nordic feed evaluation system, which are likely more representative of pasture diets with lower to moderate supplementation (
A model limitation that could explain the larger predicted intestinal starch digestion is the use of a constant value. Also, a more detailed representation of microbial populations in the rumen submodel may help improve ruminal starch outflow predictions and also improve total-tract digestibly predictions. Particularly, it has been shown that rumen protozoa play an important role in starch degradation, with protozoal concentration being positively related to ruminal pH. High forage diets appear to increase the populations of large ciliates which have a lower rumen passage rate which could increase starch degradability and even the starch content of protozoa may change according to diets (
Chemical composition of protozoal and bacterial fractions isolated from ruminal contents of dairy cows fed diets differing in nitrogen supplementation.
described that the small and medium particle outflow is sensitive to parameters controlling liquid passage. Therefore, the rate constant for ruminal liquid outflow (Kliquid, Rum) was evaluated for reparameterization (Table 4). However, Kliquid, Rum, which controls ruminal digesta retention time, remained unchanged after reparameterization at 3.27 versus the prior 3.29 ± 0.01, suggesting that Kliquid, Rum is similar for pasture-based diets and that the improvement in predictions of fiber degradation and subsequent ruminal outflow was not attributed to Kliquid, Rum modifications (Table 5).
Even though particle degradation and passage are represented in the model, the effect of mastication on particle size reduction is not well characterized for the full range of feeds in the literature (
Particle breakdown and rumen digestion of fresh ryegrass (Lolium perenne L.) and lucerne (Medicago sativa L.) fed to cows during a restricted feeding period.
). Thus, a better understanding of the particle size reduction and breakdown of forages could improve the understanding of the fermentative rumen activity and particle passage of grazed herbage from pasture-based diets.
Ruminal Nutrient Outflow
Nonammonia N and Nonammonia, Nonmicrobial N Passage
The RMSE for nonammonia N (NAN) and nonammonia, nonmicrobial N (NANMN) remained essentially unchanged (17.1 vs. 16.0%, P < 0.82; and 24.1 vs. 29.5%, P < 0.30, respectively; Table 5). Mean bias numerically increased for both variables, but slope bias decreased, suggesting that NAN and NANMN may be better represented after reparameterization, but some factors are affecting the centering of the predictions (Figure 1B, C), unlike for microbial N (Figure 1D). Removing the lowest NANMN value from the data set (78 g/d) resulted in a slight increase of CCC from 0.27 to 0.33 (Table 5); however, given the size of the data set (11 treatment means, all from 100% pasture diets) and high SD after cross evaluation (Table 9), no conclusion regarding outliers can be made with any confidence. Some of the variation among studies may be explained by the different markers used [rare earth (Yb) or transition metals (Cr and Co);
Intercept and slope scalars for crude protein degradation (KRUP, Rum and KSlpRUP, Rum), should take values of 0 and 1, respectively, if the in situ data perfectly reflected in vivo responses to changes to in situ determined RUP. Previous slope estimates were 0.00042 and the intercept was near 2, indicating that the rate constant for protein degradation was 2 times the rate determined in situ, and it is a static constant regardless of protein source and rate of degradation in situ (
). This conclusion remains the same with respect to grass protein degradation given that the refit slope value remained constant. In this case, any predicted differences in NANMN outflow between, for example, soybean meal and protected soybean meal or among forage sources, would have to be driven by differences in solubility, the effects of soluble protein on microbial expression of protein and fiber degradative enzymes, as those are the only mechanisms represented in the model. The latter would affect ruminal retention times and thus affect the extent of protein degradation.
Evaluation of the National Research Council (2001) dairy model and derivation of new prediction equations. 2. Rumen degradable and undegradable protein.
also observed problems with the use of the in situ data to predict the extent of degradation and devised an alternative scheme based solely on solubility and undegradability. Although the in situ technique is thought to be a valid method for comparing the extent and kinetics of protein degradation of different feeds in the rumen, it presents some limitations such as low reproducibility and microbial contamination of feed residuals, as discussed by
), and the relatively large variance for observed NANMN flow, it is also possible that the optimizer is placing more emphasis on the use of solubility to drive differences among ingredients than on the use of Kd. The former has a very high (and inverse) correlation with ruminal escape, with 77 to 79% of the soluble CP being degraded (
), whereas the latter is more moderately correlated with ruminal escape. At a small particle Kp of 3.3%/h (associated with ruminal liquid outflow, Table 4), and a Kd of 8.3%/h (slope of 0 and intercept of 2 per 24 h), CP escape from the insoluble pool would be approximately 29%. Given an RMSE of 30%, and correlations of NANMN with solubility and Kd, it seems likely that Kd for CP may be discounted in favor of solubility. Excluding the question of the validity of using in situ Kd to drive model predictions of degradability, the model reparameterization suggests that no adjustments relative to typical North American diets are needed to predict undegraded protein outflow from the rumen for grass-based diets. However, one must be cautious on the latter, as the number of observations in the literature for ruminal outflow from grass are very limited with considerable unexplained variation among experiments.
Ruminal NDF and ADF Outflow
The RMSE for NDF outflow decreased from 24.1 to 18.6% (P < 0.01), and mean bias decreased from 62.6 to 4.0% after reparameterization. The RMSE for ADF outflow decreased from 38.8 to 19.0% (P < 0.01), and mean bias decreased from 36.1 to 1.1%. The CCC values increased from 0.49 to 0.75 for NDF and from 0.70 to 0.74 for ADF outflow (Table 5). Improvements in fiber outflow predictions after model reparameterization (Figure 2A, B) were associated with greater intercept and slope scalar values used to adjust in situ cellulose degradation rates (KRUADF, Rum and KslpRUADF, Rum), increasing from 3.16 to 3.86 and 1.68 to 1.99, respectively, indicating that grass fiber is more degradable than fiber from forage used in North American TMR diets. A greater KRUADF, Rum intercept was required to represent the greater degradability of fiber in the animal data set. The greater slope captured the variation among pasture samples, suggesting that in situ observations captured the intrinsic variation. The increase in intercept and slope for fiber degradation explained the previous underestimation of fiber degradation with the original Molly settings, supporting that fiber from grass should perform better than expected relative to the TMR diets (Table 5).
Figure 2Observed or calculated (●, black) or residual (▲, red) versus predicted values after model reparameterization for: (A) ruminal NDF outflow (kg/d); (B) ruminal ADF outflow (kg/d); (C) fecal NDF outflow (kg/d); and (D) fecal ADF outflow (kg/d). The solid lines represent individual studies, and points represent the different treatments within each study. The dotted lines represent the line of unity. * indicates
The mean daily predicted extent of ruminal degradation was 69% for NDF and 67% for ADF; however, this increased with increasing inclusion of grass in the diets.
Increasing the water soluble carbohydrate/protein ratio of temperature pasture affects the ruminal digestion of energy and protein in dairy cows.
in: Proc. VI International Symposium on the Nutrition of Herbivores. Tropical and Subtropical Agroecosystems, Merida, Mexico. Autonomous University of Yucatan,
2003: 251-254
reported greater ruminal disappearance for NDF (76.2%) and ADF (78.4%) in 100% pasture diets. Also, ruminal fiber degradation of ryegrass changes during the season due to changes in ratios of hemicellulose to cellulose, and the degree of lignification. Seasonal changes in the effective rumen degradability were reported to range from 80% in early spring to 68% in fall, using a Kp of 5%/h (
The scalar relating hemicellulose to cellulose (KHcCs1,Rum) after reparameterization increased from 0.40 to 0.60, which suggests that the rate of degradation of hemicellulose from grass is greater than previously predicted by
for preserved forages. Although KHcCs1,Rum is better represented after reparameterization, other factors may still limit hemicellulose degradation; we expected a ratio of hemicellulose to cellulose degradation rate of around 1 (
). Interestingly, an increase in hemicellulose content with ryegrass maturity has been reported, whereas cellulose tends to be constant. Animal studies carried out in different seasons were considered in this analysis, which might explain the lower degradability predicted for hemicellulose (
). Different fibrous supplements (i.e., pasture silage and hay) were included in the various diets as well, and these have variable carbohydrate fractions depending on the maturity of the forage harvested.
Although the model predicts NDF and ADF outflow with high accuracy after reparameterization, the residuals for ruminal NDF and ADF outflow were significantly correlated with dietary RUADF (P < 0.01) indicating that in situ-derived estimates of fiber degradation did not fully capture the intrinsic digestibility of grass-based diets (Supplemental Table S4, http://hdl.handle.net/10919/103450). Temporal variation in dietary ingredients availability (i.e., supplements offered to grazing dairy cows), if it results in digestibility issues, would not have been captured in our analyses as we assumed all diets were fed as a TMR with a constant feeding rate. Therefore, any potential feed interactions would not have been captured through the in situ characterization. Also, rumen passage rate seems to be affected by the forage type, being greater in diets that include concentrates. Thus, the selection of a nonrepresentative Kp value may contribute to the observed bias (
). Future improvements could include ruminal undegradable fiber content as an input to the model to better characterize the forages used because the quality of these also change during the season (
Characterization of the nutritive value of perennial ryegrass (Lolium perenne L.) dominated pastures using updated chemical methods with application for the Cornell Net Carbohydrate and Protein System.
The RMSE for fecal DM excretion decreased from 40.3 to 17.7% (P < 0.01) after reparameterization. Similarly, RMSE for OM excretion decreased from 42.9 to 15.4% (P < 0.01). Additionally, CCC values greatly increased from 0.33 to 0.64 and 0.31 to 0.71, respectively (Table 5).
When evaluating the predictions for each study, it was evident that the
study had a great influence on the predictions (Figure 2C, 2D). Recalculation after excluding that data (without reparameterization) resulted in similar precision estimates for fecal NDF but CCC for fecal ADF predictions increased from 0.32 to 0.48 (P = 0.02; Table 5). The study of
was performed with late lactation cows in mid-summer using a low-quality grass (control pasture, 53.7% NDF and 29.2% of ADF), which likely explains the lower digestibility in that treatment (Table1). Considering that in situ rumen degradability of fiber was estimated for this study, variation in intrinsic fiber degradation with forage maturity was not captured in the inputs. The model does not attempt to represent variation in fiber degradation rate by forage type and maturity; it is assumed that information is resident in the in situ-derived rates provided as inputs. We have not explicitly evaluated the potential for use of nutrient characteristics to predict degradation rates.
Conversely, the model predicts particulate Kp from liquid passage which is influenced by DMI and diet characteristics via ruminal osmolality. Apparent Kp is also affected by particle distribution in the diet. The kinetics of particle passage given 3 particle pools and interactions with liquid passage are more difficult to compare with the literature, however Kp predictions for grass and grass silage from the Nordic feed evaluation system (
in: Sejrsen K. Hvelplund T. Nielsen M.O. Ruminant Physiology: Digestion, Metabolism and Impact of Nutrition on Gene Expression, Immunology and Stress. Wageningen Academic Publishers,
2006: 87-135
). However, after reparameterization, a value of 0.07 g/g was obtained in the current study. This can be explained by greater ruminal fiber degradation leaving the fiber remnant reaching the intestine with a greater content of lignin and reduced digestibility. Total-tract NDF digestibility predicted was 55.1% using the initial set of parameters and 65.2% after reparameterization, supporting the notion that most of grass fiber degradation occurs in the rumen. In general, total-tract NDF digestibility was greater than the 51% value previously reported for TMR diets (
). Greater intestinal digestibility may be expected with higher forage supplementation (e.g., corn silage and alfalfa hay) if ruminal degradation is more moderate, resulting in material of higher potential digestibility flowing to the intestines (
Fiber intestinal digestibility coefficient is assumed constant in the model, future work could consider partially driving ruminal degradation and intestinal digestion relationships from forage type as for other extant models (
). The latter is not a truly mechanistic approach, but it could be expanded to a representation of the amount and transit of digesta and enzymatic activity using, for example, the principles described for soluble fiber digestion (
). Although a more detailed mechanistic representation of intestinal nutrient digestion would be helpful, the overall contribution of the intestine to total-tract fiber digestion is relatively small thereby limiting the effect of any improvements.
The RMSE for fecal N output decreased from 29.5 to 16.3% (P < 0.01) (Table 5). The intestinal digestion coefficient for protein (KProtein,IntFec) increased from 71 to 79% after reparameterization (Table 4), which resulted in a decreased mean bias from 53.6 to 2.4% and an increased CCC from 0.14 to 0.29. Diets selected had a high content of soluble protein (39%), which added to a likely lower rumen passage rate and could explain a greater degradation of CP. Thus, a lower amount of CP reached the intestine (130 g/d of NANMN vs. 200 g/d for TMR diets) (
). Therefore, the increase in CP digestibility is explained by the lesser content of RUP of pasture-based diets, together with an expected greater digestibility observed in grass in a vegetative stage (
Based on the reparameterization and cross evaluation, a greater protein digestibility value should be used to represent pasture-based diets. It is important to note that residual analysis of fecal protein output found a significant relationship with dietary NDF and ADF (Supplemental Table S5, http://hdl.handle.net/10919/103450). As mentioned, fiber rumen degradation and passage are affected by forage type and by the extent of lignification due to maturity (
). Therefore, the use of a constant value for CP intestinal digestibility seems inadequate to represent the full spectrum of diets.
Blood Urea N Concentration and Urinary N Excretion
The RMSE for BUN concentrations marginally decreased after model reparameterization from 25.0 to 21.1% and it was not significant (Table 5). Mean bias decreased from 35.6 to 0.3%, and slope bias increased from 4.8 to 22.6%. The slope bias was highly affected by a single extreme value (29.7 mg/dL) from a pasture diet with 26.2% CP (
; Table 2). This single value had less effect on CCC which improved from 0.36 to 0.55 after reparameterization (Table 5). Future improvements to BUN predictions should consider that BUN changes over the course of the day associate to grazing pattern, and therefore sampling time has an important effect on BUN values (
). Thus, a mechanistic representation of urea transport from blood to milk and vice versa might be needed in Molly to improve precision of BUN predictions.
The RMSE for urinary N excretion decreased numerically from 19.2 to 15.9% after reparameterization but it was not significant. The CCC value slightly increased from 0.83 to 0.88. The latter supports the notion that the model represents the mechanism of urinary N excretion with high accuracy (Figure 1F). The rate constant for urea excretion by the kidney (KUr, BldUrin) decreased from 0.42 to 0.32 (mol−1) (Table 4), with an important reduction in mean bias from 36.5 to 3.8% for urinary N excretion. This was translated in a decrease of urinary N excretion, and an increase in BUN predictions in agreement with the observed data (Table 5). A reduced value for KUr, BldUrin after reparameterization indicates that the kidney clearance rate was reduced for those diets. This could reflect greater blood flow to the kidney when animals are consuming high N diets or different dietary mineral loads across the diet types, the latter affecting kidney filtration. The reduced clearance rate was consistent in the cross evaluations indicating the result is not unique to a subset of the data (Table 8).
discussed that urea recycling from glomerular filtrate should be considered to improve urinary urea predictions, and that NaCl played a role in renal mechanisms of urea absorption and excretion. Thus, the lower salt concentrations in grazing cow's diets, due to lower or no supplementation, may explain the lower excretion rate (
). Because urea transporters play a role in concentrating urine and are partly responsible for the transport of urea-N in the renal medulla, the representation of that mechanism using mass action kinetics in the model may be an oversimplification (
The RMSE for BW predictions significantly decreased from 8.5 to 3.2% (P < 0.01) after model modifications and reparameterization, and CCC increased from 0.59 to 0.91 (Table 5). Model predictions before reparameterization were influenced by overestimated protein degradation activity as reflected in a BW decrease of 45 kg over 14 d, and this also explained the previous overprediction of milk production. Model changes and parameterization resulted in the mean bias decreasing from 89.6 to 10.2%, explaining the improvement in predictions of BW and milk yield (Table 5). Previous work had mainly focused on ruminal fermentation and digestion. Incorporation of a target protein to DNA ratio (FPOth, DNA) stabilized body protein and blood AA concentrations and avoided inappropriate changes in body size. However, the initial estimate for the ration of 6,470 mol/mol was too low, as indicated by the derived value of 14,995 mol/mol (Table 4). Mean total blood AA concentrations were reduced from 7.5 mmol/L to 4.5 mmol/L. However, further reductions in AA concentrations are required as physiologic concentrations are approximately 2.6 mmol/L (
). The FPOth, DNA values change as animals grow, with reported muscle values around 1,000 mol/mol at 100 kg of carcass weight and increasing to 6,000 mol/mol at 400 kg (
). To properly address the protein and AA subsystem, additional data from longer-term studies supplemented with observations of N balance and blood AA concentrations are needed. It presumably would also be beneficial to de-aggregate the AA pool to reflect the effect of individual essential AA on milk protein output and tissue protein synthesis and balance. The inclusion FPOth, DNA resulted in improvements of animal BW and also proved to be a sensitive parameter relative to N metabolism and excretion and milk production and protein yield (Table 7). Although a greater value than expected was estimated by the reparameterization, it was consistent in cross evaluation (Table 8) and BW was predicted with greater accuracy (Table 9). Thus, the changes seem to be of value.
Body Condition Score
Reparameterization and model modifications resulted in the RMSE for BCS significantly decreasing from 19.0 to 14.1% (P < 0.01), and CCC value increasing from 0.31 to 0.45 (Table 5). The intercept to adjust the initial mass of adipose tissue (KiAdip) adopted a value of −164 kg (Table 4), which was previously 41.9 kg less. After KiAdip adjustment, model predictions of animal adipose tissue were closer to those reported by
for a cow of 555 kg of BW in early (47.5 kg of adipose tissue) and late lactation (80.9 kg of adipose tissue). The smaller adipose tissue mass predicted for the grazing studies used, was associated with the fact that many of the Chilean studies selected were running at early lactation, mainly from autumn calving seasons (Table 1), often with cows with lower BCS in this type of calving system (
The effect of pasture allowance and concentrate supplementation type on milk production performance and dry matter intake of autumn-calving dairy cows in early lactation.
). The improvements in BCS predictions were consistent with the cross evaluation (Table 9), supporting the usefulness of model modifications. Interestingly, slope bias was negligible, suggesting that biological processes are properly represented and mean bias observed could be addressed with future revision of additional model nutrient partitioning parameters (e.g., lipolysis and lipogenesis).
Milk Yield and Composition
Although predicting animal performance was not the main focus of this study, it was included to have a whole view of Molly predictions, including the effect of reparameterized digestive improvements and model modifications in BW and adipose tissue mass representation, on animal performance. The RMSE for daily milk yield significantly decreased from 36.3 to 20.8% after reparameterization (P < 0.01; Table 5). Also, mean bias greatly decreased from 61 to 3.2%, which indicates that milk yield was greatly overestimated before reparameterization (average of 31.5 kg/d vs. 24.5 kg/d observed). Additionally, CCC increased from 0.02 to 0.13, however, this is far from the predictions reported for US Holstein-Friesian cows on TMR diets (RMSE under 10%;
There was great variation in percentage milk components among the different animal studies. This was mainly due to the wide variety of dairy breeds used, different stages of lactation, and milk production volume (Table 2). After model reparameterization, RMSE for milk fat percentage significantly decreased from 14.6 to 12.6% (P < 0.01), whereas RMSE for milk protein percentage decreased from 9.0 to 8.8% (P = 0.57). The CCC values increased from 0.17 to 0.32, and 0.10 to 0.11 for milk fat and milk protein percentages, respectively. The yield of each milk component (kg/d) was evaluated (Table 5) given that milk composition is a function of the component yields. The RMSE values decreased for milk fat from 46.7 to 22.8% (P < 0.01), protein yield from 43.4 to 20.7% (P < 0.01), and lactose yield from 40.9 to 21.9% (P < 0.01). Similarly, CCC values increased from −0.05 to 0.18, 0.01 to 0.12 and 0.14 to 0.36, respectively.
Important improvements were observed in milk yield and milk components yield predictions (kg/d) after model reparameterization and modifications (lower mean and slope bias), with the exception of milk protein and lactose percentage. However, the accuracy of predictions was still low. It is important to note that CCC for animal performance predictions have not been reported previously; however, RMSE values reported by
were smaller than those observed in this work (about 20%). This suggests that together with the need for additional improvements in the representation of diet digestion, it is likely that other model constants and parameters derived for North American Holstein cows may require reparameterization. Milk and milk content yields in Molly are represented in a mechanistic form through the representation of mammary cells and mammary enzyme activity. Although previous attempts were made to represent Holstein and New Zealand cows, different dairy breeds used and even crossbreeds may not be well represented (
). Finally, improvements in the energy and protein balance as previously discussed will likely affect nutrient availability and uptake by the mammary gland, being required a model evaluation using data from grazing studies over a full lactation to properly represent those processes (
Global Sensitivity Analysis and 5-fold Cross Evaluation
As mentioned earlier, the model was highly sensitive to rumen pH related parameters (Table 6). This is expected given that Molly is a whole animal model, with digestive processes properly linked to animal performance. Intestinal digestive coefficients explained an important part of the variations of fecal outputs, and considering that they are assumed as constant in the model, a proper value should be used, in support of the reparameterization process. The BUN concentrations were highly related to urinary urea excretion, which support N metabolism and excretion improvements after KUr, BldUrin reparameterization (Table 7). Around 50% of milk yield and solids variations were explained by the digestive parameters, whereas the other half was associated with FPOth, DNA. This supports the usefulness of our model modifications.
No previous model cross evaluation has been performed for Molly model predictions due to this process require high computation intensity. Main findings were already included in the discussion, but it is remarkable that parameters estimate indicated that all of the parameters were very well defined by the data presenting low to moderate CV values (Table 8). Particularly, information of N passage variables was limited, which resulted in smaller CCC values and high SD (Table 9). Thus, no clear conclusions could be obtained from this information. On the other hand, the improvements in NDF and ADF ruminal outflow predictions were consistent with reparameterization, whereas accuracy of fecal output predictions was moderate and they presented a high SD (associate to the small number of observations). Animal performance predictions were consistent with reparameterization, presenting lower accuracy and moderate mean bias, suggesting the necessity of additional model parameters revision.
CONCLUSIONS
The accuracy of the Molly cow model predictions of ruminal fermentation, nutrient digestion, and performance by dairy cows consuming fresh ryegrass-based diets was evaluated, and deficiencies particular to grass-based diets were identified. No improvements were observed for rumen pH predictions after reparameterization, but ruminal acetate absorption rate appears to be larger for pasture-based diets, whereas the rate of ammonia absorption seems to be smaller. Reparameterization of ruminal protein degradation and outflow suggest that efficiency of microbial production is smaller from pasture-based diets, whereas the ruminal protein degradation rate seemed to be unaffected by protein source. However, a small amount of data was available, limiting the reliability of those parameters. Ruminal fiber degradation was greater for pasture-based diets, hemicellulose degradation in particular. Given that intestinal coefficients are constant in the model, the larger coefficients for protein and starch digestion derived should be more representative of pasture-based diets. Model modifications included in this work improved BW and adipose tissue representation of grazing cows, with subsequent improvement in animal performance predictions. Future work should evaluate other model parameters not included in this model evaluation as those related to nutrient partitioning and mammary gland representation. Model parameters that were different are recommended to be used for Molly predictions of dairy cows consuming pasture-based diets until variations between production systems are identified and unified in a sole mechanistic representation.
ACKNOWLEDGMENTS
The Chilean government National Agency of Research and Development (ANID, Santiago, Chile) and Virginia Tech (Blacksburg, VA) are acknowledged for providing scholarship and tuition support for A. G. Morales. M. D. Hanigan was partially supported by a grant from the New Zealand Agricultural Greenhouse Gas Research Centre (Palmerston North, New Zealand). Additional funding was provided by the Virginia Agricultural Experiment Station (Blacksburg, VA) and the Hatch Program of the National Institute of Food and Agriculture, U.S. Department of Agriculture (Washington, DC) via the NC-2040 and National Animal Nutrition Program regional research projects. The authors have not stated any conflicts of interest.
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