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Ellis JL, Kebreab E, Odongo NE, Beauchemin K, McGinn S, Nkrumah JD, Moore SS, Christopherson R, Murdoch GK, McBride BW, Okine EK, France J. Modeling methane production from beef cattle using linear and nonlinear approaches1. J Anim Sci 2009; 87:1334-45. [DOI: 10.2527/jas.2007-0725] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
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77
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Jalilvand G, Odongo N, López S, Naserian A, Valizadeh R, Shahrodi FE, Kebreab E, France J. Effects of different levels of an enzyme mixture on in vitro gas production parameters of contrasting forages. Anim Feed Sci Technol 2008. [DOI: 10.1016/j.anifeedsci.2008.01.007] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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78
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Kebreab E, Dijkstra J, Bannink A, France J. Recent advances in modeling nutrient utilization in ruminants. J Anim Sci 2008; 87:E111-22. [PMID: 18820154 DOI: 10.2527/jas.2008-1313] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Mathematical modeling techniques have been applied to study various aspects of the ruminant, such as rumen function, postabsorptive metabolism, and product composition. This review focuses on advances made in modeling rumen fermentation and its associated rumen disorders, and energy and nutrient utilization and excretion with respect to environmental issues. Accurate prediction of fermentation stoichiometry has an impact on estimating the type of energy-yielding substrate available to the animal, and the ratio of lipogenic to glucogenic VFA is an important determinant of methanogenesis. Recent advances in modeling VFA stoichiometry offer ways for dietary manipulation to shift the fermentation in favor of glucogenic VFA. Increasing energy to the animal by supplementing with starch can lead to health problems such as subacute rumen acidosis caused by rumen pH depression. Mathematical models have been developed to describe changes in rumen pH and rumen fermentation. Models that relate rumen temperature to rumen pH have also been developed and have the potential to aid in the diagnosis of subacute rumen acidosis. The effect of pH has been studied mechanistically, and in such models, fractional passage rate has a large impact on substrate degradation and microbial efficiency in the rumen and should be an important theme in future studies. The efficiency with which energy is utilized by ruminants has been updated in recent studies. Mechanistic models of N utilization indicate that reducing dietary protein concentration, matching protein degradability to the microbial requirement, and increasing the energy status of the animal will reduce the output of N as waste. Recent mechanistic P models calculate the P requirement by taking into account P recycled through saliva and endogenous losses. Mechanistic P models suggest reducing current P amounts for lactating dairy cattle to at least 0.35% P in the diet, with a potential reduction of up to 1.3 kt/yr. A model that integrates nutrient utilization and health has great potential benefit for ruminant nutrition research. Finally, whole-animal or farm level models are discussed. An example that used a multiple-criteria decision-making framework is reviewed, and the approach is considered to be appropriate in dealing with the multidimensional nature of agricultural systems and can be applied to assist the decision process in cattle operations.
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Odongo NE, Bagg R, Vessie G, Dick P, Or-Rashid MM, Hook SE, Gray JT, Kebreab E, France J, McBride BW. Long-term effects of feeding monensin on methane production in lactating dairy cows. J Dairy Sci 2008; 90:1781-8. [PMID: 17369219 DOI: 10.3168/jds.2006-708] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
The objective of this study was to determine the long-term effects of feeding monensin on methane (CH4) production in lactating dairy cows. Twenty-four lactating Holstein dairy cows (1.46 +/- 0.17 parity; 620 +/- 5.9 kg of live weight; 92.5 +/- 2.62 d in milk) housed in a tie-stall facility were used in the study. The study was conducted as paired comparisons in a completely randomized design with repeated measurements in a color-coded, double-blind experiment. The cows were paired by parity and days in milk and allocated to 1 of 2 treatments: 1) the regular milking cow total mixed ration (TMR) with a forage-to-concentrate ratio of 60:40 (control TMR; placebo premix) vs. a medicated TMR (monensin TMR; regular TMR + 24 mg of Rumensin Premix/kg of dry matter) fed ad libitum. The animals were fed and milked twice daily (feeding at 0830 and 1300 h; milking at 0500 and 1500 h) and CH4 production was measured prior to introducing the treatments and monthly thereafter for 6 mo using an open-circuit indirect calorimetry system. Monensin reduced CH4 production by 7% (expressed as grams per day) and by 9% (expressed as grams per kilogram of body weight), which were sustained for 6 mo (mean, 458.7 vs. 428.7 +/- 7.75 g/d and 0.738 vs. 0.675 +/- 0.0141, control vs. monensin, respectively). Monensin reduced milk fat percentage by 9% (3.90 vs. 3.53 +/- 0.098%, control vs. monensin, respectively) and reduced milk protein by 4% (3.37 vs. 3.23 +/- 0.031%, control vs. monensin, respectively). Monensin did not affect the dry matter intake or milk yield of the cows. These results suggest that medicating a 60:40 forage-to-concentrate TMR with 24 mg of Rumensin Premix/kg of dry matter is a viable strategy for reducing CH4 production in lactating Holstein dairy cows.
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80
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Odongo NE, Or-Rashid MM, Kebreab E, France J, McBride BW. Effect of supplementing myristic acid in dairy cow rations on ruminal methanogenesis and fatty acid profile in milk. J Dairy Sci 2008; 90:1851-8. [PMID: 17369226 DOI: 10.3168/jds.2006-541] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
The objective of this study was to evaluate the effects of supplementing myristic acid in dairy cow rations on ruminal methanogenesis and the fatty acid profile in milk. Twelve multiparous Holstein dairy cows (710 +/- 17.3 kg of live weight; 290 +/- 41.9 d in milk) housed in a tie-stall facility were used in the study. The cows were paired by parity and days in milk and allocated to 1 of 2 treatments: 1) the regular milking cow total mixed ration (control diet), and 2) the regular milking cow total mixed ration supplemented with 5% myristic acid on a dry matter basis (MA diet). The cows were fed and milked twice daily (feeding, 0830 and 1300 h; milking, 0500 and 1500 h). The experiment was conducted as a completely randomized design and consisted of a 7-d pretrial period when cows were fed the control diet to obtain baseline measurements, a 10-d dietary adaptation period, and a 1-d, 8-h measurement period. The MA diet reduced methane (CH4) production by 36% (608.2 vs. 390.6 +/- 56.46 L/d, control vs. MA diet, respectively) and milk fat percentage by 2.4% (4.2 vs. 4.1 +/- 0.006%, control vs. MA diet, respectively). The MA diet increased 14:0 in milk by 139% and cis-9 14:1 by 195%. There was a correlation (r = -0.58) between the 14:0 content in milk and CH4 production and cis-9 14:1 and CH4 production (r = -0.47). Myristic acid had no effect on the contents of CLA or trans-10 18:1 and trans-11 18:1 isomers in milk. These results suggest that MA could be used to inhibit the activities of methanogens in ruminant animals without altering the conjugated linoleic acid and trans-18:1 fatty acid profile in milk.
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81
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Dias R, Kebreab E, Vitti D, Roque A, France J. Application and comparison of two models to study effects of calcium sources in sheep. Anim Feed Sci Technol 2008. [DOI: 10.1016/j.anifeedsci.2007.05.006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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82
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Hill S, Knowlton K, Kebreab E, France J, Hanigan M. A Model of Phosphorus Digestion and Metabolism in the Lactating Dairy Cow. J Dairy Sci 2008; 91:2021-32. [DOI: 10.3168/jds.2007-0668] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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83
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Dijkstra J, Kebreab E, Bannink A, Crompton L, López S, Abrahamse P, Chilibroste P, Mills J, France J. Comparison of energy evaluation systems and a mechanistic model for milk production by dairy cattle offered fresh grass-based diets. Anim Feed Sci Technol 2008. [DOI: 10.1016/j.anifeedsci.2007.05.011] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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84
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France J, Keen C, Bowyer S. Communicating risk to emergency department patients with chest pain. Emerg Med J 2008; 25:276-8. [DOI: 10.1136/emj.2007.054106] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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85
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Bannink A, France J, Lopez S, Gerrits W, Kebreab E, Tamminga S, Dijkstra J. Modelling the implications of feeding strategy on rumen fermentation and functioning of the rumen wall. Anim Feed Sci Technol 2008. [DOI: 10.1016/j.anifeedsci.2007.05.002] [Citation(s) in RCA: 101] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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86
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Yang X, Yang C, Farberman A, Rideout TC, de Lange CFM, France J, Fan MZ. The mammalian target of rapamycin-signaling pathway in regulating metabolism and growth1,2. J Anim Sci 2008; 86:E36-50. [DOI: 10.2527/jas.2007-0567] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
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87
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Dias RS, Kebreab E, Vitti DMSS, Roque AP, Bueno ICS, France J. A revised model for studying phosphorus and calcium kinetics in growing sheep. J Anim Sci 2008; 84:2787-94. [PMID: 16971580 DOI: 10.2527/jas.2006-082] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
The objective of the study was to revise a model of P kinetics proposed by Vitti et al. (2000) and extend its use to study Ca flows in growing sheep. Twelve Santa Ines male sheep, 8 mo of age, with average BW of 31.6 kg were injected with 32P and 45Ca to trace the movement of P and Ca in the body. The original model had 4 pools representing the gut, plasma, soft tissues, and bone. In the revised model, instantaneous values rather than averages for pool derivatives were incorporated, and the model was extended to represent absorption and excretion of phytate P explicitly. The amendments improved the model, resulting in higher flows between plasma and bone than between plasma and tissue and, therefore, a more accurate representation of P metabolism. Phosphorus and Ca metabolism were then assessed conjointly using the revised model. The results showed that P and Ca metabolism are closely related as evidenced by the ratio of these minerals in the bidirectional flows between plasma and bone and between plasma and tissue. Phytate P digestibility was 47%, and P retention was negative (-1.4 g/d), suggesting that a feed characteristic impaired P utilization and led to P deficiency. The revised model provides an improved prediction of P and Ca metabolism that can be used to assess mineral requirements and to estimate losses to the environment.
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88
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AlZahal O, Kebreab E, France J, Froetschel M, McBride B. Ruminal Temperature May Aid in the Detection of Subacute Ruminal Acidosis. J Dairy Sci 2008; 91:202-7. [DOI: 10.3168/jds.2007-0535] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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89
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Nasri MF, France J, Danesh Mesgaran M, Kebreab E. Effect of heat processing on ruminal degradability and intestinal disappearance of nitrogen and amino acids in Iranian whole soybean. Livest Sci 2008. [DOI: 10.1016/j.livsci.2007.02.017] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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90
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Kebreab E, Odongo N, McBride B, Hanigan M, France J. Phosphorus Utilization and Environmental and Economic Implications of Reducing Phosphorus Pollution from Ontario Dairy Cows. J Dairy Sci 2008; 91:241-6. [DOI: 10.3168/jds.2007-0432] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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91
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Gill M, Beever DE, France J. Biochemical Bases Needed for the Mathematical Representation of Whole Animal Metabolism. Nutr Res Rev 2007; 2:181-200. [DOI: 10.1079/nrr19890014] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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92
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Odongo NE, McKnight D, KoekKoek A, Fisher JW, Sharpe P, Kebreab E, France J, McBride BW. Long-term effects of feeding diets without mineral phosphorus supplementation on the performance and phosphorus excretion in high-yielding dairy cows. CANADIAN JOURNAL OF ANIMAL SCIENCE 2007. [DOI: 10.4141/cjas07047] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The objective of this study was to assess the long-term effects of feeding a diet with no mineral phosphorus (P) supplementation on performance and P excretion in high-yielding dairy cows. In exp. 1, 24 primiparous (PP) and 40 multiparous (MP) Holstein cows were allocated to one of two treatments at calving: (1) regular corn silage and alfalfa haylage based milking cow total mixed ration (TMR; 0.42% P diet) or (2) milking cow total mixed ration (TMR) without supplemental mineral P (0.35% P diet) in a completely randomized design. The trial lasted until after two lactations were completed or the cow was culled. In exp. 2, eight MP Holstein cows (108 ± 8.0 d in milk) were used to determine P digestibility and retention in a completely randomized block design. In exp. 1, the 0.35% P diet cows had lower body weight, body condition score and milk urea nitrogen and higher faecal P than the 0.42% P cows. The dry matter intake (DMI) of PP cows on the 0.35% P diet was lower than that of PP cows on the 0.42% P diet. There was no difference in the DMI of MP cows. The P intake of 0.35% P diet PP cows was 30% lower than that of 0.42% P diet PP cows. The P intake of 0.35% P diet MP cows was 20% lower than that of 0.42% P diet MP. The digestibility coefficient of P for the 0.35% P diet was higher than that for the 0.42% P diet. These results suggest that the forages used in the present study contained adequate amounts of P to sustain milk production in high-yielding MP cows. However, for PP cows some mineral P supplementation is recommended especially during early lactation. Key words: Phosphorus, environmental pollution, intensive dairy operations
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93
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Ellis JL, Kebreab E, Odongo NE, McBride BW, Okine EK, France J. Prediction of methane production from dairy and beef cattle. J Dairy Sci 2007; 90:3456-66. [PMID: 17582129 DOI: 10.3168/jds.2006-675] [Citation(s) in RCA: 184] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
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) x metabolizable energy intake (MJ/d) + 1.44 (+/- 0.331) x acid detergent fiber (kg/d) - 4.16 (+/- 1.93) x 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) x 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) x 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) x 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.
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94
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Odongo N, Or-Rashid M, Bagg R, Vessie G, Dick P, Kebreab E, France J, McBride B. Long-Term Effects of Feeding Monensin on Milk Fatty Acid Composition in Lactating Dairy Cows. J Dairy Sci 2007; 90:5126-33. [DOI: 10.3168/jds.2007-0242] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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95
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Kebreab E, Dijkstra J, France J. Meta-analysis of the effect of forage type on
the efficiency of utilization of energy for milk
production in dairy cows. JOURNAL OF ANIMAL AND FEED SCIENCES 2007. [DOI: 10.22358/jafs/74482/2007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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96
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Jalilvand G, Naserian A, Odongo N, Kebreab E, Valizadeh R, Eftekhar Shahrodi E, France J. Effects of abomasal infusion of cottonseed oil and
dietary enzyme supplementation on dairy goats. JOURNAL OF ANIMAL AND FEED SCIENCES 2007. [DOI: 10.22358/jafs/66795/2007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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97
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Fathi Nasri MH, Danesh Mesgaran M, Kebreab E, France J. Past peak lactational performance of Iranian Holstein cows fed raw or roasted whole soybeans. CANADIAN JOURNAL OF ANIMAL SCIENCE 2007. [DOI: 10.4141/cjas07002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Responses of past peak lactating Iranian Holstein cows to feeding roasted whole soybean (SB), raw SB or soybean meal (SBM) supplements were evaluated. Treatments consisted of a total mixed ration (TMR) with 34% forage (21% alfalfa hay and 13% corn silage) supplemented with 11.9% SBM or 13.3% roasted SB or raw SB. Diets were offered to 18 multiparous cows assigned randomly to one of three experimental diets for a 49-d trial. Dry matter intake was not significantly different, but total and fat-corrected milk yields were higher for cows fed the roasted SB diet than the other treatments. Milk fat concentration was not significantly different among treatments, but milk fat yield was significantly higher for cows fed the roasted SB and SBM diets. Milk protein concentration was significantly decreased by the raw and roasted SB diets, but milk protein yield was unaffected. Feeding roasted SB significantly reduced rumen ammonia N, plasma urea N and milk urea N concentrations. Ruminal pH, plasma glucose and beta-hydroxybutyrate concentrations were not affected. Compared with the other treatments, roasted SB increased plasma concentration of most essential amino acids, except leucine and phenylalanine. Although caution must be taken in the interpretation of the results due to the limited number of observations in the experiment, feeding roasted SB in a diet with alfalfa hay as the primary forage was beneficial. Key words: Whole soybean, lactational performance, blood metabolite, dairy cows
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98
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AlZahal O, Kebreab E, France J, McBride BW. A Mathematical Approach to Predicting Biological Values from Ruminal pH Measurements. J Dairy Sci 2007; 90:3777-85. [PMID: 17638989 DOI: 10.3168/jds.2006-534] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
The use of continuous recording to monitor ruminal pH has received growing attention. Continuous ruminal pH data are usually summarized for each 24-h period for each cow by calculating mean pH, maximum pH, minimum pH, amount of time (min/d) below pH 5.6 and 6.0, and area (time x pH) below pH 5.6 and 6.0. In this study, a novel approach to analyzing ruminal pH is introduced. A database from 6 published studies encompassing 8 trials and 13 different treatment groups was used in a meta-analysis. Trials were selected on their ability to obtain daily pH measurements and diet analyses. A total of 613 records met the criteria for inclusion in the meta-analysis. The database was subdivided based on nonfiber carbohydrate (NFC, % of dry matter) level in the diet into low (32 to 36%, n = 105), moderate (37 to 39%, n = 326), and high NFC (>40%, n = 159). From each day of recording and for each cow, the amount of time below multiple pH points from 5.0 to 7.6 using a 0.2-unit pH interval (i.e., 5.0, 5.2, ...., and 7.6) was calculated. Sigmoidal curves were constructed to summarize daily ruminal pH records using calculated time below (min/d) as the y-variate and pH cutoff point as the x-variate. The objectives of this study were to 1) collate continuously recorded ruminal pH data from studies that used a dietary regimen to induce pH depression, 2) assess mathematical equations and subject the collated data to analysis, 3) determine the most suitable equation or equations to describe the data, and 4) derive values from the selected equation or equations that may have biological implication across dietary treatments. The analysis was performed on pooled data in each category using nonlinear modeling. Trial effect was considered as fixed and also as random. Four growth functions were considered: spline lines, Morgan, Richards, and logistic. All models had 4 parameters except the logistic equation, which had 3. The logistic and the Richards equations gave a better fit to the data than did the Morgan and spline lines. All parameter estimates were significant except for 1 parameter for the spline lines. The logistic equation uses the least number of parameters and consistently gave a better prediction. Therefore, the logistic is considered the best option to use in describing pH curves. Model-derived values that have biological interpretation such as curve inflection point, curve slope, and time and area below pH 5.6 and 6.0 were calculated for all models. Diets with higher NFC content resulted in greater depression in ruminal pH. Degree of drop in pH can be described by a shift of pH curve position toward the lower pH range, hence, by greater values of predicted time and area below most critical pH cut-off points. This shift can also be identified by a decrease in curve inflection point and curve slope. Therefore, we suggest using these model-derived biological values to summarize continuously recorded pH data. For example, the inflection points for high, moderate, and low NFC levels were 1.01, 1.17, and 1.28; respectively. This approach permits comparison of pH data across studies and helps quantify dietary effects on ruminal pH.
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99
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Kebreab E, Schulin-Zeuthen M, Lopez S, Soler J, Dias RS, de Lange CFM, France J. Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs. J Anim Sci 2007; 85:2498-507. [PMID: 17565069 DOI: 10.2527/jas.2006-738] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Success of pig production depends on maximizing return over feed costs and addressing potential nutrient pollution to the environment. Mathematical modeling has been used to describe many important aspects of inputs and outputs of pork production. This study was undertaken to compare 4 mathematical functions for the best fit in terms of describing specific data sets on pig growth and, in a separate experiment, to compare these 4 functions for describing of P utilization for growth. Two data sets with growth data were used to conduct growth analysis and another data set was used for P efficiency analysis. All data sets were constructed from independent trials that measured BW, age, and intake. Four growth functions representing diminishing returns (monomolecular), sigmoidal with a fixed point of inflection (Gompertz), and sigmoidal with a variable point of inflection (Richards and von Bertalanffy) were used. Meta-analysis of the data was conducted to identify the most appropriate functions for growth and P utilization. Based on Bayesian information criteria, the Richards equation described the BW vs. age data best. The additional parameter of the Richards equation was necessary because the data required a lower point of inflection (138 d) than the Gompertz, with a fixed point of inflexion at 1/e times the final BW (189 d), could accommodate. Lack of flexibility in the Gompertz equation was a limitation to accurate prediction. The monomolecular equation was best at determining efficiencies of P utilization for BW gain compared with the sigmoidal functions. The parameter estimate for the rate constant in all functions decreased as available P intake increased. Average efficiencies during different stages of growth were calculated and offer insight into targeting stages where high feed (nutrient) input is required and when adjustments are needed to accommodate the loss of efficiency and the reduction of potential pollution problems. It is recommended that the Richards and monomolecular equations be included in future growth and nutrient efficiency analyses.
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100
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Thornley JH, Shepherd JJ, France J. An open-ended logistic-based growth function: Analytical solutions and the power-law logistic model. Ecol Modell 2007. [DOI: 10.1016/j.ecolmodel.2006.12.026] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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