|Regression procedures for relationships between random variables
Dhanoa, M.S. ; Sanderson, R. ; Lopez, S. ; Dijkstra, J. ; Kebreab, E. ; France, J. - \ 2010
In: Modelling Nutrient Digestion and Utilisation in Farm Animals / Sauvant, D., van Milgen, J., Faverdin, P., Friggens, N., Wageningen : Wageningen Academic Publishers - ISBN 9789086861569 - p. 31 - 39.
A generic multistage compartmental model for interpreting gas production profiles
Lopez, S. ; Dijkstra, J. ; Dhanoa, M.S. ; Bannink, A. ; Kebreab, E. ; France, J. - \ 2010
In: Modelling Nutrient Digestion and Utilisation in Farm Animals / Sauvant, D., van Milgen, J., Faverdin, P., Friggens, N., Wageningen : Wageningen Academic Publishers - ISBN 9789086861569 - p. 139 - 147.
The gas production technique has become a key tool in feed evaluation and rumen fermentation studies. The value of the technique relies on modelling experimental data to obtain estimates of rumen degradation parameters. One of the first models used to describe gas production profiles was the simple exponential equation, although it has some important limitations when applied to gas production curves: (1) the intercept is positive, (2) only fits diminishing returns profiles, and (3) models gas per se (i.e. fails to link gas production to substrate degradation). The first limitation is overcome mathematically by re-parameterisation, making the intercept zero. The second limitation can be resolved by introducing a discrete lag to mimic sigmoidicity or by using sigmoidal functions. The third limitation is overcome by modelling substrate degradation from gas production profiles, so that equations are derived from mechanistic principles, and all parameters have biological meaning. The link between substrate degradation and gas production allows for extent of substrate degradation in the rumen to be determined for a given passage rate. Several multi-phase models have been proposed, but these were originally derived empirically and assumptions made a posteriori. Based on the conceptual difference between stage and phase, a multi-stage approach is proposed, a generic model presented and the accompanying equations derived. A two-stage model with four pools (substrate, intermediate products, fermentation end-products and by-products such as fermentation gas) is illustrated. An interpretation of the breakdown of polysaccharides to monosaccharides (first stage) and the fermentation of these monosaccharides to yield gas and other products (VFA and microbial matter) (second stage) is presented. Gas production profiles were used to demonstrate fitting the two-stage model and to consider its ability to describe gas production curves.
|Analysis of energy balance data from lactating dairy cows
Strathe, A.B. ; Dijkstra, J. ; France, J. ; Dhanoa, M.S. ; Lopez, S. ; Kebreab, E. - \ 2010
In: 3rd EAAP Inaternational Symposium on Energy and Protein Metabolism and Nutrition, Parma, Italy, 6 - 10 September, 2010. - Wageningen : Wageningen Academic Publishers - ISBN 9789086861538 - p. 545 - 546.
|Estimating maintenance energy using type I and type II regression models.
Dhanoa, M.S. ; Sanderson, R. ; Lopez, S. ; Dijkstra, J. ; Kebreab, E. ; France, J. - \ 2010
In: 3rd EAAP International Symposium on Energy and Protein Metabolism and Nutrition, Parma, Italy, 6 - 10 September, 2010. - Wageningen : Wageningen Academic Publishers - ISBN 9789086861538 - p. 559 - 560.
Evaluation of a mechanistic lactation model using cow, goat and sheep data
Dijkstra, J. ; Lopez, S. ; Bannink, A. ; Dhanoa, M.S. ; Kebreab, E. ; Odongo, N.E. ; Fathi Nasri, M.H. ; Behera, U.K. ; Hernandez-Ferrer, D. ; France, J. - \ 2010
The Journal of Agricultural Science 148 (2010)3. - ISSN 0021-8596 - p. 249 - 262.
thrice-daily milking - dairy-cattle - mammary development - curve - growth - yield - pregnancy - patterns - parity
A mechanistic lactation model, based on a theory of mammary cell proliferation and cell death, was studied and compared to the equation of Wood (1967). Lactation curves of British Holstein Friesian cows (176 curves), Spanish Churra sheep (40 curves) and Spanish Murciano–Granadina goats (30 curves) were used for model evaluation. Both models were fitted in their original form using non-linear least squares estimation. The parameters were compared among species and among parity groups within species. In general, both models provided highly significant fits to lactation data and described the data accurately. The mechanistic model performed well against Wood's 1967 equation (hereafter referred to as Wood's equation), resulting in smaller residual mean square values in more than two-thirds of the datasets investigated, and producing parameter estimates that allowed appropriate comparisons and noticeable trends attributed to shape. Using Akaike or Bayesian information criteria, goodness-of-fit with the mechanistic model was superior to that with Wood's equation for the cow lactation curves, with no significant differences between models when fitted to goat or sheep lactation curves. The rate parameters of the mechanistic model, representing specific proliferation rate of mammary secretory cells at parturition, decay associated with reduction in cell proliferation capacity with time and specific death rate of mammary secretory cells, were smaller for primiparous than for multiparous cows. Greater lactation persistency of cows compared to goats and sheep, and decrease in persistency with parity, were shown to be represented by different values of the specific secretory cell death rate parameter in the mechanistic model. The plausible biological interpretation and fitting properties of the mechanistic model enable it to be used in complex models of whole-cow digestion and metabolism and as a tool in selection programmes and by dairy producers for management decisions.
|Alternative regression approaches when modelling energy components
Dhanoa, M.S. ; Sanderson, R. ; Lopez, S. ; Dijkstra, J. ; Kebreab, E. ; France, J. - \ 2007
In: Energy and protein metabolism and nutrition - Eaap 124, Vichy, France, 9-13 September, 2007. - Wageningen : Wageningen Academic Publishers - ISBN 9789086860418 - p. 593 - 594.
Some methodological and analytical considerations regarding application of the gas production technique
López, S. ; Dhanoa, M.S. ; Dijkstra, J. ; Bannink, A. ; Kebreab, E. ; France, J. - \ 2007
Animal Feed Science and Technology 135 (2007)1-2. - ISSN 0377-8401 - p. 139 - 156.
in-vitro digestibility - ruminant feeds - production profiles - chemical-composition - mathematical-models - degradation - extent - rumen - fermentation - kinetics
The in vitro gas production technique is used widely in animal nutrition for feed evaluation and to study the kinetics of microbial fermentation processes in the digestive tract. This technique is based on the assumption that gas produced in batch cultures inoculated with mixed microorganisms from ruminal or hindgut contents or faeces is directly related to the amount of substrate fermented. The technique relies on mathematical modelling to estimate the rate and extent of feed digestion from cumulative gas production profiles. Section 1 of this article deals with the application of gas laws to calculate the volume of gas produced from pressure measurements when batch cultures are incubated in gas-tight bottles. Calculation of the amount of a specific gas (methane) produced at a given incubation time from total gas production and composition is presented in Section 2. Then, the definition of specific rate of substrate degradation and that of gas production are considered. Next, a piecewise linear model based on the assumption that microbial growth and fermentation follows zero-order kinetics is derived and evaluated by comparison with other non-linear models with regard to goodness-of-fit of experimental data and estimation of rate and extent of degradation in the rumen of some feedstuffs. Finally, the possibility of using procedures to account for the inevitable cyclic trends in gas production profiles by data smoothing are discussed. All these considerations provide an insight into some of the mathematical and methodological aspects of the in vitro gas production technique and should contribute to facilitating the description and interpretation of experimental data.
Functions for microbial growth
Lopez, S. ; Prieto, M. ; Dijkstra, J. ; Kebreab, E. ; Dhanoa, M.S. ; France, J. - \ 2006
In: Nutrient Digestion and Utilization in Farm Animals: Modelling Approaches / Kebreab, E., Dijkstra, J., Bannink, A., Gerrits, W.J.J., France, J., Wallingford : CAB International - ISBN 9781845930059 - p. 54 - 68.
The aim of this study was to evaluate the suitability of several mathematical functions for describing microbial growth curves. The functions considered were three-phase linear, logistic, Gompertz, Richards, Weibull and Baranyi. One data-set was used, comprising 34 curves stemming from viable count enumeration data of Yersinia enterocolitica grown on agar plates under different conditions of pH, temperature and carbon dioxide (time-constant conditions for each culture). Curves were selected to provide a wide variety of shapes with different growth rates and lag times. Statistical criteria used to evaluate model performance were based on goodness-of-fit: lowest residual mean square (RMS), extra residual variance F-test and Akaike's information criterion (AIC). The goodness-of-fit attained with all models was acceptable, with the Baranyi and three-phase linear functions showing best overall performance, followed by the Richards and Weibull, whilst the performances of the Gompertz and logistic were least satisfactory. Estimates of the maximum specific growth rate (µmax) and the lag time (T) were obtained with the six models, and then a multiple comparison was performed based on pairwise correlation analysis. Although Baranyi and three-phase linear gave lower estimates of µmax than the other four models, pairwise Pearson (R), Spearman rank-order (ρ) and Lin concordance (Rc) correlation coefficients were always greater than 0.998, 0.998 and 0.900, respectively, with a high level of statistical significance (P<0.001). These results indicate that all six models gave comparable estimates of µmax, and that all the curves were ranked in almost the same order according to the estimates of this growth attribute. However, the estimates of T varied considerably among the models, and in this case the pairwise correlation coefficients were not so high (R=0.700-0.999; ρ=0.486-0995 and Rc=0.222-0.983). In general, the Baranyi and three-phase linear gave the shortest, and the logistic model the longest, lag times. The position of the point of inflection and the different approaches used to estimate T by each model may explain the discrepancies observed among models. Our results indicate that general application of the Gompertz to describe microbial growth should be reconsidered critically, as other models showed a significantly superior ability to fit experimental data.
Comparative analysis of gas production profiles obtained with buffalo and sheep ruminal fluid as the source of inoculum
Calabrò, S. ; López, S. ; Piccolo, V. ; Dijkstra, J. ; Dhanoa, M.S. ; France, J. - \ 2005
Animal Feed Science and Technology 123-124 (2005)1. - ISSN 0377-8401 - p. 51 - 65.
in-vitro fermentation - rumen fluid - production kinetics - concentrate ratios - different forage - fed diets - cattle - feeds - digestion - degradation
An in vitro study was conducted to investigate effects of inoculum source (i.e., sheep versus buffalo rumen fluid) on gas production profiles, and to evaluate the suitability of various mathematical equations to fit the profiles and provide accurate values of degradation attributes. Incubations were completed using ruminal fluid obtained from sheep or buffalos fed the same diet (600 g/kg grass hay and 400 g/kg concentrate). Kinetics of fermentation of five feeds commonly fed to ruminants, being maize silage, grass silage, wheat straw, barley grain and a mixed hay, were studied with a gas production technique using an automated pressure evaluation system (APES). Ruminal fermentation characteristics (i.e., substrate disappearance, pH and VFA production) were determined after 120 h of incubation. Five mathematical functions (i.e., exponential, France, Gompertz, logistic, Morgan) were fitted to the experimental data to estimate rate and extent of feed degradation. Model comparison was based on goodness-of-fit assessed from analysis of residual variance and Akaike's information criterion. The logistic and Morgan functions were best overall, although the goodness-of-fit attained with all models was considered acceptable. Except for the Morgan, there were small differences among models in values derived for extent of degradation. There were differences between sources of inoculum in gas production measured at intermediate times (i.e., gas volumes with buffalo rumen fluid of 133 and 164 ml/g organic matter (OM) at 24 h for grass hay and silage, respectively, were smaller than those with sheep rumen fluid of 182 and 208 ml/g OM), but not at earlier or later incubation times. As a result of this trend, shorter half times, faster fermentation rates and higher extents of degradation occurred when feeds were incubated in sheep (estimated OM degradability was 0.308 and 0.402 g/g OM for grass hay and silage, respectively) compared with buffalo rumen fluid (0.246 and 0.330 g/g OM). Differences were larger for more fibrous substrates (i.e., grass silage, straw and hay) and negligible for barley grain.
Assessment of the nutritive value of cereal and legume straws based on chemical composition and in vitro digestibility
Lopez, S. ; Davies, D. ; Dhanoa, M.S. ; Dijkstra, J. ; France, J. - \ 2005
Journal of the Science of Food and Agriculture 85 (2005)9. - ISSN 0022-5142 - p. 1550 - 1557.
rumen degradation - gas-production - sacco degradability - ruminant feeds - barley straw - wheat-straw - rice straw - varieties - sheep - fractions
The nutritive value of 17 straws was determined on the basis of their chemical composition, in vitro dry matter (DM) digestibility and rumen fermentation kinetics (from gas production curves measured in vitro). Five roughages were from the cereal species Avena sativa (oat), Hordeum vulgare (barley), Secale cereale (rye), Triticum aestivum (wheat) and Zea mays (maize stover). The other 12 samples were legume straws, two samples from each of the species Cicer arietinum (chickpea), Lens culinaris (lentil) and Phaseolus vulgaris (bean) and one sample from each of the species Lathyrus sativus (chickling vetch), Lupinus albus (white lupin), Pisum sativum (field pea), Vicia articulata (one-flowered vetch), Vicia ervilia (bitter vetch) and Vicia sativa (common vetch). All samples were collected after harvesting from different farms located in León (northwestern Spain). Based on their chemical composition, digestibility and gas production characteristics, species could be clustered into two groups with a significant linkage distance, one for cereal straws that merged at a level of similarity of 80% and the other for legume straws with a degree of similarity of 50%. Species varied widely and significant differences (P <0.05) were observed between the two groups of straws. Legume straws showed higher crude protein (74 ± 6.1 vs 29 ± 2.2 g kg-1 DM) and lower fibre (584 ± 18.1 vs 793 ± 27.5 g neutral detergent fibre kg-1 DM) contents than cereal straws and, consequently, DM digestibility coefficients (0.670 vs 0.609; standard error of difference 0.0054) and metabolisable energy values (7.4 ± 0.15 vs 5.7 ± 0.24 MJ kg-1 DM) were significantly greater in legume than in cereal straws. Although there were noticeable differences among species within each botanical family, legume straws showed better nutritional quality than cereal straws, indicating that they could be considered promising and interesting sources of roughage for incorporation into ruminant diets
A general compartmental model for interpreting gas production profiles
France, J. ; Lopez, S. ; Kebreab, E. ; Bannink, A. ; Dhanoa, M.S. ; Dijkstra, J. - \ 2005
Animal Feed Science and Technology 123-124 (2005)1. - ISSN 0377-8401 - p. 473 - 485.
observed in-vitro - ruminant feeds - pressure transducer - production kinetics - chemical-analyses - rumen - degradation - fermentation - digestion - extent
Equations to describe gas production profiles, obtained using manual or automated systems for in vitro fermentation of ruminant feeds, are derived from first principles using a general compartmental model. The underlying pools represented are the potentially degradable and undegradable feed fractions, and accumulated gases. Equations derived and investigated mathematically include a Gompertz equation. They were obtained by allowing the fractional rate of degradation to vary with time. The equations permit the extent of ruminal degradation, and hence the supply of microbial protein to the duodenum, to be evaluated thereby linking the gas production technique to animal production.
Technical note: a proposed method to determine the extent of degradation of a feed in the rumen from the degradation profile obtained with the in vitro gas production technique using feces as the inoculum
Dhanoa, M.S. ; France, J. ; Crompton, L.A. ; Mauricio, R.M. ; Kebreab, E. ; Mills, J.A.N. ; Sanderson, R. ; Dijkstra, J. ; Lopez, S. - \ 2004
Journal of Animal Science 82 (2004)3. - ISSN 0021-8812 - p. 733 - 746.
ruminant feeds - apparent digestibility - protein degradability - bovine feces - reproducibility - prediction - kinetics - forages - models - fluid
A method is proposed to determine the extent of degradation in the rumen involving a two-stage mathematical modeling process. In the first stage, a statistical model shifts (or maps) the gas accumulation profile obtained using a fecal inoculum to a ruminal gas profile. Then, a kinetic model determines the extent of degradation in the rumen from the shifted profile. The kinetic model is presented as a generalized mathematical function, allowing any one of a number of alternative equation forms to be selected. This method might allow the gas production technique to become an approach for determining extent of degradation in the rumen, decreasing the need for surgically modified animals while still maintaining the link with the animal. Further research is needed before the proposed methodology can be used as a standard method across a range of feeds
Statistical evaluation of mathematical models for microbial growth
Lopez, S. ; Prieto, M. ; Dijkstra, J. ; Dhanoa, M.S. ; France, J. - \ 2004
International Journal of Food Microbiology 96 (2004)3. - ISSN 0168-1605 - p. 289 - 300.
predictive food microbiology - viable count data - bacterial-growth - nonlinear-regression - equation - curves - cultures - enough - batch - rates
The aim of this study was to evaluate the suitability of several mathematical functions for describing microbial growth curves. The nonlinear functions used were: three-phase linear, logistic, Gompertz, Von Bertalanffy, Richards, Morgan, Weibull, France and Baranyi. Two data sets were used, one comprising 21 growth curves of different bacterial and fungal species in which growth was expressed as optical density units, and one comprising 34 curves of colony forming units counted on plates of Yersinia enterocolitica grown under different conditions of pH, temperature and CO2 (time-constant conditions for each culture). For both sets, curves were selected to provide a wide variety of shapes with different growth rates and lag times. Statistical criteria used to evaluate model performance were analysis of residuals (residual distribution, bias factor and serial correlation) and goodness-of-fit (residual mean square, accuracy factor, extra residual variance F-test, and Akaike's information criterion). The models showing the best overall performance were the Baranyi, three-phase linear, Richards and Weibull models. The goodness-of-fit attained with other models can be considered acceptable, but not as good as that reached with the best four models. Overall, the Baranyi model showed the best behaviour for the growth curves studied according to a variety of criteria. The Richards model was the best-fitting optical density data, whereas the three-phase linear showed some limitations when fitting these curves, despite its consistent performance when fitting plate counts. Our results indicate that the common use of the Gompertz model to describe microbial growth should be reconsidered critically, as the Baranyi, three-phase linear, Richards and Weibull models showed a significantly superior ability to fit experimental data than the extensively used Gompertz
|Prediction of rumen volatile fatty acids based on milk fatty acids profile
Vlaeminck, B. ; Fievez, V. ; Dhanoa, M.S. ; Vuuren, A.M. van; Dewhurst, R. ; Souffrant, W.B. ; Metges, C.C. - \ 2003
In: Progress in research on energy and protein metabolism. Proceedings of the International Symposium on Energy & Protein Metabolism and Nutrition, Rostock-Warnemünde, Germany, 13th-18th September 2003. - Rostock-Warnemünde, Germany : Wageningen Academic Publishers - p. 569 - 572.
|Proportions of rumen volatile fatty acids in relation to milk fatty acid profiles
Vlaeminck, B. ; Fievez, V. ; Dhanoa, M.S. ; Vuuren, A.M. van; Dewhurst, R.J. - \ 2003
Communications in agricultural and applied biological sciences 68 (2003)3. - ISSN 1379-1176 - p. 325 - 328.
Three experiments were conducted in order to develop and validate principal component (PC) regressions for predicting rumen volatile fatty acid (VFA) proportions, based on a combination of milk odd and branched chain fatty acids (MOBCFA). Grass- or legume silage and concentrate-based diets were fed to rumen fistulated Holstein-Friesian dairy cows. The diets differed in silage type (Expt. 1), amount of protected starch (Expt. 2) or varied in the forage to concentrate ratio (F/C). Each experimental period lasted for 28 days. Rumen fluid and milk samples were collected at regular intervals for the determination of VFA content. It was shown that equations based on OBCFA explained 30-75% of the variation in VFA. Compared to predictions based on MOBCFA, only predictions of propionic (HPR) and butyric (BUT) acids based on milk fatty acids showed higher coefficients of determination. Prediction of BUT was the least accurate, while there were relatively accurate predictions for HPR and acetic acid (HAC). Lower values for mean square prediction error (MSPE) suggest better HAC and HPR predictions by regressions based on MOBCFA than on MFA. These results confirm the potential of MFA, particularly MOBCFA, to predict rumen VFA proportions in dairy cows
Alternatives to linear analysis of energy balance data from lactating dairy cows
Kebreab, E. ; France, J. ; Agnew, R.E. ; Yan, T. ; Dhanoa, M.S. ; Dijkstra, J. ; Beever, D.E. ; Reynolds, C.K. - \ 2003
Journal of Dairy Science 86 (2003)9. - ISSN 0022-0302 - p. 2904 - 2913.
whole-crop wheat - nutrient utilization - feeding systems - milk-production - genetic merit - cattle - grass - nitrogen - silage - fermentation
The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.
|A non-invasive approach to determining extent of degradation in the rumen
Crompton, L.A. ; France, J. ; Kebreab, E. ; Mills, J.A.N. ; Dhanoa, M.S. ; Lopez, S. ; Dijkstra, J. - \ 2001
In: Proceedings of the British Society of Animal Science, Edinburgh 2001. - Edinburgh : British Society of Animal Science, 2001 - p. 26 - 26.
A generalized Michaelis-Menten type equation for the analysis of growth
Lopez, S. ; France, J. ; Gerrits, W.J.J. ; Dhanoa, M.S. ; Humphries, D.J. ; Dijkstra, J. - \ 2000
Journal of Animal Science 78 (2000). - ISSN 0021-8812 - p. 1816 - 1828.
The functional form W = (W0Kc Wf t(c)) /(Kc t(c)), where W is body size at age t, W0 and Wf are the zero- and infinite-time values of W, respectively, and K and c are constants, is derived. This new generalized Michaelis-Menten-type equation provides a flexible model for animal growth capable of describing sigmoidal and diminishing returns behavior. The parameters of the nonlinear model are open to biological interpretation and can be used to calculate reliable estimates of growth traits, such as maximum or average postnatal growth rates. To evaluate the new model, the derived equation and standard growth functions such as the Gompertz and Richards were used to fit 83 growth data sets of different animal species (fish, mice, hamsters, rats, guinea pigs, rabbits, cats, dogs, broilers, turkeys, sheep, goats, pigs, horses, and cattle) with a large range in body size. A comparative study was carried out based on mathematical, statistical, and biological characteristics of the models. The statistical goodness-of-fit achieved with the new model was similar to that of Richards, and both were slightly superior to the Gompertz. The new model differed from the others with respect to some of the estimated growth traits, but there were highly significant correlation coefficients between estimates obtained with the different models, and the ranking of animals based on growth parameters computed with the new function agreed with the rankings computed by the other models. Therefore, the new model, with its variable inflection point, was able to adequately describe growth in a wide variety of animals, to fit a range of data showing sigmoidal growth patterns, and to provide satisfactory estimates of traits for quantifying the growth characteristics of each type of animal.
|Chemical composition and in vitro digestibility of cereal and legume straws (in Spanish)
Lopez, S. ; Ranilla, M.J. ; Davies, D. ; Llamazares, E. ; Dhanoa, M.S. ; Dijkstra, J. ; France, J. - \ 2000
In: Reunion Iberica de Pastos y Forrajes / Xunta de Galacia A Coruna : Graficias Garabal - p. 477 - 483.
|Chemical composition and in vitro digestibility of by-products (in Spanish)
Lopez, S. ; Ranilla, M.J. ; Davies, D. ; Falagan, A. ; Dhanoa, M.S. ; Dijkstra, J. ; France, J. - \ 2000
In: 3 Reunion Iberica de Pastos y Forrajes / Xunta de Galicia A Coruna : Graficias Garabal - p. 469 - 475.