Material and methods
A literature search was conducted using Scopus and ScienceDirect with the following key words: dairy cows, milk production, protein, energy, concentrate, forage, degradability. References included in the resulting papers were also checked. As a result, 261 publications (1316 treatments means) were considered for possible inclusion in the dataset. The minimum prerequisite for a published study to be included in the dataset was: that feed description in term of ingredients (% DM of the total diet), dietary CP content (g/kg DM), dry-matter intake (DMI, kg/d), milk yield (kg/d), milk fat and protein yields (g/d), and body weight (BW, kg) were reported or could be easily calculated, and that the animals were fed ad libitum. After selection, 237 publications, consisting of 1174 treatment means that satisfied the above criteria, were kept. The final list of publications used in the meta-analysis can be found in Annex 1.
The digestibility of the organic matter (OMD), CP flows at duodenum, net energy for lactation (NEL) and metabolizable protein (MP) values were calculated for all diets in the dataset using the recently updated INRA Systali feed units system (Sauvant and Nozière, 2016). Briefly, this update consisted of quantifying the effect of digestive interactions on nutrient supplies, and subsequently on NEL and MP values (see Annex 2 for further details). The required inputs to calculate these values are: BW of the animals, DMI, the proportion of concentrate in the ration, the percentages of every ingredient included in the diet (DM basis) and their corresponding tabulated feed number code from the INRA feed library (Baumont et al., 2007). Forages and concentrate ingredients listed in the publications were matched with tabulated feeds on the basis of their CP and NDF contents. For each treatment, the CP and NDF concentrations of the total diet were calculated and compared with measured chemical characteristics in the publications. If several codes were available for one ingredient (e.g. forages, soybean meal) and that no analysis was reported for that ingredient, the code was chosen to minimize the differences between the estimated and measured CP and NDF of the total diet. For the set of studies where measured values were available, the slope of the within-study relationship between estimated and observed values of: OMD (number of treatment, Nt=474) and CP flow to the duodenum (Nt=115) was tested against one (=bisector) with an F-test. Root mean square error (RMSE) was used to assess the quality of the estimates.
The full set of selected studies was coded. Unless several studies were reported within a publication, a study was equivalent to a publication. Data were coded at the level of experiments (Nexp), where an experiment is defined as a group of treatments (with a minimum of 2 treatments) relating to a particular objective within any given study. These experiment codes were subsequently used to split the within- and between-experiment variation, as recommended in the meta-analysis review of St-Pierre (2001). These codes also enabled the selection of subsets of experiments with the same objective as a means to avoid confounding factors (Sauvant et al., 2008). The two experiment types coded for were MP level and NEL level experiments. The latter pooled experiments with various inclusion levels of concentrate or various starch: fibre ratios. The two columns of codes for ‘’energy’’ and ‘’protein’’ experiments were concatenated in a ‘’energy x protein’’ column. For studies with a factorial arrangement of energy and protein levels, the code for study was used to concatenate. This increases the statistical power of the model to detect any significant interaction between MP and NEL. Experiments lacking within-experiment differences, for both variables dietary MP and NEL contents, were discarded (Nt=22). Experiments with lipids levels/sources as treatment were not selected as it was not our present objective (Nt=89). Other treatments in our database, which were not related with dietary energy or protein (Nt=238, particle size, silage hybrids, enzyme, feeding frequency, BST…) were also discarded. Consequently, from the 1174 treatments means that satisfied the original prerequisites for selection, a total of 825 treatments (Publication=168, Nexp=282) were kept (see Annex 1).
Statistical analyses were carried out using PROC MIXED of SAS (SAS Institute Inc., 2004). The first objective was to quantify, within-experiment, milk yield, milk component yields and milk composition responses to change in dietary NEL and MP contents. The model used for that purpose was Yij = μ + Si + e1.dE + p1.dP + e2.dE2 + p2.dP2 + a.dP* dE + εij,  where Yij is the milk yield, milk component yields or milk composition for experiment i and treatment j, dE and dP were the mean-centred concentrations of NEL (MJ/kg DM) and MP (g/kg DM). The values used to centre NEL and MP were 6.7 MJ/kg DM and 100 g/kg DM, respectively. These variables were centred to reduce the correlations between intercept and slope. μ is the centred intercept that gives directly the mean value of the Y variable; Si is the fixed effect of experiment i, e1 and e2 are the linear and quadratic coefficients of dE; p1 and p2 are the coefficients for the linear and quadratic effects of dP; a is the coefficient adjusting the response slope for the interaction between dP and dE; and εij the residual for experiment i and treatment j. As discussed by St-Pierre (2001), the underlying assumption for using an adjustment based on a random effect is that the observations in question are in fact a random sample from the wider population. In the present meta-analysis, the experiments selected were not picked at random. Only experiments that used dietary treatments related to amount or quality of protein and/or energy were selected. Among those experiments, we chose to discard those with dietary lipid levels/sources as treatment. Also experiments lacking variation in dietary NEL and MP contents between treatments were not retained. For these reasons, we chose to include the experiment effect as a fixed effect. Further, when the experiment effect is assumed random the statistical distribution of the adjustments for experiment should generally follow a normal Gaussian law. This was not the case for the majority of dependent variables studied in our dataset. For completeness, a comparison of fixed and random model outputs is given in Annex 3 and 4. Treatment observations were not weighted according to their standard errors because there was no benefit of doing so (see Annex 5). The same model  was used to quantify the DMI response with the exception that dietary NEL was replaced by dietary forage NDF content (FNDF, g/kg). Forage NDF was mean centred, on 250 g/kg DM. The quadratic effect of FNDF and interactions of FNDF with MP were also tested but were not found to be significant.
The second objective was to quantify, within-experiment, milk yield, milk component yields and milk composition responses to changes in NEL and MP supplies above maintenance. These co-variables were preferred over total NEL and MP supplies to correct for different energy and protein maintenance requirements, i.e. to avoid biases due to different BW and DMI. The equations and method used for calculating MP and NEL maintenances are given in full detail in Annex 2. Because there was a strong inter-experiment co-linearity between NEL supply and MP supply (by construction both contain DMI), it was necessary to centre these predictors on reference values that reduced this co-linearity (see figure 1). Centring on the global means does not achieve this. We chose to adjust MP supply by expressing it relative to the MP supply needed for an efficiency of 0.67. This efficiency was chosen because it is equivalent to an average dietary MP content of 100 g/kg DM (Sauvant et al., 2015), the reference value chosen in the concentration analysis. Moreover, the NRC (2001) also uses 0.67 as a constant MP efficiency. To centre the data, the slope (α) of the linear relation between MP above maintenance supply (Sij) and MP efficiency (Fij) was first determined (with experiments fitted as a fixed effect). The centred MP supply (=MP67) was then calculated as Sij – Si + α (Fi – 0.67) where Si is the experiment mean MP above maintenance supply and Fi is the experiment mean MP efficiency. Similarly, the centred NEL supply (=NEL100) was calculated as Sij – Si + α (Fi – 1.00) where Si is the experiment mean NEL above maintenance supply, Fi is the experiment mean milk NEL efficiency (=NEL in milk/NEL above maintenance) and α is the slope of the linear relation between NEL above maintenance supply (Sij) and milk NEL efficiency (Fij). The milk NEL efficiency of 1 was chosen because it is equivalent to a zero energy balance. Finally, responses were estimated with model  where dE and dP are NEL100 and MP67.
Akaike’s information criterion (AIC) was used to select the best model, with non-significant terms being progressively dropped. Differences in AIC greater than three between two models indicate that there is good evidence that the model with the smaller AIC is significantly better than the model with the larger AIC (Burnham and Anderson, 2002). Co-linearity between independent variables was assessed using their mutual correlations and the variance inflation factor (VIF) generated with PROC REG of SAS (SAS Institute Inc., 2004). In general, estimability is assumed acceptable when all VIF are below 10 (St-Pierre and Glamocic, 2000). Observations from model  were considered as outliers when their studentized residuals were higher than three (Sauvant et al., 2008). In this case, they were removed stepwise until there were no such outliers left. For each analysis, the percentages of outliers removed are reported in the Results section together with the RMSE.
Reliability of calculated nutritional values
The average calculated diet contents of CP, NDF, FNDF and starch were 172 (SD 22), 349 (62), 253 (71) and 234 (96) g/kg DM, respectively. The reliability of these calculated diet content was evaluated by regression of the analysed diet contents (dependant variables) on the calculated diet contents (independent variables). The slope of the global relationship between analysed and calculated CP was 0.98 (SE 0.01, number of treatment, Nt = 825, RMSE = 7) and was not different from 1 (P=0.148). Between analysed and calculated NDF the global slope was 0.86 (SE 0.02, Nt = 794, RMSE = 30) and significantly differs from 1 (P<0.001). However, for FNDF the global slope, 0.99 (SE 0.01, Nt = 691, RMSE=20), was not significantly different from 1 (P=0.361). For starch, the global slope of 0.98 (SE 0.02, Nt=373, RMSE=30) did not differ from 1 (P=0.214). The within-experiment slope between analysed and calculated OMD (mean ± SD, 69.0 ± 5.8%, Nt =474) was 0.97 (SE 0.05) and did not differ significantly from 1 (P = 0.548), with RMSE of 1.6 % units of OMD. For the 115 treatments that analysed CP flows at duodenum (mean ± SD, 3404 ± 756 g CP/d), the within-experiment slope between analysed and calculated value, 0.85 (SE 0.09) was not significantly different from 1 (P=0.119, RMSE=206).
General description of the dataset
The average year of publication was 2001 ± 8 (mean ± SD) and studies mainly originated from North America (64%) and Europe (34%). The experimental designs used were, Latin square (63.2%), randomized block design (26.4%) and change-over design (10.4%). The average number of animal used per treatments was 10 ± 7. In 74% of the treatments, animals were fed a total mixed ration, with the remaining 26% fed forage and concentrate separately. The principal diet ingredients are displayed in Annex 6. The most frequently used forages were maize silage and alfalfa silage, followed by grass silage. However the average inclusion of the latter, when present, was higher than that of maize and alfalfa silages (54 ± 20 vs 35 ± 16 and 29 ± 18 % of DM, respectively). Ground maize was the ingredient most frequently used as an energy source in the concentrate. With respect to protein sources, soybean meal (solvent extracted, expeller and extruded), followed by rapeseed meal were the most frequently used sources of rumen degradable protein (RDP). Sources of rumen undegradable protein (RUP) were mainly heat treated soybean meal, maize gluten meal, fish meal and blood meal.
Table 1 shows the animal characteristics and the milk production data. The predominant breed was Holstein-Friesian (90% of all cows) and 86% of the cows were multiparous. From the 819 treatments where stage of lactation was reported, no treatments were conducted with cows averaging under 50 days in milk (DIM) and only 64 treatments used groups of cows in late lactation (with an average >200 DIM). Thus 92% of treatments used cows in mid lactation (50<DIM<200). In most of the experiments (91%), cows were milked twice daily with the remaining 9% milked three times a day. The means of SEM reported in the publications for the dependent variables were (SD in parentheses): DMI = 0.62 kg/d (0.35, Nt = 763), milk yield = 1.07 kg/d (0.66, Nt = 794), milk fat yield = 56.9 g/d (34.5, Nt =687), milk protein yield = 38.4 g/d (30.9, Nt =695), milk lactose yield = 56.8 g/d (37.9, Nt = 411), milk fat content = 1.30 g/kg (0.63, Nt = 788), milk protein content = 0.55 g/kg (0.63, Nt = 794) and milk lactose content = 0.42 g/kg (0.29, Nt=522).
Table of contents :
Chapter 1 General Introduction
Chapter 2 Milk yield and milk composition responses to change in predicted net energy and metabolizable protein
Chapter 3 A method to estimate cow potential and subsequent responses to energy and protein supply according to stage of lactation
Chapter 4 Modelling homeorhetic trajectories of milk component yields, body composition and dry-matter intake in dairy cows: Influence of parity, milk production potential and breed
Chapter 5 Incorporation of dairy cow responses to change in dietary composition into a model that generates lactation curves of performance for cows of different potential
Chapter 6 General Discussion
Peer reviewed scientific publications
Conference and symposium proceedings