Using a meta-analysis of literature data, this study aimed to quantify the dry matter (DM) intake response to changes in diet composition, and milk responses (yield, milk component yields and milk composition) to changes in dietary net energy for lactation (NE L ) and metabolizable protein (MP) in dairy cows. From all studies included in the database, 282 experiments (825 treatments) with experimentally induced changes in either NE L or MP content were kept for this analysis. These treatments covered a wide range of diet characteristics and therefore a large part of the plausible NE L and MP contents and supplies that can be expected in practical situations. The average MP and NE L contents were, respectively (mean ± SD), 97 ± 12 g/kg DM and 6.71 ± 0.42 MJ/kg DM. On a daily supply basis, there were high between-experiment correlations for MP and NE L above maintenance. Therefore, supplies of MP and NE L above maintenance were, respectively, centred on MP supply for which MP efficiency into milk protein is 0.67, and NE L above maintenance supply for which the ratio of NE L milk/NE L above maintenance is 1.00 (centred variables were called MP 67 and NE L100 ). The majority of the selected studies used groups of multiparous Holstein-Friesian cows in mid lactation, milked twice a day. Using a mixed model, between-and within-experiment variation was split to estimate DM intake and milk responses. The use of NE L100 and MP 67 supplies substantially improved the accuracy of the prediction of milk yield and milk component yields responses with, on average, a 27% lower root mean square error (RMSE) relative to using dietary NE L and MP contents as predictors. For milk composition (g/kg), the average RMSE was only 3% lower on a supply basis compared with a concentration basis. Effects of NE L and MP supplies on milk yield and milk component yields responses were additive. Increasing NE L supply increases energy partitioning towards body reserve, whereas increasing MP supply increases the partition of energy towards milk. On a nitrogen basis, the marginal efficiency decreases with increasing MP supply from 0.34 at MP 67 = −400 g/day to 0.07 at MP 67 = 300 g/day. This difference in MP 67 supply, assuming reference energy level of NE L100 = 0, equates to a global nitrogen efficiency decrease from 0.82 to 0.58. The equations accurately describe DM intake response to change in dietary contents and milk responses to change in dietary supply and content of NE L and MP across a wide range of dietary compositions.Keywords: dairy cow, milk composition, energy, protein, meta-analysis Implications Current feed evaluation systems are not suitable to predict animal responses to dietary changes. This paper quantifies average dry matter intake, milk yield and milk composition responses to change in net energy and metabolizable protein. The equations were derived from a meta-analysis of literature studies, which assembles a large number of dairy cow rations with a large range in dietary net energy and metabolizable protein contents.

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.