Intake and nutrient supply

The INRA (Institut National de la Recherche Agronomique) feeding system (INRA, 2010) was selected to model the nutrient intake within the model. The intake when housed and at grazing is calculated based on the GrazeIn model as described in Delagarde et al. (Reference Delagarde, Faverdin, Baratte and Peyraud2011a and Reference Delagarde, Valk, Mayne, Rook, González-Rodríguez, Baratte, Faverdin and Peyraud2011b), Faverdin et al. (Reference Faverdin, Baratte, Delagarde and Peyraud2011). In simple terms, intake of the animal is the lesser of the intake permitted by the intake capacity and fill value (FV) of the feed, the HA and the intake needed to meet the requirements. The intake at grazing is calculated depending on the possible intake of the housed animal corrected for HA and time at pasture. The quality of the forage or grass is characterised by its energy value (unité fouragère lait (UFL)), protein (protéine digestible dans l’intestin (PDI)) and FV. The FV of a forage is an inverse function of its ingestibility and is calculated by the ratio of intake of the reference forage to voluntary dry matter intake of the considered forage (Faverdin et al., Reference Faverdin, Baratte, Delagarde and Peyraud2011). The quality of the concentrate is determined by its UFL and PDI. The concentrate has no fixed FV, its FV is calculated dependent on the substitution rate between concentrate and forage, which represents the metabolic regulation of intake and depends on the percentage of concentrate and the total energetic value of the diet (Faverdin et al., Reference Faverdin, Baratte, Delagarde and Peyraud2011).

Calculation of the theoretical milk yield and maximum theoretical mobilisation

In this model, the BCS change and the MY are modelled together in an interlinked way depending on the interaction between the nutrient, feed intake and partition. These two components depend mainly on following two factors.

Factor 1 – a BCS pool at calving (maximum theoretical mobilisation (theoMOBmax)), expressed in units of BCS. This BCS pool gives the theoretical maximum mobilisation of the dairy cow through the lactation.

Factor 2 – the milk yield gap (MYgap) between the theoretical milk yield (theoMY) of the cow and the MY allowed by her energy intake, expressed in kilogram of milk.

The theoMY of the cow is driven by her maximum theoretical milk yield (theoMYmax), expressed in kilogram of standard milk and is dependent on the parity and the day of lactation (LacD):

(1) $$\eqalignno{{\rm theoMY}\,{\equals}\, & {\rm coeff}\_\,{\rm parity}\,{\times}{\rm theoMYmax}\cr &{\times}\left( {0.27{\plus}6.47{\times}e^{{{\minus}0.013{\times}{\rm LacD}}} {\minus}\,6.20{\times}e^{{{\minus}0.017{\times}{\rm LacD}}} } \right)\cr &$$

for primiparous,

(2) $$\eqalignno{{\rm theoMY}\,{\equals}\, & {\rm coeff}\_\,{\rm parity}\,{\times}\,{\rm theoMYmax}\cr &{\times}\left( {0.25{\plus}2.95{\times}e^{{{\minus}0.015{\times}{\rm LacD}}} {\minus}\,2.70{\times}e^{{{\minus}0.028{\times}{\rm LacD}}} } \right)\cr &$$

for multiparous.

With coeff_parity=0.75 for parity 1, 0.92 for parity 2 and 1 otherwise (Hutchinson et al., Reference Hutchinson, Shalloo and Butler2013).

The shape of the lactation profiles originates from a previous study of Masselin et al. (Reference Masselin, Sauvant, Chapoutot and Milan1987), which described many classical lactation curve models based on the theoMYmax. The theoMYmax expresses the cow’s milk production potential in terms of her estimated yields at peak lactation in the third parity. The equations have then been adjusted using previously published data from INRA (Delaby et al., Reference Delaby, Leurent, Gallard and Schmitt2009) and Teagasc (Horan et al., Reference Horan, Dillon, Faverdin, Delaby, Buckley and Rath2004). Those data originates from experiments where cows spend most of their lactation at grazing.

The theoMOBmax (equation (3)), which is the maximum possible BCS change through the lactation, is set at calving and is always negative. The equation was developed by Delaby et al. (Reference Delaby, Horan, O’Donovan, Gallard and Peyraud2010a) for different breeds. It has been calculated using data with a large range of BCS loss and theoMYmax for primiparous and multiparous cows (Delaby et al., Reference Delaby, Horan, O’Donovan, Gallard and Peyraud2010a):

(3) $$\eqalignno{{\rm theoMOBmax}\,{\equals}\, & 2.2{\plus}{\rm parity}\,{\minus}\,0.047\cr &{\times}{\rm theoMYmax}{\times}{\rm coeff\_parity}\,{\minus}\,0.51{\times}{\rm BCS}_{{{\rm calv}}} \cr &$$

with parity=−0.1 for primiparous and +0.1 for multiparous, BCS_calv the BCS of the cow at calving and the theoMOBmax expressed in units of BCS and coeff_parity=0.75 for party 1, 0.92 for parity 2 and 1 otherwise (Hutchinson et al., Reference Hutchinson, Shalloo and Butler2013).

Calculation of the milk yield allowed by the energy intake

It has been shown in French studies at grazing (Hoden et al., Reference Hoden, Peyraud, Muller, Delaby, Faverdin, Peccatte and Fargetton1991) that the milk production of any 1 day is more influenced by the previous day’s nutrition than it is by the direct feed intake on that day. This component of individual animal performance is included in the model with the milk production allowed by the diet depending on the feedstuff ingested in the 2 previous days (Jacquot, Reference Jacquot2012):

(4) $${{\rm uflMY}\,{\equals}\,{{0.3{\times}{\rm UFLint}_{{D{\minus}2}} {\plus}0.7{\times}{\rm UFLint}_{{D{\minus}1}} {\minus}\,{\rm UFLreq}\,{\minus}\,E} \over {0.44}}}$$

With UFLint _D−1 the UFL ingested the previous day, ULFint _D−2 the UFL ingested 2 days before and 0.44 corresponding to a requirement of 0.44 UFL/kg of milk at 4% of fat content (Supplementary Equation S12).

The UFL requirement (UFLreq) consists of the energy for maintenance, gestation and growth (Faverdin et al., Reference Faverdin, Delagarde, Delaby and Meschy2010) (Supplementary Equation S1 to S6). E is a correction factor for net energy taking into account the negative effect of feeding level and concentrate feeding level has on the organic matter digestibility and energy valorisation of the ration (Faverdin et al., Reference Faverdin, Baratte, Delagarde and Peyraud2011) (Supplementary Equation S5).

The MYgap of the animal is the difference between the MY allowed by the UFL intake and the theoMY and is expressed in kilogram of milk:

(5) $${{\rm MYgap}\,{\equals}\,{\rm uflMY}\,{\minus}\,{\rm theoMY}}$$

Calculation of the daily milk yield

The animal response is calculated depending on the MYgap sign. When MYgap is positive then the cow has surplus energy to partition between additional milk and BCS deposition, when MYgap is negative the cow is in deficit of energy and adjusts milk and BCS accordingly. It is first assumed that the diet is well balanced in terms of PDI (PDIint/UFLint=100) (Vérité and Delaby, Reference Vérité and Delaby2000), with PDIint and UFLint the PDI and UFL ingested during the day.

The shape of the equations (6) and (7) has been generated to take into account the fact that the responses are linked to the potential of the animal and to the available energy. Those equations have been validated based on external data from INRA in Le Pin (Delaby et al., Reference Delaby, Faverdin, Michel, Disenhaus and Peyraud2003; Delaby et al., Reference Delaby, Leurent, Gallard and Schmitt2009).

If the energy intake is higher than the requirement for theoMY (MYgap>0), the cow is able to produce more milk than the theoMY. The extra energy is used partly to produce more milk and partly to gain body reserve (through BCS and BW gain). The MY response rule included is curvilinear, thus it increases with theoMY and with the MYgap based on the exponential equation:

(6) $$\eqalignno{{\rm bcsMYresp}\,{\equals}& \,{\rm MYgap}\cr &{\times}\left[ {\left( {0.57{\plus}0.012{\times}{\rm theoMY}} \right){\times}e^{{{\minus}0.023{\times}{\rm MYgap}}} } \right]\cr &$$

with bcsMYresp the response in kilogram of milk, this response is added to the theoMY.

If the energy intake is lower than the requirement for theoMY (MYgap<0), the cow will mobilise body reserve to compensate the MYgap and will lose body reserve (if possible). The ability to mobilise will depend on the remaining pool of body condition available (actualBCSpool) and the stage of lactation with a higher ability of the cow to mobilise in early lactation (Faverdin et al., Reference Faverdin, Delagarde, Delaby and Meschy2010):

(7) $$\eqalignno{{\rm bcsMYresp}\,{\equals}&#x0026;\,{\rm MYgap}\cr &#x0026;{\times}\left( {0.75{\plus}0.25{\times}{{{\rm LacD}} \over 7}{\times}e^{{{\minus}0.25{\times}{{{\rm LacD}} \over 7}}} } \right)\cr &#x0026;{\times}{{{\rm actualBCSpool}} \over {{\rm theoMOBmax}}}$$

with bcsMYresp being the response in kilogram of milk, LacD the day in lactation, with this response added to the uflMY.

After the 12^th week of lactation the coefficient applied on the (actualBCSpool/theoMOBmax) is set at 0.90. This is because, after week 12, the model considers the ability to mobilise the residual pool as constant and similar to the value obtained in week 12.

In a second step, the impact of the protein content of all the feed intake on the MY response is represented in the model through the equation developed by Vérité and Delaby (Reference Vérité and Delaby2000):

(8) $${{\rm pdiMYresp}\,{\equals}\,{\minus}\,6.25{\plus}{{7.55} \over {1{\plus}0.21{\times}e^{{{\minus}0.14{\times}\left( {{\rm PDI}/{\rm UFLratio}\,{\minus}\,100} \right)}} }}}$$

with pdiMYresp the response in kilogram of standard milk and PDI/UFLratio equal to PDIint/UFLint if the gap is negative, and is equal to (PDIint/UFLint)×(uflMY/theoMY) if the gap is positive.

Finally, according to the different combinations of milk gap and PDI/UFLratio, there are four situations that can occur. Resulting in the MY calculated as

• ∙ theoMY+max(bcsMYresp,pdiMYresp) if MYgap>0 and PDI/UFLratio>100,

• ∙ theoMY+bcsMYresp+pdiMYresp if MYgap>0 and PDI/UFLratio<100,

• ∙ uflMY+max(bcsMYresp,pdiMYresp) if MYgap<0 and PDI/UFLratio>100,

• ∙ uflMY+bcsMYresp+pdiMYresp if MYgap<0 and PDI/UFLratio<100.

Body condition score change

The daily change of BCS (BCSchange) in units of BCS is dependent on the UFL balance of the animal meaning the energy differences between UFL intake and UFL expenditure as milk, maintenance, gestation and growth (Supplementary Equation S7). If the cow is in a deficit of energy, the loss of BCS will be calculated as one unit of BCS equal to 250 UFL as described by Jouven et al. (Reference Jouven, Agabriel and Baumont2008) (Supplementary Equation S8). If the cow is in surplus of energy an equation (Supplementary Equation S10) has been developed to ensure that there is never a BCS >5. It integrates the higher costs of adipose tissue deposition for a cow in high condition (BCS>3.5). It is based on a basic cost of 300 UFL for one point of BCS for a cow between 1.5 and 3.5 of BCS (Jouven et al., Reference Jouven, Agabriel and Baumont2008). In the model everyday, the BCSpool is calculated as the actual BCSpool from previous day minus the BCSchange taking into account an upper bound limit of 0 and a lower bound limit of the theoMOBmax (the theoMOBmax is always negative).

When dry, the BCS change is using the same dynamic only with the component linked to milk set at 0.

On farm studies, Irish experimental study 1 (Curtins experiment)

The first experimental study has been carried out at the Animal and Grassland Research and Innovation centre, Teagasc, Moorepark, Ireland (52.17°N; −8.27°W). This experiment has been previously fully described in McCarthy et al. (Reference McCarthy, Pierce, Delaby, Brennan and Horan2013). Two different stocking rate (SR)’s have been used to evaluate the model: 3.28 cow/ha (SR1) and 2.51 cow/ha (SR2). The cows used in this experiment were based on Holstein Friesian of both North American and New Zealand origin balanced for overall genetic merit. Concentrate supplementation was similar for all treatments which started at 4 kg/day post calving and was reduced and removed totally only when herbage supply exceeded animal demand for all treatments (usually mid-March). Cows were milked twice a day and MYs were recorded individually. Milk fat and protein concentrations were determined weekly from successive evening and morning milkings. BCS was assessed every 3 weeks by the same individual throughout the study on a scale of one to five in increments of 0.25. On 1 January 2009 each SR group were composed of 31 cows and 15 pregnant heifers. The qualities of the grass and concentrate from this experiment are presented in Table 1.

Table 1

Information about the quality of the feedstuff by season for the 3 years of the simulation for the dairy lactating cow on the Irish experiment

FV=fill value.

¹ Energetic value: ‘Unité Fourragère Lait’ (UFL). 1 UFL=1700 kcal net energy for lactation.

² Proteic value: ‘Intestinal digestible protein’ (PDI).

On farm studies, French experimental study 2 (Le Pin experiment)

The objective of this experiment carried out at the INRA experimental farm of Le Pin-au-Haras (48.448°N, 0.098°E) was to evaluate over an extended period of time the ability of different breeds of dairy cows to produce and to reproduce under two feeding strategies in the context of group calving. This experiment has previously been fully described in Cutullic et al. (Reference Cutullic, Delaby, Gallard and Disenhaus2011). Since 2006, two groups of dairy cows from the Holstein and the Normande breeds were evaluated under two feeding strategies.

In early lactation during the winter period (90 days), animals of the high feeding group received an ab libitum total mixed ration (TMR) with maize silage (55%), dehydrated alfalfa (15%) (average forage quality 0.90 FV, 0.89 UFL and 76 PDI) and 30% of concentrate (average concentrate quality 1.1 UFL and 165 PDI/kg of dry matter). During the same period animals of the low feeding group were fed ad libitum with a TMR composed of grass silage (50%) and haylage (50%) without any concentrate (average of 1.07 FV, 0.92 UFL and 83 PDI). In early April when at grazing, the high feeding group of cows had access to a limited grass area of 0.35 ha/cow (permitting around 90 days of full grazing without forage supplementation) with a grass quality average of 0.98 FV, 0.91 UFL and 100 PDI. They received 4 kg of concentrate/day (average of 1.11 UFL and 136 PDI) and as soon as a grass deficit was detected, 5 to 8 kg of maize silage was added to the diet. The low feeding group of cows had access to a larger grass area of 0.55 ha/cow (permitting 180 days of exclusive grazing) with a grass quality average of 0.97 FV, 0.89 UFL and 102 PDI. They received no concentrate supplementation. Late in autumn, the grazed grass was replaced by grass silage (quality of 1.06 FV, 0.98 UFL and 67 PDI).

Model evaluation

In order to make consistent comparisons, the milk produced in the experiments was transformed into standard milk (Supplementary Equation S12). For the milk production and BCS, in both experiments, the model was evaluated on a weekly time step.

The theoMYmax for the Irish study was set for all mature cows at a mean of 37 kg (SD 5 kg) of milk/day. This potential was determined by evaluating the performance of the average actual cows through the 3 years. The average MY of the cattle was adjusted to parity 3 equivalents by assuming that parity 1 and parity 2 yield were 75% and 92% of parity 3 yields (Hutchinson et al., Reference Hutchinson, Shalloo and Butler2013). As the SRs were balanced for MY, the same theoMYmax yield has been applied across SR. Then the level of feeding effect has been included in the calculations as low (SR2) and very low (SR1) leading to a correction of the potential of 1.25 and 1.40, respectively, compared with the actual milk deliveries. These corrections were generated based on historical information. For the French study, a specific genetic index (Delaby et al., Reference Delaby, Peyraud, Foucher and Michel2010b) developed for this study was used to generate the individual theoMYmax (average of 53 kg, SD of 5 for the Holstein mature cows, average of 40 kg, SD of 4 for the Normande mature cows). The genetic index included the sire and grandsire’s genetic evaluation, the dam’s milk production over three lactations adjusted for the fixed environmental effect and the feeding treatment applied during each lactation. For the Irish data, the prediction of the model was evaluated by comparing average weekly model outputs of the subcattle v. the experimental data from the 1^st to the 40^th weeks of lactation. The simulation was run for both SR’s, and results of multiparous and primiparous cows were evaluated separately.

Using the French data the model prediction of the two different breeds and two different feeding levels was completed by comparing average weekly model outputs of the groups v. the experimental data from the 1^st to 44^th week of lactation. Based on individual genetic information available for the French data, it was possible to complete individual animal simulations (as it was possible to estimate the theoMYmax) and subsequent evaluation. The comparison between the simulation and actual data included the individual weekly average MY as well as the BCS for the 3 years. The accuracy of the simulation was evaluated per week and on a seasonal basis spring (early lactation – week 1 to 15), summer (mid lactation – week 16 to 25) and autumn (late lactation – week>25).

Statistical analyses

The root mean square error (RMSE), RPE and CCC were used to evaluate accuracy of the model when compared with the actual data. The RMSE provides information on the accuracy of the simulation by comparing term by term the actual and predicted data (Bibby and Toutenburg, Reference Bibby and Toutenburg1977). The lower the RMSE is, the more accurate the simulation. The RPE is an expression of the RMSE as a percentage of the actual data. According to Fuentes-Pila et al. (Reference Fuentes-Pila, DeLorenzo, Beede, Staples and Holter1996), a RPE <10% indicates a satisfactory prediction, between 10% and 20% a relatively acceptable prediction, and an RPE >20% suggests a poor model prediction. In this study, the RMSE and RPE were used on the comparison of the different sub cattle at the lactation week scale.

The CCC (Lin, Reference Lin1989; Nickerson, Reference Nickerson1997) evaluates the correlation between two data sets but also the deviation from the 45° line. The strength of agreement is considered as poor if the CCC is <0.65, moderate if between 0.65 and 0.80, substantial if between 0.80 and 0.90, and almost perfect if >0.90 (McBride, Reference McBride2005).