We evaluated the thermoregulation sub-model, and the feed intake and digestion sub-model, independently from other sub-models, by model comparison against experimental data and sensitivity analysis. The experimental data were not used for model calibration (i.e. independent data), which is also referred to as model validation. Independent evaluation of the energy and protein utilisation sub-model was not performed in this paper, as it requires a significant amount of detailed inputs of the thermoregulation and feed intake and digestion sub-model. Next, the energy and protein utilisation sub-model is the largest and central one. Evaluation of this sub-model, therefore, is inherently included in an evaluation of the full model reported in the companion paper (Van der Linden et al., 2017b).
3.3.1 Comparison of sub-models against independent data
Thermoregulation sub-model
The thermoregulation model was calibrated by adjusting parameters for respiration and sweating rates to fit to temperature-humidity indices (Supplementary Figure S7). After calibration, simulated heat release was compared with measured heat release from experiments. In experiments, heat release of Aberdeen Angus × Shorthorn steers (323-361 kg TBW) was measured at low temperatures (-1.1-3.1°C), with low (<7 mm) and high coat lengths (>24 mm) (Blaxter and Wainman, 1964). Heat release
ms-1) (Holmes and McLean, 1975). Coat length of the calves was not measured, but assumed to be fixed at 25 mm in model simulations. Steers and calves were expected to be below the thermo-neutral zone (TNZ) in most of these experimental treatments, and hence their measured heat release should correspond to minimum heat release simulated with the thermoregulation model.
Measured heat release and minimum heat release simulated with the thermoregulation sub-model were in agreement for steers with high coat lengths, whereas measured heat release was underestimated for steers with low coat lengths fed at sub-maintenance level (Fig. 3.3). A reduction in coat length by shaving might have resulted in a higher conductivity of the remaining coat structure. Skin temperatures of the steers were assessed reasonably by the thermoregulation sub- model (Supplementary Figure S8). Measured heat release and minimum heat release of Friesian and Jersey calves corresponded to each other, except for treatments at 20°C and at 12°C with a wind speed of 0.22 ms-1. An explanation for these deviations is that calves might have been in the TNZ instead of below. The milk-fed calves had a ME intake equivalent to 125 Wm-2, and a heat production of
Figure 3.3 Simulated heat production and measured heat production for experiments with
steers of Blaxter and Wainman (1964) and with Friesian and Jersey calves of Holmes and McLean (1975). CL = coat length
approximately 95 Wm-2, based on their growth rates and an assumed energy retention of 16 MJ kg-1 TBW. As heat production equals heat release, a measured heat release below 95 Wm-2 is not possible. Hence, the expected heat release in the TNZ is 95 Wm-2, which is higher than the minimum heat release simulated with the thermoregulation sub-model. Overall, the thermoregulation sub-model estimates minimum heat release reasonably.
Feed intake and digestion sub-model
We used the seven feed constituents and their digestion and passage rates (Supplementary Table S3) to calibrate the feed intake and digestion sub-model. Feed intake (kg DM day-1) was not compared with independent measured data, as feed intake is affected by the energy and protein requirements simulated in the energy and protein sub-model. After calibration, simulated ME contents were compared with measured ME contents from MAFF (1986) and Kolver (2000). Goodness-of-fit of the regression line is reflected by the mean absolute error (MAE, Eq. 1) and the RMSE (Root Mean Square Error, Eq. 2) (Bennett et al., 2013).
Where O is the observed value, S is the simulated value, and n is the number of observations. In case simulated data resemble measured data perfectly, the regression line passes through the origin and has a slope equal to one (Bellocchi et
al., 2010).
Simulated and measured ME contents were in agreement with MAFF (1986) (R2 adj. = 0.86; RMSE = 1.28 MJ ME kg-1 DM). The MAE was 1.06 MJ ME kg-1 DM, or 9.4% of the measured ME content. The intercept of the regression line was not significantly different from zero (P = 0.35) and its slope was not significantly different from one (P = 0.11). Simulated and measured ME contents were also in agreement with Kolver (2000) (R2 adj. = 0.91; RMSE = 0.87 MJ ME kg-1 DM). The MAE was 0.69 MJ ME kg-1 DM, or 6.4% of the measured ME content. The intercept of the regression line was not significantly different from zero (P = 0.38) and its slope is not significantly different from one (P = 0.25) (Fig. 3.4, Supplementary Figure S6 and Table S9). Hence, simulated ME contents resembled measured ones well enough. Eq. 1 MAE = Σ | O – S |
n Eq. 2 RMSE =
√
(O – S)2Figure 3.4 Simulated versus measured metabolisable energy (ME) content of 13 feed types
given by MAFF (1986) and Kolver (2000). Error bars indicate maximum and minimum simulated ME contents.
3.3.2 Sensitivity analysis
Thermoregulation sub-model
Sensitivity analysis was conducted for the thermoregulation and feed intake and digestion sub-model. For the thermoregulation model, 23 cattle-specific parameters were investigated, together with eight breed-specific parameters, weather data, and heat production (Supplementary Tables S2, S6, and S8). Each of the 31 parameters in total was decreased and increased by 10%, while all other parameters were kept at their original values (i.e. one at a time approach). We furthermore assessed lower and upper critical temperature (LCT, UCT) for a wide range of temperatures, combined with feasible ranges of other climate factors, TBWs, and heat production levels.
Breed-specific parameters affecting the LCT and UCT most were: the sweating rate, minimum and maximum conductance between body core and skin, body temperature, and conductivity of the coat during rainfall (Supplementary Figures S9 and S10). A 10% decrease or increase in body core temperature is not likely to happen, but the actual variation of other sensitive parameters is often unknown. The LCTs and UCTs calculated from minimum and maximum values of the feasible ranges for climate factors differed considerably for temperature, relative humidity, wind speed, TBW, and heat production (Supplementary Figure S11). These differences were generally larger than differences in LCT and UCT induced by a 10% decrease or increase in the most sensitive parameters.
Feed intake and digestion sub-model
For the feed intake and digestion model, parameters of 13 feed types (Supplementary Table S3) were decreased by 10% to investigate the effect on ME and digestible CP content, while all other parameters were kept at their original values. Parameters included for each of the 13 feed types are: digestion rates, DNDF passage rate, protein uptake, five out of the seven feed components (excluding UNDF and UCP), and the slope and intercept of the Lucas equation reflecting protein uptake (Lucas et al., 1961).
The ME contents of molasses (10.6%), wheat (5.3%), barley (4.4%), and concentrates (3.2%) were affected most by SNSC content, while ME contents of cereal straw (6.9%), hay (up to 5.9%), and grass (up to 5.5%) were most affected by DNDF and total CP content. Digestible protein content of all feeds was positively affected by a decrease in the intercept of the Lucas equation, and negatively by a decrease in its slope. Intercept and slope were affecting feeds with low CP contents (+80% and -90% for cereal straw) more than feeds with high CP contents (+1% and - 11% for soybean meal). Digestible protein content was also affected negatively by a decrease in CP, DCP, and SCP content (Supplementary Tables S10-S12). The analysis suggested that ME content is less sensitive to changes of input parameters than digested protein content.