### INTRODUCTION

### MATERIALS AND METHODS

### Modelling N excretion

_{FN}) (g/animal/d) since Q

_{FN}is the difference between total N intake (TNI) and digestible N intake (DNI), equation 2a:

_{UN}) (g/animal/d) can subsequently be calculated by subtracting total N retained (N

_{Ret}) (g/animal/d) for producing milk, pregnancy, growth and scruf protein, and Q

_{FN}(g/animal/d) from the total N intake (TNI) (g/animal/d), given in equation 3.

_{TN}) (g/animal/d) is calculated as the sum of Q

_{FN}(g/animal/d) and Q

_{UN}(g/animal/d), given in equation 4.

_{Ret}(g/animal/d) can be calculated for lactating, dry cows and young cows based on the NRC guidelines [14]. The scurf protein consists of protein loss from skin, skin secretions, and hair, and is calculated as 0.3×BW

^{0.60}(live weight). The retained N for milk production equals N in milk (N

_{Milk}) (g/animal/d) and is calculated by multiplying the daily milk production (g/animal/d) with the protein concentration of milk, divided by 6.38 which is the conversion factor from milk protein to N. The retained N for foetal growth in a pregnant animal (N

_{Preg}; g/animal/d) is calculated by dividing the metabolizable protein requirement for pregnancy (MP

_{Preg}) by 6.25. For cows between 190 to 279 days of pregnancy, MP

_{Preg}is computed as:

_{MPPreg}is the efficiency of use of metabolised protein (MP) for pregnancy, which is assumed to be 0.33.

_{Growth}) of lactating and dry cows is zero. In young cows, N

_{Growth}(g/animal/d) is estimated by dividing the metabolizable protein for growth (MP

_{Growth}) by 6.25. The MP

_{Growth}is computed based on equation 6:

_{g}is net protein for gain and is calculated from SWG× (268−[29.4×(RE/SWG)]). SWG is the shrunk weight gain and is assumed to equal 13.9×NE

_{Growthdiet}

^{0.9116}×EQSBW

^{−0.6837}. NE

_{Growthdiet}is the net energy requirement for growth available (Mcal/d) and calculated as (0.84 BW

^{0.355}×WG

^{1.2})×0.69. BW is the current live weight of an animal (kg) and WG is the weight gain per animal (g/d). EQSBW is the equivalent shrunk body weight and is calculated as SBW×(478/MSBW). SBW is shrunk body weight (animal weight after an overnight fast without feed or water) and being set at 96% of the current live weight. MSBW is the mature shrunk body weight and being set at 96% of the expected mature live weight (MW). The retained NE (RE) (Mcal/d) is assumed to equal 0.0635×EQEBW

^{0.75}×EQEBG

^{1.097}. EQEBW is equivalent empty body weight (weight without ingesta), and assumed to equal 0.891× EQSBW. EQEBG is the equivalent empty body weight gain, being calculated as 0.956×SWG.

### Modelling P excretion

_{FP}; g/animal/d) is calculated as the differences between daily PI (g/animal/d) and P retained (P

_{Ret}; g/animal/d) for milk production, pregnancy, and growth per day (equation 7). To calculate PI (g/animal/d), information about DMI (g/animal/d) and P concentration of the ingested DM (g/kg) is required (equation 8).

_{Milk}; g/animal/d) and is calculated by multiplying the daily milk production (kg/animal/d) with the P concentration of milk (g/kg). P retention for pregnancy (P

_{Preg}; g/animal/d) is calculated for cows in 190 to 279 days pregnancy based on equation 9:

_{Growth}) of lactating and dry dairy cows is assumed to be zero. In young cows, P retention for growth (P

_{Growth}; g/animal/d) is estimated based on equation 10:

### Data collection

### Model calibration and evaluation

_{FN}model. To calibrate the Q

_{FN}model for the Indonesian context, the data set was divided into a training data set (3/5 of the total data set) and a testing data set (the remaining 2/5). The training data set was used to estimate the intercept and the slope of equation (1a) (Table 2). The testing data set was used for model evaluation. The training and testing data were randomly selected.

_{FNPRED}; g/animal/d) using equation (2c). Following this, we compared the values of Q

_{FNPRED}with the actual measurement of faecal N from the independent data set (Q

_{FNACT}; g/animal/d). The Q

_{FNACT}values were calculated by multiplying the values of indigestible DMI (IDMI; g/animal/d) (Table 2) with the N concentration in faeces (g/kg) that was obtained from the laboratory analysis (Table 1). Finally, the proposed Q

_{FNPRED}model was statistically evaluated against the Q

_{FNACT}by using the mean average error (MAE) in equation [11] and the root mean square error (RMSE) in equation [12]. Both RMSE and MAE were presented as absolute and as relative value. The mean square error (MSE) consists of the bias error, the slope error, and the random error [22]. A low score of MAE and RMSE indicates a better model performance.

_{FN}model for smallholder dairy farms (Q

_{FNPRED}) were compared to the intercept and slope reported for the Lucas equation for N in literature [12]. The literature values for intercept and slope of the Lucas equation for N are 92% and −0.61 g N/100 g DMI, respectively.

### Effective sample size

^{2}) of the model. In this study, the R

^{2}was the R

^{2}from the regression of Q

_{FNPRED}on Q

_{FNACT}. The R

^{2}from the actual measurement of faecal N (Q

_{FNACT}) was assumed as without error (R

^{2}= 1). The Cohen method [23] was used to determine the effective sample size for Q

_{FNPRED}and Q

_{FNACT}(equation 13):

*n*is the effective sample size and

*δ*is the critical value of

*t*, and the

*t*is the critical

*t*-value in the t-test distribution given as

*t*

*and*

_{1−α}*t*

*. The δ is calculated as δ =(*

_{1−β}*t*

*−*

_{1−α}*t*

*). The*

_{1−β}*α*indicates the probability of a type I error and

*β*the probability of a type II error. The

*d*is the standardized effect size and calculated as (

*m*

*-*

_{A}*m*

*/*

_{B}*σ*) where

*m*

*and*

_{A}*m*

*are the means of populations A and B, respectively (e.g. with and without an intervention), and*

_{B}*σ*is the population standard deviation. The two populations (A and B) were assumed to have equal variances and an equal reliability coefficient,

*α*was set at p = 0.05 (one-tailed), and

*β*at p = 0.20. In this study, we calculated the effective sample sizes in order to detect a specific difference of Q

_{FN}ranging from 1 to 30 g/animal/d. All statistical analyses in the present study were performed in R (R Core Team, 2018).

### RESULTS

### Farm survey findings

### Model calibration and evaluation

_{FN}model for Indonesian smallholder dairy farms is therefore:

_{FN}model in equation 14, by comparing Q

_{FNPRED}with Q

_{FNACT}(Figure 1). The coefficient of determination (R

^{2}) of Q

_{FNPRED}and Q

_{FNACT}was 0.63 (residual standard error = 17.6, p<0.05). In this regression line, the intercept was significantly different from zero (p = 0.0003), however, the slope did not significantly differ from one (p = 0.16). The MAE was 15 g/animal/d which translates to 17% deviation of Q

_{FNPRED}from the Q

_{FNACT}. The RMSE was 20 g/animal/d which translates to 22% deviation of Q

_{FNPRED}from the Q

_{FNACT}. The bias error of the MSE was 9%, the slope error was 12% and the random error was 79%. The slope and intercept which we estimated for equation 2c were similar to those reported in literature [12].

### Effective sample size

_{FN}of different treatments was compared between Q

_{FNPRED}(i.e., derived from equation (14)) and Q

_{FNACT}(i.e., derived from measurements). The relationship between effective sample size of dairy cows (n) and a specific difference of Q

_{FN}(g/animal/d) in two alternative models (Q

_{FNPRED}; R

^{2}= 0.63 and Q

_{FNACT}; R

^{2}= 1) is illustrated in Figure 2. To detect a specific difference in Q

_{FN}of 10 g/animal/d, for example, requires 68 animals when using Q

_{FNACT}, while 107 animals are needed when using Q

_{FNPRED}. For specific differences higher than 20 g/animal/d the effective sample size did not differ much between the two models.

### Model application

_{FN}was higher for lactating cows (107 g/animal/d, 38% of TNI) than for dry cows (83 g/animal/d, 39% of TNI) and young cows (57 g/animal/d, 39% of TNI). Similarly, the average Q

_{UN}was higher for lactating cows (111 g/animal/d, 40% of TNI), than for dry cows (99 g/animal/d, 47% of TNI) and young cows (60 g/animal/d, 41% of TNI). Overall, the average Q

_{FN}was 96 g/animal/d and Q

_{UN}was 101 g/animal/d. The average N

_{Ret}was 63 g/animal/d for lactating cows (22% of TNI), 29 g/animal/d for dry cows (14% of TNI), and 30 g/animal/d for young cows (20% of TNI). In the case of Indonesian smallholder dairy farms, on average 22% of TNI was retained and the remaining 78% of TNI was found in manure, with 38% in the faeces and 40% in the urine.

_{FP}was 63 g/animal/d (89% of PI) for lactating cows, 47 g/animal/d (90% of PI) for dry cows, and 32 g/animal/d (86% of PI) for young cows. The average P

_{Ret}was 8 g/animal/d (11% of PI) for lactating cows, 5 g/animal/d (10% of PI) for dry cows, and 5 g/animal/d (14% of PI) for young cows. In the case of Indonesian smallholder dairy farms, on average 12% of PI was retained and 88% of PI was found in the manure. Average daily N and P excretion per farm (three lactating, one dry and one young cow) is approximately 947 g N and 268 g P.

### DISCUSSION

_{FN}model, and subsequently predicted Q

_{FN}, Q

_{UN}, and Q

_{FP}in our case region based on feed intake and composition, milk production and its composition, and manure composition. The Lucas equation is an important element of the Q

_{FN}model, and the model calibration for dairy cattle at the farms in the study area was essentially an evaluation of the Lucas equation for the Indonesian situation. Our estimate of true N digestibility equalled the standard value of 92% in the original Lucas equation, whereas our estimate of metabolic faecal N was −0.60 g/100 g DMI, with the standard value being −0.61 g/100 g DMI. Our estimates of true N digestibility and metabolic faecal N, furthermore, were similar to those reported in literature [12]. Hence, the standard Lucas equation for N seems to apply under a wide array of conditions, including Indonesian smallholder dairy farms [29]. Consequently, the Q

_{FN}model presented in this study can be applied under very different circumstances, and the standard values from the Lucas equation can likely be used.

_{FNPRED}model had a relatively high relative MAE (17%) and relative RMSE (22%). In literature [30] errors of 20% were found during the quantification of potential and feed-limited growth of three beef cattle breeds by a generic model which was followed by a model evaluation on independent experimental data. This error is comparable to our findings. The systematic errors (bias error and slope error) were limited and the major source of error was the random error (79%). The relatively high error could in part be attributed to the fact that some model parameters such as DDM had to be derived from literature [17,18]. The specified information of DDM for many feed types, for example the roughage, is limited for the Indonesian situation, whereas the variation in DDM quality of roughage among farmers is expected to be high. In addition, the Q

_{FNACT}that was used as actual value for model evaluation and for the estimation of the effective sample size was considered without error. In reality, the Q

_{FNACT}also has an estimation error because of errors related to sampling, to laboratory analysis and to the DDM values used to estimate Q

_{FNACT}. Hence, the MAE and RMSE of Q

_{FNPRED}when evaluated against a real direct assessment (full collection of faecal and urinary excretion separately and compositional analysis of each fraction) will likely be higher than when compared to the Q

_{FNACT}in the present study.

_{FN}was lower (96 g/animal/d) than some values reported in literature (147 to 242 g/animal/d) [5,6,8]. The difference between our estimate and these reported values could be due to the lower DMI and NI in our study. To verify this conclusion, we inserted the DMI and NI values from literature [5,6,8] into our Q

_{FN}model, and the result showed that the relative deviation of predicted Q

_{FN}values from the values reported in previous studies varied from −15% to 19%.

_{N}) by expressing excreted N as percentage of NI. In our study, this NUI

_{N}was 78% meaning that 78% of N intake ended up in manure, and only 22% in milk and meat. The NUI

_{N}in literature [5,8,32] was lower than the one found by us i.e. 70% to 72%. This could mean two things: either N losses via manure were higher from the cattle in our study caused by a low efficiency of N utilization in the animal which could be caused by limitation by other nutrients, by the genetic potential of the animals or by health-related factors [30] or it could just be that too much N was offered through the diets. These reasons imply that improving feeding management for example through nutritionally balanced rations [33], adjustment of the dairy genetics to the production potential at the present feed base and animal health care may potentially reduce nutrient excretion.

### CONCLUSION

_{FN}from dairy cattle on smallholder farms in Indonesia using readily available farm data, and applied this model, in combination with existing guidelines of the National Research Council, to predict N and P excretion in faeces and urine for 144 dairy cows on 30 farms. In conclusion, the proposed models can be used with reasonable accuracy to predict N and P excretion of dairy cattle on smallholder farms in Indonesia using readily available farm data. The model can be used as a basic tool to improve manure management and to reduce nutrient losses in Indonesian smallholder dairy farms.