Feasibility of heart girth models in estimating live weight of fat‐long‐tailed sheep

Abstract Fat deposition in the brisket of Ethiopian fat‐long‐tailed sheep may interfere with the correlation between heart girth (HG) and live weight (LW), bringing into question the accuracy of HG models for LW prediction that are currently in use. This study assessed the accuracy of published HG‐based prediction models of the live weight of Ethiopian sheep breeds. Furthermore, the study identified accurate and robust models that predict the LW of the sheep using HG. Live weight and HG of 1,020 sheep from Bonga, Adilo and Horro breeds were measured. First, data collected from the study was used to gauge the preciseness of previously published prediction models of each breed. Second, the data of individual breeds were divided into a calibration set for model construction and a validation set for model validation. Live weight was regressed on HG to construct simple linear, Box‐Cox, quadratic and allometric prediction models. Prediction error of published models was >20%. Models constructed for each breed did not differ in R2. However, only simple linear models with transformed LW (Adilo: Log10(LW) = 0.408 + 0.015*HG, Bonga: Log10(LW) = −36.6 + 0.882*HG, Horro: LW0.5 = −1.26 + 0.085*HG) had homogenous residuals and prediction error of ≤ 10%. Heart girth models currently used to predict LW of Adilo, Bonga and Horro sheep of Ethiopia are not sufficiently accurate as they have PE higher than 10%. Prediction models generated by the current study could replace the published models for an accurate estimation of LW of the three breeds for husbandry, marketing and veterinary purposes.


| INTRODUC TI ON
Live weight (LW) and LW change of sheep are important for aspects of nutrition, management, breeding and husbandry. They are vital in determining growth, feed conversion efficiency (Veerkamp, 1998), readiness for marketing or slaughtering (Sawyer et al., 1991) and adequate veterinary medications (Machila et al., 2008). Conventional weighing scales are the key standard to determine the LW of sheep provided they are well-calibrated, however, in rural areas, weighing scales are rarely used by farmers because they are expensive as well as labour and time intensive.
Scale calibration and maintenance require skilled technicians who are rarely found in rural areas. Farmers, therefore, rely on estimating weights of livestock without recourse to validated weighing methods. Eye-balling as an alternative for direct weighing of sheep to estimate LW has been demonstrated to lack accuracy and is prone to error (Machila et al., 2008). Heart girth (HG) has been repeatedly demonstrated to be a useful and robust proxy for the use of scales in LW estimation of sheep (Atta et al., 2004;Sowande & Sobola, 2008). Predictive models of LW based on HG have been reported for a mixture of Ethiopian highlands sheep as well as for individual breeds (Table 1).
Sheep, with a population of 30 million head (FAOSTAT, 2017), are the key component of the livestock farming system in Ethiopia.
They are an important source of income, meat, skin, wool and manure (Gizaw et al., 2012). Ethiopian sheep are categorized into four groups (sub-alpine short-fat-tailed, highland long-fat-tailed, lowland fat-rumped and lowland thin-tailed) based on their ecological distribution and tail types (Gizaw et al., 2012). Highland long-fat-tailed types are the best source of mutton and are well adapted to wet highlands. Adilo (also referred to as Doyogena), Bonga and Horro breeds have high growth potential highland long-fat-tailed sheep of Ethiopia (Gizaw et al., 2012).
Adilo, Bonga and Horro sheep are large, long and fat-tailed hair types with deposits of fat below the lower jaw and in the brisket (Galal, 1983). The fat deposition might weaken the correlation between LW and HG, by protecting HG from changing due to the change in LW, leading to limited predictability of the prediction models. Existing predictive models for Ethiopian sheep (Table 1) were examined and it was determined that they were generated by simply regressing of LW on HG, then models were recommended with maximum R 2 without reporting on the prediction error. Therefore, these models might result in errors higher than the accepted margins of 20% and 10% for veterinary and production purposes, respectively (Goopy et al., 2017) when predicting LW of Adilo, Bonga and Horro sheep. Another key criticism of these models is that they were not validated against independent sheep data.
Therefore, this study aimed to develop simple and robust predictive models to estimate LW in Adilo, Bonga and Horro sheep.
Furthermore, the accuracy of models developed previously for these breeds and other indigenous sheep was evaluated.

| MATERIAL S AND ME THODS
This study has been approved by the ethical committee of the International Centre of Agricultural Research in Dry Areas.

| Measurements for model development
Simultaneous measurements of LW and HG for all sheep were undertaken at their respective sites after overnight fasting. Live weight was measured gravimetrically using a portable spring-dial hoist scale (Camry, NTB, Camty company), with a capacity of 100 kg and precision of 50 g. The scale was calibrated using standard weights, after which 10 sheep were weighed in three replications to confirm the reliability of LW measurements. Scales were further calibrated at 50-sheep measurement intervals. Heart girth was measured as the body circumference immediately behind the front shoulder at the fourth ribs, posterior to the front leg using an ordinary tape held with 1kg tension using a light spring balance. Three trained persons were mainly collecting the data. One person was holding sheep and another person was taking the measurement. A third person was recording measurement data. Data were collected in 3 days (one day for each breed).

| Data analysis
Outliers in the data were screened using the interquartile range method (Zwillinger & Kokoska, 2003). Since the accuracy of weighing scales may decline with successive LW measurements of sheep, the relationship between LW and the serial number of sheep (order of sheep during the measurement process) was visually presented to depict the distribution of LW across the measurement process.
The probability distribution of LW and HG was identified using normal Q-Q plots. Thereafter, the data of the study was divided into two sets, a calibration set and a validation set for each breed using the Puchwein algorithm (Puchwein, 1988).
Linear, quadratic and allometric models, best describe the relationship between LW and HG in ruminants (Goopy et al., 2017;Lesosky et al., 2013). Therefore, a simple linear regression model, a simple linear model with Box-Cox transformed LW, a quadratic model and an allometric model (Table 2) were constructed. Optimum power of transformation of LW was identified using a likelihood maximized Box-Cox transformation (Box & Cox, 1964) with boundaries of −3 and +3 and a step of 0.1 Log-likelihood of λ was used to identify the best power of transformation.
Performance of the constructed models in predicting LW was evaluated using the coefficient of determination (R 2 ), the root mean square prediction error to standard deviation ratio (RSR), mean bias (MB), slope bias (SB), concordance correlation coefficient (CCC) and calibration error (CE). The RSR was calculated as follows: where O i is the observed value, P i is the predicted value and S O is the standard deviation of the observed values. The lower the RSR value, the better the predictability (Moriasi et al., 2007). Root mean square of the error to standard deviation ratio with a value of less than 0.7 indicates satisfactory accuracy of a model (Ibarra-Zavaleta et al., 2017).
The mean square prediction error was divided into MB and SB deviations to identify systematic biases as follows: where O i and P i are observed and predicted LWs, respectively. The validation set was used to calculate prediction error (PE) using the CE equation.

Sheep description Model
The frequency of negative residuals was presented to provide a better description of error distribution. The correlation between the residuals and LW was calculated.
Published models (Table 1) were assessed for accuracy using the data of this study. The LW of each sheep in our study was predicted using the corresponding model (considering breed and sex) and PE calculated. Data were analysed using R (R Core Team, 2017).

| Model construction and validation
The Box-Cox models of the three breeds had 95th percentile of CE ≤ 10.
Results of the residual analysis are presented in Table 3. The relation between standardized residuals and LW was moderate and positive (r = 0.43-0.65; p <.001) for all constructed models of all breeds. Residuals of all constructed models were symmetrically distributed around zero (Table 3) without any drifts (Figure 4). In the three breeds, only simple linear models with Box-Cox transformed LW had the 95th percentile of PE less than 10 (Table 3).

| Performance of published models
Analysis of residuals of the published models are presented in Table 3 and

| D ISCUSS I ON
Calibrated weight bands based on models of published studies (   it is difficult to explain the reason for their low performance. The distribution of LW in all breeds was normal with some deviation. That means a transformation of LW might be required to improve the predictability of simple linear models. That was confirmed by results of the Box-Cox transformation procedure which showed that the best transformation of LW was base 10 logarithm for Adilo and Bonga and square root for Horro. Our results showed that all constructed models of the three breeds did not differ (p >0.5) in    4   15  20  25  30  35  40  45  50  55  60  65  10  20  30  40  50  60  70   10  15  20  25  30  35  40  45  50 Residuals Edea et al (2008): Horro sheep breeding and nutrition (Goopy et al., 2017). Accordingly, Box-Cox models could be used to get a robust estimation of LW in Adilo, Bonga and Horro sheep which would improve the bargaining power of Ethiopian farmers to get better prices for their sheep and may also increase the level of trust between farmers and animal traders in Ethiopia. The results of our study do not agree with (Goopy et al., 2017) who reported that the LW of cattle could not be predicted by HG with an appropriate accuracy to provide veterinary services and improve productivity. This contradiction may be a result of differences in morphology among livestock species in their relations between LW and HG.
Positive findings of this study generate support for further research to develop robust prediction models of LW based on HG or other body measurements for sheep breeds in developing countries.

| CON CLUS IONS
Models produced in this study predicted LW of Adilo, Bonga and Horro sheep, using HG with PE less than 10% regardless of LW, age and sex. These models can be used to construct tables that contain HG corresponding to LW, thus enabling the production of calibrated weight bands of robust accuracy.

E TH I C A L S TA N DA R DS
This study has been approved by the ethical committee of the International Centre of Agricultural Research in Dry Areas.

ACK N OWLED G M ENTS
The authors acknowledge funding from IFAD as part of the project 'Improving the performance of pro-poor value chains of sheep and goats for enhanced livelihoods, food and nutrition security in Ethiopia'. We also thank the Ethiopian National Agricultural Research Centres; Bako Research Centre, Areka Research Centre and Jimma Research Centre for their support in data collection.

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
The datasets generated during and/or analysed during this study are available from the corresponding author on reasonable request.