Livestock Research for Rural Development 27 (12) 2015  Guide for preparation of papers  LRRD Newsletter  Citation of this paper 
Dhofari cattle growth curve was estimated and fitted using nonlinear function models of Gompertz, Von Bertalanffy and Logistic. Data of 2540 weight performances of 617 Dhofari cattle from birth to 228 months of age were used in this study.
Analysis revealed an initial average live birth weight of 17.8±0.99kg and of 360±23.6kg at an average age of 228 months. The estimated values of A (mature body weight) parameter ranged from 316 to 321 kg at ages ranged from 36 to 48 months. Parameters of b and k were estimated to be 2.11±0.021 and, 0.106±0.002, 0.522±0.004 and, 0.087±0.001, and 20.5±0.001 and, 0.127±0.002, for Gompertz, Von Bertalanffy, and Logistic models respectively. Inflection weights and time were found to range from 95 to 158 kg, and 5 to 9 months of age respectively. Degree of maturity (Ut) at birth was 5.59, 8.99, 12.8%, and at puberty was 36.8, 26.6, and 44.0% for Gompertz, Von Bertalanffy, and Logistic, respectively. Models used to fit the growth curve had high determination coefficients above 92% with the highest was for Von Bertalanffy (93.6%) for goodness of fit.
Keywords: degree of maturity, Gompertz, inflection point, Logistic, mature weight, Von Bertalanffy
It is important for scientists, farmers and, animal keepers to have knowledge of the growth curve characteristics for a certain cattle breed to make a reliable selection decision as they can change due to selection response (Gwase et al 2002), and for lifetime production efficiency (Salem et al 2013 and Fitzhugh 1976). Prediction of growth in animals can be found by ageweight graphical plotting using mathematical models (Bathaei and Leory 1996). These models have the ability to give a reliable description of animal growth into an understandable explanation which is vital for animal producers and farmers (Menchaca et al 1996). Estimated growth parameters such as the average mature weight (A) could be one way to make correct decision for selection for high growth rate as it possessed high additive genetic variance as shown in Nelore beef cattle (Fornis et al 2006; Mignongrastean et al 2000 ), as the high, rapid growth rate represent a major objective for meat producers from birth to slaughter weight (Chambaz et al 2001). The Dhofari cattle is an indigenous subtropical Bos indicus Omani breed which is located in the south region of the country (Mahgoub et al 2013). Omani farmers and animal producers depend on this breed for beef and milk production as a main source of red meat and dairy products (Bahashwan et al 2015). The objective of this study was to find out and predict the growth curve and related parameters of this breed using three different nonlinear model functions (Gompertz, Von Bertalanffy, and Logistic) and compare between them for the highest determination of coefficient (R²) goodness of fit with the observed growth curve.
Records of 2540 weights for 617 Dhofari cattle breed from Salalah livestock research station between 1995 to 2014 were collected from day one (birth) to 228 months of age on a monthly basis. Weights were taken by means of an automatic digital weighing scale (Iconix, New Zeland). Animals were housed in pens half shaded with one part concrete, fenced with steel pipes and utilized with automatic water supply and feeders. They were given commercial concentrate (18% crude protein, 2.5% crude fat, 7% crude fiber, 5% ash, 0.9% calcium, 0.5% phosphorus, and 11.5 MJ/Kg ME energy) with different crude protein percentages (18, 16, 14%) and, green and dry Rhodes grass hay (Chloris gayana (and quantity according to their age and condition of production based on NRC nutrient requirements tables (Taylor, 1992). Animals were vaccinated for national endemic diseases and had a good healthy condition. As a local, indigenous breed, it possessed a strong ability to withstand the hot (3040º C) temperatures during summer and the high humidity (8090%) during the rainy season (July August) with outstanding adaptive trait.
All data of means and standard errors of weights during different age stages were analyzed using SPSS (SPSS 2010). Non linear models of Gompertz, Von Bertalanffy, and Logistic were fitted to the weightage data using nonlinear regression procedure option in SPSS (SPSS 2010).
Assessment of goodness of fit among the three models was done by selecting the highest determination coefficient (R²) percentage. Models parameters (A, b, k, and M) were iterated at a set of a maximum of 150 times the initial of their values using the LevenbergMarquardt method option (SPSS 2010).
Non linear model functions
The used model functions (Gompertz, Von Bertalanffy, and Logistic) to fit the Dhofari cattle growth curve in this study with their relative important properties are presented in Table 1.
Table 1. Growth curve model equations, inflection point (weight and time) and degree of maturity. 

Model 
Equation 
Inflection time 
Inflection weight 
Degree of maturity, Ut 
Reference 
Gompertz 
Yt= A Exp(beˉkt) 
(lnb)/k 
Aeˉ¹ 
Ut= Yt/A 
Blasco et al (2002) 
Von Bertalanffy 
Yt= A (1beˉkt)³ 
(ln3b)/k 
A(8/27) 
Ut= (1beˉkt)³ 
Brown et al (1976) 
Logistic 
Yt= A(1+ eˉkt)ˉᴹ 
(lnM)/k 
A(M/M+1)ᴹ 
Ut= (1+ eˉkt)ˉᴹ 
Brown et al (1976) 
Yt= weight (kg) at time (month). A= asymptotic weight. b= scale parameter. k= maturing index. e= logarithm base. M= inflection
point. 
The observed progressive weights (Table.2) of Dhofari cattle breed through time showed an average birth weight of 17.8 ±0.99 kg, which was higher by 20% than the average found by Mahgoub (Mahgoub et al 1995) on the same breed, and a weight of 296 ±3.87kg (48 months age). It was also higher by 30% than the average found in Ndama cattle breed (Salako 2014). These high values and results found for the Dhofari cattle breed could be attributed to the difference in the environment and feed intake. The Dhofari cattle breed has a high growth trait potential especially for beef production with remarkable daily growth gain compared to temperate breeds(Friesian, Jersey, and Australian Zebu) raised at similar conditions (Lodge 1989).
Table 2. Means and standard error of Dhofari cattle weights by age. 

Age(month) 
Weight(kg) 
Std. Error 
95% Confidence Interval 

Lower Bound 
Upper Bound 

birth 
17.8 
0.997 
15.9 
19.8 
3 
88 
1.07 
85.9 
90.1 
6 
106 
1.03 
104 
108 
12 
173 
1.17 
170 
175 
24 
257 
4.09 
249 
265 
36 
284 
1.91 
280 
287 
48 
297 
3.87 
289 
304 
60 
314 
2.11 
310 
318 
72 
326 
3.43 
319 
333 
84 
338 
3.04 
332 
344 
96 
333 
3.77 
325 
340 
108 
344 
4.91 
334 
353 
120 
331 
5.4 
320 
341 
132 
357 
7.1 
343 
371 
144 
337 
6.79 
324 
350 
156 
351 
8.32 
335 
367 
168 
345 
10.5 
329 
370 
180 
349 
16.6 
316 
381 
192 
343 
16.6 
310 
376 
216 
342 
16.6 
309 
375 
228 
360 
23.5 
314 
406 
The estimated growth curve parameters (A, b, k, and M) from the three nonlinear models with their relative determination coefficient (R²) are showed in Table 3. The estimated A value did not vary much between the 3 models (316321 kg) as a mature weight of the Dhofari cows, which was higher by 7 kg than that found by Maharani (Maharani et al. 2001) in Brahman cross cows. This could be because of the Brahman cross breed low postweaning rate of gain (Lunstra and Cundiff 2003). The estimated growth rate parameter k range (0.0870.127) showed a fairly strong ability of the Dhofari cow to reach and achieve maturity weight fast, in comparison to other temperate breeds such as Holstein (Kratochvilova et al 2002), and Friesian Cross (Salem et al 2013). This could be explained by the high feed conversion rate of the Dhofari cow small size breed in comparison to the mentioned bigger size temperate breeds (Goddard and Grainger 2004). Analysis of goodness of fit for the three used nonlinear models to estimate the growth curve (Table 3.), showed a high (>93%) determination coefficient (R²), and the closest fit to the observed growth curve was for Von Bertalanffy model (94%).
Table 3. Means and standard error of Dhofari cattle growth curve parameters and coefficients of determination by different nonlinear models. 

Model 
A 
b 
k 
M 
R^{2} 
Gompertz 
319 ±1.31 
2.11 ±0.021 
0.106 ±0.002 
∞ 
0.93 
Von Bertalanffy 
322 ±1.32 
0.522 ±0.004 
0.087 ±0.001 
3 
0.94 
Logistic 
317 ±1.30 
20.5 ±0.001 
0.127 ±0.002 
2.96 ±0.030 
0.93 
A= asymptotic weight. b= scale parameter. k= maturing index. M= inflection point. R²= coefficient of determination. 
Inflection points of the Dhofari cows at which they reach their puberty weight and age for the three nonlinear models are shown in Table 4. Analysis showed that Dhofari cows reached their puberty at a range of 5 to 9 months of age with weights ranged from 95 to 158 kg. Considering the fact that analysis showed the R² was for the Von Bertalanffy model function, the most suitable estimate for the Dhofari cow’s inflection age and weight would be at 5 months of age with 95.4 kg weight. This would suggest an advantage for the Dhofari cows breed over the reported Holstein Friesian cows (Budimulyati et al 2012) who reached their puberty age later by 2 months (7 months) than the Dhofari cows. This could be a result of the negative correlation between the asymptotic mature weight and the growth rate parameters (Berry et al 2005) between the two breeds as the average mature weight of the Dhofari cattle breed is lower than the Holstein Friesian cows.
Table 4. Equation model of growth curve and inflection point of time(month) and weight(kg) for Dhofari cattle. 

Model 
Equation 
Inflection time(month) 
Inflection weight(kg) 
Gompertz 
Yt= 319 *EXP(2.11*EXP(0.106*t)) 
7 
117 
Von Bertalanffy 
Yt= 322 (10.522*EXP(0.087*t))³ 
5 
95.4 
Logistic 
Yt= 316 (1+EXP(0.127*t)ˉ2.96 
9 
158 
Yt= weight (kg) at time (month). t= time (month). 
Degrees of maturity estimates at different ages for the three used nonlinear growth curves are shown in Table (5). Results showed that Dhofari cows had an estimated degree of maturity ranged from 6 to 13% at birth and 27 to 44% at puberty which is less by only 7% compared to average temperate breeds (Hirooka and Yamada 1990).
Table 5. Degree of maturity (%) at different ages using Gompertz, Von Bertalanffy, and Logistic model 

Age (months) 
Ut.G (%) 
Ut.V (%) 
Ut.L (%) 
At birth 
5.59 
8.99 
12.8 
3 
27.6 
18.9 
21.4 
6 
33.3 
30.4 
32.1 
12 
54.1 
52.3 
55.8 
24 
80.6 
80.9 
87.2 
36 
88.9 
92.9 
97 
Ut.G= degree of maturity by Gompertz function. Ut.V= degree of maturity by Von Bertalanffy function. 
The estimated growth curves of Gompertz, Von Bertalanffy, and Logistic models for the Dhofari cattle are shown in Figure 1. They followed a typical nonlinear growth curve and fitted greatly well (R²>=93%) with highest goodness of fit was for the Von Bertalanffy (R² = 94%). All three predicted growth curves showed an accelerated growth from birth to the inflection points until they reached the mature weight (316 to 321 kg) at an average range age from 36 to 48 months, then the acceleration of growth slowed down as it finally, became constant. The three predicted growth curves slightly over estimated the observed weights from age 24 to 60 and, under estimated them after that, but with no (p>0.05) significant difference in comparison to the observed growth curve.
Figure 1. Dhofari cattle Growth curve by by Gompertz, Von Bertalanffy, and Logistic Models. 
This research was supported by Salalah livestock research station. Authors would like to thank Dr. Ahmed Bakhait Alshanfari, Dr. Hamood Alhasany and Dr. Ahmed Albakry.
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Received 29 October 2015; Accepted 29 November 2015; Published 1 December 2015