Livestock Research for Rural Development 27 (12) 2015 Guide for preparation of papers LRRD Newsletter

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Dhofari cattle growth curve prediction by different non-linear model functions

Salim Bahashwan, Abdulla Salim Alrawas, Salim Alfadli and E S Johnson1

Salalah Livestock Research Station,
P.O Box 1286, Postal code 211, Salalah, Sultanate of Oman.
saleminiom@gmail.com
1 Animal Science Department, Oklahoma Panhandle State University, P.O Box 430, Goodwell, Ok 73939. USA.

Abstract

Dhofari cattle growth curve was estimated and fitted using non-linear 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 17.80.99kg and of 36023.6kg 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 2.110.021 and, 0.1060.002, 0.5220.004 and, 0.0870.001, and 20.50.001 and, 0.1270.002, 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


Introduction

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 age-weight 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; Mignon-grastean 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 non-linear model functions (Gompertz, Von Bertalanffy, and Logistic) and compare between them for the highest determination of coefficient (R) goodness of fit with the observed growth curve.


Material and methods

Data collection and experimental procedure

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 (30-40 C) temperatures during summer and the high humidity (80-90%) during the rainy season (July- August) with outstanding adaptive trait.

Statistical analysis

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 weight-age data using non-linear regression procedure option in SPSS (SPSS 2010).

Assessment of goodness of fit among the three models was done by selecting the highest determination coefficient (R) 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 Levenberg-Marquardt 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 (1-beˉkt)³

(ln3b)/k

A(8/27)

Ut= (1-beˉkt)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.
Ut= degree of maturity(%).


Results and Discussion

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 non-linear models with their relative determination coefficient (R) are showed in Table 3. The estimated A value did not vary much between the 3 models (316-321 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 post-weaning rate of gain (Lunstra and Cundiff 2003). The estimated growth rate parameter k range (0.087-0.127) 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 non-linear models to estimate the growth curve (Table 3.), showed a high (>93%) determination coefficient (R), 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 non-linear models.

Model

A

b

k

M

R2

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 non-linear 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 R 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 (1-0.522*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 non-linear 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.
Ut.L= degree of maturity by Logistic 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 non-linear growth curve and fitted greatly well (R>=93%) with highest goodness of fit was for the Von Bertalanffy (R = 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.


Conclusion


Acknowledgement

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

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