Indian Journal of Animal Research

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Research Article

Indian Journal of Animal Research, volume 54 issue 2 (february 2020) : 259-262

Comparison and estimation of the growth curve models of Hanwoo steer (Bos taurus coreanae)

Hu-Rak Park1, Seung-Hoon Eum1, Seung-Hee Roh2, Jakyeom Seo1, Seong-Keun Cho1, Byeong-Woo Kim1,*
1Department of Animal Science, College of Natural Resources and Life Science-Life and Industry Convergence Research Institute, Pusan National University, Miryang, Gyeongnam 50463, Republic of Korea.
2Hanwoo Improvement Center, National Agricultural Cooperative Federation, Seosan 31948, Republic of Korea.
Cite article:- Park Hu-Rak, Eum Seung-Hoon, Roh Seung-Hee, Seo Jakyeom, Cho Seong-Keun, Kim Byeong-Woo (2018). Comparison and estimation of the growth curve models of Hanwoo steer (Bos taurus coreanae) . Indian Journal of Animal Research. 54(2): 259-262. doi: 10.18805/ijar.B-916.

ABSTRACT

The present study was conducted to estimate and compare the three types of growth models in Hanwoo steer (Bos aurus coreanae). The Gompertz, Von Bertalanffy, and Logistic nonlinear models were used. A total of 2,239 Hanwoo steers (Bos taurus coreanae) from 6 months to 24 months old (2003 to 2014) and 8,916 growth data from the Hanwoo improvement Center were used to estimate the growth model which included three parameters. These parameters were A, mature body weight; b, growth ratio; and k, intrinsic growth rate. Regression equations using the Gompertz, Von Bertalanffy, and Logistic models were calculated as respectively. The mean square errors (MSEs) for each model were 1945.9, 1958.7, and 1935.0, respectively. The equation using the Logistic model showed the lowest value among three models. The estimated birth weights from the Gompertz, Von Bertalanffy, and Logistic models were 50.35 kg, 36.94 kg, and 74.13 kg, respectively. Furthermore, the estimated mature weights from the Gompertz, Von Bertalanffy, and Logistic models were 919.0 kg, 1043.3 kg, and 770.0 kg, respectively. In addition, the estimated age and body weight at inflection from the Gompertz, Von Bertalanffy, and Logistic models were 349.0 days and 338.1 kg, 317.9 days and 308.2 kg, and 397.8 days and 385.0 kg, respectively. Based on the results, we concluded that the regression equation using the Logistic model was the most appropriate among the growth models for measuring data. However, further studies would be needed in order to obtain more accurate parameters using a much wider period of data from birth to shipping age. 

INTRODUCTION

Studies on the growth characteristics of domestic animals such as Hanwoo (Korean native cattle; Bos taurus coreanae) are important for assessing individual characteristics pertaining to specific breed and gender. Optimal selection of rearing management method and shipping age through the growth characteristics of steer using body weight and type in particular breeds or genders is essential in livestock production. It would be impractical to collect continuous data from birth to shipping age in order to determine the weight by age, and many difficulties can arise. Therefore, the nonlinear model is often used to estimate the growth curve as one way of estimating unmeasured value (Brown et al., 1976). Studies to estimate the growth curve of cattle using nonlinear models such as Gompertz (Winsor, 1932), Von Bertalanffy (Von Bertalanffy, 1957), Logistic (Nelder, 1961), and Brody (Brody, 1945) were conducted abroad (Brown et al., 1976; Menchaca et al., 1996; Nelsen et al., 1982) and in Korea (Cho et al., 2002; Lee et al., 2003).
        
The objective of the present study was to estimate the growth curve of Hanwoo steer using the Gompertz, Von Bertalanffy, and Logistic nonlinear models, and to compare the three models. In addition, comparison of the estimated growth curve and the actual data was performed to identify the problems with the estimated growth curve, with an aim to yield basic data for further study.

MATERIALS AND METHODS

Data
 
Total of 2,239 Hanwoo steer (weight per month) from the Hanwoo Improvement Center, National Agricultural Cooperative Federation in Korea were used to estimate the growth curve. Steers were raised from the 46th to 57th progeny test to evaluate candidate breeding bulls. Progeny test was surveyed twice a year. Measurement of body weight for progeny test was started when steers were about 6 months old. The odd number progeny test was started in May, but the even number progeny test was started in November. Each animal in the data was born from 2008 to 2014 and castrated at 5 to 6 months old. Weight was measured from 6, 12, 18 and 24 months old (for each individual, there was some difference in the time of measurement). A total of 8,955 weight data according to age by months were converted to age by day by calculating the difference between measured period and birthday.
        
Outliers that excessively deviate from the average measured month were removed. In Hanwoo steer, a measured period with a higher growth phase and a lower result than the previous records was removed, because this was considered an error. Finally, after these processes, a total of 8,916 weight-age (day) records were used for growth curve analysis.
        
Both measured age (day) and weight are summarized in Table 1. As recorded age is increased, it seems likely that the standard deviation of measured weight also increases owing to the influence of environmental factors, but the coefficient of variation does not increase.
 

Table 1: Simple statistic of measured age (day) and weight by recorded age (month).


 
Adjustment of body weight data
 
Before estimating the growth curve of Hanwoo steer, adjustment of weight data was needed, because the range of data from 2,239 steers was too broad from 2008 to 2014. Data were not considered as environmental factors used for estimating the exact growth curve. Measured weight was adjusted by group number of progeny test. Steers with the same group number of progeny test shared similar environment such as the test started in cowshed, test ended in cowshed, tested year, tested season, and birthday. The effect of the same group number of progeny test in body weight was analyzed by general linear model (GLM) procedures using SAS 9.4 package (SAS Institute, Cary, NC) and removed from measured body weight. The statistical model used for adjusting body weight was as follows:


 
The 57th progeny tested group was used for reference to estimate the effect of each progeny tested group. The effect of the 57th progeny tested group was assumed to be zero. The estimated effect of the progeny tested group is shown in Table 2.
 

Table 2: Means and effect of each group number of progeny test by recorded age (month).


 
Nonlinear model of growth curve and statistical analysis
 
There were three nonlinear models (Gompertz, Von Bertalanffy, and Logistic) used for estimating the growth curve of Hanwoo steer. All models show estimated weight by age (day) and a sigmoid curve with an inflection point exists. Each model was calculated as follows:

 
where
Wt   = weight at age t (day)
A    = asymptote for weight; mature weight
b     = constant of integration
k     =  intrinsic growth rate
e     =  natural logarithm.
 
The inflection point is where the growth curve shape changes from being concave downward to convex upward. In other words, the point where daily gain changes from increase section to decrease section is the inflection point, and daily gain becomes the highest value at that point in the growth model. t is age at inflection point (ti) when the solution of the twice differentiated growth curve equation becomes  Wti is weight at inflection point and slope at ti is daily gain of inflection point.
        
Weight-age data were fitted to three kinds of nonlinear models using SAS 9.4 (SAS Institute, Cary, NC) and nonlinear regression (NLIN) procedure with Gauss-Newton method.

RESULTS AND DISCUSSION

Growth parameters
 
Estimated growth parameters are shown in Table 3. Mature weight parameter A value was the highest in the Von Bertalanffy model and the lowest in the Logistic model. Mean square error (MSE) value was estimated as the lowest in the Logistic model. The MSE value is one of the factors that show how appropriate the nonlinear model is for data. The lower MSE value of the growth curve could be better fit for the sample population.
 

Table 3: Estimated growth curve parameters, standard error and mean square error.


 
Growth curves
 
The estimated growth curves by the Gompertz, Von Bertalanffy and Logistic models were Wt=919.0e-2.904e -0.00305t, Wt = 1040.3(1-0.671e-0.00220t)3 and Wt = 770.0(1+9.368e-0.00563t)-1 respectively. The estimated growth curve and observed weight are shown in Fig 1.
 

Fig 1: Observed weight at age (day) and estimated growthcurves of Hanwoo steer.


        
According to the fitted curve in Fig 1, there were minor differences between three models within the observed range (113 to 752 days) but at a range higher than that, significant differences between the growth curves were apparent. Each birth weight (W0) was estimated to 50.35 kg by Gompertz, 36.94 kg by Von Bertalanffy and 74.13 kg by Logistic models. Estimated birth weight was estimated to be higher than normal birth weight of Hanwoo bull in all models. Estimated weights by Logistic model at birth and mature period were estimated to be more or less the same as those of Brown (1976). Weight at shipping age (about 31 months old in Hanwoo steer, t=930) was estimated to 775.67 kg by Gompertz, 792.78 kg by Von Bertalanffy, and 733.28 kg by Logistic. Weight at shipping age was also estimated to be higher than the actual market data of 720.6 kg (Korean Institute for Animal Products Quality Evaluation, 2016).
        
For comparison between observed weight and estimated weight, weight at the main measured period is listed in Table 3. With higher than the observed range in Fig 1, three types of estimated weight were similar in the observed weight. Estimated mean weight by Logistic model was more similar than the other models of observed mean weight measured in Table 4.
 
Inflection point
 
The characteristic of inflection point is summarized in Table 5. Inflection points from the Gompertz, Von Bertalanffy and Logistic models were 349.0 days, 317.9 days and 397.8 days, respectively. Weights at inflection point from each model were 338.1 kg, 308.2 kg, and 385.0 kg, respectively. Daily gain at inflection point was highest with 1.08 kg/day in the Logistic model and lowest with 1.02 kg/day in the Von Bertalanffy model.
        
Kim et al., (2002) estimated the inflection point of Hanwoo steer raised from 1996 to 2001 at 444 days using the Gompertz model, which was approximately 100 days slower than the results of the present study.
               
In most of the period that is within the measured range, the Logistic model was satisfactorily fitted and showed the lowest mean square error among the growth models. With a range higher than that, birth weight was overestimated especially in the Logistic model. With these results, data higher than the measured range from birth to shipping age would be necessary in order to develop a more suitable growth curve for Hanwoo steer.

REFERENCES


  1. Brody, S. (1945). Bioenergetics and g Growth; with Special Reference to the Efficiency Complex in Domestic Animals. Rheinhold Publishing, New York. USA.

  2. Brown, J. E., Fitzhugh, H. A. Jr., and Cartwright T. C. (1976). Comparison of nonlinear models for describing weight-age relationships in cattle. J. Anim. Sci. 42:810-818.

  3. Cho, Y. M., Yoon,H. B; Park,B. H; Ahn B. S; Jeon B. S; and Park Y. I; (2002). Study on the Optimum Range of Weight-Age Data for Estimation of Growth Curve Parameters of Hanwoo. J. Anim. Sci. Technol. 44:165-170. 

  4. Kim, N. S., Ju J. C; Song M. K; Chung C. S; Choi Y. I; and Park C. J. (2002). Growth curve characteristics of bull and steer of Hanwoo (Korean cattle). J. Anim. Sci. Technol. 44:519-522.

  5. Korean Institute for Animal Products Quality Evaluation. (2016). 2015 Animal Products Grading Statistical Yearbook. 11th Ed. Korean Intitute for Animal Products Quality Evaluation, Sejong, Rep. of Korea.

  6. Lee, C. W., Choi J. G.; Jeon K. J; Na K. J; Lee C. Y; Yang B. K; and Kim J. B. (2003). Estimation of growth curve for evaluation of growth characteristics for Hanwoo cows. J. Anim. Sci. Technol. 45:509-516.

  7. Menchaca, M., Chase C; Jr., Olson T; and Hammond A. (1996). Evaluation of growth curves of Brahman cattle of various frame sizes. J. Anim. Sci. 74:2140-2151.

  8. Nelder, J. A. (1961). The fitting of a generalization of the logistic curve. Biometrics 17:89-110.

  9. Nelsen, T. C., Long C. R; and Cartwright T. C. (1982). Postinflection growth in straightbred and crossbred cattle. I. Heterosis for weight, height and maturing rate. J. Anim. Sci. 55:293-304.

  10. SAS Package 9.4. User’ Guide: Statistics.SAS Institute,Inc,Cary,NC.

  11. Von Bertalanffy, L. (1957). Quantitative laws in metabolism and growth. Q. Rev. Biol. 32:217-231.

  12. Winsor, C. P. (1932). The Gompertz curve as a growth curve. Proc. Natl. Acad. Sci. U.S.A. 18:1-8. 
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