#### 1. Introduction

Brahman cattle have been developed in the United States by crossing three cattle breeds namely Gir, Guzerat, and Nellore. Brahman cattle have been accepted for their environmental adaptability, longevity, mothering ability, and efficient beef production. *Balai Pembibitan Ternak Unggul dan Hijauan Pakan Ternak* (BPTU-HPT) [Breeding Center for Good Livestock and Animal Feed] Sembawa has begun to develop Brahman cattle since 2012. Since the beginning of the Brahman cattle breeding program, little research has been made to improve its biological and genetic potential.

Body weight is believed to be the most important trait in evaluating cattle producing capacity [1]. Growth can be described by using a mathematical model. The appropriate mathematical model which is biologically and analytically easy to interpret is the nonlinear model [2]. Mathematical models that are commonly used are Brody, Von Bertalanffy, Gompertz, and Logistic [3].

The application of nonlinear mathematical model had been done on some researches such in the growth of Dhofari cattle [4], Brakmas cattle [3], Lagune cattle [5], and Nellore cattle [5]. In Indonesia, the application of nonlinear mathematical models was growth and age puberty of Brahman cross cattle [2] and Frisian Holstein cattle growth [6]. The application of nonlinear mathematical model to predict growth of Brahman female cattle has never been done. Therefore, this study aimed to evaluate the application of the nonlinear mathematical model in predicting Brahman female cattle growth in *Balai Pembibitan Ternak Unggul dan Hijauan Pakan Ternak* (BPTU-HPT) Sembawa.

#### 2. Material and Methods

#### Material

The data used in this study were a form of 738 Brahman female cattle body weight, from the age of early birth (
*Balai Pembibitan Ternak Unggul dan Hijauan Pakan Ternak* (BPTU-HPT) Sembawa from 2012 to 2015.

#### Methods

#### Data collecting

The data used consisted of body weight and the age of the cattle. Cattle age data were obtained from *Balai Pembibitan Ternak Unggul dan Hijauan Pakan Ternak* (BPTU-HPT) Sembawa recordings, which were then calculated to determine the age of each cattle. Body weight data were obtained from cattle weighing recording from 2012 to 2015. The body weighing was done using a cattle scale with a 1 000 kg capacity and an error margin of 1 kg. The type of data used is cross-sectional data, in which data collection was done by measuring the weight of individual cattle in certain age group, followed by the measurement of other individual samples from within the same population [7].

#### Mathematical model

The mathematical model used in this study were Brody, Von Bertalanffy, Logistic, and Gompertz as explained by [4].

Yt is the body weight on t age; A is a mature body weight; B is the proportion of mature weight which will reach after birth weight formed by Y0 and early t (the value of integral constants); k is the animal growth rate reach on mature body weight, e is basic of logarithm (2.718282)

#### Goodness of fit

The coefficient of determination (*R*
*R*

#### Statistical analysis

One-way ANOVA was used to determine whether there is a difference in value between A, B, and k from each tested mathematical model. Duncan multiple range tests (DMRT) was used to determine whether the A, B, and k coefficient for every model was significantly different [8].

#### 3. Result and Discussion

#### Bodyweight

There were body weight variations between Brahman cattle age group. Variations of body weight in individual animal were caused by birth season, year of birth, and the mating season [9]. Indonesia has two seasons: the rainy season and dry season, there is a significant difference in cattle feed availability between these two seasons. The weaning age of Brahman cattle was 3 mo to 4 mo, in which the weaning age will affect the growth of calves after weaning [10].

Figure 1 shows the curve graph that connects between body weight and age of observed data, as well as body weight prediction results from the four mathematical models. The curve describes the pattern of growth Brahman female cattle in BPTU-HPT Sembawa. The growth curve depicted by each mathematical models followed the nonlinear growth curve patterns with depiction accuracy (*R
*

Model Brody was the most appropriate model in describing the growth curve of Brahman female cattle because it has the highest determination coefficient (*R*

#### Growth parameter

The result of parameter analysis based on Brody, Bertalanffy, Logistic, and Gompertz mathematical models are shown on Table 1. Brody models had the highest value in predicting A parameter, followed by Bertalanffy, Logistic, and Gompertz models. There are significant differences (*P *
*P *
*P *

The highest B (the proportion of mature weight which will reach after birth weight) value is achieved by Logistic models, followed by Brody, Bertalanffy, and Gompertz models. There are significant differences (*P *
*P *
*P *
*P *

The value of k (growth rate reach on mature body weight) ranged from 0.035 to 0.101. The highest value of k achieved by Logistic models followed by Brody, Bertalanffy, and Gompertz models. There is no significant (*P *

##### TableΒ 1

Brahman female cattle weight 446.85 kg at the age 4 yr to 5 yr [2] stated that cattle at the age 4 yr to 5 yr would reach mature weight. The most appropriate model in predicting the mature weight of Brahman female cattle was Logistic and Gompertz. Same results achieved by [4] and [3] which stated that the Logistic model was the most appropriate model in predicting mature weight in Dhofari and Brakmas cattle.

The *R*
*R*
*R*
*R*
*R*

#### 4. Conclusion

All the evaluated mathematical nonlinear models in this study have a high level of *R*
*R
*