Growth Analysis in Rabbit Using Gompertz Non-linear Model

An experiment was conducted to compare the growth curve of rabbit. Three breeds of rabbit,namely Indonesian Local Rabbit (IL), Flamish Giant (FG) and Rex (R) were used in the study.Individual body weights of each breed was measured from birth to 63 days of age with 3-days interval.Those periodical data were separated into different sex, be then it was averaged to analysis growthpattern. Growth curve parameters were estimated to fit growth data. There was no difference in bodyweight between sexs within breed. Indonesian local rabbit had the lowest body weight. The resultsshowed that growth curve paramaters among three breeds were significantly different (P<0.05) for bothsexes. FG had the highest value of asymptotic mature weight, followed by R and IL. In conclusion,Gompertz model was excellent fit for the growth data in rabbit with a high coefficient determination (R2= 0.999).


INTRODUCTION
In the tropic, rabbit became important small livestock and meat source. They have high productivity on reproduction but in Indonesian, rabbit development is less than poultry and ruminant. Breeding and genetic were the vital aspects of rabbit production which urgently needed in tropics to ensure a high success rate of rabbit development program. Unfortunately, there was preference in Indonesian farmers to raise exotic breed of rabbit. They had a notion that local breeds are genetically inferior. A serious consequence of this practice was the possibility loss of local germplasm. In other side, potential of imported breeds could not be optimised because their ability to adapt to tropic environment was low. Lebas et al. (1997) reported that low productivity of imported breeds as a result of unsuccessful environmental adaptation. In all cases, breed evaluation tests (local versus imported breed) should be priority to be carried out. Attention has been given to the body weight as a consequence of the growth.
Growth curve is a figure of individual ability to express its genetic potential to maximum size under the existing environmental condition. Some studies on growth curve have been reported. Suparyanto (2001) used three non-linear growth curves of Von Bertalanffy, Logistic and Gompertz to analysis the relationship of body weight and age. One of non-linear model have been used to describe growth patterns is Gompertz model. According to Lenart (2011), the Gompertz distribution was widely used to describe the distribution of adult body. This model based on the exact central moments and defined with higher accuracy approximations. By solving the maximum-likelihood estimates analytically, the dimension of the optimization problem can be reduced, both in the case of discrete and continuous data. Gompertz model has been used to analysis the growth of mice (Kurnianto et al., 1998), dog (Helmink et al., 2000) sheep (Suparyanto et al., 2001), rabbit (Blasco et al., 2003), lamb (Lambe et al., 2006), pig (Strathe et al., 2010) and cattle (Forni et al., 2009;Budimulyati et al., 2012). Several researches about growth of rabbit were analysed with Logarithmic model (Rao et al., 1997), Stochastic model (Sampaio et al., 2005) and General Linear Mixed Model (McNitt and Lukehfar, 2005).
The objective of this study was to compare growth curve of rabbit between imported and Indonesia local breeds.

Materials
Three breeds of rabbit were used in this study, namely Flamish Giant (FG), Rex (R) and Indonesian local rabbits (IL). The number of rabbit used in each genetic group of the male FG, R and IL rabbits were 16, 16 and 9 heads, respectively. Meanwhile, the female number of respective breed was 16, 12 and 8, respectively. The study was conducted in Temanggung Regency -Central Java, under temperature ranging from 18 to 25°C.

Methods
The offsprings were obtained from mating of two buck and six doe for each breed (mating ratio 1:3). After weaning, feeding was provided ad libitum by automatic feeder and drink was given by nipple. They were fed a complete, pelletized diet containing 19.71% of crude protein, 23.46% of fiber and 1.77% of fat throughout the experiment. Body weights were recorded individually at 3-days interval from birth to 63 days of age. SAS (1990) was used to analyze the data of body weights on three breed using General Linear Model (GLM). Differences between male and female body weight were tested by t-test. Growth curve parameters were estimated from average of body weights using Gompertz model (Dastidar, 2006) and analyzed using Gauss-newton method of SAS (1990). Gompertz model was chosen based on an earlier study suggesting this model provided a fit for weight data in mice compared to logistic and asymptotic models (Kurnianto et al., 1997). Growth curve parameters were used in expecting weight data within each breed. The Gompertz model was formulated as:

Data analysis
where, y t : body weight (g) at age of t (weeks); A: asymptotic (mature) weight; B: intregration constant, time scale parameter of no specific biological significance; k: growth rate constant, which a logarithmic function of degree of maturity in body weight changes linearly time unit; exp: base of natural logarithm (2.7183).
Other parameters derived from the model used were age and weight at the point of inflection designated as t i and y i , respectively. t i = 1nB/ k and y i = A / exp The deferences in mean growth parameters between sexes within breed was tested using ttest, whereas mean comparison for similar sex among breeds was tested by Duncan's range multiple test.

Body Weight
Preliminary analysis showed that there was no significantly difference of body weights between male and female at all breeds. Body weights of three breeds of rabbit from birth to 63 days of age is presented in Table 1. The average birth weight of FG was 56.16 g, IL was 53.49 g and R was 96.42 g. Birth weights showed lower body weight than the previous experiment that was 66.7 g (Sartika et al., 1998), 49.78 g (Suc et al.,1996) and61.3 g (Rahardjo, 1988), for Flamish giant, Indonesian local rabbit and Rex, respectively.
Body weights of male were not significant different in 0 until 3 days of age, while from 6 days to 63 days of age showed significant difference (P<0.05). FG show similarity to R, but not similar to IL. Except in 9 and 15 days of age, FG was similar to IL and R but did not show similarity between IL and R. In female, body weights showed significant different among three breeds (P<0.05) from birth until 63 days of age, except in 9 days of age. Birth weight of FG is differed to IL and R, but IL show similarity to R. R was similar to FG and IL, but did not showed similarity between FG and IL in 12 until 21 days of age. Meanwhile, in 24 until 63 days of age IL  show significantly difference with FG and R, but FG was similar with R. IL had the lowest body weight. According to Farrell and Raharjo (1984) local rabbit was smaller than the imported breed.

Growth Curve Paramaters
Means of growth curve paramaters for each breed are presented in Table 2. Asymptotic weight (A) among three breed were significantly different (P<0.01) for both sexes. The highest of A value was achieved by FG, in which for males and females were 1249.77 and 1521.78, respectively. Meanwhile, the smallest of A value was attained by IL, that was 558.21 for males and 559.19 for females. According to The American Rabbit Breeders Association (2011), body weight of FG achieved 5.890 g for male and 6.350 g for female. The research indicated that flamish giant was adapted with the tropic. It was stated by Brahmantiyo (2008) that FG which raised by Indonesian farmers was diverged from the pure breed character.
The growth rate constant (k) among three breed were high significantly different (P < 0.01) for both sexes. The highest and smallest k value for both sexes were IL and FG respectively. The results demonstrated that Indonesian Local Rabbit matured earlier than other breeds. It was stated by Kurnianto et al. (1998) that large of k values indicated early maturing individuals, whereas small k values indicated late maturing individuals. Point of inflection was corresponds to two parameters, namely age at point inflection (t i ) and weight at point of inflection (y i ). Autoacceleration stage was replaced be autoretardation stage in this point. This analysis showed that FG was the oldest and the largest at the point of inflection for both sexes as shown the highest t i and y i values, 41.32 days and 459.76 g; 48.12 days and 559.83 g, respectively for male and female. There was relationship between the k value and t i . The rabbit breed with higher k value reached the ti at a younger age. It was found IL had point inflection at the youngest age among three breeds.

Fitting of Growth Model
Illustration of growth patterns of this study was based on a set of data by averaging individual estimated from body weights. Mean of body weight was computed at each age for each breed. Fitted Gompertz model to body weight is illustrated in Figure 1 for male and Figure 2 for  (Lukefahr and Cheeke, 1991). The lower result might due to the heat stress factor. The means residual of estimated body weight from observed data is illustrated in Figure 3 for male and Figure 4 for female. The figures showed FG's residual was similar to R, but IL had the opposigh the Gompertz model tended to over estimated and underestimated, it provided an excellent fit for growth data as shown by the high coefficient of determination (R 2 = 0.999). According to Khan et al. (2013), the high coefficient of determination was reliable on estimation.

CONCLUSION
Indonesian local rabbit had the lowest growth performance, whereas Flamish Giant had the fastest. The import rabbit grew faster than the local rabbit of Indonesia. Gompertz model was excellent fit for the growth data with a high