### INTRODUCTION

*Longissimus dorsi*) can be good predictors of carcass composition. In this sense, the technique of real-time ultrasonography has been widely used for the evaluation of carcass and body composition, especially in beef cattle [4], small ruminants [5], and pigs [6]. This technique has been relatively less used for the description of growth patterns in rabbits and, thus, there is still much to be done.

*Oryctolagus cuniculus*) makes it impossible to obtain more reliable definitions of the right age for the slaughter of these animals. Therefore, this study aimed to identify nonlinear regression models, under the context of mixed models, to describe the growth trajectory of New Zealand White rabbits based on weight records and carcass measurements obtained using ultrasonography.

### MATERIALS AND METHODS

### Animal care

### Experiment animals and sample collection

*Oryctolagus cuniculus*), between 2018 and 2019. During the experimental period, the animals were raised in a didactic-productive module of cuniculture located at the Technical College of Bom Jesus of the Federal University of Piauí, in the municipality of Bom Jesus, Piauí, Brazil (latitude 9°04′57.8″S, longitude 44°19′36.8″W at an altitude of 277 m a.s.l.).

*ad libitum*and 150 g/shift/rabbit of pellet commercial ration was offered to the animals (minimum levels ensured: 88% of dry matter; 12% of moisture; 17% of crude protein; 3.37% of ether extract; 15% of crude fiber; 12% of mineral matter; 2% of calcium; 0.75% of total phosphorus; 0.94% of lysine; 0.63% of methionine + cystine; and 2,300 kcal/kg of digestible energy).

*Longissimus dorsi*muscle (loin eye). This anatomical region is widely used for the evaluation of finishing and muscling traits in different species.

### Statistical analyses

*A*and

*k*simultaneously.

^{2}), calculated as the square of the correlation between the predicted and observed values; mean squared error (MSE); the percentage of convergence (%C) of each model; Akaike information criterion (AIC), which is given by

*AIC*= −

*log*(

*L*) + 2

*p*, where

*log*(

*L*) is the logarithm of the likelihood function of the probability density function; Bayesian information criterion (BIC), expressed as

*BIC*= −2log(

*L*) +

*plog*(

*n*); and the mean absolute deviation of residuals (MAD), as proposed by Sarmento et al [15]. MAD is given by the following equation:

*Y*

*is the observed value;*

_{i}*Ŷi*is the estimated value; and

*n*is the sample size.

^{2}or %C, as well as lower values of MSE, AIC, BIC, or MAD indicate a better model fit. After choosing the model that best described the growth trajectories for LEA and BW of the studied animals, this model was used under the context of mixed models. For this, we considered two parameters that admit biological interpretation (

*A*and

*k*), individually or combined. In this step, we used the following criteria to determine the best model: AIC; BIC; and the residual variance (

*y*

*as the measurement*

_{ij}*j*(BW or LEA) of the individual

*i*and

*t*

*as the age of this animal (days), the regression model has residuals that follow a normal distribution, with mean zero and constant variance*

_{ij}*A*and

*k*were considered as random, with normal distribution, whereas

*B*was considered as a fixed parameter.

*y*

*) are independent regarding the index*

_{ij}*i*, but not with respect to

*j*, because at fixing

*i*, the measurements (

*y*

*) are taken longitudinally for a single animal. Therefore, it is necessary to include intra-individual variance components in the model.*

_{ij}*A*and

*k*; if

*M*= (

*Ai*;

*Ki*) is a vector of random effects and

*f*(

*yi*|

*ti*,

*N*,

*Mi*)

*ω*(

*Mi*;Σ) is the joint probability density function, where

*ω*is the joint density of

*Ai*and

*Ki*. The marginal likelihood function is given by

*N*and Σ are obtained maximizing L(

*N*; Σ) in relation to these numbers. The PROC NLMIXED procedure of the SAS software [16] minimizes numerically −L(

*N*; Σ) regarding the parameters

*N*and Σ, so that the variance-covariance matrix is approximated to the estimators obtained by the inverse of the Hessian matrix.

*A*and

*k*as random, the assumptions for these parameters are described as

*σ*

*=*

_{a,k}*σ*

*is the covariance between*

_{k,a}*A*and

*k*.

*t*(days or months) in the growth trajectory (i.e., the average growth rate of animals in the population). Regarding IP, this indicates the point where the body growth rate of the animal is the maximum (i.e., the point in which the growth switches from a fast phase to a slower phase). RGR, in turn, is the ratio of AGR to the

*ŷ*

*(predicted BW or LEA) of the selected model.*

_{i}### RESULTS AND DISCUSSION

^{2}, it is possible to note that this criterion was not so informative for LEA, as R

^{2}values are considered low for adjustment in this case (Table 3). Regarding BW, R

^{2}can be considered only to exclude some models (Richards, Meloun 1, modified Michaelis-Menten, and Santana). Therefore, the coefficient of determination is not a good indicator for model selection, because the other models (Brody, Gompertz, Logistic, and von Bertalanffy) also showed high R

^{2}values (0.98). Similar values of R

^{2}in different models have also been reported by other authors that used this criterion for the selection of models to describe the growth curve in chickens [20,21]. In these cases, it is necessary to use different criteria of adjustment, due to the low power of decision of R

^{2}[21].

*A*(Figure 1). On the other hand, the inclusion of two effects in

*A*and

*k*in the von Bertalanffy model did not show a satisfactory result, probably because the higher number of parameters makes more difficult the convergence of the model, which complicates the estimation of the error.

*A*represents the estimate of the asymptotic weight, which is interpreted as the adult weight; however, there are controversies about the optimal adult weight, which relies on the species, breed, previous selection, management system, and weather conditions. The parameter

*A*indicates the weight that the animal can reach at maturity and is useful for prediction of results and planning of the whole activity regarding the raising and breeding [22,23].

*A*.

*k*represents the growth speed to reach the asymptotic weight (at maturity). In our study, the estimate of

*k*obtained using the von Bertalanffy model was 0.01904. Animals with a high maturity rate are considered more precocious than those that have a lower maturity rate. More precocious, prolific, productive, and resistant breeds have a higher market value, as these animals can be slaughtered earlier and with higher carcass yield. This optimizes the costs with feeding (which represents 70% of the total cost of the production) without affecting the environmental and animal welfare rules [26].

*A*.

*B*is a constant of integration that is related to the initial weight of the animal and represents its degree of maturity at birth. Higher

*B*values are associated with lower birth weights in the von Bertalanffy model. In the Logistic growth model,

*B*has a fixed value of one; therefore, in this case, there is no biological interpretation [27].

*A*in the Logistic model used for LEA, the AIC, BIC, and residual variance values decreased by 13.0, 13.5, and approximately 50%, respectively, in comparison to the estimates obtained without the inclusion of random effect (Table 5).

^{2}of LEA (Figure 3). This indicates that the muscle growth of the studied animals became slower at 16 days of age (0.04 cm

^{2}/d). This can be justified by the fact that growth has allometric characteristics (i.e., the tissues have different growth rates that change in different phases of the animal life) [17].

^{2}/d). It is important to note that, at this age, the muscle mass reaches its maximum point, thus, the weight gain comes only from gaining fat. Regarding the maturity weight, the animal growth was only 9.09 g/d. From 90 days of age onwards, the weight gain decreased and was lower than that observed at 2-d-old (9.67 g/d). Thus, under conditions similar to those evaluated in this study, it would not be economically advantageous to maintain New Zealand White rabbits in the herd after 90-d-old and animals at this age should be slaughtered for meat production.