1. Introduction
Growth and development are vital traits of domestic meat animals. Although the growth and development of animals are controlled by genetic and environmental factors, the basic characteristics of the growth and development of a species or a breed of domestic animals are relatively stable.
Growth curves are commonly used to determine developmental characteristics and their cumulative changes, as well as to explore the relationship between the entire and a part of a livestock group during different growth stages. The fitting of growth curves of growth functions is an extremely effective tool for assessing different management factors for breeding purposes [
1]. Growth functions have been used extensively to represent changes in size with age, which in turn facilitates the evaluation of the genetic potential of animals for growth and matching nutrition to possible growth [
2]. Commonly used growth curve models include the Logistic, Gompertz, Brody, von Bertalanffy, and Richands models [
1,
2,
3,
4,
5]. The correlation strength among variables estimated through different models has been shown to be high. Generally, the goodness of fit of these models for growth data for various species tends to be similar to those of the Logistic, Gompertz, and von Bertalanffy models [
4]. Growth curve parameters serve as potentially useful criteria for determining the relationship between weight and age through parameter selection, and the selection of the expected value of growth curve parameters can be useful in obtaining an optimal growth curve [
4,
6]. Typically, growth curve parameters are estimated using nonlinear mathematical functions that enable data summarization from a large number of longitudinal (weight–age) data of each individual [
7]. Pala demonstrated that growth rate is related to maturity rate and mature body weight, which in turn are related to the lifetime productivity parameters of an animal [
8].
Furthermore, the posterior distribution of parameter values could be generated using the Gibbs sampling algorithm [
9,
10,
11], and a random sample of parameter estimation could be estimated according to a provided data set, which is proportional to the product of parameter probability and observation probability [
12,
13]. Moreover, the restricted maximum likelihood (REML) and Bayesian methods are widely used in animal breeding to estimate genetic parameters and variance components [
14,
15]. Carneiro reported that the Bayesian method is useful in analyzing small groups when a large amount of historical data is available [
16]. Furthermore, some scholars have proposed that sheep have a large body size that leads to better productivity [
17]; however, most studies on the animal growth curve have considered animals aged between 0 and 12 months, and only a few studies have reported the simulation of the growth curve of sheep and goats aged between 12 and 24 months.
Qianhua Mutton Merino is a newly developed, dual-purpose (meat and wool) breed of sheep that was obtained through the cross-breeding of the introduced South African Mutton Merino with the domestic Northeast China fine-fleece sheep in China in 2018 [
18]. This newly developed sheep breed dwells in the pastoral farming zone, with an over 130% lambing rate, and possesses characteristics such as strong adaptability, large body weight, rapid growth and development, high meat yield, homogeneous hair, and 66s hair as the main body. As a newly bred meat sheep breed, the exploration of the genetic characteristics of Qianhua Mutton Merino’s growth and development could reveal its germplasm characteristics, and it also may serve as a reference for improving the breeding of this sheep breed. Therefore, this study investigated the genetic relationship between the growth curve parameters of Qianhua Mutton Merino.
2. Materials and Methods
Among the core breeding group of Qianhua Mutton Merino raised by Jilin Qian’an Zhihua Breeding Sheep Breeding Co., Ltd. (Qianan, China), 896 rams and 1404 ewes born between 10 January and 13 January 2018 and exhibiting good physical condition, appetite, and health status were randomly selected and studied until 20 January 2020. All the sheep were fed in-house, and all the experimental sheep were fed diets as per the NRC (2007) standard. The sheep were vaccinated regularly and dewormed timely. The birth weight of lambs was measured before colostrum sucking within 1 h of birth, and the body weight during other periods was measured as the fasting weight before the morning feed. The body weight and bust circumference of the experimental sheep were continuously measured at 3, 6, 12, 18, and 24 months of age until January 2020.
In this study, three nonlinear models, namely, Logistics, Gompertz, and von Bertalanffy, were selected for the fitting of the growth curve.
Table 1 presents the formula and characteristics of the fitting models. In each model, W
t represents the estimation of body weight and bust circumference at ‘t’ months of age. Notably, parameter A indicates the mature weight (chest circumference); K indicates the instantaneous relative growth rate of body weight (chest circumference) relative to mature body weight (chest circumference), indicating the speed at which the animal approaches adult body weight (chest circumference); B indicates the adjustment parameter related to the initial body weight (chest circumference), determined using the initial values of Wt and ‘t’; ‘t’ indicates the age in months; and ‘w’ indicates the body weight at the inflection point (chest circumference).
The daily growth in body size is given as follows: , wherein Wt is the subsequent body size value, W0 is the previously measured body size value, and ‘t’ is the number of days.
The relative growth rate is given as follows: .
The fitting degree formula is as follows: .
Absolute growth indicates the absolute speed of livestock growth and development during a certain period, and this study assessed the daily growth to ascertain the absolute growth of the body weight and chest circumference of Qianhua Mutton Merino. By contrast, relative growth indicates the intensity of livestock growth and development. The fitting degree R2 was used to evaluate the growth curve model, wherein WP denotes the predicted average value and Wm denotes the actual average value. Notably, the closer the R2 is to 1, the better the fitting degree of growth and development is and the closer it is to its growth and development. In addition, we used the Gibbs sampling algorithm to conduct Bayes estimation for the variance and genetic parameters of the weight and chest circumference growth curves of Qianhua Mutton Merino, which will be used to design future programs involving Qianhua Mutton Merino and will provide a reference for further breeding and the scientific breeding of Qianhua Mutton Merino.
The General Linear Model (GLM) program of SPSS 25.0 (IBM) was used for the significance analysis of data combined with fixed effects, and the significance level of the fixed effect in the model was
p < 0.05. Fixed effects in the model formulas of parameters A, B, and K included sex, age, and population, while the random effects were the random additive genetic effects of animals [
17]. The univariate animal model suitable for the genetic analysis of growth curve parameters is as follows:
where ‘Y’ is the observed value vector of all traits; X is the structure matrix of fixed effects; β is the fixed-effect vector, including gender, age, etc.; Z is the structure matrix of random effects; ‘u’ is the individual additive-effect vector; and ‘e’ is the random residual-effect vector. Blup90 software was used to analyze the variance and genetic parameters.
The narrow-sense heritability of trait a was calculated as
where
and
are the estimated additive genetic variance and the estimated residual variance for trait i.
Genetic correlation between trait i and trait j was calculated as
where
is the estimated additive genetic covariance between trait i and trait j,
is the estimated additive genetic variance for trait i, and
is the estimated additive genetic variance for trait j.
Residual correlation between trait i and trait j was calculated as
where
is the estimated additive residual correlation between trait i and trait j,
is the estimated additive residual variance for trait i, and
is the estimated additive residual variance for trait j.
Phenotypic correlation between trait i and trait j was calculated as
According to the Bayes formula, if the prior probability of additive direct effects has a multivariate normal distribution, the mean is 0, the variance is σ
a2, and σ
a2 is the additive direct genetic variance; if the residual effect (posterior probability) has a multivariate normal distribution, the mean is 0, and the variance is 1
n σ
a2, where the order of the identity matrix 1n is equal to the number of individual records and σ
a2 is the residual. A contrasting analysis was conducted for the three variables, wherein the model that fitted for each feature in the univariate analysis was used. If the genetic and residual (covariance) variance matrices followed the inverse Wishart distribution, the GIBBS1F90 of Blup90 (Ignacy Misztal) program was used to estimate the marginal posterior distribution of the parameters and variance components. The GIBBS1F90 sampler was run 300,000 times, and the first 60,000 runs were discarded as the aging period [
19]. Then, the mean, SD, and 95% high posterior density (HPD) interval of all parameters were calculated for each marginal progeny.