The data used in this paper were derived from 54 F₂ full-sib families created in 2010 by the Yellow Sea Fisheries Research Institute of the Chinese Academy of Fishery Science. The dynamic genetic analysis of body weight and main length ratio was carried out using 54 full-sib families. These families were produced using a nested mating design, depending on the availability of well-liking breeders in Yantai Tianyuan Aquatic Limited Corporation. The artificial fertilization method was used to obtain eggs and sperm from breeders injected with Ovaprim (Battaglene, 1996). First, eggs were obtained from two females and stored in two different beakers. Subsequently, the male fish were stripped and the milt was divided in two. Each portion was used to fertilize one of the two females. After fertilization, individual full-sib families were incubated at 13–14°C in separate rectangular incubation net cages (80 cm×60 cm×60 cm). After ~110 h in the incubation net cages, spawn from individual full-sib families was collected and stocked in separate concrete tanks (3 m×1 m×1.5 m). To obtain similar feeding conditions, the stocking density of fish and the environmental variables were maintained at standard conditions, during the early breeding stage of all families. At the 15, 30 and 45 days after hatching, the quantity of fish in each family was normalized by randomly sampling 10 000, 5 000 and 2 000 individuals, respectively. At the 60 days after hatching, random samples of 1 000 young fish from each full-sib family were transferred to separate 12 m³ concrete tanks. At 3 months of age, 250–300 individuals were selected randomly from each family for tagging, using a visible implant elastomer (four different tags and combinations were used to distinguish different families). Fish were then transferred to a 650 m³ concrete tank with air-pumped circulating seawater for polyculture. When individuals tagged with the visible implant elastomer were 9 months of age, random samples of 50–60 individuals from each family were individually tagged again with passive integrated transponders (for distinguishing families and individuals). Individuals tagged with passive integrated transponders were transferred to a 200 m³ concrete tank for polyculture, until they reached 18 months of age. From 18 to 27 months, individuals tagged with passive integrated transponders were reared in two 400 m³ concrete tanks. Dead individuals were removed from the tank once a day. The environmental conditions were standardized during the larval and juvenile culture period at: water temperature 13–18°C, salinity 30–40, illumination intensity 500–2 000 lx, pH 7.8–8.2, and dissolved oxygen >6 mg/L. During the period 3 to 27 months, the above five indices were 15–18°C, 25–30, 500–1 500 lx, pH 7.6–8.2 and >6 mg/L, respectively.

From 3 to 27 months of age, the BW, BL and body weight (BWT) of fish were measured every three months. Each data collection was synchronous with moving ponds. A total of 50–60 individuals from each family were collected randomly at 3 and 6 months of age, and all fish tagged with passive integrated transponders were collected from 9 to 27 months of age (months of age are counted from hatching). BWT was measured using a 0.01 g precision electronic balance, and BL was measured using a Vernier caliper to the nearest 0.01 cm. The BW/BL ratio was calculated at different sampling ages. The descriptive statistics for BW/BL ratio and BWT at different growth periods are shown in Table 1.

For BW/BL ratio and BWT traits, variance components, heritability, and genetic correlations with standard errors, were estimated using the two-trait animal model AIREML, using ASReml-R software (Gilmour et al., 2009). The model can be written as:

where $u$ is the population mean, ${y_{ij}}$ is the measured value of BW/BL and BWT, ${a_i}$ is the additive genetic effect of individual as a random effect, ${f_j}$ is the full-sib family random effect, ${e_{ij}}$ is the random residual. In matrix notation the model can be written:

where $\boldsymbol y$ is the vector of observations of each trait, $\boldsymbol b$ is the vector of fixed effects, $\boldsymbol u$ is the vector of random effects, $\boldsymbol e$ is a vector of random errors, X and Z are known design matrices assigned to the observations to levels of b and $\boldsymbol u$, respectively. The mathematical expectation and variance were defined as:

where ${\boldsymbol G_0}$ is the genetic variance-covariance matrix of BW/BL ratio and BWT, ${\boldsymbol R_0}$ is the residual variance-covariance matrix of the two traits, $ \otimes $ is the Kronecker product defined by $ Var\left(\boldsymbol y \right) =$$ {\boldsymbol {ZAZ}}'\sigma _a^2 +\boldsymbol I\sigma _{\boldsymbol e}^2$, A is the additive genetic relationship matrix, I is an identity matrix, $\sigma _a^2$ is additive genetic variance, and $\sigma _e^2 $ is residual variance.

The equations of the two-trait animal model are:

Heritability (h²) and genetic correlation (r_g) can be written:

where $ {{\sigma _p^2}}$ is phenotype variance, ${a_x}$ and ${a_y}$ are additive genetic effects of x- and y-traits, and ${\rm{cov}}({a_x},{a_y})$ is covariance of ${a_x}$ and ${a_y}$. Before statistical analysis, outliers were checked using box plots and the normality of data was assessed using the Shapiro–Wilk test.

All data sets were confirmed to be normally distributed by passing the Shapiro–Wilk normality test. The descriptive statistics for BW/BL ratio and BWT are presented in Table 1. During the period of 3 to 27 months of age, the values of BW/BL ratio ranged from 0.605 6 to 0.856 7, and the BWT value from 2.979 1 to 2 031.383 2 g. In general, the BW/BL ratio increased with body weight, except at 15 and 24 months when it decreased slightly.

The results of genetic evaluation for BW/BL ratio of turbot at different sampling ages are shown in Table 2. From 3 to 27 months of age, the ranges of variance components ($\sigma _a^2$, $\sigma _f^2$ and $\sigma _e^2$) were 0.122 9–27.350 8, 0.083 4–0.130 0 and 0.213 7–47.807 3, respectively. Both $\sigma _a^2$ and $\sigma _e^2$ raised throughout the measurement period, whereas $\sigma _f^2$ did not change significantly in a specific direction. The heritability values of BW/BL ratio ranged from 0.216 8 to 0.314 8, corresponding to moderate heritability. Heritability did not change significantly in a specific direction either.

The results of genetic evaluation for BWT of turbot at different sampling ages are shown in Table 3. From 3 to 27 months, the ranges of variance components ($\sigma _a^2$, $\sigma _f^2$ and $\sigma _e^2$) were 0.101 5–49 368.553 2, 0.126 6–0.240 6 and 0.050 7–113 783.300 1, respectively. The BWT heritability values ranged from 0.270 2 to 0.347 9, corresponding to moderate heritability. Similarly to the BW/BL ratio, both $\sigma _a^2$ and $\sigma _e^2$ raised throughout the measurement period; neither $\sigma _f^2$ or h² changed significantly in a specific direction.

Genetic and phenotypic correlations between BW/BL ratio and BWT are shown in Table 4. At different sampling ages, the ranges of genetic and phenotypic correlations were 0.437 8–0.821 3 and 0.336 1–0.638 3, respectively. All genetic and phenotypic correlation coefficients were significantly different from zero at the 1% level. Genetic correlations had only two medium correlations (24 and 27 months of age) and the others belonged to high correlations (from 3 to 18 months of age), and phenotypic correlations had three low correlations (12, 24 and 27 months of age), five medium correlations (3, 6, 9 and 15 months of age) and one high correlation (18 months of age). In general, genetic correlations decreased throughout the measurement period, but phenotypic correlations did not change significantly in a specific direction.

A comparison of heritability of BW/BL ratio and BWT are shown in Fig. 2 for different sampling ages. Heritability of BW/BL ratio was lower than that of BWT, except at 3 months of age. Differences of heritability between BW/BL ratio and BWT from 6 to 18 months of age were larger than those at 3, 24, and 27 months of age.

A comparison of genetic and environmental correlations between BW/BL ratio and BWT is shown in Fig. 3 for different sampling ages. Genetic correlations were higher than environmental correlations throughout the measurement period. Differences between genetic and environmental correlations from 3 to 12 months of age were larger than from 15 and 27 months of age. The maximum of genetic correlations appeared at 12 months of age and the minimum at 18 months.