BackgroundBecause of their high economic importance, growth traits in fish are under continuous improvement. For growth traits that are recorded at multiple time-points in life, the use of univariate and multivariate animal models is limited because of the variable and irregular timing of these measures. Thus, the univariate random regression model (RRM) was introduced for the genetic analysis of dynamic growth traits in fish breeding.MethodsWe used a multivariate random regression model (MRRM) to analyze genetic changes in growth traits recorded at multiple time-point of genetically-improved farmed tilapia. Legendre polynomials of different orders were applied to characterize the influences of fixed and random effects on growth trajectories. The final MRRM was determined by optimizing the univariate RRM for the analyzed traits separately via penalizing adaptively the likelihood statistical criterion, which is superior to both the Akaike information criterion and the Bayesian information criterion.ConclusionsIn the selected MRRM, the additive genetic effects were modeled by Legendre polynomials of three orders for body weight (BWE) and body length (BL) and of two orders for body depth (BD). By using the covariance functions of the MRRM, estimated heritabilities were between 0.086 and 0.628 for BWE, 0.155 and 0.556 for BL, and 0.056 and 0.607 for BD. Only heritabilities for BD measured from 60 to 140 days of age were consistently higher than those estimated by the univariate RRM. All genetic correlations between growth time-points exceeded 0.5 for either single or pairwise time-points. Moreover, correlations between early and late growth time-points were lower. Thus, for phenotypes that are measured repeatedly in aquaculture, an MRRM can enhance the efficiency of the comprehensive selection for BWE and the main morphological traits.Electronic supplementary materialThe online version of this article (10.1186/s12711-017-0357-7) contains supplementary material, which is available to authorized users.

For body weight (BW) and morphological traits measured repeatedly during growth in Japanese flounder, random regression models (RRMs) were constructed to genetically analyse growth curves and relative growth of morphological traits to BW or body length (BL). In the RRM of growth curves, genetic effects were optimally modelled using Legendre polynomials of two orders for six growth traits. Family and permanent environmental effects remained constant for morphological traits, whereas family effects changed linearly for BWs. During the measuring periods, the heritabilities of the traits increased with age and ranged from 0.256 to 0.843 for BW, 0.379 to 0.806 for body height, 0.338 to 0.773 for BL, 0.286 to 0.665 for head length, 0.159 to 0.708 for length of caudal fin and 0.335 to 0.774 for width of caudal peduncle. Genetic correlations for each trait decreased with increased lag in days of age. In the RRM of relative growth, all morphological traits analysed were significantly associated with BW and BL. The heritabilities for the allometries of morphological traits to BWs ranged from 0.251 to 0.755, whereas those to BLs ranged from 0.412 to 0.871. The majority of genetic correlations among these allometry scalings were negative. These estimated parameters can be utilized to not only guide the efficient selection of traits, but also to genetically regulate synchronous growth of body shape with BW in Japanese flounder.

To genetically analyse growth traits in genetically improved farmed tilapia (GIFT), the body weight (BWE) and main morphological traits, including body length (BL), body depth (BD), body width (BWI), head length (HL) and length of the caudal peduncle (CPL), were measured six times in growth duration on 1451 fish from 45 mixed families of full and half sibs. A random regression model (RRM) was used to model genetic changes of the growth traits with days of age and estimate the heritability for any growth point and genetic correlations between pairwise growth points. Using the covariance function based on optimal RRMs, the heritabilities were estimated to be from 0.102 to 0.662 for BWE, 0.157 to 0.591 for BL, 0.047 to 0.621 for BD, 0.018 to 0.577 for BWI, 0.075 to 0.597 for HL and 0.032 to 0.610 for CPL between 60 and 140 days of age. All genetic correlations exceeded 0.5 between pairwise growth points. Moreover, the traits at initial days of age showed less correlation with those at later days of age. With phenotypes observed repeatedly, the model choice showed that the optimal RRMs could more precisely predict breeding values at a specific growth time than repeatability models or multiple trait animal models, which enhanced the efficiency of selection for the BWE and main morphological traits.

Genomic imprinting underlying growth and development traits has been recognized, with a focus on the form of absolute or pure growth. However, little is known about the effect of genomic imprinting on relative growth. In this study, we proposed a random regression model to estimate genome-wide imprinting effects on the relative growth of multiple tissues and organs to body weight in mice. Joint static allometry scaling equation as sub-model is nested within the genetic effects of markers and polygenic effects caused by a pedigree. Both chromosome-wide and genome-wide statistical tests were conducted to identify imprinted quantitative trait nucleotides (QTNs) associated with relative growth of individual tissues and organs to body weight. Real data analysis showed that three of six analysed tissues and organs are significantly associated with body weight in terms of phenotypic relative growth. At the chromosome-wide level, a total 122 QTNs were associated with allometries of kidney, spleen and liver weights to body weight, 36 of which were imprinted with different imprinting fashions. Further, only two imprinted QTNs responsible for relative growth of spleen and liver were verified by genome-wide test. Our approach provides a general framework for statistical inference of genomic imprinting underlying allometry scaling in animals.