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From an economical point of view, growth and developmental characters are the most important traits in farmed fish species, and persistent efforts are made to genetically improve these traits in fish breeding. Growth and developmental traits, such as body weight (BWE) and morphological traits, are measured at different times. Faster BWE growth shortens time to market and selection on morphological traits allows fish shape and size to be standardized. Growth and developmental traits are dynamic quantitative traits because they vary spatially and temporally [1]. They are also called infinite-dimensional traits, since they are expressed on a continuous time and space scale [2]. In tilapia breeding, growth and developmental traits at a specific age (in day, week, or year), such as the time to market are the main targets of genetic improvement. As such, genetic analysis of the growth and developmental process can increase the efficiency of selection compared to that of traits measured at specific ages [3].
Considerable attention has been paid to the genetic analysis of BWE and morphological traits at a specific age in breeding tilapia. In earlier studies, growth traits at specific ages were considered as separate traits and analyzed by using univariate animal models [4-13]. Subsequently, multivariate animal models were applied to estimate both the heritabilities of growth traits at specific ages and the genetic correlations between traits measured at different specific ages [8, 11, 12, 14-22]. Although multivariate genetic analysis of growth traits has improved the accuracy of parameter estimation by using more records, at multiple ages, such an analysis is strongly limited by the variable and irregular timing of these measurements [23].
For growth and developmental traits that are recorded at multiple time-points during growth, the patterns of growth curves have been shown to be heritable [2, 3, 24]. The genetic analysis of dynamic quantitative traits was initially conducted by first fitting individual growth curves and then analyzing their estimated parameters within the framework of a multivariate animal model. However, with such genetic analyses, it was not possible to determine whether some individuals had too few records to fit the growth curves. Since then, random regression models (RRM) [3, 25] were developed to dissect dynamic phenotypes into different functions that describe the effects of various genetic and environmental...