The modeling of factors is essential for estimating the components of (co)variance. Among the models tested in the present study, Model 5, which included only the fixed effects of the tank and reproductive cycle, produced genetic parameters with reliable values. Two other models, Models 1 and 3, also produced reliable estimates; however, the inclusion of age in these models was not justified because the contribution of this factor, whether linear or quadratic, was minimal for the adjustment of the models. Thus, Model 5 was selected because, in addition to generating very consistent and accurate estimates, it was the simplest model among the ones tested, meeting the criterion of parsimony.
The low importance of the age factor for the analyses was not expected because the reproductive physiology of this species is described by the increasing egg production with increasing age of females up to two or three years old, after which egg production gradually decreases with increasing age (Valentin et al. 2015). One hypothesis to explain the small influence of age on the measured variables is that the age effect is confused with the fixed effect of the reproductive cycle.
In a study by Yoshida et al. (2017) on the genetic evaluation of tilapia reproductive traits, the model used included the covariate age and location as fixed effects, obtaining estimates of genetic parameters similar to those of this study. However, Yoshida et al. (2017) did not include the reproductive cycle as a fixed effect, so the inclusion of age in the model was justified.
Traits of spawning frequency, mean spawning interval, and average egg volume showed heritability estimates of 0.15, 0.13, and 0.18, respectively. Similar heritability values were reported by Yoshida et al. (2017), with 0.14 for spawning success (0.14) and multiple spawning (0.16) in Unicaracter analysis. These low heritability estimates highlight the considerable influence of the environment on reproductive traits. However, according to the model considered for the discussions, the total egg volume presented a heritability of 0.26, a value of moderate magnitude, which indicates good possibilities of obtaining genetic gain by selecting this trait. In a study by Yoshida et al. (2017), the heritability estimate for the same trait in tilapia was much lower (0.02), whereas, in rainbow trout, Gall and Huang (1988) estimated a heritability value (0.30) similar to that of the present study.
Repeatability estimates were high for all traits, which means that it is not necessary to evaluate several cycles to accurately estimate the genetic value of the breeding stock because these animals tend to maintain the same reproductive performance for several cycles. Moreover, from the point of view of fingerling producers, high repeatability is quite interesting since animals of superior genetics can remain in the breeding stock for a long time, maintaining good production. Only a few studies have conducted the repeatability analysis for reproductive traits of aquatic species. Yoshida et al. (2017) found a repeatability of 0.28 for produced egg volume, which is below that found in the present study (0.45). Furthermore, Trong et al. (2013) observed low repeatability (between 0.04 and 0.17) for spawn success in Nile tilapia, which is different from the results obtained for the same trait in the present study (0.58). This difference between repeatability estimates was probably due to the difference in the genetic structure of the animals evaluated in different studies because the components of (co)variance were inherent to the populations for which they were estimated (Falconer, 1984).
In bi-characteristic analyses, a high negative correlation was observed between the mean spawning interval and the total egg volume (-0.99), which suggests that both traits are controlled by the same group of genes. As described by Campos-Mendoza et al. (2004), spawning in tilapia can occur at intervals of less than 21 days, which, despite resulting in a reduction in the number of eggs produced during each spawning, generates an increase in the final volume of eggs produced (Tsadik, 2008). Thus, considering each spawn separately, genetic selection to produce females that spawn at shorter intervals does not result in a practical advantage. However, considering the long reproductive period, the high frequency at which these breeders would produce eggs in a complete cycle would compensate for the drop in spawning production.
All other correlations presented high values, but they had high mean deviations. Only the correlation between total egg volume and average egg volume presented a positive and high value with good precision; however, the high correlation between these two traits was expected because they are similar and interconnected.
The results obtained in the bi-characteristic analyses converged to a clear improvement strategy for the evaluated population. Genetic selection for total egg volume can, after a few generations, result in breeders with a higher production of eggs in the reproductive cycle and smaller intervals between spawning. This will maximize the utilization of the available space and facilitate stable production, enabling the producer to achieve greater productivity with a lower number of females.