Origin and development of genetic lines

The GRO and RES lines were formed in 1998 and 2014 respectively. The GRO line was produced using shrimp from Mexico, Venezuela, Colombia, the United States, and Ecuador. The RES line is composed of shrimp with a history of resistance to WSD from Ecuador, Panama and the United States and since 2014. A more specific description of the creation of the genetic lines can be found in ^{Gallaga-Maldonado et al. (2020)} and ^{Campos-Montes et al. (2020)}.

Family management

The families were produced by artificial insemination, using a ratio of one male for every two females to form half-sib families. The inseminated females spawned in individual tanks for the counting of nauplii per family (full siblings); those spawning with less tan 25,000 nauplii being discarded for the next stage. The feeding in the larval stages was based on commercial micro-pellets with 40% to 50% protein and 8% to 10% fat, Chaetoceros microalgae, Spirulina spp., and Artemia spp., and the constitution of the diet was adapted to each stadium. The full sib families were kept in the same pond until they were marked around 60 days of age (weighing between 2 and 3 grams), using colored elastomers (Northwest Marine Technology^TM), in the last abdominal segment of the shrimp and whose color combination worked as family identification.

Management of growing ponds

Ten days after tagging, an average of 36 shrimp per family were stocked in each pond. The ponds of Sonora (WSD-presence) were of sand of 0.20 ha, with a water column of 1.4 m, at an average temperature of 32 °C and an average salinity of 33 gL^-1. The daily water exchange rate ranged from 5 to 20%. The food offered had a protein percentage between 34 and 40% at a rate of 3% of the total biomass in the pond. The stocking density in both ponds was 16 organisms/m². In Sinaloa (WSD-absence) a 4 x 16 m concrete pond was used, with a water column of 2 m and a planting density of 70 m². The water temperature was maintained at 30 °C with a salinity of 35 gL^-1, constant aeration and a daily water exchange rate of 4 to 5%. The amount of daily food offered (35 - 40% protein); it was calculated as 6% of its biomass.

Data collection for body weight at 130 days of age and survival from 70 to 130 days

After 70 days after sowing, all the organisms were recovered from the ponds, and from each one the family of origin, sex and body weight were identified. The information of individuals with deformities, without reliable identification or undefined sex was eliminated. For the estimation of the HS, the animals recovered at the end of the period were considered as alive (1) and the animals not recovered, considering the difference between the living organisms of each family and those sown, as dead (0).

Information analysis

To compare the productive behavior between both lines in both scenarios (WSD-presence and WSD-absence), the following linear model was considered:

y_ijk = µ + L_i + S_j + LS_ij + e_ijk

Where, y_ijk is the vector of observations of BW or HS, µ is the mean of the population for the variable of interest (HS or BW), L_i is the effect of the i-th line (GRO, RES), S_j is the effect of the j-th environment (WSD-presence, WSD-absence), LS_ij is the effect of the interaction between the line and pond health status, and eijk~N (0, σ²e). Sex and the pond were also included on BW. To determine differences between line and environment combinations, a Tukey test (α = 0.05) was used.

The genetic parameters for BW and HS were estimated for each line, using an animal model and restricted maximum likelihood, with the ASReml software. Considering the criteria for approximation of a binomial distribution to a normal distribution (^{Schader and Schmid, 1989}; ^{Emura and Yu-Ting, 2018}), normality was assumed in the HS analysis; the model used was:

y = Xβ + Zu +Wf + ε

Where, y is the vector of observations of (BW or HS) of both environments, β is the vector of fixed effects of each characteristic, u is the vector of random additive genetic effects of the animal, u~MVN (0, G), where G = V ⊗ A, where V is a symmetric matrix containing the (co) variances between the effects of same family animals for the characteristics in the two environments, and A is a matrix of additive relationships; ⊗ is the Kronecker product, environmental residuals, f is the unknown vector of the common family effect for all characteristics, f~MVN (0, F); where, F=C ⊗ I, where, C is a matrix of co (variances) of common family environment effects, only for BW, and I is an identity matrix of appropriate order, and ε is the vector of effects random, ε~MVN (0, R), where, R = E ⊗ I, where, E is the matrix of co (variances) of the residual effects that contains the covariances between the two characteristics, and I is an identity matrix of appropriate order, with σ₂e as the residual variance.

Finally, X, Z, and W are known incidence matrices that relate the observations to the fixed effects (which varied depending on the trait analyzed), the genetic effects of the animal, and common family environment effects, respectively. The genetic correlations between both characteristics in the line-pond combination were estimated with ASReml, using bivariate models and with the same model, but considering the y vector of information from BW and HS. No restrictions were used in the covariance structure and common family environment effects were considered independent.

In estimating the genetic parameters for BW, the fixed effects included in the model were: sex, age at harvest linear and quadratic, additionally in the case of WSD-presence; the pond effect was included (Kino and Marea Alta). Regarding the HS for the affected ponds, the only fixed effect considered was that of the pond in WSD-presence; while in the WSD- absence environment, no fixed effect was considered.

The phenotypic variance for each characteristic was estimated as the sum of the variance components of the random effects (animal genetic and common family). The h² was estimated as phenotypic variance proportion that is due to the additive genetic variance, and the r_G was estimated as the covariance divided by the product of the corresponding standard deviations. The statistical significance of the estimated parameters was based on the confidence intervals (95%), constructed with their standard errors, assuming normality. The existence of GEI was determined when r_G between environments was less than 0.80 (^{Sae-Lim et al., 2016}).

Finally, to analyze whether the behavior of the characteristics between genetic lines was similar. A comparison of the estimated r_G was made in each line (^{Nguyen et al., 2016}), such comparison was made by means of a Fisher's Z transformation (^{Rosenthal et al., 1992}) implemented in the “Cocor” package in R (Diedenhofen and Musch, 2014), a significance test for the difference between 2 correlations, based on dependent groups with 1 variable in common. For a better understanding, a diagram of the estimated genetic correlations per line is presented in Figure 1.

Figure 1 Scheme of the genetic correlations estimated in the study by genetic line r2a and r2b = Genetic correlation between environments (WSD-presence and WSD-absence) within each characteristic. r2c = Genetic correlation between WSD environments-presence of the two characteristics. r2d = Genetic correlation between WSD environments-absence of the two characteristics 

Comparison of productive behavior between lines

Descriptive statistics for BW and HS in each genetic line (GRO and RES), within environment (WSD-presence, WSD-absence) are shown in Table 1. At the same time, Figures 2 and 3 show the LSM of both lines (GRO and RES), through the environments for BW and HS. These results show differences in HS, where the GRO line has a low HS in WSD-presence; while the shrimp of the RES line have a lower HS in WSD-presence. Additionally, there is line-by-environment interaction (P <0.0001) in the two characteristics. These line-by-environment interactions highlight the importance of considering the probability of occurrence of WSD disease, when the line is chosen in the genetic improvement program (^{Sae-Lim et al., 2016}).

Figure 2 Least squares means for body weight at harvest in the growth lines and resistance to WSD, in the presence and absence of SMB in P. vannamei 

Figure 3 Least squares means for harvest survival in growth lines and resistance to WSD, in the presence and absence of WSD in P. vannamei 

Heritability for body weight at harvest

The heritabilities for BW in both lines are shown in Table 2. The common family environment effects were 0.05 in both lines. The inclusion of these effects in all the models reduced the estimation of the additive variance, according to what was presented by other authors (^{Campos-Montes et al., 2013}; ^{Montaldo et al., 2013}). The heritabilities in WSD- absence were consistent with those reported by authors such as ^{Tan et al. (2017)}, ^{Trang et al. (2019)} and ^{Ren et al. (2020}), despite the fact that the latter did not consider common family environment effects in its model; however, these heritability estimates were higher than those reported by other authors (^{Li et al., 2015}; ^{Zhang et al., 2017}; ^{Yuan et al., 2018}). On the other hand, the heritabilities for WSD-presence are similar to those estimated by ^{Caballero-Zamora et al. (2015)}, who also used data from a natural outbreak of WSD.

In the GRO line, the difference between the heritabilities for WSD-presence (0.05 ± 0.16) and WSD-absence (0.35 ± 0.15), can be an indicator of heterogeneity of variances (^{Sae- Lim et al, 2016}). In this case, in addition to changes in the additive genetic variance, the source of this heteroscedasticity may be contained in changes in the environmental variance due to the microenvironmental sensitivity of the individuals. In the case of WSD- presence, it is important to mention that the low precision in the estimate of h² may be due to the data structure resulting from the high mortality. In the RES line, the heritability estimates for BW were higher than for GRO; in addition to having better precision. On the other hand, the estimate of h² in WSD-presence (0.26 ± 0.07) is lower than in WSD- absence (0.49 ± 0.08), as in the GRO line, and the estimators of this line were consistent with other authors (^{Luan et al., 2015}; ^{Sui et al., 2016}; ^{Zhang et al., 2017} and ^{Yuan et al., 2018}).

Variations in heritability estimators for BW may be the result of the microenvironmental sensitivity of individuals (^{Sae-Lim et al, 2016}). Given the above, it is important to note that these changes in heritability can alter the response prediction accuracy to selection.

Genetic correlations for BW

The estimated rG for the BWs between environments in the GRO line was negative and not significant (P> 0.05) (-0.17 ± 0.60); although in estimates with preliminary models (data not shown) it was consistently negative. The imprecise value of the estimate may be a low value consequence of the additive genetic variance of WB in WSD-presence. It complicates the evaluation of GEI effects in this line; while in the RES line, this correlation was not different from 1 (P> 0.05) (Table 2); noting that the additive genetic effects for BW are very similar in the two environments (^{Sae-Lim et al., 2016}). In other words, there is no GEI effect on RES for BW. Considering that both lines were under the same environmental management conditions and exposed to the same pathogen (WSD), it is possible to consider that the differences in the estimators of both lines are the result of the low HS rate of the GRO line. In several studies GEI was not detected when considering environmental conditions, such as planting density (^{Campos-Montes et al., 2009}; ^{Tan et al., 2017}) or cultivation location (^{Sui et al., 2016}). Other works report possible effects of GEI for BW, considering the point values of the rG estimators. However, their standard errors do not allow defining them as significantly different from one or zero (^{Caballero- Zamora et al., 2015}; ^{Li et al., 2015}; ^{Nguyen et al., 2020}).

Heritability for survival to harvest in both genetic lines

The heritability and additive genetic correlations for HS in the genetic lines are shown in Table 3. Regarding the common family effects, these were considered independent between environments for each characteristic, and varied between 0.02 and 0.04. The estimated heritabilities for HS in WSD-presence were 0.01 and 0.11 for GRO and RES respectively; the previous ones are similar to those reported by other authors in the presence of WSD (^{Gitterle et al., 2005a}; ^{Caballero-Zamora et al., 2015}); however, they were lower than those estimated by ^{Li et al. (2015)} and ^{Trang et al. (2019)}; both in WSD controlled challenges. The results of the HS model were consistent with estimates, using univariate models, considering a binomial distribution (results not shown).

The heritabilities for HS in WSD-absence were 0.01 ± 0.03 in GRO and 0.06 ± 0.04 in RES concordant with other estimators for overall survival (^{Campos-Montes et al., 2013}; ^{Zhang et al., 2017}; ^{Ren et al., 2020}), but lower than those presented by ^{Lu et al. (2017)}, ^{Luan et al. (2020)}, and ^{Tan et al. (2017)}, where the effect of a common family environment was not included, which could have generated an overestimation of the genetic parameters.

The heritabilities in GRO were essentially zero in both environments, 0.01 ± 0.02 in SMB- presence and 0.02 ± 0.03 in WSD-absence, which represents minimal possibilities of genetic advancement by selection for this characteristic in both scenarios, which is consistent with other authors (^{Gitterle et al., 2005a}; ^{Campos-Montes et al., 2013}; ^{Li et al., 2015}; ^{Lu et al., 2017}). The minimum advance by selection could be related to the difficulty in the estimation due to the mortality rate by the statistical models (^{Vehviläinen et al., 2008}), a very low genetic proportion in the survival expression, or possibly, the damage in the structure of genetic family relationships when WSD was present.

The estimated heritabilities for HS in RES were 0.11 ± 0.06 and 0.06 ± 0.04, for WSD- presence and WSD-absence, respectively (Table 3); which were not statistically different from those estimated for the GRO line. The h² for HS in WSD-presence was higher than that estimated by ^{Caballero-Zamora et al. (2015)} 0.06 and that reported by ^{Gitterle et al. (2005b)}, who calculated values between 0.03 and 0.07. The h² for WSD-absence was concordant with other estimators for general survival in the same species (^{Campos- Montes et al., 2013}; ^{Zhang et al., 2017}; ^{Ren et al., 2020}).

The heritabilities of HS for both environments were consistent in both lines (Table 3), suggesting that there is no compression of the additive variance, in the lines, associated with the environment (^{Sae-Lim et al., 2016}). The genetic correlations between HS in WSD- presence and WSD-absence were not different from zero (P> 0.05), coinciding with that reported by ^{Vehviläinen et al. (2010)} in another aquatic species, which may suggest that survivals in both environments are independent characteristics, as suggested by ^{Thoa et al. (2015)}.

Genetic correlations between body weight and harvest survival

The genetic correlations by environment between BW and HS are shown in Table 4. For the estimation of these correlations, the common family effect was considered independent between environments.

The genetic correlation between the two characteristics could not be estimated in WSD- presence in the GRO line, possibly due to the affectation in the structure of the information associated with the high mortality presented in that line; whereas, for the RES line, it was not different from zero (0.04 ± 0.16), agreeing with the results of ^{Caballero-Zamora et al. (2015)}. In the case of WSD-absence for the GRO line, the r_G was not different from zero (-0.09 ± 0.92), unlike the one estimated in the RES line which was 0.57 ± 0.20, which was consistent with that estimated by ^{Campos-Montes et al. (2013)}, in commercial ponds, in the absence of SMB (0.56 ± 0.10). The rG estimated in the RES line was higher than that reported by ^{Yuan et al. (2018)}, ^{Gitterle et al. (2005a)} , and ^{Zhang et al. (2017)}. The differences between the genetic correlations in RES may be an indicator of changes in the variance components possibly associated with GEI, in turn related to the corresponding covariance, which would have implications in the response to correlated selection (^{Sae-Lim et al., 2016}).

Some authors highlight the importance of the creation of genetic lines in aquaculture (^{Nguyen et al., 2016}), the results of this study suggest that the selection indices for BW should take into account the genetic line used in the genetic improvement program. On the other hand, the estimation of genetic parameters related to BW must consider the presence of endemic diseases, such as WSD in shrimp culture and visualize HS in the presence and absence of WSD as independent characteristics, in both genetic lines.

In addition to changes in heritabilities and genetic correlations in both lines, their productivity was different in the environments studied, which could be interpreted as an indicator of phenotypic plasticity, which may be common in marine organisms as suggested by ^{Munday, (2013)}. It can be understood as the expression of different phenotypes in individuals with the same genotype, but under different environmental conditions (^{Munasinghe and Seneviratha, 2015}). Consequently, this phenotypic plasticity effect should be considered in shrimp genetic improvement programs, ensuring that the performance environments to be analyzed are as close to the production conditions as possible (^{Nguyen et al., 2016}).