Estimation of parameters
As presented in
Table 2, WF that included fixed weaning age effects for 7 traits, produced significantly better AIC (Akaike Information Criterion) (
Akaike, 1973) (a lower value represents a better fit in the model) than models that had random weaning age effects. The increased number of parameters due to random weaning effects in WU and WC partly contributed to the higher AICs. When included as an uncorrelated (WU) instead of a correlated (WC) random factor in the model for weaning ages, a decrease of AIC resulted. The increased estimates of phenotypic variances by WU and WC that occurred were partly due to the inclusion of weaning age variances. Estimates of phenotypic variances were increased for WF vs. WU vs. WC for all traits. Greater differences for WU vs. WC than WF vs. WU were observed in the traits except DGWT and BFAT. Direct genetic variances of the traits calculated by WF were higher than those by other models, except DGBW and BFAT. For DGPT, DGBT, DGWT, and BFAT, analysis using WF resulted in similar direct genetic variance estimates as with using WC, while WU yielded close estimates with WC for the rest of the traits. Conversely, WF produced the lowest maternal genetic variance estimates for DGBW, DGPT, DGBT, and DGWT. Overall, estimates of direct and maternal genetic variance components for the traits were generally similar across the models.
Without exception, the variances due to weaning age were increased for WU vs. WC. The estimates by WC were increased by 1.1 to 6.5 times of the estimates by WU, which descended in the order DGBW, DGBP, DGBT, DGWP, DGPT, BFAT, and DGWT. The variance of the traits including growth of suckling phase increased, and the variances of the growth as time passed after weaning were reduced. The weaning age variance of DGBW reflects the growth of the suckling period determined by weaning. That is, the weaning age decides the cutting point on the growth curve of pigs, which divides into growths of suckling and nursery. Consequently, weaning age directly affects the rate of growth during the suckling phase. Nevertheless, WU unexpectedly produced the lowest weaning age variance for DGBW. WU also produced unreasonable estimates of weaning age variance fraction and correlations for DGBW and this issue will be mentioned later. The error variances for all traits, however, were similar across the models.
The direct animal and maternal genetic heritabilities for most of the traits by WF were highest among the models, as expected from the estimates of variance components in
Table 2, whereas the standard errors of direct and maternal genetic heritabilities did not show noticeable differences across the models (SE presented only for WC). The estimates of direct genetic heritabilities by WC for DGBW, DGWP, and DGPT were 0.05, 0.13, and 0.13, respectively, which are considerably smaller than the estimates (0.06, 0.20, and 0.16, respectively) by WF and the estimates (0.24, 0.41, and 0.34, respectively) obtained by
Rosendo et al. (2007) for Large White pigs. As time elapsed from birth, the direct genetic heritabilities by all models gradually increased. Conversely, the estimates of maternal genetic heritabilities by the models decreased (0.38, 0.14, and 0.07 for DGBW, DGWP, and DGPT by WC, respectively) as the pigs aged. This decreasing tendency in maternal genetic heritability is consistent with the results of
Rosendo et al. (2007). The direct and maternal genetic heritabilities for DGBT by WC, which is used as the ADG of on-farm test pigs in Korea, were 0.20 and 0.10, respectively. The direct and maternal genetic heritabilities of BFAT by WC were 0.17 and 0.05, respectively. Back fat thickness, along with body weight, was measured on a single occasion at the end of the performance test. Therefore, it is possibly less influenced by maternal genetic effects than by direct genetic effects. Even though DGWT was a pool of DGWP and DGPT in ADG, the direct genetic heritability of DGWT was higher than that of both DGWP and DGPT. Nevertheless, both the direct and maternal genetic heritabilities of DGWT (0.21 and 0.08, respectively by WC) were considerably lower than the estimates (0.41 and 0.21) of
Rosendo et al. (2007). Further, DGBT exceeded DGBW, DGWP, and DGPT in direct genetic heritability.
The fractions of weaning age variances by WU and WC are presented in
Table 3. The values of fractions by WC exhibited the following descending order: DGWP, DGBP, DGBW, DGWT, DGPT, DGBT, and BFAT. In contrast, with WU, the fractions descended in the order DGWP, DGWT, DGPT, DGBP, BFAT, DGBW, and DGBT. Although the orders of DGWP (1st) and DGBT (6th) in WU and WC were the same, the orders of DGBP and DGBW differed between the models, leading to the largest differences in the fraction values. The largest difference occurred in the suckling phase (DGBW), and influenced DGBP and DGBT, which includes growth of the suckling phase. This could be caused by unreasonable estimates by WU, as previously mentioned. The increases of the fractions by WC over WU ranged from 1.4 to 5.5 times, and the increases in standard errors ranged from 1.4 to 5.0 times. The fractions for the ADGs and back fat thickness estimated using WC ranged from 0.09 to 0.35 across the traits. Weaning age variance fraction represents portion due to weaning in deviation of a phenotypic record from mean. The fractions for DGBW, DGWP, and DGBP were relatively high (0.22, 0.35, and 0.29, respectively). Weaning age greatly influenced post-weaning growth and provided a fair amount of variation in pre-weaning growth.
The error variance fractions for DGBW, DGWP, DGPT, DGBP, DGBT, DGWT, and BFAT, estimated using WC were 0.43, 0.38, 0.67, 0.40, 0.57, 0.54, and 0.31, respectively, and the decreases in the error variance fractions estimated using WC from WU were 0.09, 0.10, 0.05, 0.12, 0.07, 0.02, and 0.01, respectively. Consequently, including correlated rather than uncorrelated random weaning age effects in the models resulted in improvement in the fitness of the model. Even though the fractions of error variances were reduced by WC, the standard errors of the fractions slightly and insignificantly increased (data not presented).
The direct and maternal genetic correlations were estimated and compared across the models (data not presented). The estimates of the direct genetic correlations by the models were not significantly different, and the difference ranged from 0 to 0.13, which were relatively low, compared with the sizes of correlations. In the maternal genetic correlations, the estimates by WF and WU were similar, and the differences ranged from 0.00 to 0.03. However, the differences of the estimates by WF and WC ranged from 0.00 to 0.41, and further, no change of positive and negative sign in the estimates of correlations across the traits was observed except the correlation between DGWT and BFAT. The standard errors of direct genetic correlation by WC from WF and WU reduced from −0.007 to 0.019 and from −0.003 to 0.014, respectively. Further, the standard errors of maternal genetic correlation by WC from WF and WU were reduced from −0.001 to 0.006 and from −0.002 to 0.003, respectively, which were a trivial benefit from WC.
The estimates of direct and maternal genetic correlations among the ADGs by WC in
Table 4 were positive without exception, consistent with the results of
Tomiyama et al. (2009). The direct and maternal genetic correlations among the overlapped ADGs, such as DGBP, DGBT, and DGWT, were relatively high. The direct genetic correlations of DGBW with DGWP and of DGPT with DGBW and DGWP were moderate (0.48, 0.43, and 0.56, respectively). The correlations of BFAT with DGBW, DGWP, and DGBP were 0.11, 0.33, and 0.33, respectively. On the other hand, the direct genetic correlations of BFAT with DGPT and DGWT (growth in the later stage) were negative, and consistent with the estimates of
Tomiyama et al. (2009). The negative correlations implied that only the ADG of the later stage could be improved along with back fat thickness by selection on the direction of increased growth. There was, however, no significant difference from null correlations because of their large standard errors. Maternal genetic correlations between DGBW and DGWP, DGWP and DGPT, and DGBW and DGPT were lower than the corresponding direct genetic correlations. Generally, the maternal genetic correlations of BFAT with the ADGs were considerably weaker within the range of −0.03 to 0.16, which could be partly explained by the low heritability (0.05 in
Table 3) of maternal genetic effects in BFAT.
The definition of a weaning age correlation between two traits is the covariance between two traits divided by the square root of the product of the variances of the two traits due to weaning age. The weaning age correlations for the traits belong to the category of correlations due to environment or management, and summarize the relationship of traits due to weaning age effects. Generally, standard errors of the correlations were high due to small number of weaning ages (17 levels) and ranged from 0.04 to 0.32 in WU (data not presented) and from 0.05 to 0.53 in WC (presented in
Table 5). The most drastic changes in the correlations between WU and WC were observed in the correlation of DGBW with other ADGs. The correlations by WU ranged from −0.03 to −0.52. On the other hand, the correlations by WC ranged from 0.13 to 0.50. As previously mentioned, unreasonable correlation estimates were also produced by WU. Weaning weight has positive genetic and management influences on post-weaning performance (
Ward et al., 1964;
Main et al., 2004;
Smith et al., 2007;
Smith et al., 2008;
Tomiyama et al., 2010). Further, weaning weight reflects the growth of the suckling phase. Therefore, positive weaning age correlations are expected, as estimates of WC.
The weaning age correlations between ADGs of different stages (when no overlapping was allowed) by WC were low: 0.13, −0.03, and 0.09 for DGBW and DGWP, DGWP and DGPT, and DGBP and DGPT, respectively. Weaning age correlations between growths of overlapped stages by WC, such as DGBP and DGWP, and DGBT and DGWP, were high and ranged from 0.47 to 0.91. Back fat thickness had negative correlations with post-weaning growth and positive correlations with growth in the suckling phase. No research has been conducted to evaluate post-weaning performance with the growth rate of the suckling phase. Rather, influences of weaning weight or age on post-weaning growth performance have been studied.
Lynch et al. (1998) stated that weaning weight was poorly, but positively, related to post weaning performance (p> 0.10), and weaning age seemed to be more critical. Since weaning weight is a function of weaning age and the growth rate of the suckling period, the following inference from the results would be possible. The positive weaning age correlations of DGBW with other ADGs in
Table 5 reflect the positive relationship of growth of suckling with post-weaning growth due to weaning age, as was also observed in positive environmental correlations.
Environmental correlations by WC presented in
Table 5 were not significantly different from the estimates and its standard errors by WF and WU (data not presented). General trends of environmental correlations across the traits are close to that of weaning age correlations, even though some differences exist.
Weaning age effects
Weaning was most frequently done at 21 d as shown in
Figure 1, and the skewness and kurtosis of the distribution were 0.80 and −0.15, respectively, representing a lighter tail on the right side. The slope of the regression line in
Figure 1 represents the mean change in weaning weight over the weaning ages, and the thick dotted curve signifies mean weaning weight for each weaning age day. The models estimated weaning age effects for DGBT and back fat thickness and these are presented in
Figure 2. The weaning age effects of DGBT estimated using WC were generally greater than those estimated using WU. For all traits, the estimates of fixed effects deviated markedly from the estimates of random effects (data not presented). The estimates of weaning age effects for all traits by the models produced similar traces, and the differences in the estimates, however, substantially increased by WF, resulting in higher fluctuations compared with the traces by WU and WC. The averages of weaning age effects of the traits by WF and WU were zero, while the averages for DGBW, DGWP, DGPT, DGBP, DGBT, DGWT, and BFAT by WC were 7.8 g, 8.3 g, 16.3 g, 8.2 g, 9.0 g, 11.2 g, and 0.04 mm, respectively, which, although not necessarily, were not zeros due to correlated weaning ages.
The estimated weaning age effects are presented in
Table 6. The maximum values of weaning age effects for DGBW, DGWP, DGPT, DGBP, DGBT, DGWT, and BFAT were as follows: 27.4 g at 24 d, 81.6 g at 32 d, 44.7 g at 29 d, 27.4 g at 32 d, 21.0 g at 27 d, 53.0 g at 32 d, and 0.74 mm at 17 d, respectively. Similarly, the minimum values of weaning age effects for DGBW, DGWP, DGPT, DGBP, DGBT, DGWT, and BFAT were −19.5 g at 32 d, −56.4 g at 17 d, −41.9 g at 17 d, −22.4 g at 18 d, −16.5 g at 17 d, −44.7 g at 17 d, and −1.15 mm at 32 d. These results were obtained in a typical Korean swine breeding stock farm, which may have better conditions for health and management status than commercial herds. If the improvement in growth performance were partially a result of increased immunity, the active immunity, induced by delayed weaning age, could possibly expand the positive weaning age effects in commercial production systems.
The regression of weaning age effects on weaning ages are presented along with the R-square values of the regression in
Table 7. These slopes are intended to provide a reference that succinctly illustrates the rate of linear improvement in growth performance as weaning age increases. The regression coefficients of the traits were similar across the models, but the R-squares of regression on the estimates by WF were considerably smaller, implying a higher fluctuation than other models in the traces of the traits. The weaning age effects of DGPT and DGBT in Berkshire pigs increased continuously (4.41 and 1.50 g/d increase in weaning age, respectively, by WC) with some fluctuations, and BFAT was reduced by 0.106 mm/d increase in weaning age. Similar results have been reported in dietary and management experiments (
Main et al., 2004;
Fangman et al. 1996), indicating positive impacts on post-weaning weight or growth.