24th Int. Symp. “Animal Science Days”, Ptuj, Slovenia, Sept. 21st−23rd, 2016. Acta argiculturae Slovenica, Supplement 5, 183–188, Ljubljana 2016 COBISS: 1.08 Agris category code: L01, L10 ESTIMATION OF (CO)VARIANCE COMPONENTS FOR AGE AT FIRST FARROWING AND FARROWING INTERVAL IN CZECH LARGE WHITE 1 Emil KRUPA 2, Eliška ŽÁKOVÁ 3, Zuzana KRUPOVÁ 4, Monika MICHALIČKOVÁ 5 Estimation of (co)variance components for age at first farrowing and farrowing interval in Czech Large White 1 The research was supported by project QJ1310109 of the Ministry of Agriculture of the Czech Republic. This work is dedicated to Dr. Jochen Wolf. 2 Institute of Animal Science, Přátelství 815, 104 00 Prague 10, Czech Republic; e-mail: krupa.emil@vuzv.cz 3 Same address as 2, e-mail: zakova.eliska@vuzv.cz 4 Same address as 2, e-mail: krupova.zuzana@vuzv.cz 5 Same address as 2, e-mail: michalickova.monika@vuzv.cz ABSTRACT We aimed to estimate the variance and covariance components for the original and transformed age at the first far- rowing (AFF) and farrowing interval in this study. The data from 25,094 sows (77,544 observations) of the Czech Large White pig breed between January 2000 and December 2015 provided by Czech Pig Breeders Association were used for the analyses. Data higher than the median were only transformed. The farrowing interval was evaluated separately from the first to the fourth parity (FI1–FI4). The heritabilities for the original traits were very low: 0.17, 0.11, 0.07, 0.06, and 0.06 for AFF and FI1–FI4, whereas those for the transformed traits were higher: 0.19, 0.14, 0.11, 0.11, and 0.12 for AFF and FI1–FI4, respectively. The phenotypic correlations between the traits were low, but significant. The estimated genetic correlations between all the farrowing intervals were clearly lower than one, indicating that all the farrowing intervals should be treated as different traits. Using the transformation procedure decreased the skewness and kurtosis of the original data in our study. The heritabilities of the analysed farrowing intervals were only increased owing to the transformation. Key words: pigs, breeds, Czech Large White, reproduction, farrowing interval, parity, genetic parameters 1 INTRODUCTION One of the main objectives in pig breeding is short- ening farrowing intervals, which makes it possible to in- crease the number of piglets per sow per year with a sig- nificant economic impact. Age at first farrowing, which includes age at first service, conception rate, and gesta- tion length, also has been used as a measure of the repro- ductive efficiency for gilts (Holm et al., 2005). Low her- itability of the farrowing interval (usually ranging from 0.01 to 0.05; Hanenberg et al., 2001; Serenius et al., 2003) is the main problem, as it provides only a small selection progress. Besides, conventional methods routinely ap- plied to estimate breeding values and genetic parameters are based on the assumption of normal distribution of measurements. However, an extremely skewed (unbal- anced) distribution was found for farrowing interval. Wolf (2012) presented a general transformation formula for interval traits connected with reproduction in pigs, which was an adaptation of the transformation suggested by Ten Napel et al. (1995) and was applied on the wean- ing-to-first-service interval in pigs by Hanenberg et al. (2001), Holm et al. (2005), and Lundgren et al. (2010). The frequently asked question in this regard is whether the trait should be taken as a single or repeated trait if measured more than once per animal. Traits should be considered as repeated if the variances between repeated measurements are the same and if genetic correlations are equal to one (Falconer and MacKay, 1996). The ob- jective of this study was to estimate the variance and co- variance components for original and transformed data Acta agriculturae Slovenica, Supplement 5 – 2016184 E. KRUPA et al. of age at first farrowing and from the first to the fourth farrowing interval. 2 MATERIALS AND METHODS The analyses were based on performance test data for the Czech Large White (CLW) breed. Data collected between January 2000 and December 2015 were ana- lysed. All data were provided by the Pig Breeders Associ- ation of the Czech Republic. Detailed information on the pedigree and populations of the analysed breed has been reported by Krupa et al. (2015, 2016). A flexible alloca- tion of the records to herd-year-season (HYS) classes as first described by Wolf et al. (2005) was applied separate- ly for each trait and was based on the season in which the farrowing date fell: March through May (spring), June through August (summer), September through Novem- ber (autumn), and December through February (winter) of the next year. The minimum records per class were 20. Data from 78 herds (average number of observations was 308.7 per herd) were used (eight herds were excluded due to low number of observations). The total number of HYS effect classes was 999 for age at first farrowing. The average number of observations per HYS class was 24 for age at first farrowing. Two reproductive interval traits, age at first farrow- ing (AFF) and farrowing interval, were analysed. The for- mula below presented by Wolf (2012) was used for data transformation, where only part of the data needed to be transformed (observations greater than the median) to overcome the skewness and to increase the heritability of the interval traits. This approach ensured that the dif- ference between the maximum and median of the trans- formed data was equal to the difference between the me- dian and the minimum. The equation for this method then is where Z  is the transformed value and y is the original value of the trait and ymed, ymin, and ymax are the median, minimum, and maximum values. The farrowing intervals in different parities (FI1–FI4) were treated as different traits. Not all sows had data available for each trait; 6,355 sows had complete data structure (values for all traits). The five-trait animal model was used to estimate the vari- ance and covariance components for the original (AFFo and FI1o–FI4o) and transformed (AFFt and FI1t–FI4t) traits. The Pearson’s correlations coefficients between the phenotypic values of the evaluated traits were computed using CORR and the general linear model (GLM), both implemented using the statistical package SAS® (SAS In- stitute Inc., 2008); these coefficients were used to derive the fixed part of the model. After these procedures, the following effect remained in the model equations: fixed effect of the linear and quadratic regression on lactation length (used only for the farrowing interval trait), breed of service sire (four classes), mating type (two classes: artificial insemination and natural mating), random ef- fect of HYS, and random effect of the animal. The average number of sires per herd was 46.37. The average number of sires per class of the HYS effect was 6.71. The follow- ing criteria were used for the mentioned effect: breed of service sire is Czech Large White, Czech Landrace, or Duroc, the sire line is the Czech Large White breed, ges- tation length is 100–130 days, first farrowing was within 260–500 days, and farrowing interval varied from 120 to 350 days; parities greater than four were not considered. The total number of piglets born varied from 4 to 22. Af- ter applying all the criteria and forming the HYS classes, the total number of sows was 23,874. The number of ob- servations for age at the first farrowing and the farrowing interval was 76,860. Thus, the average number of litters per sow was 3.22. The pedigree was tracked back to the year 1980. The total number of animals in the pedigree was 37,199. The number of base animals (animals with both parents unknown) was 2,377. The number of inbred animals was 21,803, where 21,245 animals had less than 5 % inbreeding. The average inbreeding was 1.24 %. Vari- ance and covariance components were estimated using the restricted maximum likelihood and were optimised using a quasi-Newton algorithm with analytical gradi- ents (Neumaier and Groeneveld, 1998) as implemented in the VCE 6.0 program (Groeneveld et al., 2008). 3 RESULTS AND DISCUSSION Descriptive statistics for the original and trans- formed traits are summarised in Tables 1 and 2, re- spectively. The average length of the original age at first farrowing was 369.6 days. In previous papers, Serenius and Stalder (2004) and Serenius et al. (2004) published slightly lower ages at first farrowing for Finish Large White sows (368.5 days and 362.1 days, respectively). In contrast, Knauer et al. (2011) reported higher age at first farrowing (405.0 days) for 801 gilts of Landrace-Large White crosses. The low number of observations, differ- ences in the breeds, and the restriction for data editing               med med med medmed med yyfor yy yyyyy yyfory z )1ln( )1ln()( max min           med med med medmed med yyfor yy yyyyy yyfory z )1ln( )1ln()( max min Acta agriculturae Slovenica, Supplement 5 – 2016 185 ESTIMATION OF (CO)VARIANCE COMPONENTS FOR AGE AT FIRST FARROWING ... INTERVAL IN CZECH LARGE WHITE could explain the slight differences in age at first far- rowing between the studies. Based on original data, the first farrowing interval was 165.8 days on average. Far- rowing intervals in the next parities were slightly shorter and varied from 159.0 days (FI2o) to 157.7 days (FI4o). This was similar to the trend observed by Serenius et al. (2003) from the first to the third farrowing interval in Finish Large White sows. With regard to the transformed data, a slight decrease in the average farrowing interval over parities (from 158.6 to 153.1 days for FI1 to FI4, respectively) was observed. For all the traits, skewness as well as kurtosis and the standard deviation decreased after transformation, except for age at first farrowing, where the standard deviation as a parameter of variability remained almost the same. However, farrowing intervals slightly decreased, and the average age at first farrow- ing slightly increased to 375.7 days when comparing the original and transformed data. Nevertheless, the results indicate that the main objective of data transformation was achieved in our study. The relative proportion of phenotypic variance ex- plained by the used effects for all the traits is summarised in Table 3. The coefficient of determinations for the orig- inal data reached lower values (35 %, 28 %, 26 %, 25 % and 24 % for AFFo and FI1o–FI4o, respectively) compared to those of the transformed ones (37 %, 38 %, 38 %, 39 % and 39 % for AFFt and FI1t–FI4t, respectively). The high- est portion of phenotypic variability was explained by the HYS effect for age at first farrowing (90.5 % for original and 92.1 % for transformed age at first farrowing). The herd, year, and season effects also explained the high proportion of variability for other traits (generally more than 60 %) when they were considered as one joint ef- fect. The relatively large differences in the explained vari- ability between pairs of the original and the transformed traits were observed for the length of lactation (higher for the transformed observations) and for the mating type (higher for the original observations), especially for far- rowing interval traits. All the effects were highly signifi- cant with p < 0.001; the breed of service sire for both age at first farrowing traits and the mating type for the third and the fourth farrowing interval were significant with p < 0.05. The variance components for the original and the AFFo 1 FI1o 2 FI2o 3 FI3o 4 FI4o 5 Total number of sows 24,094 17,910 13,643 10,028 7,142 Minimum 286.00 121.00 120.00 120.00 123.00 Mean 369.57 165.84 159.00 158.09 157.71 Median 362.00 154.00 151.00 150.00 150.00 Maximum 500.00 350.00 346.00 350.00 344.00 Standard deviation 35.71 31.49 25.13 24.56 24.00 Skewness 1.03 2.44 3.14 3.26 3.32 Kurtosis 0.99 6.91 12.33 13.13 14.05 1 original age at first farrowing, 2 original first farrowing interval, 3 original second farrowing interval, 4 original third farrowing interval, 5 original fourth farrowing interval. Table 1: Descriptive statistics for the original data AFFt 1 FI1t 2 FI2t 3 FI3t 4 FI4t 5 Total number of sows 24,094 17,910 13,643 10,028 7,142 Minimum 286.00 121.00 120.00 120.00 123.00 Mean 375.73 158.63 154.65 153.88 153.11 Median 362.00 153.00 151.00 150.00 150.00 Maximum 438.00 186.03 182.00 180.00 177.00 Standard deviation 36.57 13.33 11.12 10.39 9.59 Skewness 0.09 0.31 0.56 0.54 0.50 Kurtosis −0.42 −0.24 −0.76 −0.74 −0.71 1 transformed age at first farrowing, 2 transformed first farrowing interval, 3 transformed second farrowing interval, 4 transformed third farrowing interval, 5 transformed fourth farrowing interval. Table 2: Descriptive statistics for the transformed data Acta agriculturae Slovenica, Supplement 5 – 2016186 E. KRUPA et al. transformed traits are shown in Tables 4 and 5. The esti- mated heritabilities for the original traits were low with a tendency for heritability of the first farrowing interval to be greater than that at the subsequent intervals. Simi- lar values were reported by Serenius et al. in 2003, with similar inclination (0.13, 0.06, 0.00, and 0.04 from the first to the fourth farrowing intervals). Serenius et al. claimed that this tendency might have been caused by was 0.10, 0.03, and 0.02 from the first to the third far- rowing intervals, respectively, when the length of lacta- tion was assumed as an effect in the model (0.00, 0.02, and 0.00 from the first to the third farrowing intervals, respectively, when lactation length was not considered as an effect in the model). Cavalcante-Neto et al. (2009) also estimated a heritability of 0.02 for the first farrow- ing interval in a Brazilian commercial hybrid when the AFFo AFFt FI1o FI1t FI2o FI2t FI3o FI3t FI4o FI4t LL - - 6.56 13.02 12.83 22.31 11.24 21.49 17.67 30.33 HYS 90.51 92.12 74.98 72.38 69.90 68.53 68.97 69.54 60.64 60.39 BSS 0.12* 0.10* 2.09 2.01 2.34 1.64 1.21 0.91 1.07 0.50 MT 6.68 5.37 12.84 9.83 13.62 6.66 17.47* 7.43* 17.94* 7.23* TNB 2.69 2.40 3.52 2.76 1.31 0.85 1.10 0.64 2.68 1.55 * (p < 0.05). All other effects are highly significant (p < 0.001). LL: Length of lactation, HYS: Herd-Year-Season, BSS: Breed of service sire, MT: Mat- ing type, TNB: Total number of born piglets. For traits abbreviations, see Tables 1 and 2. Table 3: Relative proportion of phenotypic variance explained by effects for all traits AFFt FI1t FI2t FI3t FI4t Additive genetic effect (Heritability) 0.19 ± 0.011 0.14 ± 0.010 0.11 ± 0.011 0.11 ± 0.012 0.12 ± 0.013 Proportion of variance for HYS effect 0.18 ± 0.008 0.08 ± 0.006 0.08 ± 0.007 0.08 ± 0.008 0.06 ± 0.008 Proportion of variance for residual effect 0.63 ± 0.011 0.78 ± 0.010 0.81 ± 0.010 0.81 ± 0.012 0.82 ± 0.013 For traits abbreviations, see Table 2. Table 5: Variance components for the transformed traits AFFo FI1o FI2o FI3o FI4o Additive genetic effect (Heritability) 0.17 ± 0.011 0.11 ± 0.010 0.07 ± 0.009 0.06 ± 0.010 0.06 ± 0.011 Proportion of variance for HYS effect 0.16 ± 0.007 0.06 ± 0.006 0.05 ± 0.005 0.05 ± 0.005 0.03 ± 0.005 Proportion of variance for residual effect 0.67 ± 0.012 0.83 ± 0.010 0.88 ± 0.010 0.89 ± 0.010 0.91 ± 0.011 For traits abbreviations, see Table 1. Table 4: Variance components for the original traits the decreasing numbers of observations in later parities, leading to a deterioration of the data structure, i.e., fewer observations per HYS class leading to poorer connect- edness of the data. However, in our case, it is likely that it was caused because the total number of observations decreased but the number of observations within a joint HYS effect class did not decrease (average number of ob- servation per class was 24, 23, 22, 22, and 22 for AFF and FI1–FI4) due to flexible HYS class formation. In addi- tion, genetic relationship among herds is sufficient in the Czech Large White population, as observed in our previ- ous study (Krupa et al., 2016). Our results for the original farrowing interval are also consistent with the outcomes reported by Tholen et al. (1996), where the heritability permanent effect was not considered in the model, and estimated it to be 0.00 when this effect was added to the model. All the above-mentioned results were estimated for non-transformed data. The transformation procedure had negligible influ- ence on the heritability of age at first farrowing, and the heritability of the transformed AFF was very similar to that of the original one (0.17 and 0.19 for AFFo and AFFt, respectively). Transformation of the farrowing interval had a higher positive impact: heritability of FI1t–FI4t was 0.14, 0.11, 0.11, and 0.12, respectively. Proportions of the variances of the HYS effect were low (0.03–0.18) and were similar in the original and transformed traits. Proportions for residual variances reached high values Acta agriculturae Slovenica, Supplement 5 – 2016 187 ESTIMATION OF (CO)VARIANCE COMPONENTS FOR AGE AT FIRST FARROWING ... INTERVAL IN CZECH LARGE WHITE for all the traits. The phenotypic and genetic correlations between the analysed traits are summarised in Tables 6 and 7. The phenotypic correlations were slightly higher for the transformed traits, but had very low values. The genetic correlations between AFF and FI1–FI4 traits were low or moderate, whereas those between the FI1– FI4 traits showed high values (0.66–0.94); all the values were clearly lower than one. The phenotypic Pearson’s correlation coefficients between a pair of original and transformed traits were also calculated. The correlation coefficients reached values of 0.93, 0.83, 0.82, 0.81, and 0.80 for the original and transformed AFF and FI1–FI4, respectively. All the phenotypic correlation coefficients were highly significant (p < 0.001). Previously, Serenius et al. (2003) reported phenotypic and genetic correla- tions of farrowing interval between different parities. The genetic correlations estimated in their study varied be- tween parities from −0.28 to 0.84, but with large standard errors and correlations between the fourth and previous farrowing intervals fluctuating around zero. Consistent with our results, Serenius et al. (2003) also found low phenotypic correlations between parities, and based on the fact that the genetic correlations between farrowing intervals were estimated to be lower than one, concluded that farrowing intervals over parities should be treated as different traits. This is in agreement with our results for the farrowing intervals. Further, Hanenberg et al. (2001) also evaluated farrowing interval and its parts as gesta- tion length, interval from weaning to first mating, and interval from first mating to farrowing on different pari- ties and observed high genetic correlations among pari- ties for all the studied traits, except for interval from first mating to farrowing. 4 CONCLUSIONS Using the transformation formula decreased the skewness and kurtosis of the original farrowing interval data. 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