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Genetic Analysis of Dystocia and Calf Mortality in Israeli-Holsteins by Threshold and Linear Models

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Genetic Analysis of Dystocia and Calf Mortality in Israeli-Holsteins by Threshold and Linear Models J. I. WELLER 1 I. MISZTAL and D. GIANOLA Department of Animal Sciences University of Illinois Urbana 61801 AB ST R ACT
Calvings of 106,751 Israeli Holstein heifers were analyzed for dystocia and calf mortality, scored dichotomously, and a composite trait, scored trichotomously. Dystocia was also studied with 146,973 second and third parity records. Models fitted included herd-year-season, sex of calf, calving age, calving month, sire of cow, sire of calf, and groups of sire of cow and of calf. Herd-year-season, sire of cow and calf, and residuals were ran- dom with diagonal variance-covariance matrices. Herd-year-season variance was assumed to be 10 of the residual com- ponent. Other variance components were estimated by REML for linear models and by the counterpart of REML for thres- hold models. Heritability estimates were two to five times greater in threshold than in linear models, but correlations between corresponding sire evaluations were all >.9. Linear model sire evalua- tions were skewed positively, whereas threshold model evaluations had sym- metrical distributions. Heritability for dystocia was greater in first than in later parities. Correlations between first and later parity sire evaluations were <.5. Thus, the genetic control of dystocia seems to be different for heifers and cows. Correlations between sire of cow and calf evaluations were <.3. Correla- tions between dystocia and calf mortality evaluations were about .7. Received January 7, 1988. Accepted May 9, 1988. 1 Institute of Animal Sciences, Agricultural Re- search Organization, The Volcani Center, Bet Dagan, Israel 50250.
INTRODUCTION
Dystocia (DC) and calf mortality (CM) are of major economic importance to dairy far- mers. These traits have low heritabilities, high genetic correlation, and significant residual cor- relation (1, 2, 13, 17, 18, 19, 20, 21). Many studies have found the effect of sire of calf to be larger than that of the sire of the cow (1, 13, 17, 18, 19, 21). Although both traits are scored categorically, most studies have used standard mixed model methodology, even though this assumes the data to have a continuous distribu- tion. Theoretical problems involved in this type of analysis have been described at length (6, 7). Several studies have suggested that the thres- hold model (TM), which assumes the existence of an underlying normal variable, is theore- tically appropriate and computationally feasible for genetic analysis of categorical traits (3, 4, 6, 7, 8, 9, 10, 11, 14, 15, 16). However, only a few studies have actually applied this model to analysis of field data (4, 11, 14). Because TM equations are nonlinear and involve normal probability functions, computational com- plexity and computing resources required are greater than in a linear model (LM) analysis. Furthermore, TM genetic evaluations also require accurate estimates of variance compo- nents in the underlying scale. Although meth- ods have been developed that are similar to REML, computations are more complex than those in standard REML algorithms (9, 10). Limitations in computing resources may pose a serious problem for sire evaluation based on large field data sets. However, recent develop- ments in computers and programming tech- niques have made large-scale TM analyses feasible (16). The objectives of this study were to com- pare TM and LM analyses of calving traits using a large field data set of Israeli Holsteins, to esti- mate genetic parameters for these traits and to find the model of choice for routine genetic evaluation. 1988 J Dairy Sci 71:2491-2501 2491
2492 WELLER ET AL.
M TERI LS ND METHODS
Data were 347,691 first through third parity calvings of milk-recorded Israeli Holsteins, calving between January 1978 and June 1985. Both DC and CM were scored as dichotomous traits. Dystocia was scored as 0 if the calving was normal or as 1 if it was difficult; CM was scored as 0 for a live birth or as 1 if the calf died within 48 h of birth. Records were deleted from the analysis for the following reasons: 1) sire of cow or of calf was unknown, 2) mul- tiple births, 3) either CM or DC was undefined, 4) the calf was abnormal or died due to causes not related to calving, 5) abortions, 6) calvings of daughters of sires with less than 20 daughter calvings, and 7) calvings in which the sire of the calf sired less than 20 calves. Dystocia was recorded in all but two calvings. However, 2.1% of the records were deleted because either calf fate was unknown, the calf was abnormal, it died due to causes unrelated to calving, or it was aborted. There are no natural service matings in Israel, and about 1000 inseminations are performed for each young sire tested. Therefore restrictions 6 and 7 eliminated 1274 observations, consisting of recording mistakes, progeny of a few matings from imported semen, and progeny of sires tested at the boun- daries of the time period considered. In total, 27% of the records (93,967) were deleted, mostly because the sire of the calf was unknown. All analyses were by both TM and LM. Dystocia was analyzed using all parities to- gether and first and later parities separately. Based on these results, it was decided to analyze CM using only first parity calvings. Because these traits have a high genetic correla- tion, a composite trait (CT) was also analyzed. In the LM analysis, CT was the sum of the DC and CM scores; thus, each calving received a score of either 0, 1, or 2. In the TM analysis, it was assumed that these tbree classes were ordered so that the model included two thres- holds. Thus five analyses were run for each of the two statistical methods: 1) DC, all parities; 2) DC, first parity; 3) DC, later parities; 4) CM, first parity; and 5) CT, first parity. The fol- lowing model was used for analysis: Yijklmnopq = HYSi + GSj + SIREjk + GSC I + SCIm + S n + A o + Mp + eijklmnop q [1] where: Yijklmnopq = record on cow ijklmnopq; HYS i = random effect of herd-year- season i; GSj = fixed effect of group j of sires of cows; SIREjk = random effect of sire of cow k in group j ; GSC 1 = fixed effect of group 1 of sires of calves; SClm = random effect of sire of calf m in group l; S n = fixed effect of sex n; A o = fixed effect of calving age o; Mp = fixed effect of calving month p; and eijklrnpopq = random residual. Calving seasons were October to March, and April to September. Sires were grouped by year of birth, with all sires born prior to 1972 in group 1. Groups 2 to 7 included all sires born during each subsequent 2-yr interval. Twelve classes were defined for calving month. Be- cause HYS was random, there was no con- founding between HYS and calving month. The first 10 calving ages were for primiparous cows representing calving ages from
2
to 30 mo. The 1st also included cows calving prior to 21 too, and the lOth included cows that calved after 30 mo. In the all parities analysis, second and third parity cows were included in classes 11 and 12, respectively, regardless of calving age. In the latter parity analysis, only two classes were defined for this effect. Analysis was facilitated by assuming that all random effects were mutually uneorrelated with diagonal dispersion matrices. It was fur- ther assumed that the variance of the HYS effect was known and equal to 10% of the residual variance. This value is similar to esti- mates calculated from US data (4). Using these Journal of Dairy Science Vol. 71, No. 9, 1988
GENETIC ANALYSIS OF CALVING TRAITS 2493 assumptions, HYS effects, which had many levels in all analyses, could be absorbed. The assumption of diagonal dispersion matrices was inaccurate for the SIRE and SC effects, because sires were related. The assumption of zero correlation between effects was also an approximation, because several studies have found nonnegligible correlations between SIRE and SC effects (13, 17, 18, 21). A program based on principles described by Misztal et al. (16) and adapted to the CRAY XMP-48 supercomputer, was used for analysis. The SIRE, SC, and residual variance compo- nents were estimated by REML for LM model analyses and by the counterpart of REML for TM (9). After absorption of HYS effects, coefficient matrices were inverted at each round of iteration for both models. In TM analyses, interation involved Fisher's scoring and a modification of the expectation-maximization (EM) algorithm for variance components (16). Two to three EM rounds were performed per round of Fisher scoring iteration. At least six rounds of REML iteration in LM and six rounds of Fisher scoring iteration in TM were com- pleted for each analysis. Iteration stopped when the change in all variance components was less than 1 of the values in the previous round. Sire evaluations were computed as the sum of the sire and sire group effects. Heritability (h 2) as a trait of the cow was calculated as: h 2 = 4 VAR(SIRE)/ [VAR(SIRE) + VAR(SC) + VAR(HYS) + VAR(E)] [2] where VAR(SIRE), VAR(SC), VAR(HYS), and VAR(E) are the SIRE, SC, HYS, and residual variance components, respectively. Herita- bility as a trait of the calf was computed in a similar manner except that VAR(SC) replaced VAR(SIRE) in the numerator. Threshold model heritabilities for dichotomous traits were also obtained dividing LM estimates by: z2/[p(1 - p)] [3] where z is the ordinate of the standard normal density function corresponding to p, the ob- served incidence in the first category (3). For CT, a trait with two thresholds, a formula of Gianola (7) was used. The unit of measurement of estimates and predictions in TM is the residual standard devia- tion. To facilitate comparison between LM and TM estimates, the TM solutions were multiplied by the square root of the corresponding LM residual variance component so that the units of the two models would be equivalent. Results obtained with the two different methods of analysis were compared in terms of ratios of variance components (heritability), the variance and skewness of the estimates and evaluations, and correlations between the solutions or evaluations. Although all sires included in the full data set had 20 or more calving records, some sires in the first and later parity subsets had less than 20 records. Therefore, correla- tions between sire evaluations were also com- puted for sires with at least 20 records in both analyses, and for sires with repeatability based on LM greater than .6. Repeatability was calcu- lated as 1 - PEV/VC, where PEV is the predic- tion error variance of the SIRE or SC effect, and VC is the corresponding variance compo- nent. The PEV was computed as the diagonal dement of the inverse of the coefficient matrix at the final round of iteration times the residual variance.
R SU LTS
Basic statistics for the edited data set are in Table 1 for all parities combined and for first and later parities separately. Incidences of DC and CM for all parities were 5.1 and 5.4 , respectively; the incidence of either DC or CM in a single calving was 7.9 . Frequencies were higher for heifers, which is consistent with pre- vious studies (1, 4, 13, 17, 20, 21). The distribution of records by level of fixed effects is presented in Table 2 for all parities combined, and for first and later parities separately. The ratio of male to female calves was 1.114, which is consistent with the general situation in the Israeli Holstein popula- tion. Calvings were less frequent in the early summer months because fertility is lowest in late summer. Ten rounds of Fisher scoring iteration for TM and nine rounds of REML iteration for LM were performed for the analysis of DC in the complete data set. Computing times on a CRAY XMP-48 were about 12 and 4 rain for TM and LM, respectively, and less for the single Journal of Dairy Science Vol. 71, No. 9, 1988
2494 WELLER ET AL. TABLE 1. Basic statistics of the data sets analyzed. Parity All 1 2 + 3 Incidence ( )
of: Dystocia 5 08
8.05 2.92 Calf mortality 5.43 7.66 3.81 Dystocia + calf mortality 2.59 4.17 1.44 Number
of:
Records 253,724 106,751 146,973 Herd-year-seasons 8053 5882 7748 Sires
of cow
436 377 399 Sires of calf 386 329 368 parity analyses. Computing times on most standard mainframe computers would be larger (16). Estimates of SIRE and SC variance compo- nents, as a fraction of the residual variance, and of heritabilities are in Table 3 for all analyses. Variance component estimates by LM were similar to those found in previous studies (1, 2, 13, 18, 19, 20, 21). Heritability estimates were higher for TM than for LM in all cases. The TM heritability estimates obtained using the coun- terpart of REML were in most cases slightly lower than the values obtained from the LM estimates using the equations of Dempster and Learner (3) and Gianola (7). Except for the analysis of CM by TM, the SC variance compo- nent was always larger than the SIRE compo- nent. The SIRE and SC variance component estimates for DC based on later parities were less than a third of the corresponding first parity estimates with TM and even less for LM. Variance components using first parity records were also larger than with all parities included. Heritability of CT was higher than that of CM in both LM and TM. It was higher than that of DC only as a trait of the SIRE in the LM analyses. Solutions for fixed effects for first parity DC and CM are presented in Table 4. Similar trends were evident for both TM and LM and for both traits. As in previous studies (2, 4, 13, 14, 18, 19, 20, 21), incidence of both DC and CM was higher for births of male calves. Dysto- cia and CM occurred in 10.9 and 10.2 of male calves and in 5.0 and 4.9 of female calves. As expected, both DC and CM tended to decrease with increasing calving age. Dystocia was lowest in June and highest in February and March. For CM May was most favorable and February least favorable. These results differed from the effect of season on production and fertility. Due to heat stress, both production and fer- tility are lowest in Israel in the late summer. No clear trends were evident for the group of SIRE or SC solutions. Correlations between TM and LM estimates of fixed effects are given in Table 5. Correla- tions are not given for the effects of sex for all analyses and calving age for the later parity analysis because there were only two levels for each of these effects. The correlations for GS ranged from .87 for later parity DC to .99 for first parity DC, CM, and CT. The correla- tions for GSC ranged from .75 for all parity DC to .99 for first parity CM. These results suggest that estimates of genetic trends by LM and TM may be different. This point is being investigated further. Correlations for age and calving month were all greater than .98. Correlations between estimates of fixed effects in the three DC analyses and in the three first parity analyses, separately for TM and LM, are given in Table 6. None of the cor- relations between first and later parity esti- mates of fixed effects for calving difficulty differed from zero (P>.05). Correlations between the DC and CM solutions were high for calving age and month but were not significant for group effects with the exception of GSC by LM. Journal of Dairy Science Vol. 71, No. 9, 1988
GENETIC ANALYSIS OF CALVING TRAITS TABLE 2. Distribution of records by level of fixed effects. 2495 Parity All 1 2 + 3 Group of sires of cow 1 121,110 35,296 85,814 2 35,312 14,749 20,563 3 47,575 24,755 22,820 4 29,387 19,152 10,235 5 15,390 8241 7149 6 4753 4558 195 Group of sires of calf 1 46,041 18,641 27,400 2 26,876 14,271 12,605 3 42,960 22,282 20,678 4 90,317 45,705 44,612 5 18,470 3414 15,056 6 15,792 1576 14,216 7 13,261 862 12,399 Sex Male 133,805 55,361 78,444 Female 119,919 51,390 68,529 Calving age, mo <22 963 963 . . . 22 6609 6609 ... 23 27,704 27,704 ... 24 31,897 31,897 . .. 25 18,386 18,386 ... 26 10,017 10,017 . . . 27 5536 5536 ... 28 3126 3126 . .. 29 1816 1816 . . . >29 697 697 2nd parity 91,448 ... 911448 3rd parity 55,525 ... 55,525 Calving month January 27,575 11,233 16,342 February 24,061 9491 14,570 March 22,042 9233 12,809 April 17,306 8026 9280 May 15,040 6921 8119 June 11,623 4966 6657 July 13,457 5242 8215 August 16,532 6380 10,152 September 24,051 10, 335 13,716 October 26,546 11,159 15,387 November 26,892 11,470 15,422 December 28,599 12,295 16,304 Variances and skewness values of the SIRE and SC evaluations sums of the corresponding sire and group solutions) are in Table 7 for both the TM and LM analyses. Similar results were obtained for the SIRE and SC solutions and therefore are not presented. In all cases, vari- ances derived from TM analyses were higher than the corresponding LM values, even though the residual variance was set equal for compari- son purposes. As expected from the magnitude Journal of Dairy Science Vol. 71, No. 9, 1988

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