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Department of Dairy Science, Virginia Polytechnic Institute and State University, Blacksburg 24061-0315
Corresponding author: B. G. Cassell; e-mail: bcassell{at}vt.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: incomplete pedigree • inbreeding depression • milk yield • days to first service
Abbreviation key: ABTK = Animal Breeders Toolkit, AIPL = Animal Improvement Programs Laboratory, DTS = days to first service, SM = summit milk yield
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The method of VanRaden (1992) will estimate inbreeding for animals with very limited pedigree information. Such estimates vary less for animals with the same birth year than would be expected of inbreeding coefficients calculated from complete and accurate pedigrees of the same animals. VanRaden’s procedure produces higher estimates of inbreeding than true values for animals whose parents were less related than average for their birth year and underestimates inbreeding when parents were more closely related than average. The magnitude of overestimates is limited by average relationship, but underestimates of inbreeding could be quite large for highly inbred animals with limited pedigree data. Thus, VanRaden’s approximations may be inappropriate in studies of inbreeding depression. Our purpose in this study is to present a method to evaluate the amount of information in a pedigree for estimation of inbreeding coefficients. We also compare estimates of inbreeding depression for interval to first breeding and summit milk yield based on inbreeding adjusted and unadjusted for unknown ancestors in field data on Holstein and Jersey cows.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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We developed a method to calculate the percentage of information available for detection of inbreeding in each of the pedigrees used in this study. The calculations are best viewed as a quantitative measure of our ability to declare an individual to be non-inbred based on pedigree information available. The method accounts for all possible combinations of missing ancestors in a five-generation pedigree. Extension of the procedure to more or fewer generations is straightforward. Figure 1
shows the abbreviations used in this explanation, and equation [1] provides the basis of our calculations.
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 | ([1]) |
F(x) is the inbreeding coefficient of individual x, n is the number of Mendelian segregations separating parents of X through common ancestor a, F(a) is the inbreeding coefficient of that ancestor, and summation is across all independent paths through all common ancestors. This equation is sometimes expressed with the exponent n + 1 and no division by 2.
For S in Figure 1
to be a common ancestor to S and D, he would need to appear as SD, SSD, SSSD, or any of the other males on the maternal side of the pedigree. If S and SD were the same individual, one Mendelian segregation would separate S from D, and the relationship would contribute (1/2)n = (1/2)1 = 0.5 to the numerator of Equation 1. If SD were missing, we could not declare S = SD or S 
SD, although the latter decision is frequently made by default with missing ancestors. The loss of SD also means loss of SSD, SSSD, SDSD, and all female ancestors as well. Such loss would impact efforts to estimate inbreeding in X or to declare X non-inbred. Table 1 shows 15 possible positions where S might appear on the maternal side of the pedigree of X as well as the possible contribution to inbreeding if S was the same as the animal in each of those positions. The total possible contribution of all such common ancestor locations is 2.0. If some of those maternal ancestors were missing, the sum would be reduced. The information lost by such missing ancestors could be estimated by ratio of the sum of contributions of males that remain to the maximum value of 2.0 if all male ancestors were present.
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shows the possible contribution of each paternal ancestor, male or female, to the numerator of equation 1, assuming that the maternal side of the pedigree is complete for five generations. The sum of all possible paths through all possible ancestors of both sexes in any generation in a five-generation pedigree is 12.0. That total is useful as a standard for "complete" pedigree information, but could not occur in calculations of actual inbreeding coefficients. Animals cannot be their own parents. For this reason, our approach to evaluating completeness of pedigree information really measures the relative amount of information available to declare an animal non-inbred.
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shows the information loss associated with combinations of missing information on paternal and maternal sides of a pedigree. If the paternal side of the pedigree was complete for five generations (expected for a cow sired by an AI bull), but identification of DD was unknown, 39.6% of opportunity to declare an animal non-inbred would be lost through loss of SDD, DDD, SSDD, and so forth. If some paternal information, such as DDS were also missing, total loss of opportunity to declare an animal non-inbred would appear at the intersection of column DSS and row DD, 49.5% information loss. Such a pedigree could be considered to be (1 - 0.495) x 100 = 50.5% complete.
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The Data and Calculation of Inbreeding
Data for this study were provided by Dairy Records Processing Center (DRMS), Raleigh, North Carolina, and consisted of first services to sires in AI performed on Holstein and Jersey cows with records processed at Raleigh in 1995 through 1998. Data were originally created for sire fertility evaluations calculated by DRMS Raleigh, and included herd, sire, cow identification, date of birth, date of calving, interval to first breeding, date and result of insemination, service sire identification, and summit milk yield (SM). Editing procedures eliminated records for missing sire or dam identification, services to bulls not in AI, missing or invalid information on herd or parity, any evidence of crossbreeding of cow or fetus, and interval to first breeding less than 20 or greater than 220 d. Approximately 40% of original data were removed by our edits, leaving 1,780,283 first services on 1,213,475 Holstein cows and 115,344 first service records on 77,379 Jersey cows. Holstein data included 441,096 registered and 772,379 grade cows, while Jersey data included 62,491 registered and 10,289 grade cows.
Pedigree files maintained by the AIPL, ARS, USDA, Beltsville, Maryland, for USDA genetic evaluations of dairy cattle in the fall of 1999 provided pedigree data for all Holstein and Jersey cows involved in this study. The AIPL pedigree files were updated well after DRMS Raleigh files were created, ensuring that all cows in DRMS data passing edits for inclusion in genetic evaluations had pedigree data as complete as available information would allow. The AIPL uses the method of Wiggans et al. (1995) to calculate inbreeding coefficients with average relationships replacing missing ancestors. These inbreeding coefficients, hereafter called AIPL inbreeding, were retrieved along with pedigree data. We constructed five-generation pedigrees and used the procedures of Golden et al. (1995) in the Animal Breeders Tool Kit (ABTK) to calculate inbreeding coefficients without the use of average relationships for missing pedigree data. These estimates are hereafter called ABTK inbreeding. We also merged pedigree data on cows in the DRMS Raleigh data with the AIPL pedigree data of the service sire contained in each reproductive record to construct a pedigree of the fetus. We calculated ABTK inbreeding of the fetus, but AIPL estimates of inbreeding in the fetus were not available.
Pedigree files were used to determine the percentage of pedigree completeness using the procedure described earlier. Following these calculations, Holstein-grade herds were divided into three categories based on completeness of pedigree. Group 1 included those herds in which more than 85% of cows had 30% or less ancestor information for estimating inbreeding in their pedigrees. Herds in group 2 included 85% or more cows with 31 to 70% pedigree completeness. Group 3 herds had the most complete pedigrees, with 85% or more cows with 71 to 100% of pedigree information available. Thus, some cows in each herd could have had pedigrees more or less complete than the standard met by 85% of cows in the herd. Registered Holstein herds were in a separate group because most registered cows had complete data. Jersey herds, which included some grade Jerseys, were not subdivided because only small numbers of Jersey cows had substantial missing pedigree data. The base for pedigree data from AIPL was 1960. Most cows in this study had birth dates in the early to mid 1990s, allowing opportunity for full five-generation pedigrees if the necessary ancestor identifications were reported through DHI over the years.
Estimation of Inbreeding Depression
Multiple records were available on individual cows and a repeatability mixed model was used to estimate the effects of inbreeding on days to first service (DTS) and SM. Summit milk was defined as the average of the two highest test-day milk weights out of the first three test days recorded for each cow. Effects of inbreeding on DTS and SM were estimated using MTDFREML (Boldman et al., 1995) and the following mixed model in matrix form:
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where Y is a vector of observations, X, Z, and W are incidence matrices associating vectors of fixed effects and covariates (b), additive genetic effects (u), and permanent environmental effects (p) with the observations, and e is a vector of residual errors. The model is further specified as an animal model for repeated records on single traits.
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In this representation, Yijkl is DTS or SM from the lth record of the kth cow in her jth parity calving in the ith herd-year season, HYSi is the random effect of herd-year-season of calving, Pj is the fixed effect of the jth parity (1 through 4), Fk is inbreeding estimated by the AIPL or ABTK methods for cow k, ß is the regression of DTS or SM on inbreeding, Ak are the random, additive effect of genes of cow k, PEk are random permanent environmental effects of cow k, and Eijkl is random residual error associated with record l on cow k. Three generations of pedigree data were included in the relationship matrix for all analyses. Data files were too large to include all animals in the analyses. We created subsets for registered Holstein, grade Holstein, and Jersey cows by randomly selecting complete herds with at least five observations per herd-year-season, subject to the restriction that resulting datasets include between 70,000 and 80,000 records (approximately 50,000 cows).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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shows the amount of pedigree information present for registered Holstein, grade Holstein, and Jersey cows. Pedigrees were most complete (97.7%) in registered Holsteins, where over 83% of cows had all ancestors identified in their five-generation pedigrees. Almost no registered Holsteins had less than 70% of pedigree data available. Pedigree information on Jerseys was nearly as complete. More than 80% of these Jerseys were registered, and the grade Jerseys were apparently in herds where pedigree data were valued and maintained carefully. Pedigrees on grade Holsteins averaged slightly less than 50% complete. Two thirds of male and female ancestors were present in the average grade Holstein pedigree, but the location and combination of missing ancestors reduced the information available to declare these cows non-inbred by more than 50%. For grade Holsteins, the ABTK estimate of inbreeding (where missing ancestors were ignored), was less than half the estimate the AIPL method, where average relationships were assumed for missing ancestors. However, when pedigree data were complete, or nearly so as in registered Holsteins, the two methods produced very similar average estimates of inbreeding, 3.64% for ABTK and 3.50% for AIPL. If pedigree files were identical for AIPL and ABTK methods, average inbreeding should be very close for the two methods for cows with complete pedigrees. The method we used to construct pedigree files for the ABTK method included some ancestors born prior to 1960, causing slightly higher inbreeding for registered Holsteins by the ATBK method. We did not observe the same effect in Jerseys, where AIPL inbreeding was 4.16% compared with 4.10% for ABTK. Jersey pedigrees were slightly less complete than registered Holstein pedigrees, perhaps allowing the missing information feature of the AIPL method to overshadow any additional pedigree data available to the ABTK method.
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includes the same cows as Table 4, grouped by percentage of pedigree information available. When the percentage of pedigree information available was less than 30%, the ABTK method detected almost no inbreeding, regardless of breed or registry status. Inbreeding coefficients by the AIPL method averaged 3.55% for Jerseys, 2.67% for registered and 2.75% for grade Holsteins for cows with least pedigree information available. At the other extreme, 87% of Jersey cows had over 70% of pedigree data available, and averaged 4.27 and 4.56% percent inbreeding by the AIPL and ABTK methods. Estimates of inbreeding in the most complete pedigree group for Holsteins were higher for registered cows (3.71 and 3.53% for AIPL and ABTK methods, respectively) than for grade Holsteins (2.89 and 2.06 for AIPL and ABTK methods, respectively). The AIPL and ABTK inbreeding coefficients for grade Holsteins with more than 70% pedigree information present were more different than for registered Holsteins and Jerseys with the most complete pedigrees. About half of the grade Holsteins in the group with most complete pedigrees had complete five-generation pedigrees, but about 25% had 90 to 99% percent of pedigree information present, and another 25% had 80 to 89% of pedigree information present. Very few of the grade cows in the most complete pedigree group had 70 to 79% of pedigree information present.
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), leaving a pedigree 60.4% complete. Maternal ancestry is not required of records used in genetic evaluations in the United States, so such an omission could be common in AIPL pedigree files. Loss of this specific ancestor may not conceal much inbreeding, as these females are unlikely to appear on the paternal side of a pedigree created by use of registered bulls in AI. Male ancestors of those missing cows, however, would also be missing and might conceal some inbreeding.
We used DTS and SM to compare estimates of inbreeding depression across breeds and percentages of pedigree information available. Table 6 shows that DTS was longest for registered Holsteins (93.4 d) and shortest for Jerseys (84.4 d). Differences in interval to first breeding for registered and grade Holsteins may reflect management strategies, such as use of more expensive semen in registered cows and an intentional delay before first service for a positive energy balance or strong estrus display before breeding. Means in Table 6 are not adjusted for herd effects. Removal of cows with extremely long intervals to first breeding did reduce means and standard deviations of DTS. Inbreeding depression was estimated from data with extreme DTS removed.
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shows summary statistics and inbreeding depression for DTS and SM for the samples of data created for analysis in grade Holsteins. Three datasets of approximately 50,000 cows each were created. At least 85% of cows in a herd were required to have the pedigree completeness percentage indicated for a herd to be assigned to a group. All cows and records from that herd were included, rather than just those cows with the indicated pedigree completeness. Our intent was to maintain the integrity of each herd. For the least complete group, only 5.6% of cows had inbreeding estimates above 0.0 for the ABTK method, but 99.9% of these same cows had inbreeding estimates above 0.0 by the AIPL method. In the most complete pedigree group, the AIPL method actually produced a lower percentage of cows with 0.0 inbreeding (98.0 vs. 99.9%), because there were sufficient pedigree data to declare some animals non-inbred. Average and standard deviation of inbreeding by the ABTK method increased with more complete pedigrees. Inbreeding estimated by the AIPL method changed slightly (not consistently increasing) with more pedigree information, but standard deviation of inbreeding increased considerably from least to most complete pedigrees. Days to first service was longest for the groups with the most complete pedigree data. Summit milk yield increased as the amount of pedigree data increased, perhaps reflecting better management conditions in herds with more complete pedigree data.
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Estimates of inbreeding depression in grade Holsteins was nonsignificant for the two groups of herds with least pedigree information available for both AIPL and ABTK methods of estimating inbreeding. Inbreeding depression in DTS was significant and unfavorable (P < 0.01) in herds where over 85% of cows had at least 70% of pedigree information present in five-generation pedigrees. Inbreeding depression for SM was significant (P < 0.01) for all three groups of herds, and by either method in estimating inbreeding except for the 0 to 30% pedigree group with AIPL inbreeding. All estimates of inbreeding depression were unfavorable, but less damaging when more pedigree data were available. For SM, use of inbreeding coefficients from animals with limited pedigree data would have lead to an overestimate of the negative effects of inbreeding in these data samples. For DTS, limited pedigree data likely would have produced nonsignificant inbreeding effects if data from all three groups of herds had been pooled.
Table 8 shows the same results as Table 7, but for registered Holstein and Jersey cows. We did not examine inbreeding depression using AIPL estimates of inbreeding for Jerseys. Means for DTS were higher for registered Holsteins (88.6 d) than for Jersey (82.0) or for grade Holsteins (83.6 to 86.7 d, Table 7) and were more variable. Mean SM was similar for the group of grade Holsteins with most complete pedigree data and registered Holsteins. Heritabilities for DTS were 0.03 for both registered Holsteins and Jerseys, a slightly lower estimate than for two of the three grade Holstein groups in Table 7. However, heritability for SM was higher in both registered Holsteins and Jerseys (0.10 or 0.11) than for grade Holsteins (0.07 to 0.08). Accuracy of pedigree information may contribute to the difference for SM, but heritabilities for DTS do not support that conclusion.
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. The (nonsignificant) estimate of inbreeding depression for registered Holsteins was very similar (0.03- or 0.02-d increase in DTS per 1% increase in inbreeding) for ABTK and AIPL estimates of inbreeding. Average inbreeding was similar for the two methods (3.67% for ABTK and 3.51 for AIPL) as would be expected for registered cows with very complete pedigree information. Inbreeding depression for SM was highly significant (P < 0.01) for both Jerseys and registered Holsteins and was similar (-0.07 to -0.08 kg per 1% increase in inbreeding) for both breeds. The estimate of inbreeding depression in grade Holsteins with most complete pedigrees was -0.06 kg per 1% increase in inbreeding. One interesting comparison in these results is between the group of grade Holsteins with most complete pedigree data and registered Holsteins or Jerseys. Heritability of DTS for the grade cows was 0.07, and inbreeding depression for DTS was significant (P < 0.01) with 0.15-d increase in DTS per 1% increase in inbreeding. Heritability for the same trait in registered Holsteins was less than half as large, 0.03, while inbreeding depression of 0.02 or 0.03 d increase per 1% increase in inbreeding was not significant. Jersey results for DTS were similar to registered Holsteins. These results could be attributable to the sample of data analyzed or to differences in how the trait is expressed in registered and grade Holsteins. Days to first service is a management decision, affected by biological processes. It is possible that the role of biology in expression of DTS is greater in grade Holsteins, or these grade Holsteins at least, than in these registered Holsteins. Both the grade and registered Holsteins produced the same significant inbreeding depression for SM, -0.06 kg per 1% increase in inbreeding. We conclude that inbreeding depression can be estimated accurately from grade data, but pedigrees must be nearly complete for several generations. There is evidence to suggest that for some traits such as DTS, groups of cows can be managed for different purposes, and genetic components affecting the resulting phenotypes may be affected.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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We present a method of measuring the completeness of pedigree data and demonstrate its utility for editing data before estimating the effects of inbreeding. Our method could be coupled with current algorithms for estimating inbreeding with little additional computational investment. Replacement of missing ancestors with average relationships for animals born in the same year, currently used by AIPL, cannot replace missing information in a manner useful for estimating inbreeding depression. Statistical properties of the AIPL inbreeding coefficients depend on the proportion of pedigree information available. Unusual behavior of regression coefficients can be expected, especially in pedigrees with large amounts of missing information. The AIPL method has merit for other applications, but not for estimation of inbreeding depression. Grade cows with relatively complete pedigree data are useful for estimating inbreeding depression, but should not be used for that purpose unless the pedigrees are complete.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Received for publication March 13, 2003. Accepted for publication April 28, 2003.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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