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Institut für Tierzucht und Tierhaltung der Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
1 Corresponding author: ksanders{at}tierzucht.uni-kiel.de
| ABSTRACT |
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Key Words: exclusion probability genetic response missing sire information wrong sire information
| INTRODUCTION |
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The second source of pedigree errors is missing sire information (MSI). In contrast to WSI, until now there has been comparatively little information on the extent and impact of this source of error, but as discussed by Harder et al. (2005), the proportion of MSI can be substantial. Harder et al. (2005) pointed out that MSI influences the variance of estimated sire breeding values and reduces the response to selection.
The objective of the present study was to estimate the proportion of wrong sire information in the Angeln dairy cattle population using molecular marker information. Furthermore, the consequences of WSI and MSI on the genetic gain were investigated by deterministic simulation.
| MATERIALS AND METHODS |
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et al. (1998) reported that 40% of the Angeln population had proportions ranging from 13 to 37% of genetics from other cattle breeds such as Red Holstein, Swedish Red and White, and Finnish Ayrshire. The breed is listed in the database of the European Association of Animal Production (EAAP, 2004), where additional information about it can be found. In the present study, a daughter design was used (Weller et al., 1990) in which 5 paternal half-sib families with a total of 805 daughters were selected. The family size ranged from 123 daughters in family 1 to 199 daughters in family 4; the average was 161 daughters per sire.
Genotyping Process
In 2000, blood samples of the daughters were collected on 41 farms, and semen samples were taken from the 5 sires. No blood samples of the daughters dams were available. The DNA was extracted using the silica-gel method following Myakishev et al. (1995). The DNA extraction was carried out as follows: 325 µL of whole blood (containing 50 mM EDTA) or semen was mixed with 650 µL of bind mix in a 1.5-mL minicentrifuge tube. The combination was incubated in a hybridization oven at 37°C for 15 min (lysis), and the pellet was collected by centrifugation at 5,000 rpm for 10 s in an Eppendorf centrifuge (Eppendorf AG, Hamburg, Germany). The supernatant was poured off. This procedure was conducted 3 times. The pellet was resuspended in 1.0 mL of guanidine solution by vortexing and was incubated in a hybridization oven (37°C). The supernatant was then poured off. The guanidine washing procedure and the incubation were then repeated. The pellet was resuspended in 1 mL of propanol wash, incubated in a hybridization oven, and centrifuged at 5,000 rpm for 10 s. The supernatant was then poured off. This washing procedure was conducted twice. Finally, the pellet was dissolved in 1 mL of ethanol (once) and centrifuged; the supernatant was poured off. The probe was dried for 45 min under vacuum in an exsiccator. The pellet was then resuspended in 400 µL of Tris-HCl buffer (pH 8.0) and dissolved overnight at 4°C.
The 805 daughters and the 5 sires were genotyped for 16 microsatellite markers. These markers are located on 5 different chromosomes (BTA6, 14, 16, 18, and 27) and were selected from previously published bovine marker maps (USDA cattle genome marker maps: http://www.marc.usda.gov/genome/genome. html; INRA BOVMAP database: http://locus.jouy.in-ra.fr/). (The properties of the involved markers will be described in the Results section.) They were chosen because of their highly polymorphic character, and their genotypic information will be used in a subsequent QTL mapping project. The PCR for the microsatellite markers was completed on an MJ Research PTC-200 thermocycler (Global Medical Instrumentation Inc., Ramsey, MN). The electrophoresis of the fluorescent-labeled microsatellite markers was carried out using the MegaBACE 500 Analysis System (Amersham Biosciences Europe GmbH, Freiburg, Germany) and analyzed with the MegaBACE Genetic Profiler Software Suite v2.2 (Amersham Biosciences Europe GmbH). The genotypes were transferred into the ADRDB database (Reinsch, 1999) and checked for agreement with the Mendelian laws of inheritance with the program GEN-CHECK (Bennewitz et al., 2002). To exclude genotyping mistakes, animals involved in conflicts were genotyped for a second time. However, most conflicts (i.e., a violation of the Mendelian laws of inheritance) remained after the second genotyping. Within the set of conflicts that remained unsolved, a paternity was declared wrong if a conflict between a daughter and its putative sire was observed at
3 loci.
Marker Characteristics and Estimation of Pedigree Errors
The allelic frequencies were estimated by maximum likelihood with the following log-likelihood function (Brka et al., 2002):
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where
, where n = number of the different alleles at the particular marker, ni = number of allele i from the founder animals (i.e., either from founder sires or unequivocally descending from unknown dams), and nij = number of half-sibs that share the same heterozygous genotype with their sire. This formula is tailored to a half-sib structure because it allows the use of genotypic information of those daughters with alleles whose paternal origin cannot be unequivocally determined.
For a single locus, the exclusion probability is defined as the probability that a putative conflict between a sire and a daughter occurs in the case of a true non-paternity and is calculated from the frequencies of the different marker alleles. Exclusion probabilities for each marker were calculated for the whole population (PEpop) and each single family (PEfam(i)). Following the S-notation given by Dodds et al. (1996), PEpop was estimated for a single locus as
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where
where pi = frequency of allele i, n = number of distinct alleles, and t = arbitrary non-negative integer (Dodds et al., 1996).
The family-specific exclusion probability (PEfam(i)) was estimated following Ron et al. (1996):
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where qi is the sum of the frequencies of the 2 alleles of sire i.
Extending this to multiple loci, the method described by Ron et al. (1996) was followed to calculate a combined exclusion probability for the whole population (CPEpop):
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where m = number of genotyped loci and PEpop(j) = exclusion probability for the population at locus j. The combined exclusion probability for each family (CPEfam(i)) was calculated as follows:
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where PEfam(i)j = exclusion probability for family i at locus j.
The power of this study was defined as the probability of detecting a nonpaternity given a random case of non-paternity. In a first step, the probability of nonpaternity in the case of zero to 3 loci showing a conflict was calculated. In the next step, the power was calculated as the sum of the probabilities showing a conflict at more >2 loci given a random case of nonpaternity. These probabilities can be calculated from the individual marker exclusion probabilities. One minus these probabilities of all included loci is equal to the power of this study.
Effect of Pedigree Errors on Selection Response
Following Mrode (1996), the selection response (
G) per generation can be defined as
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where i = intensity of selection,
a = additive genetic standard deviation, and R = reliability of the estimated breeding value; therefore,
represents its accuracy. Assuming that only progeny records contribute to the EBV of a sire, R is defined as (Mrode, 1996)
![]() | [1] |
where N = number of potential progenies per sire and t = intraclass correlation, which is one-quarter of the heritability in the case of a half-sib progeny group.
The impact of WSI and MSI can be illustrated by a small example. Assume a population consisting of 2 paternal half-sib groups, each of 100 daughters. Further, assume a WSI and an MSI, both of 10%. In this case, 90 daughters are assigned to each sire (MSI = 0.10), but only 81 daughters are correctly assigned to each sire (WSI = 0.10), and 9 daughters are assigned to the wrong sire, respectively. Similar to Visscher et al. (2002) it was assumed that i and
a were not affected by WSI. Therefore, the impact of WSI and MSI on the selection response can be expressed as
![]() | [2] |
Subscript e denotes pedigree errors. The efficiency of a breeding plan with respect to the genetic gain with pedigree errors relative to a situation with no pedigree errors can be estimated as (Visscher et al., 2002):
![]() | [3] |
where R is the reliability without pedigree errors.
To investigate the impact of different WSI and MSI on the response to selection, the efficiency was calculated for a number of configurations that might reflect a general dairy cattle breeding scheme based on progeny testing, including the situation that can be found in the Angeln population. Different values for heritability (h2 = 0.10, 0.25, and 0.50) and for the progeny group size (n = 10, 50, and 100) were used in the calculations. The proportion of WSI was varied in 6 steps (WSI = 0.05, 0.07, 0.10, 0.15, 0.20, and 0.30), and for MSI, 4 different values were chosen (MSI = 0.10, 0.20, 0.30, and 0.40).
Additionally, as suggested by an anonymous reviewer, the different impacts of MSI and WSI on the efficiency can be derived analytically by taking the first derivative of the square of Equation (1) with respect to (1 MSI) and to (1 WSI), respectively (see Appendix).
| RESULTS AND DISCUSSION |
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3 loci, corresponding to a power of 0.83.
Proportion of WSI
Table 3
shows the putative WSI of the Angeln population for varying numbers of conflicts. Of 805 animals, 10.8% showed conflicts at
1 loci. None of the animals showed conflicts for
8 of the 16 markers. The final WSI in the Angeln population was estimated to be 7%, bearing in mind that an unknown proportion of the WSI might be erroneously declared as WSI (i.e., reflecting a Type I error). For the 5 different families, the estimated proportions of WSI were 4.07, 5.56, 11.11, 11.56, and 5.67%, respectively. The estimated WSI in the Angeln population is in accordance with the literature reports for other breeds (Visscher et al., 2002; Ron et al., 2003; Weller et al., 2004).
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The present study pointed out that WSI and MSI combined their effects on the genetic gain. The calculations showed that the impact of WSI was more harmful than that of MSI. The first derivation of Equation 1 showed, either with respect to (1 MSI) or with respect to (1 WSI), that the effect on the efficiency of WSI was around 1.4 times more harmful as MSI, assuming large progeny groups (see Appendix). Increasing the number of daughters per sire decreases the influence of WSI and MSI, especially in the case of a low heritability (Table 4
). The results of the calculations presented in Figure 1
and Table 4
are in agreement with Van Vleck (1970a, b) and Christensen et al. (1982), who concluded that a trait with a lower heritability and WSI >0 had higher losses in the genetic gain than traits with a higher value of heritability. Harder et al. (2005) showed similar results for MSI, which reduced the genetic gain, especially for traits with low heritabilities.
| CONCLUSIONS |
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3 loci showing a conflict, was 0.83. Additionally, it was shown that WSI and MSI had an influence on reliability and on genetic gain in the Angeln dairy cattle breed and combined their effect on genetic gain. The impact of WSI on the efficiency is around 1.4 times more harmful than the impact of MSI. If a reduction in the loss of genetic gain is desired, especially for low heritable traits caused by incorrect paternity, breeding organizations must check their recording and verification systems to decrease the proportion of wrong and missing pedigree records or to increase the number of daughters per sire. | APPENDIX |
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, where Re = reliability with pedigree errors (Equation 2 in the main text) and R = reliability without pedigree errors (Equation 1 in the main text). Using Equations 1, 2, and 3 and defining x = (1 MSI) and y = (1 WSI), the square of the efficiency is given by
![]() | [A1] |
where N = number of potential progenies per sire and t = intraclass correlation.
Taking the first derivative of Equation A1 with respect to x yields with some algebraic operations:
![]() | [A2] |
Setting x = y = EG = 1 (i.e., no pedigree errors) results in
![]() | [A3] |
Taking the first derivative of Equation A1 with respect to y yields, after some algebraic operations,
![]() | [A4] |
Setting x = y = EG = 1 (i.e., no pedigree errors) results in
![]() | [A5] |
Equations A3 and A5 show that the increase of MSI and WSI (i.e., a decrease of x and y) results in a loss of EG2, that is equal for
, respectively. Hence, for large N, the impact of WSI on EG is around 1.4 (i.e.,
) times as harmful as MSI.
| ACKNOWLEDGEMENTS |
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Received for publication January 7, 2005. Accepted for publication September 1, 2005.
| REFERENCES |
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, T., N. Reinsch, and E. Kalm. 1998. Auswirkungen der Rassenzusammensetzung auf Merkmale der Tagesmilchmenge und auf die Zellzahl beim Angler Rind. Arch. Tierz. 41:201209.This article has been cited by other articles:
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J. A. Woolliams Technical Note: A Note on the Differential Impact of Wrong and Missing Sire Information on Reliability and Gain J Dairy Sci, December 1, 2006; 89(12): 4901 - 4902. [Abstract] [Full Text] [PDF] |
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K. Sanders, J. Bennewitz, N. Reinsch, G. Thaller, E.-M. Prinzenberg, C. Kuhn, and E. Kalm Characterization of the DGAT1 mutations and the CSN1S1 promoter in the German Angeln dairy cattle population. J Dairy Sci, August 1, 2006; 89(8): 3164 - 3174. [Abstract] [Full Text] [PDF] |
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