Relationship between bull dam herd characteristics and bias in estimated breeding value of bull

The objective of the study was to relate estimated breeding values (EBVs) of the parents’ 305-days protein production and the bull dam herd-year characteristics to the empirical bias in pedigree indices (difference between the pedigree index and the final proof) of young bulls. Two animal model evaluations were carried out; one included records up to 1990 and the other up to spring 1992. The final data set included 242 bulls with pedigree indices, final proofs, parents’ EBVs, production and herd information (the size, the average production and the intraherd standard deviation) of the dams. The average empirical bias in pedigree indices was 13.6 kg. The correlation between the final proof of the bull and the EBVs of the bull sire or dam were 0.45 and 0.17, respectively. The low correlation with bull dam EBV indicates the unreliability of the bull dam EBVs. Size of the herd and the standard deviation of production in the herd when bull dam produced its third lactation were correlated with the empirical bias in pedigree index. Pedigree indices of the bulls coming from small herds with high intraherd standard deviation were more biased than those from the big herds with low intraherd standard deviation. The best bulls, when grouped according to their final proofs, were sons of the highest EBV sires. EBVs of bull dams did not differ in the highest and the lowest final proof groups, but the dams of the best bull group had a higher first lactation record than the dams of the other bull groups.


ntroduction
In 1990, an animal model was adopted for dairy cattle evaluation in Finland.Economically the most important trait in the evaluation is 305-days protein yield.Some problems connected to evalu- ation of young bulls entering artificial insemi- nation (AI) in Finland have been indicated by Uimari and Mäntysaari (1993).The empirical accuracy (r = 0.37) of the young bull's pedigree index (the average of estimated breeding values (EBVs) of parents) calculated as a correlation between pedigree index and final proof (EBV of a bull when daughter information is available and the accuracy of the estimate approaches to 1) was less than what was expected from the amount of information available (r = 0.61).The reduction was attributed to the selection of young bulls based on pedigree index.The other problem indicated was an empirical upward bias (5 kg) in pedigree indices calculated as a difference be- tween pedigree index and final proof (Uimari and  Mäntysaari 1993).This bias influenced bull's EB V when only a small number of daughters was available.Biased pedigree indices for production traits in animal model evaluation have also been reported by Ferris and Wiggans (1991), Mao et al. (1991) and Van Der Werf et al. (1994).
Bias in pedigree index is caused by errors in parents' EBVs.Because of the large number of offspring, EBV for bull sires can be considered quite reliable, ifno systematic preferential treat- ments for daughters of bull sires exist.The more likely source of bias is the evaluation of bull dams.Biased cow EBV can be caused by hetero- geneous intraherd variance (Brotherstone and  Hill 1986, Vinson 1987).To address this problem, several statistical methods has been developed (Brotherstone and Hill 1986,Wiggans and  Vanraden 1991, Gianola et al. 1992, San Cristobal et al. 1993).In Finnish evaluations the problem of heterogeneous variances has been ad- dressed by Mäntysaari and Sillanpää (1993).With a crude precorrection of records by within herd standard deviation, they could reduce the bias in pedigree indices by 6%.A higher reduc- tion in bias (20%) in Dutch evaluations was ob- served when within herd variances were standardized using a slightly different approach (Van  Der Werf et al. 1994).
Another possible source of bias is preferential treatment of phenotypically superior cows.The degree of bias in bull dam evaluations de- pends on whether cow has received preferential treatment only in later lactations or in all lacta- tions and also ifthe relatives have received preferential treatment (Kuhn et al. 1994).Largest potential sources of bias arise with preferential treatment of the cow and its multiple daughters made possible with embryo transfer (Kuhn et al.  1994).One way to handle this situation is to try to identify herds where preferential treatment is a possibility and reject these herds as sources of bull dams (Van Vleck 1986).The relationship between the intraherd variance and bias in the evaluation has been shown to be significant (Wilhelm and Mao 1989).Thus, preferential treat- ment and heterogeneous intraherd variance are not separate problems, because the reason for high intraherd variance could be genetic or en- vironmental, i.e., different management for different animals.
The objectives of this study were 1) to deter- mine the correlation between EBV of bull and EBVs of parents, 2) to relate the characteristics of the bull dam herd to the empirical bias in pedigree indices of young Al bulls and, 3) to deter- mine the characteristics of the herds of genetically best bulls.

Material and methods
Two different estimated breeding values (EBV, and EBVj) of 305-days protein production for each animal were calculated.Evaluation 1 was based on a data set of production records up to 1990.Evaluation 2 was based on the informa- tion available in spring 1992 (official dairy evaluation in April 1992).For both evaluations, records were multiplicatively precorrected for the effects of calving season and lactation number by calving age.This was done to par- tially standardize the variances of records in dif- ferent lactations and calving months.Precorrec- tion factors were obtained from an earlier animal model run without precorrection.The evalu- ation model used was a single trait animal model with repeated measurements.Heritability used was 0.30 and repeatability between recods was 0.50.The model and the technique to solve for EBVs was the same as in official national evalu- ation (Mäntysaari and Stranden 1991; Uimari  and Mäntysaari 1993).No adjustment was ap- plied for intraherd variances.
From these two evaluations, Ayrshire bulls born between 1984-1986 that had no daughters in the evaluation 1 but that had a repeatability over 0.9 in the evaluation 2 were chosen for closer Vol.4: 462-472.inspection.In the following, these bulls will be called as young bulls and their EBVs from evaluations 1 and 2 will be referred as pedigree indeces and final proofs, respectively.For the young bulls the dams' herd characteristics and production information were examined.Herd characteristics studied were the number of cows in the comparison group, i.e., herd-year size, and average and standard deviation of 305-days protein production within herd-year.Bull dam pro- duction information included the first three 305days protein production records if available.
Correlations were calculated between the two different EBVs of young bulls (the pedigree index and the final proof), EBVs of dams and sires, and empirical bias in pedigree indices of young bulls (difference between the pedigree index and the final proof).Multiple regression techniques were used to determine ifthe empirical bias can be explained by different herd characteristics and dam records.The preliminary model included herd-year size, average herd-year production, intraherd standard deviation and production of dam.Similar model, with the pedigree index included as an independent variable, was used to predict the final proof of the young bull.The data were further divided into three groups of equal size based on the empirical bias or on the final proofs.The average bias, EBVs of young bull, sire and dam, production of dam and herd char- acteristics were computed for each group.

Results
Totally 242 young bulls did not have any daugh- ters in the evaluation 1 and had repeatability over 0.9 in the evaluation 2 and were included in the further analysis.The average number of daughters in the evaluation 2 for these young bulls was 187.The EBVs of young bulls, EBVs of their sires and dams and the production and the herd characteristics ofbull dams are given in Table 1.
The empirical bias was 13.6 kg which is over two times larger than what were reported by Ui-  mari and Mäntysaari (1993).The reasons for this change are the different heritabilities used in evaluations (0.25 and 0.30) and different sets of bulls considered.The average EBVs ofbull sires changed approximately -2 kg from the evalu- ation 1 to the evaluation 2. The reduction in bull dam evaluation was more substantial, falling from 23.1 kg down to 16.8 kg, this being a res- ult of the information from grand progeny.The difference between the first and the later lacta-Table 1. Averages and standard deviations (SD) of 305-day protein production evaluations 2 (EBV) of 242 young bulls and their parents, production records and herd characteris- tics of bull dams.

Variable
Mean SD EBV,), evaluation 2: data from 1978-1992(Final proof and EBV 2 ).b 232 observations for 3 rd lactation.c Standard deviation ofprotein production within herd-year..89 a Evaluation 1: data from 1978-1989 (Pedigree index and EBV,), evaluation 2: data from 1978-1992 (Final proof and EBV 2 ).b Not significantly different from zero (P = 0.05).tion records of dams was relatively small caused by the precorrection of the records for calving season and for lactation number by calving age, as explained earlier.The average herd size and the intraherd standard deviation were fairly con- stant, but the average production of herd increased slightly over production years of bull dams.
Correlation between pedigree index and final proof was 0.47 (Table 2) giving the empirical repeatability of 0.22, which is higher than what was reported in a previous study (Uimari  and Mäntysaari 1993).Again, this is due to increased heritability and different set of bulls used in this study compared to a previous one.The correlation between sire EBVs was 1.00 indicating that the difference found in Table 1 between average EBVs of bull sires is constant across all bull sires.However, the correlation less than 1.00 between EBVs of bull dams indicates that the reduction in bull dam EBVs has not been con- stant for all bull dams.No correlation between EBVs of bull sire and bull dam was found.The correlation between pedigree index and the parent EBV,s reflects the relative accuracy of the parents' EBVs giving more weight for sire information in pedigree index and thus higher cor- relation between pedigree index and sire EBV, than pedigree index and dam EBV,.More inter- esting was the low correlation (0.17) between bull's final proof and his dam's EBV, illustrat- ing inaccurate evaluation ofbull dams.The mod- erate positive correlation between sire EBVs and bias (0.19) implies that the sons of the sires with high EBV tended to have bigger bias than the sons of the sires with moderate or low EBV, thus some overestimation of the bull sire EBVs may exist.Also a moderate correlation existed between dam's EBV, and its son's empirical bias (0.25), but no correlation was found between empirical bias and dam's EBV 2 .
Using the full multiple regression model (in- cluding the third year herd characteristics and the third production record of the bull dam) only the herd-year size and intraherd standard devia- tion were found to be significant in describing empirical bias (Table 3).Therefore another ana- lysis was done using model which included population mean, herd-year size, and intraherd stand- ard deviation only.The regression of empirical bias on intraherd standard deviation in the herd- year after third calving of the dam was 0.15 indicating a positive relationship between bias and intraherd standard deviation, for example, 10kg difference between herd-year standard deviation corresponded to 1.5 kg bias.The negative regression coefficient for herd-year size (-0.15)indic- ates that bulls coming from small herds tend to have more upward biased pedigree indices than bulls coming from big herds.When the first or Significance levels: *** P = 0.001, ** P = 0.01, * P = 0.05, + P = 0.1, NS the variable is not significantly different from 0.
* Standard deviation of protein production within herd-year.
the second herd-year size and intraherd stand- ard deviation were used as independent vari- ables both came up to be nonsignificant.Overall, the coefficients of determination for the models were very low.For the best fitting model the co- efficient was only 0.06, thus even the best mod- el was rather poor in explaining the variation in empirical bias.
Using the final proof as a dependent variable the bulls coming from the large herds with small herd-year standard deviation maintained their pedigree index better than bulls coming from small herds with large intraherd standard devi- ation.
When bulls were classified according to the empirical bias in pedigree index, both the aver- age of final proofs and the average of pedigree indices varied significantly among the groups (Table 4).However, based on the averages of pedigree indices in each category, the expecta- tions of the bulls in high bias category had been much higher than in the medium or the low bias categories.These expectations have been caused mainly by outstanding bull damEBVs, although the mean EBV of bull sires has been higher in high bias group than in others.Bulls in the high bias group had dams with higher 3 rd production than bulls in the medium and the low groups.The only herd characteristics which varied ac- cording to empirical bias was intraherd stand- ard deviation when bull dam produced its 3 rd lactation record.
Young bulls with the highest final proofs were the progeny of the top matings, as was expected (Table 5).A significant difference (14.5 kg) was found between EBVs of the sires of the highest and the lowest bulls.Conversely, the difference between the averages of dam's EBV! in the high- est and the lowest ranking bull groups was not significant, but the difference in the first lacta- tion records between the best and the other bull groups was significant.However, no significant difference in the first lactation record was found between the low and the medium bull groups.No other significant differences were found be- tween herd characteristics of the three bull groups.

Discussion
The regression of recent on early EBVs provide a simple test to detect either inappropriate vari- ance components used in evaluation or bias as- sociated with EBVs (Reverter et al. 1994).The regression coefficient calculated from our data set for 242 young bulls was 0.65, which was sig- Table 4, Averages of 305-day protein production evaluations* (EiBV) and herd characteristics of bull dams for young bulls divided into three equal size groups according to empirical bias (standard errors in parentheses).Significance levels of the difference between Low and High groups: *** P < 0.001, ** P < 0,01, * P < 0.05, NS the difference is not significant.
b Standard deviation of protein production within herd-year.
nificantly (P = 0.001) different from the expected value of I (Reverter et al. 1994).The other simple method suggested by Reverter et al.  (1994) is the correlation between subsequent EBVs, which has an expected value equal to the square root of the ratio of the mean repeatabilities of the evaluations.The correlation between pedigree index and final proof for the 242 young bulls was 0.47 which is significantly different from the expected value of the 0.65.These two simple statistics indicate that the 13.6 kg empirical bias in pedigree indices was significant.
High correlation (0.45) was found between BRY, of the bull sire and final proof of his son.
On the contrary, weak correlation (0.17) was found between EBV! ofbull dam and final proof of its son.The conclusion from these correlations is that EBV of a bull dam is a fairly poor indicator of its son's final proof and that the se- lection of bull sires is crucial for genetic progress.On the other hand, no better criteria for bull dam selection thanEBVs, even if biased, are available, so breeders must rely on those.
The only significant effects found in predict-Table 5. Averages of 305-day protein production evaluations" (EBV) and herd characteristics of bull dams for young bulls divided into three equal size groups according to final proofs (standard errors in parentheses).Significance levels of the difference between Low and High groups: *** P < 0.001, ** P < 0.01, * P < 0.05, NS the difference is not significant.
ing the empirical bias using the multiple regression technique were the herd-year size and the intraherd standard deviation at the third lactation of the bull dam.The birth year of the young bull was not related to the lactation history of the dam, as was done by Wilhelm and Mao  (1989).In our data set, the bull dams were se- lected after four lactations, on average, before the son was bought for AI-use.Only 22% of the bull calves were born at second or third calving of their dams.However, we believe that the moment when the bull calf is sold to be unimpor-tant compared to the moment when the cow is promoted to be a bull dam.
When bulls were grouped according their final proofs, the average EBV of the sires of the highest group bulls differed significantly from the average EBV of the sires of the lowest group bulls.On the contrary, no significant difference was found between average EBV of bull dams of different bull groups.This provide an indic- ator of the difficulty in distinguishing the very best bull dams from all selected bull dams.It may be beneficial to select bull dams based on their first lactation records.This can be supported by the significant variation in the first lactation records of bull dams between different final proof groups found in this study as well as other evidences which have shown that the EBVs based on the first lactation records are more reliable predictors of the bull dams' true genetic values than EBVs based on all lactation records (Rothschild et al. 1981, Pedersen 1991, Män- tysaari and Sillanpää 1993).Early selection can also be more efficient than selection based on all lactation records even when bias occur (Weigel et al. 1994).However, when biases occur in all lactations including the first lactation or within cow families, selection based on first lactation EBVs is less efficient than selection on EBVs based on all lactation records (Weigel et al. 1994).Other herd characteristics did not vary significantly according to final proof, so although the bulls coming from small herds with high intraherd standard deviation more likely have upward biased EBVs than other bulls, this does not mean that the final proof of those bulls will necessarily be lower than other bulls.
Mäntysaari and Sillanpää (1993) tested sev- eral models describing the management effect and found that the most effective way to reduce bias is to separate first lactations from the later lactations into different herd-years.Such def- inition lead to significantly smaller bias in pedigree indices of young bulls.They suggested that an interaction between lactation number and herd yields presumably causes larger differences in different lactations in herds with high produc-tion.This phenomenon might explain why in Tables 4 and 5 the first lactation production of bull dams does not reach the same level as the second and the third lactation protein production although the records were multiplicatively precorrected before running the evaluation.Multiplicative correction factors for lactation number effect, however, did not completely cor- rect the interaction and thus a division of herdyear effects by lactation number seemed advis- able, as has been adapted in Finnish dairy cattle evaluations since fall 1993.

Conclusions
According the results the Al co-operatives should select the young bulls from the matings of the animals having the highest estimated breeding values.The use of the outstanding bulls as bull sires is the most important factor in genetic progress as long as the evaluation of bull dams is less reliable.Because the herd size and the intraherd standard deviation at bull dam's third lactation appeared to be related to biased pedigree indices of young bulls, Al co-operatives would be well advised to take a more critical view on pedigree indices of young bulls coming from small herds with high within herd standard deviation.Finally, possibility for selection of bull dams based purely on first lactation records should be studied.

Table 2 .
Correlations between empirical bias, 305-day protein production evaluations* (EBV) of young bulls and their parents.

Table 3 .
Regression coefficients of different multiple regression models explaining the empirical bias and the final proof in 305-day protein production evaluations of young bulls.