Application of the direct sire comparison method to the Finnish dairy cattle population

Data, consisting of a total of 400542 first lactation records completed in 1975 through 1982, were utilised for development of a model for ranking sires. Using the principle of direct sire comparison method (BLUP), sire evaluations were calculated assuming three models. Model 1 included random terms for sires and maternal grandsires (MGS) of cows, fixed sire and MGS groups within the three breeds and fixed two-year classes within herds. A two-year period within a herd was used to increase the number of records in a class. In model 2 genetic groups were only for breeds. Model 3 included fixed breed groups and herd-year classes. Relationships among bulls were used in all models. About 83, 13 and 2 % of cows making the records were of the Finnish Ayrshire (FAy), the Finnish Friesian (FFr) and the Finncattle (Fc), respectively, whileabout 2 % were of various crossbreds. About 20 % of the herd-year classes had cows of more than one breed. Practically all of the male ancestors of bulls and about 70 to 85 % of maternal grandsires of cows were identified in recent years. About 7 % of the total variation for fat corrected 305-day milk (FCM) production was accounted for by years within herds. The fraction of records lost in editing was 4 % for models 1 and 2, and 11 % for model 3. Assuming model 3, the average numbers of daughters for bulls of the FAy-, FFrand Fc-breeds were 130, 152 and 44, respectively. Average number of records in a herd-year class was about 3.6 in recent years. The additive genetic superiority of the FAy-breed in FCM-production to the FFrand Fc-breeds was 84 and 860 kg, respectively. Joint use of bull groups and relationships among males (model 1) tended to underevaluate the youngest bulls and overevaluate the oldest bulls belonging to previous generations. Based on the results and the breeding structure in the Finnish dairy cattle population, model 3 was chosen to be used in official sire evaluation.


Introduction
A variant of the herdmate comparison method replaced the daughter-dam comparison in dairy sire evaluation in Finland in 1950.The change in evaluation method was, in part, a result from the studies by Dr. Varo (e.g., VARO 1952).The herdmate method was used with some modifications (e.g., VARO 1958, LINDSTRÖM et ai. 1973)for about 30 years.Beginning in the spring of 1981, dairy sires have been evaluated using the direct sire compari- son method which by statistical definition produces the best linear unbiased prediction (BLUE) of a sire's breeding value (HENDERSON 1973).
The mixed model used is the maternal grandsire model, similar to that in the Northeast United States (EVERETT et al. 1979).As generally known, the operational model is largely dictated by the structure of the population.Thus, it is questioned whether groups for sires and grandsires are necessary in the model under the Finnish data structure.Due to the small herd size, a fixed two-year period within a herd (H2Y-effect) is used in the model to account for differences between herds and years.After a poor fodder crop in the year of 1981, however, it was questioned whether the H2Y-effect should be replaced with the herd-year effect.This assumes that year effects share an important portion of the total variation for milk production records.On the other hand, replacing the H2Y-class by the HY-class, variance of error of prediction for sire proofs may increase because of loss of more records, and because the number of records for a young bull to be proved as well as in a herd-year subclass would decrease.
The objective of this paper is to present the structure of data and results from the comparison of three alternative models, and to propose a model suitable for ranking sires in the Finnish dairy cattle population.

Structure of dairy cattle population and breeding in Finland
In 1982 the Finnish dairy cattle population consisted of some 680000 cows, of which 43 % were milk recorded (BOA 1983).In practice all recorded cows have for the past 10 years been bred by artificial insemination (AI).Of the milk recorded cows 81 % was Finnish Ayrshire (FAy), 16 % Finnish Friesian (FFr) and 2 % Finncattle (Fc).The average number of cows in a herd was 12.2, and has steadily increased from 1975 through 1982 by 0.4 cows a year (BOA 1976-1983).In 1982 the majority, 77 %, of recorded cows was in herds with 10 or more cows.
Positive assortative mating for milk yield is probable since according to recommendations cows within a herd should be bred as follows: 1) 15 to 20 % of best cows should be bred by selected bulls, 2) 15 to 20 % of the poorest cows should be bred by bulls of a beef breed, and 3) the rest of the herd, 60 to 70 %, consisting of mediocre cows and all heifers, should be bred randomly by young bulls.The breeding advisors of the Finnish Animal Breeding Association (FABA) have made specific mating plans in about 25 % of the recorded herds.The fractions of recorded cows bred by selected and beef bulls have recently averaged about 35 and 6 %, respectively (CAAIS 1983).
To avoid an increase of inbreeding and to simplify the work of the AI-technicians, bulls and cows are assigned to 3 breeding groups within each breed.The breeding group is determined according to a sire's group.General recommendation for AI-technicians is that a cow belonging to a group should be bred by a bull from another group.The prospective AI-bulls, however, are generally from planned matings in which both the cow and bull belong to the same breeding group.It has also been the policy to occasionally introduce imported semen to the FAy-and FFr-breeds from superior bulls of corresponding breeds.The imported semen is restricted to high quality cows, mainly to bull dams.
About 200 to 250 young bulls are annually proved for dairy characteristics.All of these bulls have passed the performance test in which culling, about 20 %, is mainly on growth rate.First inseminations, about 1500 to 2000 per young bull, are generally completed in about 6 months.Young bulls are usually used to cows within a certain geographical area, within an AI-stud.Due to collaboration between Al- studs, there are essentially 4 areas in the country in terms of progeny testing youngs bulls.After having collected about 20000 to 40000 doses of semen, the bulls are slaughtered at the age of about 3 to 4 years.
Once the young bulls are proved, about 10 % of them are selected.The semen storage of selected bulls is used in about 2 years to cows across the whole country.
The described structure of breeding leads to a distinct pattern in the age distribution for sires represented with first lactation daughters during one year.Bulls obtaining their first proof in a year t, were born on the average 6 years earlier, in a year of t-6.Selected bulls may obtain their second batch of first lactation daughters after about 5 years, i.e., they were born on the average in a year of t-ll.Referring to the amount of semen available for and usage of selected bulls, it is obvious that the critical and most important part of sire evaluation is selection and correct ranking among the youngest classes of bulls.
The structure of the breeding program in Finland is similar to those in Sweden (DANELL and   ERIKSSON 1982) and in Norway (FIMLAND 1976).The breeding program differs, however, from that in North America where the fraction of young bulls progeny tested is smaller and the number of lifetime first inseminations by selected bulls is larger than in North Europe (e.g., CUNNINGHAM 1983).

Materials and methods
The basic data set for the sire evaluation in the spring of 1983 consisted of a total of 400542 first lactation 305-day milk records.About 83, 13 and 2 percents of the cows making the records were of FAy-, FFr-and Fc-breeds, respectively, while about 2 percent were of various crossbreds (Table 1).Lactations were completed in 1975 through 1982.Data included about 24000 herds and 7000 bulls of which about 2200 bulls had 20 or more progeny.
Four traits, 4-% fat corrected milk (FCM), protein, fat and milk yields in kilograms were included in sire evaluation.All traits were preadjusted for age-season of calving subclass effect with multiplicative correction (MC) factors which are estimated in every sire run.Age of calving consisted of 16 one-month classes, 21 months and younger through 36 months and older.Season of calving consisted of 6 two-month periods starting from January.Records were also adjusted for days open with MC-factors.The days open effect was coded to 20 ten-day periods, from 20 to 210 or more days after calving.
Table 1.Percent of first lactation cows of the FAy-, FFr-or Fc-breed, or  The Finnish Ayrshire (FAy)    Determined by a combination of the breed of the sire and the breed of the maternal grandsire.

"
Records of cows with identified sire and maternal grandsire.
Alternative models for sire evaluation Three models, which differed in grouping of sires and/or in classes accounting for herd and year effects, were compared.In describing the models, a detailed equation will be presented only for model 3 to which a reference will be made in the context of models 1 and 2. Due to editing, the size of data used in the final run was smaller for model 3 than for models 1 and 2 (Table 2).
In model 1, which was used in the officially approved sire evaluation until the fall of 1983, sires were assigned within each breed to 5 groups according to their year of birth.The first two groups consisted of selected bulls whereas the last two groups comprised young bulls having their first batch of daughters only.The middle group may include bulls from both of the two classes.This pattern arises from the breeding structure of young and selected bulls as described previously.The equation included a fixed term consisting of a period of two consecutive years within a herd, the H2Y-effect.A two-year period was used to increase the number of records in a H2Y- class.
Equation for model 2 was the same as for model 1 except that no grouping of bulls within a breed was used.Based on several papers (e.g., HENDERSON 1973, KENNEDY and MOXLEY 1975, THOMPSON 1979, JENSEN 1980, KEN- NEDY 1981, QUAAS and POLLAK 1981, DEMPFLE 1982, FAMULA and VAN  VLECK 1982, FAMULA et al. 1983, POLLAK and QUAAS 1983, SWALVE and BRUNS 1983) it seems that joint use of bull groups and relationships among males is difficult to justify under the Finnish breeding structure.Sires, and paternal and maternal grandsires of the young bulls were perfectly known in Table 2. Size and structure of the data for the three models used in sire evaluation in the spring of 1983.the Finnish data.Due to the breeding structure, bulls for later use are selected from the youngest two or three classes of young bulls, all of which are the progeny of highly selected bull sires and dams.Thus, it seems that use of bull groups jointly with relationships among bulls, would improve only slightly, if at all, the accuracy of prediction of a sire's genetic merit.Groups for the three breeds remained in the model, however, because all records are included in the same run irrespective of the breed.This is dictated by the relatively small number of records for the FFr-and Fc-breeds in general, and also because about 20 % of the herd-year classes had cows of more than one breed (Table 3).Connectedness of the data between breeds comes mainly through mixed herds because the fraction of crossbred cows was relatively low (Table 1).Connections among young bulls within a breed in one geographical area are provided through the use of relationships among male ancestors of the bulls.This is further strengthened because about 70 to 85 % of a cow's maternal grandsires were identified in the recent years (Table  4).In addition, the use of selected bulls across the whole country also adds to the connectedness of the data.

Item
Table 3. Percent of herd-year classes having first lactation cows of one, two or three combinations of breeds in different years.

A combination of
Percent of herds with a certain combination breeds for sires of of breeds by the year the lactation was cows in one herd initiated 1977 1978 1979 1980 1981 1982" The Finnish Ayrshire (FAy) 73.0 72.5 72.0 69.9 69.2 73.1 The Finnish Friesian (FFr)   7.6 8.1 8.4 8.6 8.5 11.2 The Finncattle (Fc)   2.6 2.1  The Finnish Friesian (FFr)     hi is a fixed effect of the ith herd-year, gj is a fixed effect of the jth breed of sires, Sjk is a random effect representing one-half the additive genetic merit of the kth sire within the jth breed, gl is a fixed effect of the Ith breed of maternal grandsires (MGS) of the cows making records, sim is a random effect representing one-half the additive genetic merit of the mth MGS within the Ith breed, and e ijklmn is a random residual associated with the record of the nth cow.
The one-year period for the FiY-effect included 305-day lactation records initiated in the interval of May Ist through April 30 th.This period was chosen because then a maximum number of cows produce the major part of the 305-day lactation by the fodder crop harvested in one year.All relationships among bulls were utilized as described by HENDERSON (1975) and EVERETT et al. (1979).
Relative variation of year effects within herds First lactation 305-day milk production records initiated in 1978 through 1981 by cows of FAy-breed were used to estimate the magnitude of relative variation for years within herds.Data included a total of 195478 records which were preadjusted with MC-factors for age-season of calving subclass effect and for days open effect.A simple random model including herds and years within herds was assumed.Thus, the residual component of variation includes both genetic and non-genetic effects.The model assumed and structure of data are implicit from Table 5.

Results and discussion
Relative variation of year effects within herds The importance of years in affecting a cow's milk production was evaluated by the percent of total variation accounted for by years within herds which was about 7 % for traits of FCM, milk and fat production, and was about 9 % for protein production (Table 5).Variance due to herd effects accounted for a large portion, about 36 % of the total variation, for traits other than protein production.
The fraction of total variation accounted for by herd effects in this study is in general agreement with the value of 1/3 summarized by CHRISTENSEN  (1980) based on several studies.The magnitude of variance due to year effects within herds in this study suggests that this effect should be included in the model jointly with herd, as a herd-year subclass effect.Use of fixed HY- classes in the model in place of H2Y-effects can be expected to improve the efficiency in removing the bias caused by year effects on sire proofs.
Consequences of replacing H2Y-effect by HY-effect in the model Total number of records lost.In editing the data for a sire run, a record with no contemporary record in a herd-year class is lost.The same is true if all records in one HY-class are made by paternal half-sisters.Referring to Table 2, about 4 % of records were lost when a two-year period within a herd was used (models 1 and 2), in comparison to 11 % of records lost when using HY-effect (model 3).The number of records lost reduced with time, about 11 %in 1977 and 7% in 1981 (Table 6).The percent of records lost in this study is equal to or less than the percentages of records lost for the models assumed in Sweden (DANELL and ERIKSSON 1982) and in the Northern United States (JENSEN 1980).
Number of records lost in a progeny group.When H2Y-effect was replaced by HY-effect in the model, the reduction in the average number of daughters was about 9 % for young bulls having at least 20 progeny (Table  2).Due to the relatively large number of progeny, the number of daughters lost is negligible relative to the accuracy of sire proofs for milk production traits.The number of daughters for young bulls of FAy-and FFr-breeds is about three to four times, and for Fc-breed about equal to that deemed sufficient (HEIDHUES et al. 1961) and obtained (EVERETT et al. 1979) in the Northeast United States.Relatively large number of progeny for bulls is favored in Finland because bulls are evaluated also for low-heritability traits such as fertility (see Appendix).
Size of HY-subclass relative to the accuracy of sire proofs.In direct sire comparison, a progeny record is deviated from the average of all contempor- ary records in one herd-year subclass.Intuitively, it is expected that the estimated average of a HY-subclass, and consequently a deviation from the average, is more accurate with many contemporary records than with only a 2) Represents the percent of records lost in editing (see text for details).
few.The same relation can be expected to be expressed in the accuracy of sire proofs as well.
Excluding the records lost in editing, the average number of records was 5.1 in a H2Y-class and 3.5 in a HY-class (Table 2).The fraction of larger HY- classes tended to increase in the most recent years, however, and the average number of records in a HY-class in 1981 was 3.65 (Table 6).
Using parameters applicable to the Finnish dairy cattle population, a simulation study was conducted to determine the effect of the size of herdyear class on the accuracy of sire proofs.Increase of herd-year size from 2 to 3 records resulted in greatest reduction in the standard deviations of error of prediction (OJALA et ai. 1983).Increase in the number of records in a HY- class above 4 or 5 records improved the accuracy of sire proofs only slightly.This is in general agreement with the study by HENDERSON (1974).It is obvious, however, that regarding the accuracy of sire proofs, the effect of the number of progeny is much more important than the size of herd-year class.
Sire proofs under the three models The proof for a bull is g + s which is the predicted difference (PD) of one- half of a bull's additive genetic merit from the average of all sires in a run.To Table 7. Averages and standard deviations of predicted difference for bulls of FAy-, FFr-and Fc-breeds.Trait and model Average (x) and standard deviation (s) of predicted difference'* for the breeds of " Predicted difference of one-half of a bull's additive genetic merit from the average of all sires in a run.
provide a stable and predetermined range and distribution, evaluations for sires are standardized within each breed to a relative scale, i.e., to be distributed normally with mean 100 and standard deviation 10.Parameters necessary to calculate a standardized evaluation, an index, were estimated from the set of sires with at least 20 daughters (Table 7).
Differences between breeds.Average PD of FCM for bulls of the FAy-, FFr-and Fc-breeds represents the average of one-half the additive genetic merit of the breeds (Table 7).Thus under model 3, the additive genetic superiority of the FAy-breed in first lactation 305-day FCM to the FFr-and Fc-breeds was 84 and 860 kg, respectively.The genetic differences in FCM between the three breeds were slightly smaller than the corresponding differences, 104 and 873 kg, from the raw averages for the three breeds (Appendix).The observed differences between the three breeds are under the assumption that breeds of cows, defined by the breed of sire, are as in Table 1.The fraction of crossbred cows of all cows was small, however, and was the largest for the FFr-breed.About 17 % of the cows whose sire was a FFr-bull were crossbreds, the majority being of the FFr by FAy type.Standard deviation of PD for FCM was about 160 kg for FAy-bulls (Table 7).This implies that the standard deviation of additive genetic values is about 320 kg.In comparison to the FAy-breed, the corresponding variation was slightly larger in the FFr-breed, but was considerably smaller in the Fcbreed.Standard deviations of PD for FCM did not change much under any of the three models in any of the breeds.
Differences between bulls born in different years.Averages of FCM-index for the two youngest classes of FAy-bulls increased when bull groups were deleted from the model (Figure 1).Indexes for the very youngest bulls increased the most, about 3 units on the average.As a result of this change, the averages of FCM-index for the oldest classes of bulls decreased slightly.Thus, joint use of bull groups and relationships among males tended to underevaluate the youngest bulls and overevaluate the oldest bulls belonging to previous generations.This is an unfavorable situation with regard to sire selection, and grouping of bulls does not under the Finnish breeding structure serve the purpose originally proposed by HENDERSON (1973).
Replacing the H2Y-effect by the HY-effect in the model resulted in a similar effect in the averages of FCM-index for bulls of different ages, as mentioned in the previous paragraph.Also in this case the increase in the average index for the very youngest bulls was the largest, about 4 units (Figure 1).It should be noted, however, that the number of bulls in the youngest group was incomplete.These bulls also were those whose daugh- Figure 1.Average of standardized predicted difference of FCM for FAy -bulls born in different years.
ters completed their lactations during the poor fodder year of 1981, and consequently, probably suffered the most from not having the fixed herd-year effect in the model.Even though the numbers of FFr-and Fc-bulls in a year class were relatively small (Table 2), changes in the models tended to have similar effects in all breeds.
The proposed model.Model 3 was chosen because it seemed to fit the structure of the data most appropriately.Replacing H2Y-class by HY-class in the model can be anticipated to improve the efficiency in removing the possible bias caused by year effects on sire proofs.Even though the total number of records decreased, the number of daughters for young bulls to be proved remained relatively large.Model 3 also proved to be most appropriate with.regard to nominating new selected sires.
Publication of sire evaluations Sire evaluations are published for bulls having at leat 20 daughters.The overall index was the main criterion in nominating the best bulls (Appendix).The weights needed in constructing the overall index were calculated by MÄNTYSAARI (1983) based on the principle of selection index, i.e., making use of heritabilities and economic values for the traits, and genetic correlations among the traits.The nine subindexes included in the overall index, and deviations for fat and protein percents are also listed in the sire summary.
Due to standardization, the subindexes should be within a range of 70 and 130 units in 99.74 % of the cases.It is observed, however, that some very high indexes may exist (Appendix).This suggests that sire proofs for the trait in question are not normally distributed.In recent years, especially high indexes have been obtained in FCM-trait for FAy-bulls in the breeding group C. This, and the high peak in Figure 1 for bulls born in 1974 or 1975, could be partly explained by a succesful import of semen from the Norwe- gian bull, A. Tier.In the fall of 1983, new FAy-bulls with high FCM-index was obtained also in the breeding group D. Vuonna 1981 aikaisemmin käytetty sonnien jälkeläisarvostelumenetelmä korvattiin uudella lineaarisen, kiinteitä ja satunnaistekijöitä sisältävän mallin (BLUP = Best Linear Unbiased Prediction) hyväksikäyttöön perustuvalla ns.suoran vertailun menetelmällä.Käyttöön otettu menetelmä sellaisenaan on yksiselitteinen, mutta myös laskentamallin on oltava hyvin todel- lista tilannetta kuvaava, ennen kuin voidaan laskea varmat ja harhattomat arvostelut.
A p p e n d i x .
Model 3 was modified from model 2 by changing the H2Y-class to the herd-year class.The equation for model 3 is: yijklmn +gj + S jk S lm e ijklmn where yijklmn is a 303-day first lactation record adjusted for age-season of calving and days open effects,

Table 4 .
Percent of identified maternal grandsires (MGS) of cows for different breeds in different years.

Table 5 .
The relative magnitude of total variation accounted for by herds and years within herds.
% 11 Data include 305-day first lactation records initiated by FAy-cows in 1978 through 1981, records are preadjusted for age-season of calving effect and for days open effect by multiplicative correction factors.

Table 6 .
Distribution of records in different size ofherd-year (HY)subclasses in different years.Percent of records in different size of HY in the years of herd-year