Estimation of genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers

Genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers were estimated with the REML method using the AI algorithm and animal model. The data consisted of 38 679 first lactation test-day milk yields of 4205 cows from 231 herds in three geographical regions (North Savo, Central Ostrobothnia and Lapland). To identify different test days, records were numbered according to the days in milk after calving, and were further categorized into three part-lactations according to the test-day classification. Expressions in the three part-lactations were considered as separate traits, and tests were treated as repeated observations within the trait. Heritability estimates for test-day milk yield varied between 0.11 and 0.17, being lowest at the beginning of lactation. Genetic correlations between test-day milk yields at different trimesters ranged from 0.64 to 0.91, being highest between consecutive trimesters. Standard errors of the estimates of genetic parameters varied between 0.02 and 0.08. Genetic interrelationships differed from 1.0, supporting the assumption that genetic variation exists in the shape of the lactation curve. The necessity of considering deviations from the general lactation curve in the test-day model, e.g. fitting random regression coefficients, is discussed.

In Finland, as in many other countries, the estim- ation of breeding values for production traits of dairy cattle is based on 305-day lactation records of milk, protein and fat production, and on the protein and fat percentages in the corres- ponding milk.For milk-recorded herds, indi- vidual milk yields are measured every month at regular (approximately 30-day) intervals, and the concentrations of protein and fat in milk every other month.The lactation records are formed by combining the first ten monthly test-day yields, weighted by the length of the testing periods, into a measure of production.
In estimation of breeding values and in an- imal selection scheme it is advantageous to use the original test day measurements rather than the entire lactation production.There is then no need to combine individual test-day results into an entire lactation yield nor to extend incomplete lactation records.In the test-day model, the specific environmental conditions of the sample day can be accounted for by modelling the contem- porary group to include all the animals sampled on a certain test day within the herd.This should result in smaller residual variance (Ptak and Schaeffer 1993).In the test-day model the amount of information is greater; instead of one measure ofproduction per lactation, all information obtained during lactation can be used and the accuracy of evaluations may improve (Pan- der et al. 1992, Ptak andSchaeffer 1993).Furthermore, it is possible to weight test-day meas- urements according to their (co)variance struc- ture (Ali and Schaeffer 1987).
When the animal evaluation is based on 305day production, a common underlying lactation curve for all animals is assumed.In the test-day model, factors for modelling the curve of lacta- tion can be included (Ptak and Schaeffer 1993), and different lactation curves can be delineated for different subgroups if necessary.The use of continuous evaluation and the test-day model rather than one-shot evaluation would make it possible to obtain updated evaluations of a particular herd immediately after each new test day.Solutions for herd-test day effects and indi- vidual animal deviations from the predicted production can be used in dairy management and to detect problems in herd feeding or health pro- grammes.
In most studies the variance components of test-day measurement data have been estimated for either individual test days or for yields cu- mulated periodically (see review by Swalve 1995 b).Heritability estimates for the mid-part of lactation are of the same order of magnitude as those estimated for 305-day production, and considerably lower for the beginning and end of lactation (Meyer et al. 1989, Pander et al. 1992, Swalve 1995 a).Genetic correlations between consecutive test days are close to unity, decreas- ing when the distance between test days increas- es (Meyer et al. 1989, Pander etal. 1992, Kahten- brink and Swalve 1993, Rekaya et al. 1995).Genetic relationships between test-day yields and the entire lactation production depend on the stage of lactation, being lowest during the first two test days and highest during the mid-part of lactation (Pander et al. 1992, Kahtenbrink andSwalve 1993).
One parameter of the lactation curve that is of economic importance to the dairy producer is persistency (Graven and Baptist 1976).Gener- ally persistency describes how sharply the lacta- tion curve peaks, and how strong the decrease in daily production is after the peak.Cows main- taining consistently high production throughout lactation are consideredpersistent.First lactating cows are usually more persistent than cows in later parities (Danell 1982).At the same level of production, persistent cows are under much less physiological stress, and thus metabolic dis- orders or problems with health and fertility are less probable (Leukkunen 1985, Swalve 1995 c).
It is much easier to meet the feeding requirements of a persistent cow, and therefore it is possible to keep the proportion of roughage in the daily diet high (Danell 1982, Leukkunen 1985, Swalve 1995 c).This has economic import- ance, especially in geographical areas where self-sufficiency in feedstuff production is based on hay and silage, and grain or concentrates being mainly bought elsewhere.Persistency cor- relates favourably with 305-day milk yield and the test-day milk production, except in early lactation (Danell 1982, Swalve 1995 c).
The shape of the lactation curve can be estimated with various mathematical models, of which those widely used are Wood's gamma function (Wood 1967) and the multiple regres- sion model (Ali and Schaeffer 1987).As there is evidence of genetic variation in persistency (Danell 1982), individual differences in the shape of the lactation curve may have to be con- sidered.This can be done with a multitrait model in which each test-day yield is considered as a different trait.Another alternative is to use a single-trait model in which test-day yields are considered as repeated observations and indi- vidual deviations from the general lactation curve are accounted for by estimating lactation curve parameters within cows (Schaeffer and Dekkers 1994).The breeding value of an animal is then a combination of the genetic value determining the height of production and the genetic value of the shape of the lactation curve.
Here, heritabilities were estimated for testday milk yields at different stages of the lacta- tion of Finnish Ayrshire heifers with a test-day model, and the genetic correlations between test- day milk yields at different stages of lactation were determined.The need to include lactation persistency in the breeding value estimation is discussed in the light of the results.

Material and methods
Test day data were extracted from the national milk-recording database in three geographical regions (North Savo, Central Ostrobothnia and Lapland).For this study, the data were restrict- ed to the first lactation records of Ayrshire cows calving between April 1991 and March 1995.As in the national milk recording system, cows pro- ducing less than 6.0 kg of milk on a test day were considered dry.To enable the computations to be made with a multitrait model, the data were further edited with respect to the number of an-imals in the contemporary comparison group, only the herds with more than three heifers calv- ing in each herd-year class being included in the analyses.A total of 38 679 test day milk pro- duction records for 4205 cows from 231 herds were used in the estimation of genetic parameters.
Test days (TD) were identified by number- ing records according to the days in milk (DIM) after calving.Equal 30-day intervals were used to classify test days 1-9; the test made during days 271 to 305 after calving was classified as test day 10.If a cow's two successive test-day samples fell in the same test-day class, only the last one was considered.For the estimation of genetic parameters, the test-day classes were further grouped into three part-lactations accord- ing to the stage of lactation.The first trimester consisted of the first two test days (1-60 DIM), the second trimester ranged from the third to sixth test day  and the last trimes- ter from the seventh to tenth test day (181-305 DIM). No resriction was made according to the number oftest day records during lactation. Te average test-day milk production peaked during 31-90 days after calving and then declined quite linearly to the end oflactation (Fig. 1).The vari- ances of the test-day milk yields were fairly Fig.l.Lactation curve for milk yield from average phenotypic test-day milk production (n = 38 679).
Table 1.Number of observations (N), means and standard deviations (SD) of test-day milk yield classified according to days in milk (DIM).
Test day (DIM) N Mean SD 1.
Characteristics of the data are presented in Table 1 and Table 2. Genetic parameters were estimated using a multitraitanimal model in which expressions in each trimester were considered as repeated ob- servations of a different trait.The statistical model used for describing the test-day milk yield for each trait was:  y Ukimno = test -day yield (milk kg), HD = fixed effect of herd, i= 1-231, I AGE.= fixed effect of calving age, j = 1-8, DCC k -fixed effect of days carried calf, for traits 2 and 3, k = 1-5, YS = fixed effect of calving year-season, 1= 1-23, b = regression coefficient for test-day milk pro- duction on days in milk (DIM), D1M..., = days in milk at test, ijklmno J HY m -random effect of herd-calving year, pe n -random effect of permanent environment, a n = additive genetic effect of animal, e.. = random residual error pertaining t0y....The effect of calving age was divided into eight classes according to the age of the heifer on the day of calving (Table 3).As the effect of pregnancy on milk yield cannot be found in the 7 738 21.9 4.5 2.  15 959 21.9 4.5 3. (TD7-TD10) 14 982 18.1 4.6 first trimester, its effect was considered only in later trimesters.The DCC effect was divided into five classes according to the duration of preg- nancy on the sample day (Table 3).The calving year-seasons were classified into bimonthly periods within each calving year across herds, forming 23 calving year-season classes.From the lactation curve, estimated by phenotypic test-day means, production was observed to be approximately linearly dependent on the time from calv- ing to sample day within each trimester (Fig. 1).Therefore DIM was included as a covariate in the model. Calving years, each from April to March and the years from 1991 to 1995, were classified within herds to form 867 herd-calving year classes. The vriances Var(hy)=l®HY 0 , Var(pe)=l®PE 0 , Var(a)=A®G 0 and Var(e)=l®R 0 were assumed where I is an identity matrix and A is the additive relationship matrix of animal effects.
The matrices HY 0 , PE 0 , G 0 and R 0 are matri- ces of order 3, describing the (co)variance struc- ture of the traits.For computational reasons, pedigree information from the dam side was re-  stricted to include only female relatives whose first production year was 1982 or after.Cows with records were daughters of 681 sires and 3202 dams.On average sires had 6.2, and dams 1.3, daughters in the data.The total number of dam-daughter pairs with records in the dataset was 570.The structure of the pedigree informa- tion is presented in Table 4.
Variance components were estimated with the restricted maximum likelihood (REML) method using the AI algorithm (average information).The average information matrix is taken as an average from Fisher's information matrix and the Newton-Raphson second derivative matrix (Johnson and Thompson 1995).Standard errors of the estimates of heritabilities and genetic cor- relations were estimated using the elements of the inverse of the average information matrix and a Taylor series expansion.

Results and discussion
Variance components and estimates of heritabilities and repeatabilities for test-day milk yields at different stages of lactation are presented in Table 5. Heritability estimates were 0.11, 0.17 and 0.17 for the first, second and third trimesters, respectively.Standard errors of the estim- ates of heritabilities were 0.02 for all three trimesters.Repeatability estimates within trimes- ters ranged from 0.52 to 0.71 (Table 5).Genetic correlations between trimesters were 0.88, 0.64 Table 5. Variance components for herd-year (HY), perman- ent environment (pe), animal effect and residual, and estim- ates of heritabilities and repeatabilities for test-day milk yield in lactation trimesters.and 0.91 between the first and second, the first and third and the second and third trimesters, respectively.Standard errors of the estimates of genetic correlations were low, ranging from 0.03 to 0.08.Additive genetic variance was lowest during the first trimester, increasing towards the end of lactation.Residual variance, in contrast, was considerably higher at the beginning oflactation than in the following two trimesters, indicating that the model did not describe early lactation as well as it did the rest of lactation (Table 5).

Variance
Heritabilities are typically estimated for individual test days (Meyer et al. 1989, Pander et al. 1992,Kahtenbrink and Swalve 1993, Reents et al. 1994, Rekaya et al. 1995, Swalve 1995 a) or for cumulated or averaged yields in standard- ized intervals (Kahtenbrink andSwalve 1993, Swalve 1995 a, b).Somewhat higher heritabilities for test-day milk production are presented in the literature than those found in three trimes- ters in this study.The definitions used in the records vary, however, and the statistical models and methods of estimation differ from those used here (see review by Swalve 1995 b).Espe- cially test-day milk production at mid-lactation is reported to be much more heritable than was found here (Pander et al. 1992, Kahtenbrink andSwalve 1993, Swalve 1995 b).Comparison with estimates of heritabilities for 305-day milk pro- duction is invalid, because the trimesters are assumed to be different traits.However, with the Table 6.Variance components for herd-year (HY), perman- ent environment (pe), animal effect and residual, and estim- ates of heritabilities and repeatabilities for test-day milk yield in lactation trimesters when fixed herd effect was ex- cluded from model.aid of heritabilities and repeatabilities it was possible to construct selection indices for cumu- lative yields over each period.The squared ac- curacy of such indices (comparable to h 2) would then be 0.14, 0.22 and 0.23 for the first, second and third trimesters, respectively.In the literature, higher heritabilities are es- timated for the test-day records with herd-test day models than for the traditional herd-yearseason (HYS) classification (Swalve 1994, Rekaya et al. 1995).In our study the herd-test day classification could not be used because of the small size of the contemporary comparison group; the random herd-calving year (HY) was used as a contemporary comparison group instead.The fixed herd effect was included in the model to account for between-herd variation.Such an HY definition pools together the test months of a period of one year or more, and hence does not have the accuracy of even HYScalving groups in other studies.
Exclusion of the fixed effect of herd in the model affected heritability estimates (Table 6).When the herd effect was removed from the model, herd-year variation increased significantly.There was also some increase in the additive genetic variance, with a decrease in the compo- nent of permanent environmental variance.It was assumed that ignoring the fixed herd effect would make it impossible to fully differentiate between the part of the variation due to between-herd dif-ferences and the part due to the within-herd variation between calving years.Part of the be- tween-herd variation seemed to enter the additive genetic component, and the effect of per- manent environment became less detectable.No change in residual variance component was noted, thus leading to overestimation of herit- abilities when the fixed herd effect was excluded from the model (Table 6).On the other hand, the structure of the data could have caused problems in distinguishing the effects of the factors in the model.Because the young sires in the Attest- ing program (artificial insemination) are used for only limited periods, and possibly in only a few herds, the low heritability estimates may result from the fact that sires and herds and/or sires and calving year-season effects are confounded.

Conclusions
As a result of lower additive genetic variance and higher residual variance, the heritability es- timate for test-day milk production in the first trimester of lactation was lower than that in the two following trimesters.The first test-day yield at the beginning of lactation, which is often sam- pled only a few days after calving, is presum- ably a less reliable measure of test-day milk pro- duction than later yields.Many environmental factors, such as feeding before calving, may significantly affect the cows' performance on the first test day.The variation caused by these nuis- ance factors might be very hard to account for, and at least was not distinguished by the model used here.This was indicated by the larger re- sidual variance for the first trimester than for the other two trimesters.
Genetic correlations between the trimesters of the lactation were estimated to range from 0.64 to 0.91, being highest between consecutive trimesters.The fact that the interrelationships between different parts of lactation were lower than one indicates that the shape of the lactation curve is not genetically the same for all the indi- viduals.Furthermore, estimating breeding values and ranking animals on the basis of test-day records for the first two test days may not al- ways lead to selection of the same animals that would have been selected if the decisions had been based on the later test day records.
On the basis of these results, it would be reasonable to take individual deviations from the general lactation curve into account either by estimating regression coefficients describing the lactation curve within cows, as in an approach chosen in Canada (Jamrozik et al. 1995), or by considering individual test-day observations as different traits.Fitting random regression coef- ficients to describe the individual lactation curves would enable lactation persistency to be included as a new trait in animal evaluation.The animal's breeding value for test-day milk pro- duction would be determined by two components: one determining the genetic mean production throughout lactation and another describing the genetic value of the shape of the lactation curve.Problems in defining the contemporary comparison groups in test-day models, the possibility of reducing the number of regression parameters in the lactation curve submodel and establishing the genetic background of the shape of the lactation curve in the Finnish dairy cow population are subjects that need to be studied in the future.SELOSTUS Ayrshire-ensikoiden koelypsykohtaisen maidontuotannon perinnölliset tunnusluvut laktaation eri vaiheissa Anne Kettunen ja Esa A. Mäntysaari

Table 2 .
Number of observations (N), means and standard deviations (SD) of test-day milk yield in trimesters grouped according to test day classification (TD).

Table 3 .
Classification of calving age (AGE) and days car-

Table 4 ,
Structure of pedigree information.