Genetic Correlations Among Body Condition Score, Yield, and Fertility in First-Parity Cows Estimated by Random Regression Models

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1 J. Dairy Sci. 84: American Dairy Science Association, Genetic Correlations Among Body Condition Score, Yield, and Fertility in First-Parity Cows Estimated by Random Regression Models R. F. Veerkamp,* E. P. C. Koenen, and G. De Jong *Institute for Animal Science and Health, ID-Lelystad, PO Box 65, 8200 AB Lelystad, The Netherlands NRS, PO Box 454, 6800 AL Arnhem, The Netherlands ABSTRACT Twenty type classifiers scored body condition (BCS) of 91,738 first-parity cows from 601 sires and 5518 maternal grandsires. Fertility data during first lactation were extracted for 177,220 cows, of which 67,278 also had a BCS observation, and first-lactation 305-d milk, fat, and protein yields were added for 180,631 cows. Heritabilities and genetic correlations were estimated using a sire-maternal grandsire model. Heritability of BCS was Heritabilities for fertility traits were low (0.01 to 0.07), but genetic standard deviations were substantial, 9 d for days to first service and calving interval, 0.25 for number of services, and 5% for firstservice conception. Phenotypic correlations between fertility and yield or BCS were small ( 0.15 to 0.20). Genetic correlations between yield and all fertility traits were unfavorable (0.37 to 0.74). Genetic correlations with BCS were between 0.4 and 0.6 for calving interval and days to first service. Random regression analysis (RR) showed that correlations changed with days in milk for BCS. Little agreement was found between variances and correlations from RR, and analysis including a single month (mo 1 to 10) of data for BCS, especially during early and late lactation. However, this was due to excluding data from the conventional analysis, rather than due to the polynomials used. RR and a conventional five-traits model where BCS in mo 1, 4, 7, and 10 was treated as a separate traits (plus yield or fertility) gave similar results. Thus a parsimonious random regression model gave more realistic estimates for the (co)variances than a series of bivariate analysis on subsets of the data for BCS. A higher genetic merit for yield has unfavorable effects on fertility, but the genetic correlation suggests that BCS (at some stages of lactation) might help to alleviate the unfavorable effect of selection for higher yield on fertility. Received October 26, Accepted May 25, Corresponding author: R. F. Veerkamp; r.f.veerkamp@id. wag ur.nl. (Key words: body condition score, genetic selection, fertility, dairy cows) Abbreviation key: CI = interval first to second calving; DFS = interval calving to first service; DLS = interval calving to last service; EB = energy balance; FSC = first-service conception; MGS = maternal grandsire; NS = number of services. INTRODUCTION Genetic selection for yield alone increases feed intake but also results in a larger negative energy balance (EB) and more body tissue mobilization during lactation. This follows from the size of the genetic correlation between yield and feed intake (i.e., the expected correlated response in feed intake from selection on yield alone can not completely cover the extra requirements for the increased yield) and is also illustrated by the negative genetic correlation of yield with 1) measures of EB, 2) BW (change 2 and 3) BCS (Veerkamp, 1998). Even though a negative EB during early lactation is normal for mammals (Robinson, 1986), magnitude and duration of the negative EB are generally related to reduced health and fertility (DeRouen et al., 1994; Harrison et al., 1990; Treacher et al., 1986; Waltner et al., 1993). However, these studies investigate phenotypic or environmental correlations only, and so far only a few studies indicate a genetic correlation between EB and fertility. For example, bulls with a very high EBV for dairy form (low BCS) had daughters with more reproductive problems (Rogers et al., 1999) and a more positive EB, a higher BW during lactation or BW gain all had a favorable genetic correlation with days until first luteal activity ( 0.40 to 0.80) (Veerkamp et al., 2000). Body condition score is widely used in many species to assess body composition and energy balance status of animals. Body condition score is easy to measure on a large scale and is sufficiently accurate to indicate a major part of the variation in body reserves between animals of a similar breed (Enevoldsen and Kristensen, 1997; Gregory et al., 1998; Lowman et al., 1973; Wright and Russel, 1984). Several studies indicate that the 2327

2 2328 VEERKAMP ET AL. heritability for BCS is as high as for milk yield when using trained scorers (Gallo et al., 1999; Koenen and Veerkamp, 1998; Veerkamp and Brotherstone, 1997). Dairy cattle breeders are used to routinely scoring of linear type traits that represent biological extremes for body, udder, feet, or leg characteristic (e.g., Brotherstone et al., 1990). Recently, studies in the United Kingdom and the Netherlands (Jones et al., 1999; Koenen et al., 2001) demonstrated that BCS from the linear type scoring system had similar heritability (0.3 to 0.4), indicating that a considerable genetic variation exist for BCS. The value of EBV for BCS might be that it serves as indicator for fertility traits and might therefore help to select those cows that increase yield without poorer EB and worse fertility. To test this hypothesis, genetic correlations among yield, BCS, and fertility are required. However, a priori, it might be expected that the correlation between BCS and fertility depends on the stage of lactation that BCS is measured. This is probable because the effect of BCS change and because of the timing of BCS recording and the first insemination. Pryce et al. (2000) showed some initial evidence for changes in genetic correlation as a function of lactation stage of BCS recording. In this study, CI was regressed on EBV for BCS at different lactation stages. The latter were estimated using random regression models even though individual daughters had a single measure for BCS available (Jones et al., 1999). The first objective of this study was to estimate the genetic correlation between BCS, fertility, and milk yield. The second objective was to investigate the use of random regression models to estimate the genetic correlation between BCS and other traits that are measured as a single lactation score (fertility and 305-d yield). Condition Scores MATERIALS AND METHODS During type classification, body condition was scored for first-parity cows from October 1998 through September Twenty experienced type classifiers of NRS were trained to score body condition during two sessions. Condition scoring was based on the system described by Lowman et al. (1973) and is described in more detail by Koenen et al. (2001). For practical reasons, i.e., similarity to scoring of other type traits, a 1 to 9 scale was used with increments of one point, rather than the more commonly used 1 to 5 scale with increments of a quarter or half. In total, 126,546 Black-and- White cows that had at least 50% Holstein genes were scored between DIM 1 and 305. To optimize analyses, small herds and herds with natural services only were excluded by selecting herds with >10 records and daughters of at least three sires, respectively. Selecting daughters of sires with 15 daughters reduced the dataset to 91,738 cows from 601 sires and 5518 maternal grandsires. Fertility and Milk Yields Insemination and calving records were extracted from the national database a few months after finishing BCS recording. For this reason, only 12,209 of the 91,738 cows with a BCS record also had a second calving. Most cows did not have the opportunity for a second calving yet, and therefore fertility and yield data was extracted for additional daughters of the 601 sires. These daughters calved in other herds (i.e., herds not participating in type classification) or in the same herds but in previous years. Initially, all daughters with 50% Holstein genes that calved in the period October 1997 through January 1999 were included. The number of cows was reduced by selecting herds that had cows with a BCS observation or herds with 3 cows with a first insemination record. Fertility data were extracted for 177,220 cows, of which 67,278 also had BCS (24,460 cows with BCS but no fertility data were included, these had calved after January, 1, 1999). Finally, 305-d milk, fat, and protein yields during first lactation were added for 180,631 cows. Three types of fertility traits were derived from calving and insemination data: 1) interval traits, 2) all-ornone traits, and 3) counts. Interval traits were days to first service (DFS), calving interval (CI), and days open. Days open was calculated as the number of days between the last service date and calving date for cows with a first service (DLS), and for cows with a CI (DLScon). First-service conception (FSC) and nonreturn to first service (FSC56) were the all-or-none traits. When cows had more than one service than FSC = 0, and when cows had only 1 service and a next calving than FSC = 1, for all other cows FSC is considered missing. Similarly, FSC56 was scored as zero when cows had more than one service, as one when cows had only 1 service and this service was more than 56 d of the data cutoff point, and missing for others. Number of services (NS) was counted for all cows with a first service, all cows with a second calving (NScon), and for those cows that had their last services more than 56 d before the data cutoff point (NS56). ANALYSIS Repeatability Model for BCS Variance components were estimated in ASREML (Gilmour et al., 1999) first using a model with one addi-

3 GENETICS OF BODY CONDITION SCORE 2329 tive genetic effect for BCS during lactation. An extension to this model, i.e., considering BCS during lactation stages as different traits, is described later. The first model used for BCS assumes homogeneous genetic variances during lactation, and a genetic correlation of unity between all lactation stages. Therefore this model is called a repeatability model. A sire-maternal-grandsire (MGS) model was used: Y ij = fixed effects + SIRE sire + ¹ ₂ SIRE mgs + e ij, where the random sire effect is identified by sire and MGS (SIRE sire or SIRE mgs, respectively), and therefore each animal in the pedigree obtains one estimate for the additive genetic effect. This SIRE effect is assumed to be normally distributed with a mean of zero and var(sire) = S and var(e) = E. The heritability (h 2 ) for trait Y is defined as 4 S/(E S). The pedigree file included 7441 male animals and their relationships. Heritabilities were estimated for each trait separately (BCS, fertility, or yield). Fixed effect included were Holstein percentage (50, 62.5, 75, 87.5, and 100%), year month of calving (23 levels), herd (15,025 levels), and a quadratic polynomial regression on age at calving. For BCS two effects were added: the effect of classifier (20 levels) and a fourth-order (cubic) regression on DIM that BCS was recorded. Repeatability Model for BCS with Yield and Fertility Genetic and phenotypic correlations among fertility traits, BCS, and yield traits were estimated using the model described previously in a series of bivariate analyses. The disadvantage of bivariate analyses is that bias might exist due to selection in the data, e.g., farmers can use BCS or yield information when making insemination decisions, therefore a seven-trait analysis, including DFS, CI, FSC, BCS, milk, fat, and protein was also performed. In this analysis, it was computationally too demanding to fit MGS, and therefore SIRE sire was included as the only random effect. Random Regression Model for BCS The previous model assumed one sire effect for BCS during the whole lactation, although repeated daughter records per sire exist. This assumption might not be optimal as discussed previously; genetic differences in BCS loss during lactation might exist, and the genetic correlation between BCS and a second trait (yield or fertility) might not be constant during lactation. A common approach would be to consider every BCS at each lactation stage as a separate trait and then to estimate the genetic covariances between lactation stages (envi- ronmental covariances between lactation stages are not estimable because there was a single record per cow only). However, several disadvantages of this approach (e.g., Veerkamp and Thompson, 1999) can be overcome by random regression models (Kirkpatrick and Heckman, 1989; Kirkpatrick et al., 1994; Schaeffer and Dekkers, 1994). Therefore, the random sire term for BCS in the previous model was replaced by random regression components: Y ij = fixed effects + n SIRE im φ m (DIM j ) + e ij. m=1 SIRE im are random regression coefficients (including the intercept), that are assumed normally distributed with a mean of zero and a (co)variance matrix of order n. The values φ m (DIM j )(m= 1 to n) are the design values of the orthogonal Legendre polynomials (Ambramowitz and Stegun, 1965), and e ij are the residuals. The additive genetic effects the order of the polynomial was increased from intercept only (denoted as L0) to polynomials of order 4 (denoted as L4). Initially, the log-likelihood and eigenvalues of the additive genetic covariance matrix were used to obtain the most parsimonious covariance function. Subsequently, (co)variances for BCS at DIM = 1, 20, 40 to 300 were calculated from this function, and were visually compared with estimates obtained from a conventional analyzer dividing the BCS data over 10 mo of lactation. The same fixed effects were used as in the random regression model. Ideally, all 10 mo should be analyzed simultaneously (i.e., each month as a trait), but a 10- trait analysis was computationally not feasible. Therefore, single-trait analyses were performed to obtain variances for each month of lactation, and two five-trait analyses were performed to obtain variances for even and odd months simultaneously (e.g. mo 2, 4, 6, 8, and 10 were analyzed as five traits in one analysis). Random Regression with Yield and Fertility To obtain genetic correlations of BCS at different DIM with lactation yield or fertility, the random regression model was extended to multitrait analysis. The estimated covariance matrix (M) combines the variance for the second trait (σt), 2 the covariance function for BCS (containing (co)variances for n random regressions σbcs 2 n ), and the n covariances between the covariance function and the second trait: σ 2 T σ T,BCS1 σ 2 BCS M = σ T,BCSn σ BCS1 BCS n... σbcs 2 n

4 2330 VEERKAMP ET AL. Table 1. Number of records, mean and standard deviation for BCS, and 305-d lactation yeilds for milk, fat, and protein. The phenotypic (σ p ) and additive genetic standard deviations (σ a ) were estimated with a sire and a sire-maternal-grandsire model. N Mean σ p σ a h 2 BCS 91, Milk (kg) 180, Fat (kg) 180, Protein (kg) 180, Estimated SE of the heritabilities were To obtain genetic correlations between the second trait and BCS at DIM = 1, 20, 40 to 300, the (co)variance matrix was obtained as M V M, where Φ 1 (1) Φ... (1) Φ n (1) V = 0 Φ 1 (...) Φ... (...) Φ n (...) 0 Φ 1 (300) Φ... (300) Φ n (300) For comparison, genetic correlations were estimated also in a series of two-trait analyses (a fertility or yield trait with BCS in one particular month), and a fivetrait analysis (fertility or yield with BCS in mo 1, 4, 7, and 10). Repeatability Model RESULTS The BCS was based on a single score during lactation, whereas the 305-d milk yields combined several test days. Nevertheless, the heritability for BCS of 0.38 (Table 1) was only slightly lower than the heritability estimates for yield (0.39 to 0.48). The genetic standard deviation for BCS was 0.87 on the 1 to 9 scale. Fertility traits had a low heritability (Table 2), but had consider- Table 2. Number of records, mean, and standard deviation for fertility traits. The phenotypic (σ p ) and additive genetic standard deviations (σ a ) were estimated with a sire and a sire-maternal-grandsire model. N Mean σ p σ a h 2 DFS 1 (days) 177, CI (days) 56, DLS (days) 177, DLScon (days) 56, NS 177, NScon 56, NS56 173, FSC 122, FSC56 176, DFS = Interval calving first service; CI = interval first and second calving; DLS = interval calving to last service; NS = number of services; FSC = first-service conception; con and 56 indicate if a next calving or no return in 56 d was used. 2 Estimated SE of the heritabilities ranged from to able genetic standard deviations of, for example, 9 d for DFS and CI, 0.25 number of services, and 5% for FSC. A higher Holstein percentage was associated with lower BCS, higher yield, and poorer overall fertility (Table 3). Compared with a 50% Holstein cow, a 100% Holstein cow produced 231 kg more milk, but took 4.7 d longer to first service and had a 6.5% poorer conception at first service, resulting in a 7.2 d longer CI. Repeatability Model for BCS with Yield and Fertility Phenotypic correlations between BCS and fertility were low, and phenotypic correlations between yield and fertility did not exceed 0.20 (Table 4). However, genetic correlations between yield and fertility ranged from 0.34 to Genetic correlations of BCS with interval fertility traits ranged from 0.41 to The high genetic correlations among fertility traits (Table 5) showed a close association between the fertility traits. The genetic correlation between milk yield and fat yield was low (0.41) compared with the correlation between milk yield and protein yield (0.84). Genetic correlations between BCS and 305-d milk, fat, and protein yields were negative, 0.30, 0.27, and 0.31, respectively (Table 5). Random Regression Model for BCS The genetic variance for BCS over DIM is shown in Figure 1. Models L1 and L2 gave reasonable flat curves, whereas model L3 gave more variable estimates for the genetic variance. During the start of the lactation, less genetic variance is shown. When increasing the order of the polynomial regression, the difference in log-likelihood between L2 and L3 was 6.5, which makes model L3 significantly better (P = 0.011). The four individual eigenvalues of the additive genetic variance matrix of L3 explained 98, 1.2, 0.6, and 0.016% of the variance, suggesting little importance of the fourth term, although it improved the likelihood significantly. Estimates for model L4 did not converge. Variances from univariate analysis of BCS in each lactation month showed a similar pattern during early lactation as from L3 (Figure 2), but in last two lactation months univariate variances dropped considerably, whereas L3 variances increased. However, when BCS data in more months were considered simultaneously in the two fivetraits analysis, results similar to model L3 were obtained. The covariance functions were used to calculate genetic correlations between BCS observations at different DIM (results not shown). Correlations decreased with increasing time between DIM and with order of fit, e.g., the genetic correlation for BCS at d 1 and at d

5 Table 3. Effect of Holstein percentage on BCS, 305-d lactation yields, and fertility traits. 1 GENETICS OF BODY CONDITION SCORE 2331 Holstein BCS Milk Fat Protein DFS CI DLS DLScon FSC FSC56 % (1 9) (kg) (kg) (kg) (d) (d) (d) (d) NS Nscon NS56 % % Approx. SED DFS = Interval calving first service; CI = interval first and second calving; DLS = interval calving to last service; NS = number of services; FSC = first-service conception; con and 56 indicate if a next calving or noreturn in 56 d was used. 300 was 0.95, 0.94, and 0.85 for L1, L2, and L3, respectively. Comparing these correlations with those from the two five-trait analyses they were relatively close. The genetic correlations from the two five-trait analyses ranged between 0.83 and 0.98 but were more variable over time, most likely due to the sampling errors. Random Regression with Yield and Fertility Genetic correlations between BCS at different DIM and full lactation yield or fertility traits were estimated with L2 and L3, but only analyses with CI, FSC, milk, and fat stayed within the parameter space (i.e., matrix positive definite) when L3 was used for BCS. The genetic correlation between BCS in early lactation and 305-d lactation fat yield was smaller than for BCS in later lactation (Figure 3). This suggests that selection for a high-lactation fat yield has less effect on BCS during early lactation, than selecting for milk or protein yields. When BCS was measured before d 100 (i.e., the first insemination), more value as predictor of conception at first service (FSC58) was shown compared with BCS later during lactation, as shown by the close to zero correlation after d 100 (Figure 4). This explained the zero correlations between average BCS during lac- tation and FSC56, as the correlation was zero after about d 100. For DFS, little effect existed on the genetic correlation as a function of lactation stage for BCS. With L3, the genetic correlation over time differed very little from L2 for CI. For protein the curve followed the curve of milk very closely. Compared with L2, L3 gave correlations with milk closer to zero for BCS during early lactation and closer to 1 for FSC (Figure 5). During early and late lactation very little agreement existed between the correlations coming from the two-trait analysis and L3 (or L2). However, close agreement between the correlations from the five-trait analysis and L3 existed (Figure 5). DISCUSSION Heritabilities and genetic standard deviation confirmed a considerable genetic component to BCS. A difference of three standard deviations for BCS on the scale used in this study equaled to more than 1.25 units on the more usual 1 to 5 scale. The genetic correlation between BCS and yield was clearly negative. Using the genetic parameters a 0.38 units lower BCS was expected on average during lactation for every 1000 kg of milk extra milk. An increase in Holstein percentage Table 4. Phenotypic (r p ) and genetic correlation (r g ) among fertility traits, and 305-d milk, fat and protein yields, and BCS. r p r g 1 BCS Milk Fat Protein BCS Milk Fat Protein DFS CI DLS DSLcon NS NScon NS FSC FSC Estimated SE of the r g were close to DFS = Interval calving first service; CI = interval first and second calving; DLS = interval calving to last service; NS = number of services; FSC = first-service conception; con and 56 indicate if a next calving or no return in 56 d was used.

6 2332 VEERKAMP ET AL. Table 5. Genetic (below diagonal) and phenotypic correlation (above diagonal) among days to first service (DFS), calving interval (CI), first-service conception (FSC), and 305-d milk, fat, and protein yields. DFS CI FSC BCS Milk Fat Protein DFS CI FSC BCS Milk Fat Protein Estimated SE of the r g ranged from 0.01 to 0.1. also reduced BCS: one unit when going from 50 to 100% Holstein. A simultaneous increase in Holstein% and genetic merit for yield implied that a reduction in BCS was expected over time and that management norms for BCS need to be adapted to this change. One BCS observation at a random moment during lactation is not expected to predict phenotypic fertility performance accurately. Therefore, it is not surprising that the phenotypic correlation between fertility and BCS was low. The phenotypic lactation yield is also unlikely to be a major source of variation in fertility as it explains less than 4% of the between cow variation (after adjustment for fixed effects). Genetic correlations between yield and fertility were clearly undesirable in this study and were close to the values reported by others (e.g., Bagnato and Oltenacu, 1993; Boichard and Manfredi, 1994; Campos et al., 1994; Grosshans et al., 1997; Hoekstra et al., 1994; Pryce et al., 1998; Seykora and McDaniel, 1983; Van Arendonk et al., 1989). The genetic correlation between CI and BCS was close to 0.56 (± 0.10) in UK data (Pryce et al., 2000). For the other interval traits DFS and DLS, similar high correlations were found with BCS. Hence, BCS can serve as a predictor for the EBV for interval traits, albeit with an accuracy not higher than the genetic correlation. This is illustrated for CI in Figure 6 using standard selection index equations to calculate the accuracy. When >100 daughters had CI recorded, the additional benefit of BCS records on the accuracy was limited. However, for selection among young bulls when only a few daughters had the opportunity to have a next calving or selecting a cow on own performance, predicting CI from BCS was more accurate than from records for CI. Also, DFS and FSCONC can be used as predictor for CI. These traits had a lower heritability than BCS, but higher genetic correlation with CI, and are therefore more accurate with a large number of records. However, up to 50 daughters, a combination of BCS with FSCONC and DFS was most accurate. A combined analysis of all these traits should therefore be considered. However, these sums did not consider the genetic correlation with yield yet. Ideally, predictors of fertility should have a high correlation to that part of fertility that is independent of yield. This was, for example, also shown for DMI. The correlation between DMI and days to first luteal activity was 0.04, but decreased to 0.49 after adjusting for yield (Veerkamp et al., 2000). Thus, the contribution of BCS to the total breeding goal will be more important than the prediction of fertility alone. Figure 1. Genetic variance for BCS at different lactation stages (DIM), using polynomials ranging from first to third order (L1 ot L3). Figure 2. Genetic variance for BCS at different lactation stages (DIM), using random regression polynomials the third order (L3), and estimates in each month of lactation from univariate analysis (UNI), or two five-trait analysis (MT) fitting even and odd months together.

7 GENETICS OF BODY CONDITION SCORE 2333 Figure 3. Genetic correlation between BCS at different lactation stages (DIM) and 305-d milk, fat, and protein yields. A random regression model with a third-order polynomial (L3) was used for BCS. Rather than absolute BCS, BCS loss might be important for robustness of dairy cows (Bourchier et al., 1987; Butler and Smith, 1989; Lalman et al., 1997; Senatore et al., 1996; Whitaker et al., 1989; Wildman et al., 1982). However, correlations between BCS in early and late lactation were close to unity in this study, and others (Jones et al., 1999; Koenen and Veerkamp, 1998; Koenen et al., 2001), suggesting little genetic variation in BCS change compared with the variation in level of BCS. Still, in this study, BCS during early lactation showed a stronger association with FSC than BCS in later lactation, a result also reported by others (Pryce et al., 2000), and correlations with the yield traits changed according to DIM for BCS also. Therefore, random regression models might help to predict BCS at that moment during lactation that the genetic correla- Figure 5. Genetic correlation between BCS at different lactation stages (DIM), and first-service conception (FSC), and 305-d milk yield (milk) using different models: 1) Model L3 with FSC or milk, 2) twotrait analysis (2T), taking each month of lactation for BCS with FSC or milk, and 3) a five-trait analysis (5T), mo 1, 3, 7, and 10 for BCS plus milk or FSC (L3 milk ; 2T milk ; 5T milk ; L3 FSC ; 2T FSC ; 5TFSC ). tion is highest with fertility. The increase in the genetic correlation between 305-d protein yield and BCS towards the end of the lactation, poses the question how persistency of milk yield affects yield, fertility, and BCS in the next lactation. Selection for a high-lactation protein yield decreased BCS during the whole lactation, but especially at the end of the lactation. Further analysis should therefore include fertility in the subsequent lactation and probably a multitrait random regression model to investigate the role of persistency of yield. Choosing the appropriate order of fit for the random regression model is not easy. A significant increase in the log-likelihood was obtained by L3 compared with L2, but the fourth eigenvalue was very small. Hence, Figure 4. Genetic correlation between BCS at different lactation stages (DIM), and days to first-service (DFS), calving interval (CI), first-service conception (FSC), and FSC using no return 56 d (FSC56). Model L2 was used for BCS. Figure 6. Accuracy of the breeding value for CI as a function of the numbers of daughters that have CI, condition score, days to first heat (DFS), first-service conception (FSCONC), or a combination recorded. ( CI; BCS; DFS + FSCOWC; BCS + DFS + FSCONC).

8 2334 VEERKAMP ET AL. in breeding values for BCS from L2 or L3 probably differ little. Using variance components from conventional models as a guideline to select the appropriate order of fit for random regression models proved awkward in this study. Correlations from a multitrait analysis were so close to unity that models were overparameterized and variance components had to be bended at the boundary of the parameter space. To overcome these convergence problems, and to overcome computational difficulties, subsets of the data were used in single-trait analysis (to obtain variances) or two-trait analysis (to obtain covariances). The results of these subsets of data provided, however, poor benchmark values for random regression models. The univariate analysis showed a decrease in genetic variance in the last month, whereas L3 and the two five-trait analyses showed a similar increase in genetic variance in the last 2 mo (Figure 2). Also genetic correlations from two-trait analysis provided poor benchmark values for the RR model (Figure 5). A probable reason might be that only a selected group of cows (e.g., cows not culled for disease yield or any other reason) will have data in the last month of lactation, hence, choosing order of random regression models on similarity of the variance components with overparameterized multitrait models, or analysis that ignore large parts of the data is not advised. The RR model provided a more satisfactory fit. REFERENCES Ambramowitz, M., and I. A. Stegun Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dover Publications Inc., New York, NY. Bagnato, A., and P. A. Oltenacu Genetic study of fertility traits and production in different parities in Italian Friesian cattle. J. Anim. Breed. Genet. 110: Boichard, D., and E. Manfredi Genetic analysis of conception rate in French Holstein cattle. Acta Agric. Scand. Sect. A, Anim. Sci. 44: Bourchier, C. 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