Application of multiple-trait random regression animal model to predict genetic production traits in Iranian Holstein dairy cattle

Nowadays production of dairy cattle has become a sophisticated money-making industry throughout the world. For many producers, production traits, e.g. milk, fat and protein yield still form the cornerstone of many breeding plans. In general, no breeding plan could be sustained without genetically addressing and exploring these traits. A recent study indicated that, milk yield per cow per lactation has become more than doubled in the last 40 years (Oltenacu and Broom, 2010). Prediction breeding values constitute the main part of most breeding plans. In order to predicting breeding values, genetic parameters of traits should be known. These genetic parameters can be estimated (since their real values are unknown) using suitable breeding designs and statistical models. In recent years, Test Day (TD) models received lots of attention to evaluate genetic potential of dairy cattle by many breeders and researchers around the world (Pool et al., 2000; Swalve, 2000). This method of genetic evaluation is almost grasped worldwide instead of classical 305 day based genetic evaluation. Test day model has some advantages in respect to 305 day based method, amongst them are: computation and considering environmental factors that could affect the performance of cows throughout the lactation (Ptak and Schaeffer, 1993), increasing accuracy of genetic evaluation due to increasing the volume of data per animal (Carvalheira et al., 1998), lack of need to extend uncompleted milking period and reducing the cost of recording (Bilal and Khan, 2009).

Various TD models have been recommended for genetic evaluation of dairy cattle (Swalve, 2000). Among the models that consider TD records, random regression model (RRM) has been widely shown to increase the accuracy of breeding value predictions in many countries (Strabel et al., 2004). Mathematical solid foundation of RRM and its application in current evaluation of dairy cattle and other species throughout the world is doubtless. The use of RRM makes it possible to study changes in TD records over time and a better understanding of lactation genetics (Swalve and Guo, 1999). Therefore, at the present, the random regression TD model is referred to be the most precise model for estimation of production traits in dairy cattle (Lidauer and Mäntysaari, 1999).

Though, applying animal model to evaluate Iranian Holstein dairy cattle production traits goes back to 1994 (Safi Jahanshahi et al., 2003). There have been scant studies in which multiple-trait RRM has been adopted. Due to this fact, the objective of the current study was to predict production traits genetic parameters in Iranian Holstein dairy cattle using multiple-trait random regression animal model (MT-RRAM). 

In this study, records of milk production, protein and fat yield of Iranian Holstein dairy cattle during 2005 to 2010 in Iran Breeding Centre, located in Karaj, Iran was used. In order to edit and explore fixed effects on each trait, GLM procedure of SAS (Version 9.1, 2003) was used. All records spanned between 5 to 305 days of milk (DIM) belong to cows having age 22 to 33 month and their milk yield, fat and protein percentage were in the range of 2 to 48 kg, 1.5 to 9% and 1 to 7%, respectively. Cows were assigned to one of the three subclasses of age at calving (<26, 26-30 and >30 months) and to one of four seasons of calving (spring, summer, fall and winter). In order to increase accuracy of prediction, records of those animals which possess at least 8 records for all traits (to get rid of missing values) and their first record was registered before first 60 DIM. In order to maximum application of the covariance among animals, a big pedigree file spanned 1990–2010 was used. Finally, a data file contained 30729 daughters with 276962 records, gathered over 79 herds. Pedigree file included 691 sires and 26042 dams (Table 1).

Multiple-trait random regression animal model was fitted to data in REMLF90 (Misztal et al., 2002) program and Restricted Maximum Likelihood (REML) method was adopted to estimate the parameters. In this research, for milk and protein yield three order (4 covariates) of Legendre polynomial (Kirkpatrick and Heckman, 1989) was adopted but for fat yield Lidauer-Mäntysaari (1999) function (LM) was used. Finally, the model equation was: 

 

Where y_jklmr is the observation of r^th trait; yc_j is the fixed effect of j^th year of calving; htd_k is the fixed effect of k^th herd-test-day; S_ln is the n^th fixed regression coefficient specific to age-season subclass l; a_mn is the n^th random regression coefficient of additive genetic effect of cow m; pe_mn is the n^th random regression coefficient of permanent environmental effect of cow m; Q_nr(t) is the n^th coefficient (constant, quadratic, cubic, quartic) of Legendre polynomials matrix or LM evaluated at DIM t; and e_jklmr is the random residual effect.

In matrix notation, the following random regression model was fitted: 

 

b = a vector of fixed effects; s = a vector of fixed regression coefficients; a = a vector of random regression coefficients (RRC) for animal genetic (AG) effect; p_e = a vector of RRC for permanent environmental (PE) effect; e = a vector of residual effects; W, Z, and X = incidence matrices relating observation to respective effects.

Also it was assumed that random effects had following (co)variance structure: 

 

Where G = Relationship matrix across all animals; Ka and Kp_e = a 12 by 12 covariance matrices of RRC for additive genetic and permanent environmental effects, respectively; R = a 3 by 3 diagonal matrix of residual variances; I = the identity matrix and, ⊕ depicts the Kronecker product operator. Based upon predicted (co) variance components, heritability (as function of DIM 305 day) for all traits and also genetic correlation among traits obtained using following formula (Jakobsen et al., 2002):

 

 

Ka_pq indicates a matrix of additive genetic (co)variances between traits p and q. Note that i=j if observations were on the same day, and i≠j if observations were on different days (Jakobsen et al., 2002). 

Table 1: Description of data set used for estimation of variance components

In general, the average of milk, fat and protein yields were 31.5, 1.063 and 0.958, respectively. Over the period considered, milk yield showed a consistent decline. The year of calving solution for 2005 was 0.59, it became 0.00 in 2008 and finally in 2010 it obtained -0.87. Even though these values for fat yield (from 0.85 to 0.81) and protein yield (from 0.77 to 0.76) were positive, but they fairly showed a reducing trend. About the effect of age-season of parturition, as it is expected, it was observed that with increasing age of animal in parturition, though negligible, but continuously these values showed an increasing trend. For instance, predicted milk yield for different classes/categorizations of age of parturition, were 32.07, 32.59 and 33.20, respectively.

Results of this study indicated that predicted genetic variances during lactation period increased at the end of lactation period. In comparing the trend of predicted genetic variances for all traits, it was observed that similar to their phenotypic trend (results not reported), milk and protein yield traits had higher similarity than fat yield trait in terms of their genetic variances trend. Concerning to predicted environmental variances for all production traits in this study like trend were observed in such a way that the minimum and maximum values for this components were observed at the middle and beginning of lactation period, respectively (results not reported). Such trend has been reported for Tunisian and Marco Holstein dairy cattle (Hammami et al., 2008; Tijani et al., 2010) which are in agreement with our results.

Heritabilities of milk production traits as a function of DIM are shown in Figure 1. The heritabilities of milk, fat and protein yields as a function of DIM were estimated between 0.12 to 0.25, 0.08 to 0.15 and 0.09 to 0.22, respectively. Previous estimates of heritability of milk yield [fat and protein yields] in Iran were 0.09 to 0.23 [0.06 to 0.12 and 0.07 to 0.23] with a multiple-trait random regression sire model (Bohlouli and Alijani, 2012). Heritability for milk yield assessed by Penasa et al. (2010) in the Italian dairy cattle was 0.09 to 0.28. For milk and protein yields, there are higher heritability estimates than for fat yield based on DIM, which are in accordance with many other similar investigations (Strabel et al., 2004; Zavadilová et al., 2005; Hammami et al., 2008). For all traits, predicted heritabilites over 20 to 35 DIM obtained downwardly which could be due to high amount of permanent environmental variance over this period; however, predicted genetic variances for fat trait with a little discrepancy was identical to protein yield (Table 2). The difference between fat and protein in terms of predicted environmental effect was obvious which culminated in having low amount of heritability for fat trait in comparison with protein trait. In general, predicted heritabilities and genetic variances for fat yield and protein yield showed similar trend, in such a way that their maxim values for both traits can be seen at the end of lactation period. In case of milk yield, the maximum values of predicted heritability and genetic variance observed in middle of lactation (140 to 150 DIM), which showed a declining trend over course of DIM and it became almost relatively constant at the end of lactation period. For milk yield, the main reason for this trend of change of genetic variance, could be due to sharply reduction of permanent environmental effect which itself can be as a function of animal adaptation.

The range of predicted heritability for total milk production across different literatures have been diverse e.g. 0.14 (Strabel et al., 2004) to 0.55 (De Roos et al., 2001). In this study, these values for milk, fat, and protein yields (0.32, 0.32, and 0.33) were slightly higher than the results obtained with a multivariate model (Razmkabir, 2005) on the same population used for this study. Our results were comparable with 0.30, 0.27, and 0.28 obtained by Muir et al. (2007) in Italian Holsteins using multi-lactation RRM. However, heritabilities of yield traits for the Iranian Holsteins were larger than those reported in Tunisian Holsteins (Hammami et al., 2008) and Polish Black and White cattle (Strabel and Jamrozik, 2006).

So far many studies have pointed out lacking consistency among days over lactation period (Jakobsen et al., 2002; Zavadilová et al., 2005; Hammami et al., 2008). Based upon the results of Table 3, the maximum genetic and permanent environmental correlations observed for consecutive days (close to unity). These results are in agreement with other studies (Jakobsen et al., 2002; Zavadilová et al., 2005). However, the magnitude of these variations was different across traits. For example, genetic correlation between 5 and 305 days of lactation period for milk yield and fat yield predicted 0.19 and 0.27 respectively, whereas, for protein yield genetic correlation for the same period (5 and 305 DIM) predicted 0.64, almost 3 times of value predicted for milk yield (the data are not presented). In general, the association between TD records in relation with increasing the interval between DIM is not linear. For example in the case of milk yield, it is observed that with increasing the interval between DIM, the amount of genetic correlation reduced in such a way that for DIM 130 and 140 the minimum value (0.1) turned out, but around 280 DIM, it gradually increased (0.23) and again at end of lactation period a reduction trend was observed (Fig. 2). However, Jamrozik and Schaeffer (1997) and Rekaya et al. (1999) observed negative correlations for extreme parts of the lactation when working with random regressions. The correlation between permanent environmental effects decreased much faster than additive genetic effects as TD got further apart (Table 3). 

Table 2: Estimates of variance components and heritability for daily milk yields on selected days in milk (DIM) and 305-day milk, fat and protein yields

Table 3: Genetic (above diagonal) and permanent environmental (below diagonal) correlations (×102 ) on selected days for milk, fat and protein yields

Table 4: Heritability (on the diagonal), genetic (above diagonal), and permanent environmental (below diagonal) correlations for 305-d milk, fat, and protein yields

 

Fig. 1: Heritability estimates of test-day milk (squares), protein (triangles), and fat (circles) yields

 

Fig. 2: Genetic (RG) and permanent environmental (RPE) correlations between test-day milk yield at different stages of lactation

 

Fig. 3: Additive genetic (RG) and permanent environmental (RPE) correlations between a given DIM* and the remaining part of lactation between milk and fat yield (squares), milk and protein yield (triangles), and fat and protein yield (circles). *DIM: 35 (solid), and 185 (open)

 

About all traits, like genetic correlations, predicted environmental correlation obtained positive (>0.2) value. Exception for fat yield, predicted environmental correlation for other traits obtained higher values than their corresponding genetic correlation for the same interval of DIM. This point should be taken into account in running secure sustainable breeding plans.

The results of prediction of genetic and permanent environmental correlations among traits across different days of lactation period are presented in Table 3. The genetic correlation between milk yield with fat and protein yields ranged from 0.01 (for 5 and 170 DIM) to 0.85 (for the end of lactation) and 0.06 (5 and 140 DIM) to 0.93 (for the end of lactation), respectively. Range of these values concerning correlation between fat and protein yield showed a bit constant trend (0.27 to 0.90). Overall, the maximum genetic correlation between traits was observed for similar DIM and increased toward the end of lactation. High genetic correlations between adjacent test days imply that any both traits are influenced by similar genes (Ilatsia et al., 2007).

The ranges of genetic and environmental correlations among traits for whole lactation period (305 day) were 0.76 to 0.93 and 0.87 to 0.97, respectively (Table 4). In agreement with other researches (Jakobsen et al., 2002; Zavadilová et al., 2005; Hammami et al., 2008) the maximum value belonged to the amount of milk and protein yields and the minimum value belonged to milk and fat yields. About permanent environmental correlation (Table 3), the maximum and minimum values observed for milk and protein yields and milk and fat yields, respectively. This parameter predicted positive and in concordance with genetic correlation, as DIM increased toward the end of milk production, it increased as well. Overall, the amount of permanent environmental correlation across traits predicted higher than genetic correlation. 

Based upon results of this study, building up breeding plan based upon single trait analysis makes less sense since genetic and environmental correlation is not taken into account. For genetic evaluation of Iranian Holstein of dairy cattle, we recommend to resort on multiple-trait random regression model for those sorts of traits which can be calibrated in this model. Moreover, as can be seen, genetic correlations among yields in different stages are positive and higher than 0.3 for most of the lactation and suggesting that selection for increased milk yields in each part of lactation have a positive effect on other traits in the other parts lactation. 

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