Random regression animal models for genetic evaluation of test-day milk yield and milking duration in Saudi dairy goats

Milking duration is among the most important functional traits in dairy cattle and small ruminant (sheep and goats). It is well known in practice that long milking animal are not desirable. Therefore, genetic selection against this characteristic would be appreciated by farmers. Milking duration for dairy goats ranged from 1.5 to 4.88min/milking for different types of milking parlor (Mottram et al., 1991). Milking time of Alpine dairy goats ranged from 1.79 to 2.32 min/milking across different vacuum level of milking machine. Milking time for cows producing 9 to 11 kg of milk should not exceed 4.25 minutes, with an additional ¾ minute for each additional 4.5 kg of milk harvested (Matthew, 2001).  Most of milking characteristics can be measured as a threshold traits classifying cows into categories, or alternatively recording duration in time quantitatively for each cow during routine test day. Different approaches are described by Banos and Burnside (1992). Zwald et al., (2005) found that average milking duration for a single milking  was 4.5 min. Estimated heritability of milking duration was 0.17 and predicted transmitting abilities of individual sires ranged from -0.48 min for sires with the short time milking daughters to 0.59 min for sires with the long time milking daughters. A recent approach has been to use Covariance Functions (CF) (Kirkpatrick and Heckman, 1989) and Random Regression models (RR) (Henderson, 1982 and Schaeffer and Dekkers, 1994). The equivalence of CF and RR has been described by many authors (e.g. Meyer and Hill, 1997; Van der Werf et_al1998). Recentally sire evaluation using animal model (Mallick et al., 2018) play an important role in estimating several genetic parameters in dairy cattle.

The objectives of the current study were to estimate (co) variance components of the multi-lactations data with random regression models and to characterize some genetic aspects of test-day milk yield and milking duration across lactation in Saudi dairy goats.

Data consisted of 17324 test day records (TDR) on daily milk yield (Mk_Kg/day) and milking duration (DR_min). The current data set involved the 1^st, the 2^nd and > the 3^rd lactation of Aradi dairy goats located in Al-Hassa governorate located in eastern area of kingdom of Saudi Araba provided by Training Station of Agricultural and Veterinary Research at King Faisal University (KSA). All studied traits were recorded on each test day between 5 and 180 days in milk (DIM). Does had to have at least two lactations, while the average was 3.7 lactations with 7.16 test-day records.  Data were recorded on does kidding between 2010 and 2015. Number of TDR per lactation was not less than five observations. Days in milk (DIM) were classified into 12 groups with two weeks interval.  Structure of the current data set is given in Table 1.


 
Statistical analysis
 
Random regression (RR) models have been suggested for genetic analysis of test day (TD) yields by Schaeffer and Dekkers (1994) and Swalve (1995) because of their ability to model a separate lactation curve for every animal. Single trait RR models were applied to first lactation milk, fat and protein of test-day yield data with different functions for fixed and random regressions (Jamrozik and Schaeffer, 1997 and Jamrozik et al., 1998). In the simulation study of Strabel and Misztal (1999), RR models were significantly better than an analysis of 305d in terms of correlation between estimated and true breeding values.

The random regression model used in the study was

 
Where:- Y_ijklm is the m^th test day observation of k^th doe in l^th lactation, HTD^_il is the independent fixed effect of ith herd-test-date for l^th lactation, a_klo is the O^th random regression coefficient of additive genetic effect of k^th doe in l^th lactation on DIM,Y_klo is the oth random regression coefficient of permanent environmental effect of k^th doe in l^th lactation on DIM, n_p is the number of parameters fitted in days in milk function, β_jlo  is the o^th fixed regression coefficient of j^th DIM of l^th lactation, X_klmo is the o^th dependent trait on DIM and ε_ijklm  is the random residual.
 
The following (co)variance structure was assumed:
 

 
Where : G = genetic covariance matrix between random regression coefficients and traits, A= additive numerator relationship matrix, I= identity matrix, P = permanent environmental covariance matrix among random regression coefficients and traits and E = residual variance for lactation and assumed to be constant throughout the lactation due to program limitations. Variance-covariance parameters for each of the current longitudinal traits (daily milk yield and milking duration) were estimated using the software package, DFREML (Meyer, 1998 Version 3ß). Random regression model was used with cubic as the order of polynomial fit that achieved the highest correlations between random regression coefficients. Cubic random regression was mostly used in several pervious research works. Permanent environmental effect was presented as a ration between permanent environmental variance to total phonotypic variance.

Results of RR animal model were used for analyzing the relationship between MK and DR (Table 2). Heritability of daily milk yield (h²_MK) ranged from 0.15 to 0.54 (mean = 0.34+0.04). Estimates of h²_MK increased linearly from the 2^nd DIM group till end lactation. Estimates of h²_MK across different DIM groups were moderately high during the last lactation months (>0.40). Estimates of test day milk yield found in the present study are agreement with results of Rupp et al. (2011) of the first parity on Alpine and Saanen breeds. Maroteau et al. (2014) found that heritability estimates for test-day milk were 0.24 and 0.22 in Alpine and Saanen goats using repeatability animal model. The flattest shapes were observed during early production while the rapid increase of genetic variance occurred at the end of lactations. 

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Variations in milk yield due permanent environmental conditions were reduced with progressing days in milk (Table 2). Variations in milk yield due to permanent environmental effect were high (not less than 50%) within early months of lactation. Whereas the corresponding estimates of additive variances were slightly low among the first four groups of DIM. Phenotypic variance of daily milk yield increased markedly after the 7^th DIM group showing high variation with advancing lactation months. Dahiya et al. (2003) found that, several non-genetic and environmental factors had significant effect of performance of dairy animals.

Estimates of h2DR (Table 2) were very low during early lactation months (from 0.01 to 0.11) and were intermediate across the 2^nd half of lactation (from 0.35 to 0.39). Heritability estimate for milking duration was low during the first half of lactation while it increased during the beginning of the 2^nd half of lactation. Zwald et al. (2005) found that low heritability estimates for milking time may be due to the wideness of the interval between positive and negative predicted transmitting ability or breeding values that associated with increase estimates of permanent environmental effect. Moore et al., (1983) found that estimated heritability of the “2-min milk” was 0.23, which was significantly higher than the corresponding estimate of 0.13 for milking duration. Upadhyay et al., (2014) reported that, some udder characteristics had significant effect on several milk ability traits in Indian local dairy goats.

Estimates of permanent environmental effect (PEDR) for milking duration were high during both ends of lactation ranging from 0.52 to 0.73 and from 0.50 to 0.56 during the first and the last three months of lactation, respectively. On the other hand, PEDR decreased greatly at the middle of lactation arriving to 0.35 during the 6^th month of lactation. It appears that environmental conditions had a great contribution in variations of milking duration among different months of lactation.
 
Estimates of heritability and permanent environmental effect within parities
 
Estimate of random regression heritabilities and permanent environmental effects for milk yield and milking duration within parities across DIM groups are presented in Table 3. Estimates of h²_MK within 1^st and 2^nd parities were higher than within others. Estimates of h²_MK within the 1^st parity ranged from 0.24 to 0.36 across lactation months except DIM1,2 and the highest values were obtained during the mid-lactation (DIM5,6). Most h²_MK estimates were high in the 2^nd parity arriving to 0.48 with small variations among estimates across lactation. On the other hand, estimates for h²_MK were low within later parities. Zavadilováet_al(2005) reported that additive genetic variances using random regression increased with parity and heritability estimates increased in turn, especially from the 2^nd to the 3^rd lactation. The present results indicate the importance of genetic evaluation of populations within parity.     

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Estimates of PEMK (Table 3) were obviously low within the 2^nd parity and across the middle of the 1^st parity. Contribution of the permanent environmental variation on MK across DIM groups were magnified during the later parties where h²_MK estimates were decreasing.

Results of heritability estimates of milking duration (h²_DR) within different lactations were mostly near to zero while the corresponding estimates of P_EDR were high. Some high values for h²_DR were obtained slightly during edges of the 1^st lactation (from 0.13 to 0.21 and 0.13 to 0.20), and during the 2^nd half of the 2^nd lactation (0.12 to 0.27). Milking duration may have an intermediate optimum, because most producers prefer does with relatively uniform milking duration. However, selection for extremely short milking duration may be undesirable, because an antagonistic relationship may exist with general udder health (Zhang et al., 1994). Estimates of PEDR were relatively high reaching 0.80, 0.59 and 0.67 within the 1^st, 2^nd and the later parity, respectively. These results refer to the impact of some environmental conditions which may affect the extent of genetic improvement of this trait across and within all lactations.
 
Random regression covariance between and within traits
 
Estimates of additive genetic correlations for MK decreased in magnitude with increasing interval between measurements (Fig 1). Additive genetic correlations between early and late measures of MK were low and directly changed to negative direction. Therefore, MK in early and late stages of lactation could be considered as different traits. Estimates of additive genetic correlations between measures of DR were around unity across all lactation months. These results may indicate the effectiveness of early selection based on milking duration. On the other hand, R_PeMK appeared to show approximately similar trend to R_AMK during most parts of lactation months. Relationships between milking duration and milk yield were positive across all DIM groups (Fig 2).





Fluctuation in relationship of MK and DR was obtained during early months of lactation. While changes of the corresponding estimates during the 2^nd half of lactation was in flattest shape till the end lactation. In general additive relationship between MK and DR was not less than 0.73. These results may suggest that high milk production tend to be inheritable along with long milking duration.               

Estimates of permanent environmental correlations between MK and DR increased linearly with progressing lactation months. Therefore, milking duration may have an intermediate optimum trait in selection programs, because low producer does that consume long time during milking will disrupt parlor flow and reduce parlor efficiency. 

Estimates of correlations R_BVDR*MK between expected breeding values of milking duration with milk yield are shown in Fig 3. Changes were characterized into two phase, the 1^st was in curve shape and ranged from 0.41 to 0.68 (mean R_BVDR*MK = 0.52) and the 2^nd was in flattest shape and ranged from 0.75 to 0.83 (mean R_BVDR*MK = 0.81). It appears that milking durations generally tended to be transmit across generations along with high milk production.

The results show that genetic improvement of both daily milk yield and milking duration is possible and that enhancement of environmental conditions during milking process is the important factor for assessment genetic programs. Milk yield could be considered as different traits along the trajectory especially during early and late of lactation.

My sincere thanks and appreciation to the Scientific Research Deanship - King Faisal University for provide all necessary materials to conduct this study. In addition, my sincere thanks and appreciation to all employees of the training agricultural and veterinary research station - King Faisal University to provide all the services that have contributed significantly to the completion of the search.