Comparison of breeding value for test day milk yield and test day energy corrected milk yield in Mehsana buffaloes

Introduction

Rapid population growth in India has led to a significant rise in demand for milk and dairy products. Milk plays a critical role in addressing nutritional insecurity, especially in rural areas where livestock are a key source of food and income. Although India ranks first globally in milk production, the share of dietary energy from dairy is only 4.4%, compared to 14.0% in developed countries (FAO, 2013) [2] . The per capita dietary energy intake projected for 2030 is 2860 kcal/person/day in developing countries, compared to 3430 kcal/person/day in developed countries (FAO, 2012) [1,3] . Milk composition varies by species and breed. While water is the major component, the nutritional value depends on fat, protein, SNF, and lactose. Emphasis on milk quantity over quality has negatively impacted both nutritional content and marketability. The energy value of milk can be estimated based on the concentrations of fat, protein, and lactose (Perrin, 1958) [4] . Although incorporating energy balance into breeding programs is ideal, direct measurement remains expensive and complex (Hüttmann et al., 2009) [5] . Energy corrected milk yield accounts for fat and protein content, offering a more accurate reflection of nutritional value. In a largely vegetarian country like India, milk contributes an average of 134 kcal energy, 8 g protein, and 7.3 g fat per capita daily (FAOSTAT, 2012) [3] . Considering the potential of milk to mitigate bio-energy insecurity, an attempt was made to utilize energy corrected milk yield as a trait for evaluation of Mehsana buffalo which can aid in genetic improvement focused on energy output. Buffalo milk is more energy-dense than cow milk, with higher fat and protein content (FAO, 2013) [2] . It is also more efficient for dairy processing (Ménard et al., 2010) [6] .

Model used

Where, y thijkl = the test day milk yield of k th animal made on t th days in milk (DIM) Herd j = herd as fixed effect with subclass j Owner h = owner as random effect with subclass h HYMR i = herd * year of milk recording * month of milk recording as random effect with subclass i 𝛽 𝑙 = fixed regression coefficients 𝑢 𝑘𝑙 and𝑝𝑒 𝑘𝑙 = the l th random regression for animal additive genetic and permanent environmental effects, respectively, for animalk ∅ ktl = the l th Legendre polynomial for the test day record of animalk made on t th day inmilk nf = the order of polynomials for DIM nr = the order of polynomials for animal and peeffects e thijkl = the random residual effect

The DIM was transformed using Legendre polynomials of 'n' order as described below. However, the second order of LPs were used in the present study.

The matrix φ is of order t (the number days in milk) by k (order of fit) with element φ ij = φ j (α t ) equals the j th Legendre polynomial evaluated at the t th standardized DIM. Consequently, α t is the t th DIM standardized to the interval for which the polynomials are defined.

In matrix notation, φ = MΔ, where M is the matrix containing the polynomials of the standardized DIM values and Δ is a matrix of order k containing the coefficients of Legendre polynomials. The elements of M can be calculated as m ij = (α i (j-1) ,i = i = 1,...,t; j = 1,..., k).

Here, standardized DIM can be calculated after calculating the total milk yield from the known part of lactation length, the rest of the unknown lactation part up to 300 days lactation lengths were estimated by the prediction equations (Habib et al., 2019) [12] . Legendre polynomials were calculated for matrix Δ. The j th

Legendre polynomial evaluated at DIM t (Pj(t)), can be evaluated by the formula given by Abramowitz and Stegun (1965) [13] .

Sire Evaluation

Estimated variance and covariance components were used in breeding value estimation of breeding bulls using univariate Best Linear Unbiased Prediction (BLUP) model for test dayrecords. The 305 days milk yield breeding value and standard error for individual animals were estimated by sum of multiplication of 305 days solutions of Legendre polynomials to random effect solutions of individual animals.

Best Linear Unbiased Prediction (BLUP) method (Mrode, 2014) [14] Univariate model Breeding value of each sire was obtained as BLUP solutions for the animal genetic component in the model. Three solutions corresponding to each order of Legendry polynomial was obtained from BLUP analysis and EBV for each DIM and 305 days was calculated as below: Each animal has an order of polynomials for animal and pe effects regression coefficients as solutions for animal and permanent environmental effects. These are not useful for ranking animals and need to be converted to breeding values for any particular day of interest. Usually, in dairy cattle, values are calculated for 305 days' yield.

The estimated breeding value from days 5 to 309for animal k (EBV k305 ) is calculated as:

Where, t = a row vector of order of polynomials for animal and pe effects with the j th elements equal to the sum of the j th orthogonal polynomial from days 5 to 309 û k = vector for the regression coefficient of animal k

Reliability of EBV

Where, G = variance component of sire Predicted Error Variance (PEV) = square of standard error Here, standard error obtained by the sum of multiplication of n th order of Legendre polynomials to n number of breeding value solutions.

Comparison of TDMY and TDECM for Sire Evaluation

Sires were evaluated for test day milk yield (TDMY) and test day energy corrected milk (TDECM) and thereafter ranked as per their genetic merit. The comparison of TDMY and TDECM for sire evaluation was judged by using the following criteria:

Rank correlation

The Spearman's correlation was used to judge the effectiveness between breeding values of sires derived by TDMY and ECMY models. The rank correlation estimated as per Steel and Torrie (1960) [15] :

Where r s = rank correlation coefficient n = number of sires under evaluation d i = difference of rank between paired items under two models

The significance of rank correlation was tested by t-test as given below and it was compared with t-table value with (n-2) degree of freedom:

Where, n = number of animals

Results and Discussion

The minimum, maximum, average values of EBV and the number of sires above and below the average of breeding value for 305D MY and 305D ECMY of Mehsana buffalo bulls predicted through univariate BLUP are presented in Table 2. The average EBV for 305D MY was found higher compare to transformed traits for milk energy correction. But, the estimates of maximum EBV for 305D ECMY found slightly higher than 305D MY except for 305D 6% FCMY and highest breeding value (437.09 kg) found for the sire of 305D ECMY1. Similar to present study, Prajapati et al. (2018) [16] reported maximum, minimum and average EBV (Kcal) for fat based energy corrected milk were 1472.75, 978.94 and 1185.70 respectively for Mehsana buffalo. Earlier, Sathwara et al. (2019) [17]

Rank correlation of sires' estimated breeding values for different traits

Rank correlation coefficients of 305D MY and 305D ECMY for all the sires (118 sires of daughters whose records were used for analysis) as well as for top and bottom 75%, top and bottom 50%, top and bottom 25% and top and bottom 10% sires based on their breeding values irrespective tore liabilities and greater than or equal to 60% reliability of EBVs estimated and are presented in Table 5 and6 respectively. The rank correlation of sires EBVs between 305D MY and 305D ECMY for all sires, top 75%, top 50%, top 25%, top 10%, bottom 75%, bottom 50%, bottom 25% and top 10% were found highly significant for all traits while it was significant for top 10% bulls. The rank correlations of sire EBVs between 305D MY and 305D ECMY with greater than or equal to 60% reliability, were found highly significant for all sires, top 75%, top 50%, bottom 75%, bottom 50% and bottom 25% whereas correlation was significant for top 25% and bottom 10% except for 305D 4% FCMY and 305D 6% FCMY while non-significant for top 10% for all traits and bottom 10% for 305D 4% FCMY and 305D 6% FCMY. The above results indicated the huge changes in ranking of sires if selected based on 305D ECMY as compared to selected based on 305D MY in Mehsana buffalo. CVB feed, 2016 [11] 6.

SCM (lb) 12.3 * Fat (lb) + 6.56 * SNF (lb) 0.0752 * Milk yield (lb) Tyrrell and Reid, 1965 [9]

Conclusion

High magnitude of change in ranking of sires if daughters selected based on ECMY as compared to MY may lead to change in the genetic gain under large-scale field-based animal breeding programmes. Thus, bulls selected for MY may produce less milk energy efficient daughters and it is required to select the bulls for 305D FPCMY for energy efficiency of milk yield. Hence, selection for energy corrected milk yield will require the use of different sires based on the ranking of sires for different traits. The selection based on TDMY is expected to result faster genetic gain in Mehsana buffalo. However, the selection of sire based on energy corrected milk is expected to the higher energy efficiency of milk and it may provide higher total revenues to farmers in context to fat or energy efficient milk.

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