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Cuban Journal of Agricultural Science

Print version ISSN 0864-0408On-line version ISSN 2079-3480

Cuban J. Agric. Sci. vol.54 no.4 Mayabeque Oct.-Dec. 2020  Epub Dec 01, 2020



Multi-trait selection in Holstein cows

A. Hernández1  *

Raquel Elena Ponce de León1

1Instituto de Ciencia Animal, Apartado Postal 24, San José de Las Lajas, Mayabeque, Cuba.


The phenotypic and genealogical data of 1 571 Holstein cows located in three livestock enterprises during the years 1984 to 2016 were used. The purpose of this study was to carry out the multi-trait selection of dairy production, reproduction and longevity traits by means of the preparation of selection indexes (SI) through the analysis of main components (MC). Correlations and breeding values (BV) were estimated for the traits: cumulative milk production up to 305 days (BVL305), duration of lactation (BVDL), age at first parturition (BVAP1), gestation parturition interval (BVGPI), accumulated milk per life (BVTML) and productive life (BVPL) by means of a multi-trait animal model. The SPSS statistical package was used to perform the MC analysis, for which the BV were standardized, and the Kaiser criterion was used to select the MC that explains the greatest genetic variation. The genetic correlations between L305, TML and DL showed mean values (0.55, 0.47 and 0.27), and between GPI and PL of 0.29. The first two main components (MC1, MC2) were those that obtained the Kaiser criterion and explained 53.7 % of the total variance of the BV. Linear correlations between BVs with each main component showed that L305, DL and TML were related with the MC1, and GPI and PL to MC2. It is concluded that in Holstein cows it is possible to perform multi-trait selection by constructing selection indexes based on the first two MCs, since they showed considerable genetic variation.

Key words: main component analysis; dairy cattle; selection indexes

Genetic evaluation is a process that allows obtaining the breeding value of the animals for one or more characteristics and in that way selecting as reproducers those with the greatest genetic merit (Ruales et al. 2007). The mixed model methodology allows obtaining the BLUP (Best Linear Unbiased Prediction) or MPLI (Best Linear Unbiased Prediction) of the breeding value of the animals evaluated based on their own records and their relatives records (Kennedy et al. 1988).

The traditional selection indexes (Smith 1936 and Hazel 1943) are used to select animals by linear combinations of breeding values with economic weights. However, it is sometimes difficult to obtain the economic weights (the information is not available), in addition to being subject to constant market variations.

An alternative was to develop an index in which each trait had a weight to obtain the gain desired by the farmer without considering the relative importance of the traits in an economic sense (Rouvier 1969 and Yamada et al. 1975). Pesek and Baker (1969) suggest that the farmer should specify the amount of improvement required for each characteristic to achieve the desired gain. Thus, the desired gain is incorporated with the estimates of the genetic parameters in the selection index.

Recently, several countries such as Brazil and India have incorporated the main component analysis (MC) in the construction of selection indexes in dairy cattle (Bignardi et al. 2012 and Khan et al. 2013). Authors such as Buzanskas et al. (2013) stated that the use of MC is a methodology to build linear combinations between the breeding values of the available traits in a database, taking into account the eigenvalues of the main component and the eigenvectors of the traits in each main component, which are variability measures. The great advantage of this procedure is that the eigenvectors are orthogonal, that is, they are not correlated and therefore they can be added together, in this way the selection based on the index maximizes the genetic merit for the included characteristics.

This study was carried out with the purpose of carrying out the multi-trait selection of milk production, reproduction and longevity traits in Holstein cows by means of the preparation of selection indexes (SI), through the analysis of main components.

Materials and Methods

Description of the database. The information on milk production and reproduction, which was registered in the Sistema de Control Pecuario (SISCOP), of Holstein cows with parturitions between 1984 and 2016 was used. These cows were located in three livestock enterprises (Empresa Pecuaria Genética de Matanzas in Matanzas province, Los Naranjos in Mayabeque and Camilo Cienfuegos in Pinar del Río) in the western region of the Republic of Cuba.

The records of live animals were used as well as of those that had caused leave. From the milk production data file (live + pouled) were obtained the traits: Cumulative milk production up to 305 days (L305), duration of lactation (DL) and age at first parturition (AP1). While, from the reproduction data file (live + pouled) the gestation parturition interval (GPI) was calculated. From the file of pouled of milk production, accumulated milk for life (TML) was calculated; as well as the longevity trait called productive life (PL) determined as the months from the first to the last parturition.

Creation of contemporaries groups. A general linear model (GLM) was used using the statistical package SAS (2013) version 9.3 to define the significant fixed effects (P <0.01) to be included in contemporaries group (CG). The herd-year- parturition season combination was considered as CG and those groups made up of less than 3 animals were eliminated. Two parturition seasons were determined: the rainy (from May to October) and the dry (from November to April).

Subsequently, all the files were joined, leaving only those cows that had BV information for all the studied traits. The final file showed a total of 1,571 Holstein cows. The pedigree file was made up by a total of 153,963 individuals. The pedigree information reached the grandparents, through the maternal and paternal lines.

Correlation estimation. The ASREML program (Gilmour et al. 2003) was used to estimate the genetic and environmental correlations and the breeding values (BV) using the following multi-trait animal model:

y1y2y3y4y5y6= x1000000x2000000x3000000x4000000x5000000x6b1b2b3b4b5b6  +  z1000000z2000000z3000000z4000000z5000000z6a1a2a3a4a5a6+ e1e2e3e4e5e6


yi =

vector of observations for the i-th trait

bi =

vector of fixed effects (herd-year-parturition season and parturition age as linear and quadratic covariates) for the i-th trait

ai =

vector of the random effects of the animal for the i-th trait

ei =

vector of random residual effects for the i-th trait

xij y Zij =

design matrices relating data to fixed and random effects, respectively

The main components analysis was carried out using the SPSS (2002) statistical package version 11.5. This analysis was performed as a way to condense or summarize the information contained in several original variables (in this case the BVs) into a smaller group of new composite dimensions or variants called main components, with minimal loss of information, and to explore the relations between the BVs obtained from the single- trait analysis BVL305, BVDL, BVTML, BVAP1, BVGPI, BVPL, to explain the data structure (Hair et al. 2009).

Due to differences in units of measurement, the BVs for all traits were standardized. The Kaiser (1960) criterion was used to select the main component that explains the highest genetic variation in the data. This criterion takes into consideration only those main components with eigenvalues above unity. The eigenvalue of a main component is associated with the variance of all the traits included in the main component. Each eigenvalue is associated with a unit vector called an eigenvector (Rencher 2002). The eigenvectors have the strength and direction of the variance of each trait with the main component. In this study, a variable correlation matrix was used to obtain eigenvalues.

The first main component explains the largest percentage of the total variance of the BVs. The second explains the second largest percentage, until all the variance in the database is explained.

Each main component can generate a new value called the main component score, which is the sum of the standardized BVs of the weight of each trait by its respective standardized score coefficient (SSC). In this way, the main component can be used as an index to evaluate animals, for multiple traits. The standardized scoring coefficients of each BV in each main component were obtained using the following formula:

SSCij =eigenvectorijeigenvaluej



Standardized scoring coefficients of the BVs of each trait in the j-th main component

The main component (index) score was calculated as: MPjl= i=1ji=1lSSCijVGil 

Where :


Main component score (index score) for the l-th animal in the j-th main component


Standardized scoring coefficients of the BVs of the i-th trait in the j-th main component

BVil =

Standardized estimated breeding value of the i-th trait in the l-th animal

Results and Discussion

Correlation estimation. The estimates of genetic and environmental correlations in Holstein are showed in table 1. The genetic correlations between cumulative milk up to 305 days, milk production per life, and duration of lactation were moderate, so that selection for milk production will also improve, in some way, the accumulated milk per life and the duration of lactation. While, the genetic correlation of accumulated milk up to 305 days with the rest of traits was low, this implies that these traits will change almost independently of the milk production.

Table 1 Estimates of genetic (above the diagonal) and environmental (below the diagonal) correlations and standard errors (±) in traits of milk production, reproduction and longevity of Holstein cows. 

Traits L305 DL TML AP1 GPI PL
L305 0.47±0.01 0.55±0.01 -0.20±0.01 0.09±0.01 0.12±0.01
DL 0.35±0.01 0.27±0.02 -0.06±0.01 0.20±0.01 0.21±0.02
TML 0.36±0.01 0.24±0.01 -0.29±0.01 -0.03±0.01 0.05±0.02
AP1 0.01±0.01 0.02±0.01 -0.09±0.01 -0.09±0.02 -0.11±0.02
GPI 0.07±0.01 0.17±0.01 -0.10±0.01 -0.03±0.01 0.29±0.01
PL 0.10±0.01 0.10±0.01 0.75±0.01 -0.13±0.01 0.05±0.01

L305: accumulative milk production up to 305 days, DL: duration of lactation, TML: accumulative milk per life. AP1: age at first parturition, GPI: gestation parturition interval, and PL: productive life.

The previous results show that the Holstein cows with the highest accumulated productions up to 305 days were not the longest-lived. These corroborate previous studies carried out in our country in the same breed (Ponce de León and Guzmán 1993); as well as in the Siboney de Cuba breed (Ponce de León et al. 2002) where antagonistic values were found in the genetic correlations between milk in first lactation and longevity (-0.60 to -0.64 and from -0.30 to -0.61, respectively).

The previous performance is probably due to the fact that there was no differential treatment for cows with high production. They are disadvantaged in the diet because the amount of concentrate offered is in correspondence with the average of the high group, which is lower than their average milk production, and therefore they do not cover their nutritional requirements. This causes that the cows with high production had reproductive problems (they do not show heat and are not pregnant) so they are the most likely to cause loss.

The genetic correlations of age at first parturition with L305 and TML were moderate and negative, which shows that these traits, to some extent, will change in the opposite direction. Similar results were seen in the Holstein in Ethiopia by Ayalew et al. (2017) where the estimates of the genetic correlations between AP1 and L305 were -0.24 ± 0.11.

Several authors (Ettema and Santos 2004, Ojango et al. 2005 and Ruiz et al. 2007) reported that the effect of age at first parturition on longevity and yield of the productive life of the animal was maximized at an age of 20 to 36 months in the first lactation. On the other hand, Buzanskas et al. (2010) suggest that animals that give birth at a young age are more probable to have better reproductive yield for a long time.

The analysis of multi-trait data, used in this study, is useful in the selection of the best animals for replacement, since in advance it allows knowing the possible effect of the selection for milk production on the reproductive and longevity traits studied. Authors such as Unalan and Cebeci (2004) refer to the importance of these analyzes by providing estimates of reliable and unbiased genetic parameters. On the other hand, the variance-covariance estimates help to evaluate the magnitude of the genetic correlations between the traits that are the objective of selection, which allow establishing a total merit index for the precise evaluation of the genetic merit of the animals in the herd. .

Main components analysis The main component analysis showed that the first two main components (MC1, MC2) reached eigenvalues higher than the unit, thus fulfill the Kaiser criterion (table 2). These explained 53.7 % of the total variance of the breeding values. The results of this study correspond to others where it was also shown that with the use of MC analysis the dimensionality of traits can be reduced.

Table 2 Eigenvalues for each main component, total and accumulated proportion of the additive genetic variance, from the first to the sixth main component (MC1-6), in Holstein cows 

Components Eigenvalues
Total % of the variance additive genetic % accumulated
MC1 2.098 34.972 34.972
MC2 1.127 18.781 53.753
MC3 0.974 16.232 69.985
MC4 0.938 15.632 85.617
MC5 0.509 8.479 94.096
MC6 0.354 5.904 100.000

According to the Bignardi et al. (2012) studies in Holstein cows, only two MCs were required to summarize the genetic variation of the bulls among the 10 traits evaluated (10 monthly milk productions). In Canchim cows, Buzanskas et al. (2013) reported that 73.37 % of the total variance of the breeding values of three reproductive traits and one growth trait was explained by two MCs. Also in Mambí de Cuba cows (3/4Holstein 1/4Cebú), Hernández and Ponce de León (2018) reported that 53.1 % of the total variance of breeding values was explained by the first two MCs, in dairy production, reproduction and longevity traits.

The linear correlations between the BV of the studied traits in Holstein cows with each main component (table 3) showed that the traits related to milk production and the duration of lactation are highly related to MC1 while GPI and PL were more associated with MC2.

Table 3 Linear correlations of the standardized BV with the main component 1 and 2 (MC1-2), in Holstein cows 

BV Components
BVL305 0.842 -0.159
BVDL 0.717 0.337
BVTML 0.728 -0.478
BVGPI 0.284 0.564
BVPL 0.255 0.639
BVAP1 -0.446 0.184

The weights of these indexes are standardized scoring coefficients (SSC) for each standardized BVB in Holstein cows (table 4). The highest of the absolute values of the SSC is the one of high relative importance of the standardized BV in the main component. This importance is explained by the higher linear correlation between the traits with the main component (table 3).

Table 4 Standardized scoring coefficients (SSC) of each estimated standardized BVfor all traits in each main component (MC1-2), in Holstein cows 

BV Standardized scoring coefficients
BVL305 0.401 -0.141
BVDL 0.342 0.299
BVTML 0.347 -0.424
BVGPI 0.135 0.500
BVPL 0.122 0.567
BVAP1 -0.213 0.164

The main component score (index value) for each Holstein animal, in each main component, was calculated as:

MC1= 0.401 (BVL305) + 0.342 (BVDL) + 0.347 (BVTML)

MC2= 0.500 (BVGPI) + 0.567 (BVPL)

In Holstein cows, the selection for BVL305, BVTML and BVDL by MC1 could be carried out separately from the selection for BVGPI and BVPL by MC2 considering the linear correlation between the BV with each main component (table 3). This corresponds to the genetic correlations between the studied traits (table 1) where there was a mean genetic correlation between L305, TML and DL (0.55, 0.47 and 0.27) and between GPI and PL (0.29).

Using main component analysis, animals can be selected based on just two scores generated by MC1 and MC2 instead of the six breeding values. According to Buzanskas et al. (2013) when using this approach, the animals can be selected in a balanced way since the scores of each main component are linear combinations of all the breeding values of the evaluated traits, and not empirical weights typically used in improvements programs. .

The authors cited above stated that the use of MCs is a methodology to build linear combinations between the breeding values of the traits available in a database, taking into account the eigenvalues of the main component and the eigenvectors of the traits in each main component, which are measures of variability. In this way, traits with low heritability estimates, which are rarely taken into consideration in a direct selection process, can be included in the main component.

In the Holstein cows analyzed in this study, the MC1 can be considered a genetic index of milk production because it favors genetically superior animals for BVL305, BVTML and BVDL; while the MC2 can be a genetic index related to reproduction and longevity that would consider the VGIPG and VGVP.


The results show that in Holstein cows it is possible to perform multi-trait selection by constructing selection indexes based on the first two MCs, since they showed considerable genetic variation.


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Received: April 15, 2020; Accepted: July 31, 2020


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Los autores declaran presentar contribución igualitaria en la concepción de la investigación, obtención y procesamiento de los datos y redacción del documento

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