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Journal of Animal Science - Animal Genetics

Estimates of genetic parameters for growth traits in Brahman cattle using random regression and multitrait models1

 

This article in JAS

  1. Vol. 93 No. 8, p. 3814-3819
     
    Received: Apr 01, 2015
    Accepted: June 16, 2015
    Published: August 3, 2015


    2 Corresponding author(s): ricardo@dracena.unesp.br
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doi:10.2527/jas.2015-9164
  1. T. S. Bertipaglia*,
  2. L. O. D. Carreño*,
  3. R. R. Aspilcueta-Borquis*,
  4. A. A. Boligon,
  5. M. M. Farah*,
  6. F. J. Gomes*,
  7. C. H. C. Machado,
  8. F. S. B. Rey* and
  9. R. da Fonseca 2§
  1. * São Paulo State University “Júlio de Mesquita Filho” (UNESP), Jaboticabal, São Paulo, 14884-900, Brazil
     Federal University of Pelotas (UFPel), Rio Grande do Sul, 96010-970, Brazil
     Brazilian Association of Zebu Breeders (ABCZ), Uberaba, Minas Gerais, 38022-330, Brazil
    § São Paulo State University “Júlio de Mesquita Filho,” Dracena, São Paulo, 17900-000, Brazil

Abstract

Random regression models (RRM) and multitrait models (MTM) were used to estimate genetic parameters for growth traits in Brazilian Brahman cattle and to compare the estimated breeding values obtained by these 2 methodologies. For RRM, 78,641 weight records taken between 60 and 550 d of age from 16,204 cattle were analyzed, and for MTM, the analysis consisted of 17,385 weight records taken at the same ages from 12,925 cattle. All models included the fixed effects of contemporary group and the additive genetic, maternal genetic, and animal permanent environmental effects and the quadratic effect of age at calving (AAC) as covariate. For RRM, the AAC was nested in the animal’s age class. The best RRM considered cubic polynomials and the residual variance heterogeneity (5 levels). For MTM, the weights were adjusted for standard ages. For RRM, additive heritability estimates ranged from 0.42 to 0.75, and for MTM, the estimates ranged from 0.44 to 0.72 for both models at 60, 120, 205, 365, and 550 d of age. The maximum maternal heritability estimate (0.08) was at 140 d for RRM, but for MTM, it was highest at weaning (0.09). The magnitude of the genetic correlations was generally from moderate to high. The RRM adequately modeled changes in variance or covariance with age, and provided there was sufficient number of samples, increased accuracy in the estimation of the genetic parameters can be expected. Correlation of bull classifications were different in both methods and at all the ages evaluated, especially at high selection intensities, which could affect the response to selection.



INTRODUCTION

Beef cattle breeding programs have generally selected for growth traits such as weight or weight gain at certain ages. These traits are easy to measure, have medium to high heritability, and respond well to selection, thereby resulting in genetic progress (Bertipaglia et al., 2012; Boligon et al., 2009). For genetic analyses, weights at different ages are widely used, particularly in traditional multitrait models (MTM).

However, another methodology, random regression analysis (random regression models [RRM]; Kirkpatrick et al., 1990), has become popular. It allows us to analyze data taken repeatedly over the productive life of the animal and allows for the prediction of a genetic growth curve as a whole value, avoiding the use of adjusted weights. In addition, RRM takes into account the covariance between any 2 age measures (Meyer and Hill, 1997) and is widely used in beef (Albuquerque and Meyer, 2001a,b; Meyer, 1999, 2001, 2003; Nobre et al., 2003) and dairy cattle (Kirkpatrick et al., 1994; Jamrozik et al., 1997; El Faro and Albuquerque, 2003) studies.

Through RRM, it is possible to describe the behavior of the variance components, more accurately estimate and predict parameters and breeding values, and identify the growth stages in which there are greater genetic variability changes in the growth curve. The RRM has frequently been used in Brazilian Nellore cattle studies, but there are no similar studies for Brahman cattle. Because this methodology can describe the changes in the variances of BW with age (Albuquerque and Meyer, 2001a; Boligon et al., 2009), it can help identify genetically superior animals at a young age. Therefore, RRM is important to Brazilian Brahman improvement programs.

The objective of this work was to estimate genetic parameters for Brahman cattle weights between 60 and 550 d of age using both RRM and MTM to aid in developing breeding program guidelines and compare the estimated breeding values obtained using these 2 methodologies.


MATERIALS AND METHODS

Animal Care and Use Committee approval was not necessary for this study because the data were obtained from an existing database.

Data and Management

Data on purebred, registered Brahmans born between April 2001 and April 2013 in the Southeast and Midwest regions of Brazil were obtained from the Brazilian Association of Zebu Breeders (Uberaba, Brazil). Weight measurements were taken an average of every 3 mo, ranging from 39 to 430 kg. Weaning was conducted at an average of 205 d. All animals were bred using either AI or controlled, natural breeding and were raised on pasture and nursed by their dams. Only animals that were nursing or weaned were considered in this data set.

The contemporary groups (CG) for each of the methods were defined as follows:

  • RRM: animals born on the same farm (5 farms), sex (41,961 females and 36,680 males), season of birth (53,708 born in the rainy season and 24,933 born in the dry season), year of birth, weighing station (48,859 measurements in the rainy season and 29,782 measurements in the dry season), and year of weighing for a total of 527 GC levels and

  • MTM: animals born on the same farm (5 farms), sex (10,629 females and 6,771 males), season of birth (10,702 born in the rainy season and 6,698 born in the dry season), year of birth, weighing station (11,200 measurements in the rainy season and 6,200 measurements in the dry season), and year of weighing for a total of 100 GC levels.

The data file for the RRM analysis contained only animals with more than 4 weight measurements; there were at least 3 animals per age class, and each CG must have contained a minimum of 2 bulls and 8 animals. For MTM, the data file contained a minimum of 2 bulls and 3 animals per CG. After the restrictions for consistency, the RRM used 78,641 weight measurements between 60 and 550 d of age from 16,298 cattle and the MTM used 17,385 weight measurements between 60 and 550 d of age from 12,925 cattle.

The final RRM file contained 6,377 (39.10%), 6,572 (40.30%), 3,183 (19.50%), and 1,296 (1.00%) animals with 4, 5, 6, and 7 to 10 records, respectively. The average weight for RRM was 223.54 kg with a SD of 73.11 kg. For MTM, the average weight was 191.72 kg with a SD of 76.17 kg. The relationship matrix for RRM contained 24,931 animals with 8,081 dams and 900 bulls, and the matrix for MTM contained 21,701 animals with 8,253 dams and 859 bulls, for a total of 4 and 6 generations for both.

All data file manipulations and the statistics obtained were performed using R software (R Development Core Team, 2013).

Analysis

The matrix representation of the models for RRM and MTM isin which y is the vector of observations; b is the vector of fixed effects; a is the vector of random coefficients for additive effects; m is the vector of random coefficients for additive maternal effects; p is the vector of random coefficients for animal permanent environmental effects; e is the vector of residual effects; and X, Z1, Z2, and W1 are the corresponding incidence matrices.

For both RRM and MTM, the CG fixed effect (farm, sex, year of birth, and year and weighing station) was included. For RRM, the age at calving (AAC) was nested into the animal’s age class (linear and quadratic effect) as a covariable. Ten age classes were formed with 6,766 to 9,121 measurements for each class, so as to have at least the minimum number of animals in each class. The AAC was nested to estimate the influence of maternal age on the growth of the progeny, because this is not constant over time. Additive genetic (a), maternal genetic (m), and animal permanent environmental (p) effects were all considered random effects.

Orthogonal Legendre polynomials about the age at weighing were used as the fixed effect model for calculating the population’s mean curve in the RRM analysis. For the analysis of the 3 random effects (additive genetic, maternal genetic, and animal permanent environmental), Legendre polynomials of orders 3 (quadratic), 4 (cubic), and 5 (quartic) were used. The residual variances were modeled using classes with 1 and 5 levels. The 5-level class was constructed by grouping nearby ages to the following age classes—60 to 120, 121 to 205, 206 to 365, 366 to 450, and 451 to 550 d of age—aiming to verify whether the residual variances change with age.

Covariance components were estimated using the animal model for RRM and MTM with the maximum restricted likelihood on WOMBAT (Meyer, 2007). The RRM results of each selection criterion are expressed as a comparison between them, because lower values of Bayesian information criterion (BIC; Wolfinger, 1993) indicate the best fit. The RRM citation in this study follows the standard , referring leg to the Legendre polynomials and the order of the covariance function for the additive genetic effect (ka), maternal genetic (km), animal permanent environmental (kp), and structural residual variance (r).

For MTM, additive genetic, maternal genetic, animal permanent environmental effects and weights adjusted to 60, 120, 205, 365, and 550 d of age were considered. The age of the animal at weighing and AAC (linear and quadratic effect) were covariates.


RESULTS AND DISCUSSION

For RRM, according to the BIC, the most appropriate model was the order of 4 to all effects: additive genetic, maternal genetic, animal permanent environmental, and residual variance with 5 levels (leg444_5). The means and SD in both methods increased with age, showing the growth trend (Table 1).


View Full Table | Close Full ViewTable 1.

Number of records, mean, SD, and heritability for BW at 60, 120, 205, 365, and 550 d of age with the random regression and multitrait models

 
Model used2
Random regression model
Multitrait model
Weight1 N Mean3 SD3 h2 N Mean3 SD3 h2
W60 129 85.52 18.08 0.60 1,427 85.46 15.48 0.47
W120 159 134.18 21.59 0.34 4,782 131.11 22.69 0.44
W205 176 192.26 29.71 0.50 5,939 190.89 31.56 0.50
W365 203 237.96 40.87 0.67 2,920 245.01 43.16 0.62
W550 112 317.81 47.08 0.75 2,317 317.03 59.03 0.72
1W60 = BW at 60 d of age; W120 = BW at 120 d of age; W205 = BW at 205 d of age; W365 = BW at 365 d of age; W550 = BW at 550 d of age.
2N = number of records; h2 = additive heritability with SE ranging from 0.008 to 0.045.
3Expressed as kilograms.

The additive heritability estimates ranged from 0.34 to 0.75 for RRM (Fig. 1) and from 0.47 to 0.72 for MTM. The high heritability value may reflect the additive genetic variance, and therefore, selection for weights could be efficient if performed at 120 d of age, as it was in this period in which the additive heritability estimates were growing, allowing identification of the genetic merit of animals for growth traits.

Figure 1.
Figure 1.

Estimates of additive heritability, maternal heritability and estimates of animal permanent environmental variance as a proportion of total phenotypic variance for BW of cattle at different ages obtained with the random regression model. h2a = estimates of additive heritability; h2m = estimates of maternal heritability; p2 = proportion of animal permanent environmental variance in relation to the total phenotypic variance.

 

These results are lower when compared with studies for weights with Nellore with RRM (0.12 to 0.22) and MTM (0.11 to 0.25; Nobre et al., 2003). However, similar estimates (from 0.32 to 0.43) were found with MTM in Brazilian Brahmans (Faria et al., 2011), and in a study of the same population in a bivariate analysis (Bertipaglia et al., 2012), lower estimates for BW at 550 d of age (0.48) were obtained.

Although selection for BW at 120 d of age (W120) should be efficient, in practice it would be difficult to carry out because the culled animals would remain in the herd until weaning (205 d); there is no cost advantage to perform selection at this age. Therefore, selection at 205 d is more feasible than that at 120 d of age, because the culled animal could be sold and heritability is higher. Besides, the genetic correlations between BW at 205 d of age (W205) and BW at 550 d of age (W550; a weight at an age closer to slaughter) are greater than that between W120 and W550 (Table 2).


View Full Table | Close Full ViewTable 2.

Estimates with the random regression model and multitrait model (in parentheses) for additive genetic correlation (above the top table diagonal), maternal genetic (below the top table diagonal), and animal permanent environmental (random regression model only, in the bottom table) for BW from 60, 120, 205, 365, and 550 d of age

 
W60
W120
W205
W365
W550
Weight1 Additive genetic and maternal genetic correlations
W60 0.42 (0.82) –0.08 (0.81) –0.06 (0.46) –0.12 (0.58)
W120 0.50 (0.70) 0.83 (0.86) 0.62 (0.67) 0.51 (0.52)
W205 0.20 (0.54) 0.94 (0.88) 0.87 (0.74) 0.77 (0.62)
W365 0.09 (0.49) 0.84 (0.84) 0.96 (0.94) 0.93 (0.87)
W550 –0.16 (0.51) 0.70 (0.82) 0.89 (0.96) 0.96 (0.80)
Animal permanent environmental correlations
W60 0.93 0.89 0.85 0.79
W120 0.98 0.76 0.53
W205 0.83 0.43
W365 0.60
W550
1W60 = BW at 60 d of age; W120 = BW at 120 d of age; W205 = BW at 205 d of age; W365 = BW at 365 d of age; W550 = BW at 550 d of age.

The estimate of maternal heritability was nearly constant for all ages, with a maximum at 140 d for RRM (0.08; Fig. 1) and at 205 d (0.09) for MTM. This differs from other estimates found for the Brahman breed (0.11 and 0.18, respectively; Pico et al., 2004; Kriese et al., 1991), which decreased with age. However, results similar to this study were observed in a bivariate analysis, with a maximum maternal heritability for W205 (0.13 and 0.14; Plasse et al., 2002). The results of this study show that maternal effects begin to decline after weaning and remain nearly constant as a residual effect throughout the life of the offspring. Therefore, according to MTM, greater selection response for maternal ability can be expected if the selection is performed based on weaning weights, because at weaning, maternal heritability is at the maximum.

For RRM, a better age for selection to maximize the direct response would be at 140 d of age (or at approximately 120 d of age). The maternal ability measure at 120 and 205 d of age would be the same because the genetic maternal correlation is 0.94 (Table 3). Calf weighing is more frequently done at 205 d than at either 120 or 140 d, and because the genetic correlation between W120 and W205 is so high and the maternal heritability is about the same at W205 as W120 (or BW at 140 d of age), it would be more practical to perform selection for maternal ability at 205 d.


View Full Table | Close Full ViewTable 3.

Percentages and numbers of bulls (in parenthesis) that would be selected in common based on breeding values obtained with the random regression and multitrait models for BW from 60, 120, 205, 365, and 550 d of age for 5, 10, 20, and 50% selection intensities

 
Percentage of bulls selected
Weight1
Selection intensity W60 W120 W205 W365 W550
5% (192) 8% (16) 53% (101) 49% (95) 48% (93) 39% (75)
10% (384) 17% (67) 58% (225) 50% (193) 51% (197) 43% (166)
20% (768) 32% (251) 63% (487) 58% (446) 57% (443) 52% (402)
50% (1,920) 58% (1,113) 79% (1,516) 76% (1,453) 73% (1,417) 72% (1,380)
1W60 = BW at 60 d of age; W120 = BW at 120 d of age; W205 = BW at 205 d of age; W365 = BW at 365 d of age; W550 = BW at 550 d of age.

The proportion of animal permanent environmental variance in relation to the total phenotypic variance with RRM ranged from 0.15 to 0.34 (Fig. 1). This permanent environment variance is higher in the progeny’s early life because at this stage, the animal is more susceptible to environmental variations, which will be reduced over time.

The estimates of additive genetic correlation (Table 2) between BW at 60 d of age (W60) and other weights (Table 2) for RRM range from low negative to positive average (–0.06 to 0.42). This differs from the values found with MTM (0.46 to 0.82), showing that RRM is unreliable for extremes of the age range, especially if there is a dearth of data at these ages. When comparing the 2 methods, the best was MTM (–284,783.417 versus –63,139.794), according to the BIC. Similar results were observed for Brahmans with MTM (0.51 to 0.79; Faria et al., 2011). The negative estimates in this work as well as the estimates found in the literature with RRM (–0.48 to 0.05) between weight at 100 d and other ages (Mota et al., 2013) is unexpected and may reflect the smaller amount of information for W60. Another issue could be the use of orthogonal polynomials for cattle growth data, such as variance and covariance inconsistencies at extreme ages, because of the greater emphasis placed on polynomial observations located at the extremes of the curve (Meyer, 1999).

Estimates of additive genetic correlation using RRM and MTM between weights at 120 (0.83, 0.62, 0.51; 0.86, 0.67, 0.52); 205 (0.87, 0.77; 0.74, 0.62); and 365 d (0.93; 0.87), respectively, with subsequent ages were of medium and high magnitudes in both models. This suggests that the same genes control genetic effects on these ages and that selection for weights at these ages can have the same effect on weights at later ages. The later the selection is performed, however, the greater the correlation between weights at advanced ages. Nonetheless, later selection may not be desirable because of the difficulty in handling and the increased production costs associated with older animals. These results are in agreement with others studies (0.44 to 0.98; Albuquerque and Meyer, 2001a; Dias et al., 2006; Boligon et al., 2009).

The estimates of maternal genetic correlation between W60 and the other ages (Table 2) ranged from low negative to medium positive (–0.16 to 0.50) and were lower than those obtained through MTM (0.51 to 0.70). This may be a reflection of the low number of weight measurements at 60 d of age. The estimates of maternal genetic correlations between other ages were of high magnitude and similar for both RRM (0.70 to 0.96) and MTM (0.80 to 0.96). This suggests that the genetic potential possessed by the dam for maternal ability (milk and protection, among others) has an additive association with the offspring’s weight. This is a residual effect at older ages and decreases with age. These results agree with studies on Nellore using RRM (above 0.70; Nobre et al., 2003).

The animal permanent environmental correlations with RRM (Table 2) showed moderate to high estimates between weights of medium to high magnitude (0.43 to 0.98). These results highlight the importance of the permanent environmental effect. Permanent environmental factors influencing early ages may be reflected in weights at older ages by its residual effect.

To compare the 2 methods, percentages and numbers of bulls that would be selected in common based on their breeding values estimated with RRM and MTM at standard ages for different selection intensities were calculated (Table 3). By increasing the selection intensity, the correlation of ranking bulls on different methodologies was lowered. This is because the higher the bull selection intensity, the more specific the selection of the best breeding values and the less probable the concordance of the methods in few animals. This result was consistent for all columns (Table 3).

By analyzing the rows, it is easy to see the effect of the amount of available data. Body weight at 60 d of age and W550 were the traits with less data (Table 1). For each selection intensity (row), lower correlations were found for these traits. Therefore, for a more comprehensive agreement between the methods, a large amount of data should be available for genetic evaluation, especially for high selection intensities. With the amount of data used in this study, the 2 methods would provide quite different results regarding the selected animals. However, the method that would maximize the genetic progress could be determined only by a simulation study.

Conclusions

The RRM adequately modeled changes in variance or covariance with age, with an order of 4 to all effects: additive genetic, maternal genetic, animal permanent environmental, and residual variance with 5 levels; however, the best model was multitrait, according to BIC. Using either methodology, selection for weight could be efficient if performed at 120 d of age, a period in which the estimates of additive heritability were growing, thereby allowing for identification of an animal’s genetic merit for growth characteristics.

The RRM adequately modeled changes in variance or covariance with age in a Brazilian Brahman cattle population, allowing the identification of the ages where heritability estimates and genetic correlation were maximum. The analysis of the results indicates that the breeding scheme that is usually used for Nellore cattle in Brazil would serve as well for the breeding programs for Brahman cattle.

Selection based on any weight from weaning on will affect the weight at older ages. Therefore, selection index and line creation should be used to attempt to control the excessive increase in the female’s weight due to selection. In application of high selection intensity, differences were observed in the classification of bulls when comparing RRM and MTM methodologies. For smaller data sets, as in this study, the MTM performed better and should be preferred to RRM.

The weights analyzed in this study could be used as selection criteria to improve the growth characteristics of this population of Brazilian Brahmans.

 

References

Footnotes


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