Efectos geneticos directos y maternos para caracteristicas de crecimiento de bovinos Indubrasil.
Many researchers around the world have shown that direct and maternal genetic effects significantly influence early (pre-weaning) and late (post-weaning) growth of cattle [33, 34] and other animal species, including sheep (Ovis arles) [26, 59]. During the last decade, there have been significant efforts in Mexico directed towards the estimation of genetic parameters of growth traits in various Bos taurus and Bos indicus beef breeds, such as: Tropicarne , Simmental , Nelore , Charolais , Sardo Negro , Brahman , Guzerat , Brangus/Salers , Limousin  and Charbray . However, there is no information in the scientific literature related to the magnitude and importance of direct and maternal genetic effects (heritability) for growth traits of Indubrazil cattle raised in Mexico, although this breed, along with the Brahman, is one of the two major Zebu breeds in this country. Indubrazil is a beef cattle breed from Brazil and is the result from crosses between Gyr, Guzerat and Nelore cattle. It was introduced to Mexico (sires and cows) from 1945 to 1946. The breed was distributed from Yucatan, along the Gulf of Mexico coast, to Coahuila and Nuevo Leon, in Northern Mexico. This Zebu breed has shown good adaptability to a wide range of environmental conditions of Mexico. In the tropical areas, is well accepted by dual-purpose cattle producers because they use it to obtain Brown Swiss x Zebu and Holstein x Zebu crosses for milk and calf production. The "Asociacion Mexicana de Criadores de Cebu" has an Indubrazil database with approximately 168,760 registered cattle .
One of the few studies conducted with Indubrazil cattle not done in Mexico is the work reported by Santos et al. , who evaluated the influence of direct and maternal genetic effects on weaning weight of animals reared in the State of Bahia, Brazil. However, it is necessary to know the direct and maternal heritability of other growth traits (e.g., birth and yearling weights) which also affect the efficiency of beef production systems, in order to establish successful breeding programs. In addition, genetic parameters are specific to each cattle population and heavily influenced by the environment. Hence, the objective of the present study was to estimate, fitting animal models, the variance components and genetic parameters for birth, weaning and yearling weights of Indubrazil cattle reared under tropical conditions of Mexico.
MATERIALS AND METHODS
Location and climate
The current study was conducted at Playa Vicente Research Station from the National Institute for Forestry, Agriculture and Livestock Research (INIFAP). The experimental site is located at 17[degrees] 19' NL and 95[degrees] 41' WL, at 95 meters above sea level, in the Municipality of Playa Vicente, in the State of Veracruz, Mexico. The climate is tropical wet , with mean annual temperature and precipitation of 26.8[degrees]C and 2200 mm, respectively .
Records of 598 Indubrazil calves born during a 27-year period (1980-2006) were analyzed. These calves were produced from 35 sires and 281 dams. Sires were mated to dams mainly through artificial insemination, but there was also some natural mating.
From birth to weaning, calves were reared with restricted suckling, which lasted one hour (h) in the morning (07:00 to 08:00 h) and one h in the afternoon (17:00 to 18:00 h). The rest of the day (d) the calves were kept in rotational grazing on African Star grass (Cynodon plectostachyus). Weaning was performed at seven months of age, on average. Fifteen d before and 30 d after weaning, calves were supplemented with 1 kg/calf/d of a concentrate feed with 18% crude protein, 70% total digestible nutrients and 2.7 Mcal of metabolic energy/kg of dry mater. From weaning to yearling, the calves were still maintained in rotational grazing on African Star grass.
The evaluated traits were: birth weight, weaning weight adjusted to 205 d and yearling weight adjusted to 365 d. Weaning and yearling weights were linearly adjusted as recommended by the Guidelines for Uniform Beef Improvement Programs .
Before estimating variance components and genetic parameters, preliminary statistical analyzes were performed for each trait, in order to determine which fixed effects were significant sources of variation. For this purpose, the Mixed procedure (PROC MIXED) was implemented in the SAS program . PROC MIXED computations are based on likelihood principles  to obtain (restricted) maximum likelihood estimates of the variance component parameters. The DDFM = Satterth option of the Mixed procedure of SAS was used for computing the denominator degrees of freedom for the tests of fixed effects. The DDFM = Satterth option (a general Satterthwaite approximation) implemented here is intended to produce an accurate F approximation. The fixed effects included in the full model were: year of birth (1980, 1981, ..., 2006), birth season (December to May; June to November), calf sex, first-order interactions derived from these three effects, and cow age at calving in d as a linear and quadratic covariable. In addition, the preliminary full model included sire as a random effect. To determine the final models, sequential analyzes were performed by removing from the full model not significant interactions and covariates (P > 0.05). The final model for birth weight resulting from these preliminary analyzes included year of birth, birth season, calf sex, year of birth x birth season interaction, and the age of dam at calving, as well as sire as a random effect. The final model to analyze weaning weight was similar to the model for birth weight, but instead of year of birth x birth season interaction it included year of birth x calf sex interaction. For yearling weight, the final model was similar to the model to analyze birth weight, but it did not include year of birth x birth season interaction.
Animal models in matrix notation
After a series of preliminary analyzes with different variants of the animal model, the following models were assumed: y = Xb + [Z.sub.1]a + [Z.sub.2]m + e, with cov(a,m)= A[[sigma].sub.am], y = Xb + [Z.sub.1]a + [Z.sub.2]m + [Z.sub.3]c + e, with cov(a,m) = A[[sigma].sub.am], and y = Xb + [Z.sub.1]a + e, for birth weight, weaning weight and yearling weight, respectively. In these models, y is a vector of observations for each one of the different traits, b is a vector of fixed effects, a is an unknown random vector of direct additive genetic effects, m is an unknown random vector of maternal additive genetic effects, C is an unknown random vector of maternal permanent environmental effects, e is an unknown random vector of temporary environmental effects, and X, [Z.sub.1], [Z.sub.2] and [Z.sub.3] are known incidence matrices relating records to b, a, m, and c, respectively. It was assumed that direct additive genetic, maternal additive genetic, maternal permanent environmental and residual effects were normally distributed with mean 0.
The variance-covariance structure (V) assumed in the weaning weight analysis was:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where A is the Wright's additive relationship matrix  among all animals in the pedigree, [[sigma].sup.2.sub.a] is the direct additive genetic variance, [[sigma].sup.2.sub.m] is the maternal additive genetic variance, [[sigma].sup.2.sub.c] is the maternal permanent environmental variance, [[sigma].sup.2.sub.e] is the residual variance and [I.sub.c] and [I.sub.n] are identity matrices of size equal to the number of dams and the number of observations, respectively.
Estimation of variance components
Variances and (co)variances were estimated with Derivative-Free REML , using the MTDFREML program . It was assumed that convergence was reached when the variance of minus twice the logarithm of the likelihood in the simplex was less than [10.suo.-12]. After the program converged for the first time, several restarts were performed to ensure a global rather than a local maximum had been reached. In each new analysis, parameter estimates obtained in the previous analysis were used as initial values. Solutions of random effects were obtained from the last iteration cycle where a global maximum was reached.
Estimates of genetic parameters
Estimates were obtained for phenotypic variance ([[sigma].sup.2.sub.p] = [[sigma].sup.2.sub.a] + [[sigma].sup.2.sub.m] + [[sigma].sub.am] + [[sigma].sup.2.sub.c] + [[sigma].sup.2.sub.e]), heritability for direct additive genetic effects ([h.sup.2.sub.a] = [[sigma].sup.2.sub.a] / [[sigma].sup.2.sub.p]), heritability for maternal additive genetic effects ([h.sup.2.sub.m] = [[sigma].sup.2.sub.m] / [[sigma].sup.2.sub.p]), correlation between direct and maternal additive genetic effects ([r.sub.am] = [[sigma].sub.am] / [([[sigma].sup.2.sub.a] [[sigma].sup.2.sub.m]).sup.1/2]), fraction of phenotypic variance due to maternal permanent environmental effects ([c.sup.2] = [[sigma].sup.2.sub.c]/ [[sigma].sup.2.sub.p]), and residual variance as proportion of phenotypic variance ([e.sup.2] = [[sigma].sup.2.sub.e] / [[sigma].sup.2.sub.p]). Standard errors for estimates of genetic parameters were approximated and were calculated using the average information matrix  and the Delta Method . Additionally, total heritability estimates ([h.sup.2.sub.t]) were calculated using the following equation: [h.sup.2.sub.t] = ([[sigma].sup.2.sub.a] + 0.5[[sigma].sup.2.sub.m] + 1.5[[sigma].sub.am])/[[sigma].sup.2.sub.p].
RESULTS AND DISCUSSION
Descriptive statistics and data structure are shown in TABLE I. Means and standard deviations of weights at birth, weaning and yearling were: 32.3 [+ or -] 5.27, 182.5 [+ or -] 30.00 and 220.7 [+ or -] 43.00 kg, respectively. The coefficients of variation for weaning weight and yearling weight were greater than the coefficient of variation for birth weight, as expected. The number of calves, sires and dams was 598, 35, and 281, respectively. The pedigree file consisted of 796 animals. TABLE II presents estimates of variance components and genetic parameters for each of the analyzed growth traits.
The direct genetic effect for birth weight was found to be moderately heritable, with a heritability estimate of 27%, which suggests that birth weight can be modified through selection. Present estimate of direct heritability is within the range of direct heritability estimates of 0.37, 0.33, 0.33, 0.28, 0.32, 0.28 and 0.31 reported for American , Venezuelan [42, 43], South African  and Mexican  Brahman cattle, as well as for Brazilian Nelore  and Gyr  cattle. Rios-Utrera  in a review of estimates of genetic parameters reported that unweighted means obtained from estimates of direct heritability for birth weight were 0.32 for Brahman and 0.34 for Nelore cattle. Mercadante et al.  and Lira et al.  reported average estimates of direct heritability for birth weight with values of 0.33 (weighted mean) and 0.34 (unweighted mean), respectively, for different Bos indicus beef breeds. In contrast, Estrada-Leon et al.  for Mexican Brahman, and Martinez-Gonzalez et al.  for Mexican Nelore cattle reported estimates of direct heritability for birth weight with values of 0.56 and 0.59, respectively. However, according to Meyer , these heritability values could be overestimated because correlations between direct and maternal effects for birth weight obtained by these authors were considerably high and negative (-0.55 and -0.90, respectively), inflating the estimate of the direct additive genetic variance.
The maternal genetic effect was less heritable than the direct genetic effect, having a low heritability estimate. The estimate of maternal heritability for birth weight obtained in the present study is within the range of estimates reported in the literature, but most of literature estimates are lower than the one reported here. Albuquerque and Meyer , Arnason and KassaMersha , Diop et al.  and Salces et al.  reported estimates of maternal heritability for birth weight with values of 0.01, 0.02, 0.03 and 0.02 for Nelore, Boran, Gobra and Brahman cattle. On the other hand, several authors [12, 13, 15, 22, 29, 39, 40] have obtained estimates of maternal heritability for birth weight similar to the one reported in the present investigation, with values ranging from 0.11 to 0.18. The unweighted means of maternal heritability estimates reported by Rios-Utrera  for Brahman (0.10) and Nelore cattle (0.09) and by Lira et al.  for different Bos indicus breeds (0.09) were also similar to the corresponding estimate obtained in the present study.
The estimate of the genetic covariance between direct and maternal effects was practically zero, with a value of -0.00039 [kg.sup.2]. Together, direct and maternal genetic effects explained 37% of the phenotypic variance of birth weight, so that about 63% of the total variation was due to unknown environmental and genetic effects. The estimate of total heritability for birth weight was moderate (0.32).
In contrast to the findings for birth weight, maternal heritability (0.09) for weaning weight was similar to the corresponding direct heritability (0.11). The low direct heritability for weaning weight estimated in the present paper suggests that selection to improve this trait would be lowly effective for the Indubrazil herd under study. Several authors have also reported low estimates of direct heritability (0.11 to 0.17) for weaning weight of Nelore, Guzerat, Tabapua, Brahman and Indubrazil cattle [12, 16, 25, 36, 40, 44, 45, 53, 54, 57]. Some other researches obtained estimates of direct heritability for weaning weight close to zero in different Zebu breeds [4, 14, 37, 42, 43]. In Mexico, by contrast, for Guzerat  and Nelore cattle  were reported higher estimates of direct heritability for weaning weight (0.53 and 0.43, respectively). The difference between these two estimates and the estimate of the current study may be due, in addition to the difference in the breeds tested, to the type of animal model used, since it has been shown that when the model does not include maternal effects (genetic and permanent environmental), as with the animal model adjusted for Martinez-Gonzalez et al.  and Medina-Zaldivar et al. , direct heritability is overestimated (biased).
The magnitude of the maternal genetic effect for weaning weight suggests that Indubrazil cows in the experimental herd under study had low maternal (milking) ability, but there is enough maternal genetic variation (54.6 kg2; TABLE II) to increase milk yield of cows, though genetic progress probably would be slow. For other Zebu breeds, as well as for the experimental Indubrazil herd evaluated, it has been found that maternal genetic effects for weaning weight are lowly heritable, since scientific literature reports heritability values of 0.05, 0.03, 0.01, 0.10, 0.03, 0.04, 0.06, 0.10 for Indubrazil , Gyr , Guzerat , Tabapua , Bermejo Zebu , Brahman , Boran  and Nelore  cattle, respectively.
Maternal permanent environmental variance as a proportion of the total variance
The maternal permanent environmental effect was a minor source of variation for weaning weight. This result suggests that the loss or bad condition of molars and/or permanent injuries due to accidents or diseases were minimal in dams, or if these problems occurred, they were harmless and did not affect the weaning weight of their calves. Unlike the findings of the present study, in which the maternal permanent environmental effect was practically zero for weaning weight (corresponding variance= 0.02 kg2; TABLE II), other researchers [7, 16] have reported values ranging from 0.04 to 0.17.
Correlation between direct and maternal genetic effects
The estimate of the correlation between direct and maternal effects for weaning weight was relatively low (-0.27). This estimate is similar to the weighted value (-0.23) reported in a published review of genetic parameters for Zebu cattle , as well as to the estimates obtained in studies by Cabrera et al.  (-0.20), Elzo and Wakeman  (-0.22) and Gunski et al.  (-0.24). Conversely, other researchers [8, 15, 19, 29, 41, 45] found more intense genetic correlations, with values of -0.46, -0.90, -0.58, -0.70, -0.57 and -0.68. However, Meyer  reported that strongly negative estimates of the direct-maternal correlation can be partially explained by unaccounted ranch practices, such as inappropriate identification of management groups, increasing the covariance between paternal sibs in contemporary groups. Therefore, strongly negative estimates of the direct-maternal correlation do not always are a true sign of genetic antagonism between growth and maternal ability. The moderate antagonism between direct and maternal effects found in present study may be related to adaptive mechanisms of Zebu cattle to tropical conditions. In extreme environments, preserving animal size within certain limits may have adaptive advantages from a genetic viewpoint .
The genetic effects (direct and maternal) for weaning weight explained 20% of the total variation, so weaning weight depended on a higher proportion of unknown genetic and environmental effects. The estimate of total heritability for weaning weight was 11%.
The direct genetic effect for yearling weight proved to be a lowly heritable component, with a value of 13%. Compared with weights at birth and at weaning, yearling weight was mainly determined by unknown environmental and genetic effects. The direct heritability estimate for yearling weight found in the current research suggests that this trait can be improved by applying selection. Moreover, comparison with other estimates reveals that present estimate of direct heritability is within the range of corresponding estimates (0.08 to 0.17) reported in the literature for Tabapua , Guzerat , Brahman  and Nelore  cattle, although some other studies have reported little higher estimates for other Bos indicus breeds [8, 27]. Estimates of direct heritability for yearling weight of Indubrazil cattle were not found in the scientific literature, suggesting that such estimates are rare or that there have not been previously reported values.
For birth weight and weaning weight, the direct genetic effect was of greater importance than the maternal genetic effect. Also, there was no maternal permanent environmental effect on weaning weight. In general, estimates of direct and maternal heritability for Indubrazil cattle found in the present study are within the range of estimates reported for different Zebu breeds reared in Mexico and other countries. The magnitude of the estimates of direct heritability for weaning weight and yearling weight suggests that implementation of a selection program to improve these characteristics in our experimental herd would be feasible.
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Angel Rios-Utrera (1) *, Victor Delio Hernandez-Hernandez (1), Eugenio Villagomez Amezcua-Manjarrez (2), Juan Prisciliano Zarate-Martinez (1) and Jose Alfredo Villagomez-Cortes (3)
(1) Campo experimental La Posta, Instituto Nacional de Investigaciones Forestales, Agricolas y Pecuarias (INIFAP). Kilometro 22.5 carretera federal Veracruz-Cordoba, Paso del Toro, municipio de Medellin de Bravo, Veracruz, Mexico, 94277. Telephone: +55 (229) 2622222, * email@example.com. (2) Centro Nacional de Investigacion Disciplinaria en Microbiologia, Instituto Nacional de Investigaciones Forestales, Agricolas y Pecuarias (INIFAP). Kilometro 15.5 carretera Mexico- Toluca, Col. Palo Alto, Cuajimalpa, Distrito Federal, Mexico, 05110. Telephone: +55 (55) 36180800. (3) Facultad de Medicina Veterinaria y Zootecnia, Universidad Veracruzana. Miguel Angel de Quevedo, Esquina Yanez, Veracruz, Veracruz, Mexico, 91710. Telephone: +55 (229) 9342075.
Recibido: 28 / 02 / 2012. Aceptado: 07 / 06 / 2013.
TABLE I DESCRIPTIVE STATISTICS AND DATA STRUCTURE FOR BIRTH WEIGHT (BW), WEANING WEIGHT (WW) AND YEARLING WEIGHT (YW) OF INDUBRAZIL CATTLE REARED IN MEXICO Trait BW, kg WW, kg YW, kg Descriptive statistics Mean 32.30 182.53 220.73 Minimum value 19 101 93 Maximum value 50 317 397 Standard deviation 5.27 30.0 43.0 Coefficient of variation, % 16.32 16.45 19.49 Data structure Calves, number 598 598 598 Sires, number 35 35 35 Dams, number 281 281 281 Animals in the pedigree, number 796 796 796 TABLE II ESTIMATES OF VARIANCE COMPONENTS AND GENETIC PARAMETERS (a) FOR BIRTH WEIGHT (BW), WEANING WEIGHT (WW) AND YEARLING WEIGHT (YW) OF INDUBRAZIL CATTLE REARED IN MEXICO BW WW Variance components, [kg.sup.2] [[sigma].sup.2.sub.a] 5.98 65.73 [[sigma].sup.2.sub.m] 2.16 54.60 [[sigma].sub.am] -0.00039 -16.069 [[sigma].sup.2.sub.c] -- 0.02 [[sigma].sup.2.sub.e] 14.43 482.15 [[sigma].sup.2.sub.p] 22.58 586.44 Genetic parameters [h.sup.2.sub.a] 0.27 [+ or -] 0.19 0.11 [+ or -] 0.11 [h.sup.2.sub.m] 0.10 [+ or -] 0.08 0.09 [+ or -] 0.09 [r.sub.am] 0.00 [+ or -] 0.63 -0.27 [+ or -] 0.86 [c.sup.2] -- 0.00 [+ or -] 0.06 [e.sup.2] 0.64 [+ or -] 0.14 0.82 [+ or -] 0.10 [h.sup.2.sub.t] 0.32 0.11 YW Variance components, [kg.sup.2] [[sigma].sup.2.sub.a] 132.73 [[sigma].sup.2.sub.m] -- [[sigma].sub.am] -- [[sigma].sup.2.sub.c] -- [[sigma].sup.2.sub.e] 881.53 [[sigma].sup.2.sub.p] 1.014.25 Genetic parameters [h.sup.2.sub.a] 0.13 [+ or -]0.08 [h.sup.2.sub.m] -- [r.sub.am] -- [c.sup.2] -- [e.sup.2] 0.87 [+ or -] 0.08 [h.sup.2.sub.t] 0.13 (a) [[sigma].sup.2.sub.a] = direct additive genetic variance, [[sigma].sup.2.sub.m] = maternal additive genetic variance, [[sigma].sup.2.sub.c] = maternal permanent environmental variance, [[sigma].sup.2.sub.e] = residual variance, [[sigma].sup.2.sub.p] = phenotypic variance, [h.sup.2.sub.a] = direct heritability, [h.sup.2.sub.m] = maternal heritability, [c.sup.2] = maternal permanent environmental variance as a proportion of phenotypic variance, [e.sup.2] = residual variance as a proportion of phenotypic variance, [h.sup.2.sub.t] = total heritability.