DOI: 10.5216/cab.v14i2.13571

EFFECT OF SEVERAL STRUCTURES OF CONTEMPORARY
GROUPS ON ESTIMATES OF (CO)VARIANCE AND GENETIC PARAMETERS FOR WEANING WEIGHT
IN NELLORE CATTLE

Lillian Pascoa^{1}, Arcadio de los Reyes^{2},
Mauricio A. Elzo^{3}, Jorge Luiz Ferreira^{4}, Luiz A.F.
Bezerra^{5}, Raysildo Barbosa Lobo^{5}

ABSTRACT

We used actual and adjusted weights
to 120 d and 210 d of age of 72,731 male and female Nellore calves born in 40
PMGRN - *Nellore Brazil* herds from
1985 to 2005 aiming to compare the effect of different definitions of
contemporary groups on estimates of
(co)variance and genetic parameters. Four models, each one with a different
structure of contemporary group (*CG*),
were compared using the Akaike Information Criterion (AIC), the Bayesian
Information Criterion (BIC), and the Consistent Akaike Information Criterion
(CAIC). (Co)variance estimates were obtained using a derivative-free restricted
maximum likelihood procedure. Estimates of (co)variances and genetic parameters
were similar for the four models considered. However, the BIC and CAIC
indicated that the most appropriate model for this Nellore population was the
one that considered *CG* to be random,
and sex of calf to be fixed and separate from *CG*, in which *CG* was
defined as the group of calves born in the same herd, year, season of birth
(trimester), and undergone the same management.

--------------------

** **beef cattle; contemporary
groups; information criteria.

EFEITO DE DIFERENTES MODELOS SOBRE AS
ESTIMATIVAS DE (CO)VARIÂNCIAS E PARÂMETROS GENÉTICOS PARA PESOS ATÉ A DESMAMA
EM GADO NELORE

RESUMO

Com o objetivo de se comparar o ajustamento de modelos com diferentes
definições de grupos contemporâneos sobre as estimativas de (co)variâncias e
parâmetros genéticos para pesos padronizados e reais aos 120 e 210 dias de
idade, analisaram-se dados de 72.731 bezerros Nelore, machos e fêmeas, nascidos
de 1985 a
2005 em 40 rebanhos integrantes do *PMGRN
- Nelore Brasil*. Foram comparados quatro modelos incluindo diferentes
estruturas de grupos contemporâneos (*CG*),
julgados pelos critérios de informação de Akaike, Bayesiano e modificado de
Akaike. As estimativas foram obtidas pelo método da máxima verossimilhança
restrita livre de derivadas. As estimativas de (co)variâncias e parâmetros
genéticos foram similares entre os modelos, porém os critérios de informação
(BIC, CAIC) indicaram que o modelo mais adequado é o que considera o grupo
contemporâneo como efeito aleatório, sendo este constituído pela concatenação
dos efeitos de rebanho, ano de nascimento, grupo de manejo e efeito sazonal de
trimestre de nascimento, e com efeito do sexo do bezerro independente do *CG*.

---------------------

PALAVRAS-CHAVE: critérios de informação; gado de corte; grupos
contemporâneos.

INTRODUCTION

The
structure of contemporary groups (*CG*)
is of primary importance for genetic evaluation of animals under selection;
they are crucial to avoid potential biases in genetic evaluations due to
differential treatment of animals in a population (VAN VLECK, 1987).

Contemporary
groups have usually been considered as fixed effects in beef cattle genetic
evaluations. This has been based on HENDERSON (1973) statement that in sire models,
genetic predictions of sires would be associated to contemporary group effects,
and to eliminate this bias, CG needed to be defined as fixed effects.
Currently, the model of choice is an animal model where individuals are assumed
to represent a random sample of the genetic material in a population; however, *CG* continues to be considered as fixed
effects.

Some
authors have found that random *CG*
effects yield a better adjustment than models with fixed *CG* in various animal species. In small herds, BABOT et al. (2003)
managed to estimate genetic values for litter size in herds with insufficient
number of animals per *CG* using
simulated data, whereas VASCONCELOS et al. (2005) estimated genetic values for
milk production in dairy cattle in Portugal using contrast models. Treating *CG* as random effects was also found to
be advantageous by GONZÁLEZ-RECIO &
ALENDA (2005) when analyzing binary reproductive traits in Spanish dairy
cattle, by WOLF et al. (2005) for growth and litter size in swine
utilizing a multi-trait animal model, and by LEGARRA et al. (2005) for milk
production in ewes using a Bayesian approach.

To
obtain the best possible estimates of (co)variance and genetic parameters it is
important to define mathematical models that fit the available data as
accurately as possible. This will in turn yield the most accurate genetic
predictions given the available information. Thus, the objective of this study
was to compare models with different definitions of contemporary groups on
estimates of (co)variances and genetic parameters for actual and adjusted
weights at 120 and 210 d of age in Nellore cattle in Brazil.

MATERIAL AND METHODS

Actual and adjusted weights at 120 d (AW120,
RW120) and 210 d (AW210, RW210) from 72,731 male and female Nellore calves born
between 1985 and 2005 in 40 herds from PMGRN-Nellore Brazil were used in this
study. Actual weights were the closest ones to 120 d and 210 d within the
intervals of 120 ± 90 d and 210 ± 90 d, respectively. Calf ages were expressed
as deviations (CAD) from 120 d and 210 d. Adjusted weights were computed by
interpolation between a prior and a posterior weight to the standardized age
(120 d or 210 d), allowing a maximum interval of 195 d between these two
weights (± 90 d plus an additional 15 d due to possible management changes).
Birth weight was used as the prior weight for AW120 when there was no other
weight (actual birth weight or breed mean: 33 kg for males, and 31 kg for
females) to compute the interpolation. Computations were similar to PMGRN
(LÔBO, 1996):

* *where,
AW = adjusted weights at
standard ages (AW120 or AW210); W = actual weight; Wp = prior weight; I =
interval in days between W and Wp; A = standard age (120 d or 210 d);
Aw = age at measurement of W.

The
effect of age of cow in years was grouped into six classes (DAC): 1 = 2 yr; 2 =
3 yr; 3 = 4 yr; 4 = 5 yr; 5 = 6 to 9 yr; and 6 = 10 yr and older cows.

Four
structures of contemporary groups were defined by concatenation of individual
effects, starting from a base subclass (CG_{B}), as follows:

CG_{B}:
herd – year of birth – management group at each age.

CG_{1}: CG_{B} – semester of
birth.

CG_{2}: CG_{B} – trimester of
birth.

CG_{3}: CG_{1} – sex of calf.

CG_{4}: CG_{2} - sex of calf.

Based on these four CGs (CG_{1} to CG_{4}),
four analytical models were defined:

M_{1}: Weight = α + CG_{1} + SC + DAC + ε

M_{2}: Weight = α + CG_{2} + SC + DAC + ε

M_{3}: Weight = α + CG_{3} + DAC + ε

M_{4}: Weight = α + CG_{4} + DAC + ε

where,
Weight = actual or adjusted weight at 120 d or 210 d of age; α = constant; CG = contemporary
group; SC = sex of calf; DAC = class of cow age at calving, and ε = random residual effect. In
addition, models for actual weights included age of calf at weighing (CAD),
modeled as a cubic polynomial regression, and expressed as a deviation from 120
d or 210 d.

A minimum of five observations per contemporary
groups were required. Calves in CG with less than five observations were kept
in the database but their weights were set to zero, thus their genetic
evaluations were computed using solely information from their relatives. This
allowed us to have the same inverse of the relationship matrix (A^{-1})
with 119,586 animals in all analyses.

Models
for the estimation of (co)variances and genetic parameters for AW120, RW120,
AW210 e RW210 using single-trait analysis, considering CG fixed (1) or random
(2), were as follows:

y = Xb + Z_{1}d + Z_{2}m
+ Z_{3}pe + e
(1)

y = Xb + Z_{1}d + Z_{2}m
+ Z_{3}pe + Z_{4}c + e (2)

where,
y = vector of observations; b = vector of fixed effects, including CG (Equation
1), and the effects of SC, DAC, and a cubic polynomial regression on CAD for
the analysis of actual weights (Equations 1 and 2); d, m, pe, c and e = vectors
of additive direct genetic effects, additive maternal genetic effects, maternal
permanent environmental effects, contemporary group, and residual, respectively;
and X, Z_{1}, Z_{2}, Z_{3} e Z_{4}, are known
incidence matrices relating observations in vector y to vectors b, d, m, pe,
and c, respectively. The assumptions of
these models were:

for
model 2, where, A = matrix of additive relationships among individuals; I = identity
matrices of appropriate order, σ²_{d}, σ²_{m}, σ²_{pe}, σ²_{c} and σ²_{e} = additive direct genetic variance, additive
maternal genetic variance, permanent environmental variance, contemporary group
variance, and residual variance, respectively; and σ_{d}_{m}= covariance
between direct and maternal genetic effects.

Models
were compared using the logarithm of the likelihood function (logL), using the
Akaike Information Criterion (AIC; AKAIKE, 1972), the Bayesian Information
Criterion (BIC; SCHWARZ, 1978), and Consistent Akaike Information Criterion
(CAIC, BOZDOGAN, 1987). The CAIC gives higher penalties to hyperparametrized
models compared to AIC. Thus, BIC and CAIC favor parsimonious models. These
criteria are defined as follows:

AIC = -2logL + 2k

BIC = -2logL + klog(n)

CAIC = -2logL + k(log(n)+1)

where,
k = number of estimated parameters; n = number of observations; logL =
logarithm of the likelihood function.

Models
with lower values of these information criteria are considered to better fit
the data.

Estimates
of (co)variances and genetic parameters were obtained using a derivative-free
restricted maximum likelihood procedure (DFREML; SMITH & GRASER, 1986). Computations
were carried out using the MTDFREML (Multiple Trait Derivative Free Restricted
Maximum Likelihood; BOLDMAN et al., 1995) software package using a single-trait
animal model. Because comparisons among animals were done within contemporary
groups, the variance due to CG, in
those models that considered CG to be random, was not included in the
phenotypic variance.

RESULTS AND DISCUSSION

Model Fitting

Values for the information criteria AIC, BIC and
CAIC obtained using models 1 through 4 with CG either fixed or random are
presented in Table 1 for 120 d and in Table 2 for 210 d of age. By any of these
criteria, better fitting models have smaller values.

In all cases, the criterion AIC had the smallest
values for models with *CG *fixed. On
the other hand, BIC and CAIC, by imposing higher penalties than AIC for models
with higher number of estimated parameters, favored models with random *CG*. These results were in agreement with
results from the literature. UGARTE et al. (1991), working with simulated data,
and VISSHER & GODDARD (1992), working with dairy data from small herds,
estimated lower prediction error variances (PEV) and mean squared errors (MSE)
for models with random CG. Contrarily, VALVERDE et al. (2008), using Braunvieh
cattle weaning weight data, found somewhat higher accuracies of genetic
predictions for direct genetic effects when CG were considered fixed, and no
difference between models with CG fixed or random for maternal genetic effects.

For weights at 120 d (AW120 and RW120), the criteria
BIC and CAIC indicated that models with trimester seasonal effect had the best
fit when CG was random (Table 1). A similar result was obtained for weights at
210 d (AW210 and RW210; Table 2). However, when CG was fixed, the best fitting
models were those with semester seasonal effects for 120 d (AW120 and RW120),
whereas for weights at 210 d, model M_{2} (trimester) was better than M_{1}
(semester), but model M_{3} (semester) was better than M_{4}
(trimester) for AW210 and RW210. On the other hand, REYES et al. (1998) found
out that it was better to consider trimester over semester when they compared
the efficiency of two fixed effects models containing season (trimester or
semester) as part of the structure of contemporary groups for weaning weight in
Nellore cattle.

According to the BIC and CAIC criteria, models that
had sex of calf effect separated from CG, provided a better fit to the data.
These models allowed the construction of contemporary groups with larger number
of individuals and permitted better genetic connections among CG and higher
accuracies of prediction of genetic evaluations. These results are in agreement
with those found by REYES
et al. (2006) for growth between birth and weaning in a multibreed Nellore x
Hereford cattle population.

Among models with random CG, model M_{2} was
the most parsimonious and provided the best fit. Thus, for 120 d and 210 d of
age and actual or adjusted data, results here suggest that models that had
random CG with trimester seasonal effect, and sex of calf effect separated from
CG effect were the most appropriate for growth from birth to weaning in Nellore
cattle.

Tables 3 and 4 present the estimates of
(co)variances and genetic parameters for the four traits in this study (AW120,
RW120, AW210 e RW210). Estimates for each trait differed little among models.

Estimates of σ²_{d, }σ²_{m}_{, }h²_{d } and h²_{m} were larger in models with semester of birth
season effect in CG (M_{1} and M_{3}) than those obtained in
models with trimester of birth season effect in CG (M_{2} e M_{4}).
On the other hand, estimates of σ²_{pe }and σ²_{e} were similar in all
models. These results may have been due to greater variation among weights when
the period of time (season effect) considered in CG was longer.

Estimates of σ²_{d, }σ²_{m, }h²_{d}_{ }and h²_{m} for weight at 120 d and 210 d of age were similar in models that included or not the
effect of sex of calf within CG (M_{2} vs M_{4} and M_{1}
vs M_{3}). Estimates of σ²_{e} ranged from 118.61 to 163.01 kg^{2 }for
actual and adjusted weights at 120 d (W120), and from 223.99 to 292.43 kg^{2
}for actual and adjusted weights at 210 d (W210), with smaller values in
CG of larger size, i.e., those in models that considered semester seasonal
effects and sex of calf separately from CG.

Models that considered CG random yielded higher
estimates of σ²_{d, }σ²_{m, }h²_{d}_{ }and h²_{m} , and lower estimates
of σ²_{e} than models that considered CG fixed. Larger
estimates of σ²_{d} and smaller values of σ²_{e} in models with random CG were also obtained
for weaning weights in Braunvieh cattle in México (VALVERDE et al., 2008).
Literature values reported higher values of heritability estimates for models
with fixed CG than for models with random CG (PHOCAS & LALOE, 2003;
CHANVIJIT et al., 2005; VALVERDE et al., 2008). However, these lower heritability
estimates for models with random CG were computed with phenotypic variances
that included the variance due to contemporary group (σ²_{c}), which is not
appropriate because comparisons among animals evaluated genetically occur
within contemporary groups.

Estimates for σ²_{d} ranged from 56.20 to 68.17 kg^{2} and
estimates for σ²_{m} from 24.86 to 29.67 kg^{2} for weight
at 120 d of age (W120). For weights at 210 d of age (W210), σ²_{d} estimates ranged from 116.61 to 155.44 kg^{2}
and estimates of σ²_{m} ranged from 41.91 to 52.05 kg^{2}.
Estimates of σ²_{dm }were negative, ranging from -38.61 to -20.84 kg^{2} for W120 and
from -38.94 to -21.41 kg^{2}
for W210. These estimates indicated antagonism between additive direct and
maternal genetic effects, in agreement with previous beef cattle research
(FERREIRA et al., 1999; LEE & POLLAK, 2002; ROSALES et al., 2004). This
implies that if producers perform selection for growth in calves without
considering maternal additive genetic effects, this may produce a decrease in
milk production of future mothers and a reduction in weaning weights of their
progenies (VALVERDE et al., 2008).

Estimates of σ²_{pe} ranged from 30.38 to 33.97 kg^{2} for
W120 and from 66.59 to 74.27 kg^{2} for W210. These estimates were
higher than those reported by GARNERO et al. (2001) for weights at 120 d of age
(19.1 kg^{2}) and at 220 d of age (48.01 kg^{2}).

Direct heritability estimates ranged from 0.22 to
0.28 for W120 and from 0.25 to 0.32 for W210. Estimates of maternal
heritabilities ranged from 0.10 to 0.12 for W120 and from 0.09 to 0.11 for
W210. MARCONDES et al. (2002) and SIQUEIRA et al. (2003) found similar
estimates of direct heritability for W120 (0.24 and 0.29, respectively), and of
maternal heritability (0.08) in Nellore cattle. GARNERO et al. (2001) also
estimated values of heritability for direct genetic effects (0.19) and for
maternal genetic effects (0.06) similar to those obtained here.

Differences among estimates of (co)variances and
genetic parameters were small across models in this study, perhaps due to the
utilization of the same matrix of additive relationships. However, one could
expect that estimates from models that yield better fit would be more accurate
and reliable.

CONCLUSIONS

*CG* and sex of calf
separated from *CG*, where *CG* was defined as a group of calves born
in the same herd, year, season measured as trimester of birth, and had the same
management. Estimates of (co)variances and genetic parameters, predictions of
breeding values, and ranking of animals obtained with the best model are
expected to be more accurate and reliable.

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