Estimation of animal × environment interaction in Czech beef cattle

The objective was the estimation of animal × environment interaction for weaning weight (WWT) of the most frequent breeds of beef cattle in the Czech Republic. The environment was represented by 3 areas: Mountain (1), Foothills (2) and Lowland (3). A pairwise analysis was carried out between the areas: 1 vs 2 (n=5 149) and 2 vs 3 (n=4 971) for the estimation of (co)variance components and genetic correlations between the environments. A multiple-trait animal model was used where weaning weights in different areas were considered as different traits. The direct and maternal heritability estimates of WWT were for area (1): 0.12 (direct) and 0.05 (maternal); for (2): 0.26 and 0.11 (direct), 0.10 and 0.11 (maternal) and for (3): 0.26 (direct) 0.03 (maternal). Direct and maternal genetic correlations were between: 1 and 2 0.98 and 0.65 respectively, with standard deviations 0.03 and 0.37 respectively, and between 2 and 3: 0.82 and 0.50 respectively, with standard deviations 0.12 and 0.31 respectivly. The magnitude of the across-areas genetic correlation indicates that the animal by environment interaction was not biologically important and can be ignored in the evaluation of beef cattle in the Czech Republic.


Introduction
Correct estimation of genetic parameters is the basic step for the estimation of breeding value and subsequent selection of parental pairs.This estimation of genetic parameters is related to the representativeness of the data set and with the appropriate choice of a statistical model.When constructing the model for estimation of genetic parameters, estimation of breeding values of individual animals and genotypic value of populations, which comprises many fixed and random effects, it is assumed in beef cattle breeds that there exist no genotype by environment interactions, i.e. that the reaction of the performance and adaptability of individual animals or breeds to different environmental conditions (nutrition, climate, altitude above sea level, precipitation, temperature, soil structure and quality) is identical.It means that the performance level of breeds in different environmental conditions is not different.However, it follows from the experience gained in the Czech Republic and in other countries that it is not the case because e.g. the animals of breeds of medium-frame beef cattle have optimum performance in mountain locations while the animals of large-frame breeds are better adapted to lowland conditions and animals of some breeds are so adaptable that hey have more or less the same performance in any environmental conditions.
The knowledge of animal × environment interaction and its extent in those breeds of beef cattle that are mostly kept under extensive conditions in the Czech Republic is a crucial problem for the estimation of breeding value of animals, genotype value of populations, selection and hybridisation.If existing animal × environment interactions are neglected, great inaccuracies may arise in the breeding of beef cattle.
The objective of this paper was to test whether there exists any animal × environment interaction for weaning weight in the main breeds of beef cattle kept under the conditions of the Czech Republic.

Genotypes
Field test data on animals of the following beef cattle breeds were used: meat-type Simmental, Hereford, Aberdeen Angus, Charolais, Blonde d'Aquitaine and Piemontese.Each animal possessed an 88-100 % gene share of the breeds concerned.Data were adjusted so that the components of variance among all considered effects would be estimable (VOSTRÝ et al. 2007).The data set comprised: animals from of sires who had at least 5 offspring with performance testing records and whose offspring were always present in two studied environments, animals forming a group of contemporaries that contained 5 animals at least, animals from of mothers who had at least two offspring and one half-sister.The set of pedigrees was formed by attributing two generations of ancestors to the information on animal performance.

Localities
Environmental conditions in the Czech Republic were classified into three localities according to the evaluation of less-favoured areas (LFA) (http://ec.europa.eu/agriculture/consultations/lfa/consultationdoc_en.pdf ).Locality 1 comprised mountain areas.These areas represent land at of altitudes more then 500 m above sea level, and with more than 50 % of agricultural land on slopes higher than 7 degrees.Locality 2 was described as less-favoured areas, i.e. the territory with a lower production potential.Locality 3 represented intensive production areas with the high production capacity of soil (hereinafter localities 1, 2 and 3) (VOSTRÝ et al. 2008).Table 1 shows the characteristics of a sampling set for the particular localities.

Model
The estimation of animal × environment interaction was done separately between two environments (1 × 2, 2 × 3).To estimate the animal × environment interaction the same trait in two different environmental conditions it was considered as two traits.The estimation of genotype × environment interaction was done by a multi-trait animal model (DE MATTOS et al. 2000): where yi and yj are vectors of the observed values in environments i and j; bi and bj are the vectors of fixed effects (combined effect of sex and litter size, effect of mother's age, effect of the group of contemporaries and effect of breed) in environments i and j; ai and aj are the vectors of random additive genetic effects in environments i and j; mi and mj are the vectors of random additive maternal effects in environments i and j; pei and pej are the vectors of random effects of mother's permanent environment in environments i and j; ei and ej are the vectors of random residual errors in environments i and j, Xi, Xj, Zi, Zj, Mi, Mj, Wi and Wj are the known incidence matrices of fixed and random effects in environments i and j.
We assume that random effects show the normal distribution of frequencies with zero average and with the following variance-covariance structure: , , where σ 2 di and σ 2 dj are the additive genetic variances of direct effect for environments i and j; σ 2 mi and σ 2 mj are the additive genetic variances of maternal effect for environments i and j; σdi,mi and σdi,mj are the genetic covariance of direct and maternal effect [Cov(d,m)] for environment i and j; σdi,dj and σmi,mj are the covariance between direct or maternal effect for environment i and j; σdi,mj is the covariance between direct effect in environment i and maternal effect in environment j; σdj,mi is the covariance between direct effect in environment j and maternal effect in environment i; σ 2 pei and σ 2 pej are the variance of the effects of permanent maternal environment; σ 2 ei and σ 2 ej are the variance of the effect of residual errors; A is the relationship matrix and I is the identity matrix.
The computation programme VCE5 (KOVAČ et al. 2002) was used for the estimation of variance and covariance components.The other population parameters were derived from the estimated variance-covariance components (WILLHAM 1979).

Results and discussion
Table 1 shows descriptive characteristics of sampling sets.The table documents that the data sets for two-trait analyses between localities 1 vs 2 and 2 vs 3 showed approximately identical values in these characteristics.Markedly lower values of localities particular characteristics were computed in the set for the analysis of 1 vs 3. The table also indicates the existence of a marked disproportion among the numbers of animals, sires and groups of contemporaries in the data set for the analysis of localities 1 and 3.These set showed no meaningful results.This disproportion significantly influenced the estimation of variance components of the given set and that did not make sense.For this reason the analysis between localities 1 vs 3 will not be mentioned any more.The estimations of mean values and standard deviations within the localities were done only in the analyses of 1 vs 2 and 2 vs 3.In a comparison of 1 vs 2 average live weights reached higher values in more favourable localities (locality 2).On the contrary, a higher value was reached by locality 2 in a comparison of localities 2 vs 3. The comparison of standard deviations showed that in localities with lower average live weight locality 1 in the comparison of localities 1 vs 2, or locality 3 in the comparison of localities 2 vs 3, had higher values of variability.Similar values for beef cattle breeds were published e.g. by JAKUBEC et al. (2003), VOSTRÝ et al. (2007) and PILARCZYK and WÓJCIK (2008).
The results of bivariate analysis for the estimation of animal × environment interaction in conditions of the Czech Republic are summarized in Table 2. Total phenotypic variance among the particular localities ranged from 1 008.50 to 1 113.80 when the lowest value was reached in locality 1 and the highest value was computed for locality 3. The values of residual variance showed a similar trend.Locality 2 was the only exception, for which the lowest value of residual variance was estimated (602.39).The estimates of direct heritability coefficients among the localities amounted to 0.11 to 0.26.The estimates of maternal heritability coefficient were in the same range as the estimates of direct heritability coefficients from 0.03 to 0.11.The coefficients of direct or maternal heritability had similar values like those reported by MEYER (1997), ROBINSON (1996), WALDRON et al. (1993) andSZABÓ et al. (2007), who estimated heritability coefficients in the range from 0.15 to 0.57 for the direct effect and from 0.16 to 0.4 for the maternal effect.A comparison of the values of standard deviations with the coefficients of direct heritability shows that the estimations of coefficients hd 2 are statistically significant.The estimates of maternal heritability coefficients reached statistical significance only in locality 2. VAN VLECK (1963) suggested that significant differences between the heritability coefficients of one trait in two environments might signal the existence of genotype × environment interaction.A comparison of direct heritability estimates in two-trait analyses revealed pronounced differences (0.12 vs 0.26 and 0.11 vs 0.23).But this considerable variation need not be necessarily caused by the existence of genotype × environment interaction.
Large variation was also observed in the coefficient of genetic correlation between direct and maternal effect (rdm).Estimation of rdm for localities 1 and 3 resulted in zero to medium positive values, i.e. 0.01 and 0.28, respectively.However, estimation of rdm in locality 2 turned out a negative (−0.19) and a positive (0.22) value.These genetic correlation between direct and maternal effect fitted into estimates the large range of values published by the above-mentioned authors (−0.594 to 0.223).Unlike the other coefficients, the estimates for genetic correlation between direct and maternal effect was not significantly different from zero.
A similar trend as in rdm was observed in the ratio of permanent maternal environmental variance to total phenotypic variance (c 2 ), in which differences among localities and analyses were smaller than in rdm, but for locality 2 similar values were estimated in both analyses.The values of c 2 in the particular analyses ranged from 5 to 15 %.DE MATTOS et al. (2000) reported c 2 -estimates in the range of 14 to 17 % for the Hereford and DONOGHUE and BERTRAND (2004) computed c 2 -estimates between 7 and 17 % for Charolais breed.Similar to direct and maternal heritability estimates of coefficients c 2 were significantly different from zero.
Genetic correlation between localities for directs effect was estimated to be 0.98 (1, 2) and 0.82 (2, 3) respectively, and for maternal effects 0.65 (1, 2) and 0.50 (2, 3) respectively.ROBERTSON (1959) recommended to use a multi-trait model for evaluation of the performance of animals across different conditions when performance in different environment is considered to be a different trait.He also stated that the genotype × environment interaction for two environments was not biologically significant if the genetic correlation was higher than 0.80 between the some trait in the two different environments.The estimates of genetic correlation for direct effect exceeded this critical value while estimates for maternal effect were lower (0.65 and 0.50 respectively).Considering the standard errors, the estimates of genetic correlation for maternal effect obviously was not statistically significant.
From these results it can be concluded that weaning weight of beef cattle kept in the Czech Republic is not influenced by animal × environment interaction.Applying the bivariate analysis, DE MATTOS et al. (1996) analysed weaning weight in the Hereford breed in different localities in Uruguay, LEE andBERTRAND (2002) andDE MATTOS et al. (2000) in USA, Canada and Uruguay.These authors estimated genetic correlations for direct and maternal effects to be 0.80 and higher.They concluded that weaning weight of the Hereford breed was not influenced by the genotype × environment interaction under their conditions.On the contrary, HYDE et al. (1998) estimated the genetic correlation for direct genetic effects between conditions of the USA, Canada, Australia and New Zealand to be 0.70 for the Charolais breed while the significance of genotype × environment interaction was confirmed.
According to DE MATTOS et al. (2000) no papers were published dealing with the animal × environment interaction in which the efficiency of sire, sire-maternal grandsire and animal models was compared.FERREIRA et al. (1999) reported large differences in the estimation of breeding value by different models.
The analysis showed that for weaning weight, considered as a different trait in different environmental conditions, of the beef cattle kept in the Czech Republic the estimates for genetic correlation for direct effect were higher than 0.80.Therefore weaning weight in beef cattle kept under the conditions of the Czech Republic is not influenced the animal × environment interaction.The magnitude of the across-areas genetic correlation indicates that the animal by environment interaction was not biologically important and can be ignored in the evaluation of beef cattle in the Czech Republic.

Table 2
Estimated genetic effects for the particular localities Genetische Parameter für die Lokalitäten