With the objective to verify the existence of the interaction genotype X enviroment, under
the form of heterogenity of variances for the milk production in buffaloes and its impact in
the genetic evaluation of the animals, using the Bayesiana inference by means of Gibbs
Sampler, form used 5,484 registers of referring milk production to the productions of 2.994
females predominantly Murrah, calves of 150 sires, mateds with 1130 matrices, whose birth
had occurred between the years of 1974 and 2004. The records had been proceeding from
the Programa de Melhoramento Genético de Bubalinos (PROMEBUL) with the addition of
records proceeding from the flock of the EMBRAPA Amazônia Oriental - EAO, located in
Belém, Pará, State. Class of herd-year of birth had been established and in accordance with
the standard deviation of milk production of each class had been classified in class of high
and low phenotypic standard deviation. Later the data had been analyzed disrespecting and
considering the standard deviations class. The used model used the referring fixed effect to
the herd-year class, month of parity and covariable age of the female to the birth and length
of the lactation, beyond the random effect of animal, permanent environment and temporary
environment effects. For the fixed effect uniform was assumed distribution to priori and for
the components of (co)variances, had been assumed distributions priori inverse qui-square
and inverted Wishart. The observed averages and shunting line-standard for milk
production in the class of high, low standard deviation and in general analysis, had been
equal 1870,21±758,78, 1900,50±587,76 and 1885,48±677,98, respectively. The posterior
averages for the components of variances had been bigger in the classroom of high standard
deviation. The genetic correlation for milk production between standard deviation classes
was equal the 0,58. The correlations of Spearman between the breeding values for the milk
production obtained in general analysis with the values in the class of high and low standard
deviation were 0,94 and 0,93 , respectively, for all the sires. For one it shows of the 10
better sires, the same correlations had been equal 0,94 and 0,47, respectively. Such results
disclose presences of heterogenity of variances between herds and this heterogenity of
variances is resultant of environmental factors, that can take to a wrong classification of the
breeding value to best sires for the production milk.
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