2.4. Deregression of Estimated Breeding Values

A Herdbook has been in place for the Ramo Grande breed since 1995, where animals are registered after being classified according to morphology and type at around 2 years of age. Animals are scored for nine body conformation traits, and to enter the Herdbook they must receive a total type score of at least 75 in a maximum of 100 possible points. As part of the on-going management program of this breed, phenotypic data has been collected since 1996, including measurement of the following traits:

Estimated breeding values (EBV) are routinely predicted for these traits using univariate Animal Models with fixed and random effects specific for each trait. The linear mixed models used for analyzing the various traits were as follows.

(1) Analysis of type score, temperament, age at first calving, longevity and number of calvings:

(2) Analysis of calving interval:

(3) Analysis of live weight at 4 months and carcass weight/day of age:

where:

‘y’ is the vector of observations;

‘b’ is the vector o fixed effects;

‘a’ is the vector of additive direct genetic effects;

‘m’ is the vector of additive maternal genetic effects;

‘p’ is the vector of permanent maternal environmental effects;

‘e’ is the vector of residual effects;

‘X, Z_a, Z_m, e, Z_p’ are known incidence matrices relating the fixed effects (X) and each of the random effects (Z_a, Z_m, e, Z_p) with the vector of observations ‘y’.

Variance components were estimated and breeding values predicted with the BLUPF90 package [25].

For the genome-wide association analyses, EBVs of the genotyped bulls were obtained from the published annual evaluations, which are based on phenotypic records collected on an average of 55.5 ± 91.3 offspring per bull. These EBVs were then used to compute deregressed EBV (DEBV), calculated by applying the procedure described by Garrick et al. (2009) [26], considering that the fraction of genetic variance not explained by markers (c) was 0.10. The deregression procedure of Garrick et al. (2009) [26] takes into consideration the estimated reliability of the EBV, thus accounting for the amount of information available on relatives of the evaluated individuals, which in our case included phenotypic records on a total of 2332 offspring of the genotyped bulls. The deregression step also eliminates shrinkage inherent to the computation of EBV, and therefore deregressed EBV behave as though they were observations with a heritability equal to the reliability of the deregressed EBV [27].