Common use of Statistical Methods Clause in Contracts

Statistical Methods. Two statistical methods were used to perform the GWAS, namely weighted single-step GBLUP (WssGBLUP; ▇▇▇▇ et al. 2012) and ▇▇▇▇▇▇ (▇▇▇▇▇▇ et al. 2011). The model adopted for WssGBLUP was: y=1µ+Zaa+e, where y is the vector of phenotypes, µ is the overall mean, a is the vector of additive genetic effects, 1 is a vector of ones, Za is an incidence matrix relating the phenotypes to a, and e is the vector of residuals. The covariance between a and e was assumed to be zero and their variances were considered to be Hσ 2 and Iσ 2, respectively, where σ 2 and σ 2 are the direct additive and residual variance, respectively, H is the matrix which combines pedigree and genomic information (▇▇▇▇▇▇▇ et al. 2010), and I is an identity matrix. The SNP effects (û) were calculated as in Stranden & ▇▇▇▇▇▇▇ (2009): û=DP’[PDP’]-1ag, where D is a diagonal matrix that contains the weights for the SNPs, P is a matrix relating genotypes of each locus (coded as 0, 1 or 2 according to the number of copies of allele B) and ag is a vector with the estimated breeding values of genotyped animals. D, â and û were iteratively recomputed over three iterations. In the first iteration (w1), the diagonal elements of D (di) were assumed to be 1 (i.e., the same weight for all markers). For the subsequent iterations (w2 and w3), di was calculated as: di=ûi2pi(1-pi), where ûi is the allele substitution effect of the ith marker, estimated from the previous iteration, and pi is the allele frequency of the second allele of the ith marker. The WssGBLUP was adopted using two sets of data, one considering all available phenotypic information (SI; n=45,000) and another considering phenotypes just from genotyped animals (SII; n=2,000). The three different weights for the SNPs (w1 to w3) and the two sets of data (SI and SII) resulted in six different solutions for the SNP effects obtained under the WssGBLUP method. BayesC was applied under the model: