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The mean pairwise relationship coefficient, from the A matrix computed for the "combined" prediction approach, between dent lines was 0.46 with standard deviation of 0.38, and between flint lines 0.49 with standard deviation of 0.32.
The mean kinship coefficient value was 0.64.
The average of the maximum genetic relationship coefficient (amax) within and between groups for five groups formed by K-means clustering in Limousin and Simmental animals.
This means that some pairs of individuals sharing rare alleles can show an unrealistic inflated value of their genomic relationship coefficient.
The following regression equation of application of RSM resulted in an empirical relationship: Coefficient of determination (R) = 0.98; adjusted R = 0.97; coefficient of variation (CV) = 1.77%; SS, sum of squares; DF, degree of freedom; MS, mean square.
Precision was measured by the mean squared error (MSE) of the relationship coefficients in predicting the true IBD relationships, relative to MSE obtained from using pedigree only.
Because the relationship coefficients are expressed relative to the current population, the mean of the off-diagonal elements (left panel) is −(1 + f)/ n, which is essentially 0 for populations with hundreds of lines or more.
In accordance with Observation 3, we find a close relationship (R2 ≥ 0.6) between the mean clustering coefficient mean (ClusterCoef ) and (1 + Heterogeneity)2 × Density.
However, eight of the 28 relationships had mean correlation coefficients that differed significantly from zero (Figure 4a and Table S4a).
Mean coefficient of variation: the mean coefficient of variation across all transcripts.
The mean hydrodynamic coefficient of the particles was obtained from the diffusion coefficient using Stokes Einstien relationship.
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