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Table 2 Moments of genotypes’ distributions depending on genotype codification

From: Approximated prediction of genomic selection accuracy when reference and candidate populations are related

Expectations Genotype codification
x tim  = a tim  − 2p tm x tim  = (a tim  − 2p tm )/σ tm
E[X im ] 0 0
E[X 2 im ] σ 2m 1
E[X 4 im ] σ 2m 1/σ 2m
E[X im X jm ] 2a ij σ 2m 2a ij
E[X im X 3 jm ] \( \frac{1}{2}\alpha_{ij}^{13} \sigma_{\text{m}}^{2} - \frac{1}{4}\gamma_{ij}^{13} \sigma_{\text{m}}^{4} \) \( \frac{1}{2}\alpha_{ij}^{13} /\sigma_{\text{m}}^{2} - \frac{1}{4}\gamma_{ij}^{13} \)
E[X 2 im X 2 jm ] \( \frac{1}{2}\alpha_{ij}^{22} \sigma_{\text{m}}^{2} - \frac{1}{4}\gamma_{ij}^{22} \sigma_{\text{m}}^{4} \) \( \frac{1}{2}\alpha_{ij}^{22} /\sigma_{\text{m}}^{2} - \frac{1}{4}\gamma_{ij}^{22} \)