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Table 3 Two-locus genotype probabilities as functions of characteristic parameters

From: Mendelian sampling covariability of marker effects and genetic values

L1

L2

Probabilities

BB

BB

\([D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i)(1- p^{{\mars}}_j)][D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i)(1- p^{{\venus}}_j)]\)

AB/BA

\([-D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i) p^{{\mars}}_j] [D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i)(1- p^{{\venus}}_j)]+[D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i)(1- p^{{\mars}}_j)][-D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i) p^{{\venus}}_j]\)

AA

\([-D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i) p^{{\mars}}_j][-D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i) p^{{\venus}}_j]\)

AB/BA

BB

\([-D^{{\mars}}_{i,j}+p^{{\mars}}_i (1-p^{{\mars}}_j)][D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i)(1- p^{{\venus}}_j)]+[D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i)(1- p^{{\mars}}_j)][-D^{{\venus}}_{i,j}+p^{{\venus}}_i (1-p^{{\venus}}_j)]\)

AB/BA

\(\begin{aligned}&[D^{{\mars}}_{i,j}+p^{{\mars}}_i p^{{\mars}}_j][D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i)(1- p^{{\venus}}_j)]+[D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i)(1- p^{{\mars}}_j)][D^{{\venus}}_{i,j}+p^{{\venus}}_i p^{{\venus}}_j]\\&\quad+[-D^{{\mars}}_{i,j}+p^{{\mars}}_i (1-p^{{\mars}}_j)][-D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i) p^{{\venus}}_j]+[-D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i) p^{{\mars}}_j][-D^{{\venus}}_{i,j}+p^{{\venus}}_i (1-p^{{\venus}}_j)]\end{aligned}\)

AA

\([D^{{\mars}}_{i,j}+p^{{\mars}}_i p^{{\mars}}_j][-D^{{\venus}}_{i,j}+(1-p^{{\venus}}_i) p^{{\venus}}_j]+[-D^{{\mars}}_{i,j}+(1-p^{{\mars}}_i) p^{{\mars}}_j][D^{{\venus}}_{i,j}+p^{{\venus}}_i p^{{\venus}}_j]\)

AA

BB

\([-D^{{\mars}}_{i,j}+p^{{\mars}}_i (1-p^{{\mars}}_j)][-D^{{\venus}}_{i,j}+p^{{\venus}}_i (1-p^{{\venus}}_j)]\)

AB/BA

\([D^{{\mars}}_{i,j}+p^{{\mars}}_i p^{{\mars}}_j][-D^{{\venus}}_{i,j}+p^{{\venus}}_i (1-p^{{\venus}}_j)]+[-D^{{\mars}}_{i,j}+p^{{\mars}}_i (1-p^{{\mars}}_j)][D^{{\venus}}_{i,j}+p^{{\venus}}_i p^{{\venus}}_j]\)

AA

\([D^{{\mars}}_{i,j}+p^{{\mars}}_i p^{{\mars}}_j][D^{{\venus}}_{i,j}+p^{{\venus}}_i p^{{\venus}}_j]\)

  1. Nine classes of two-locus genotypes (L1, L2) for offspring in a full-sib family and the probability of each class as a function of the parental LD D and the A-allele frequency \(p_i\) at locus i (the superscripts indicate the sex of the parent and the subscripts indicate the locus)