Figure 1.

The network model. Left panels refer to the possible gametes produced by either bivalent pairing or quadrivalent pairing in parent P₁, where the four homologous/homeologous chromosomes are labeled by different colors. The right panel refers to the directed acyclic graph of the model for N_o = 3 offspring at N_t = 3 marker loci, where the rectangles denote known dosage data, the circles random variables, and the solid arrows probabilistic relationships described in the Methods section. Conditional on the chromosome pairings $V={\left\{V_{\mathrm{o}}\right\}}_{\mathrm{o}=1}^{{\mathrm{N}}_{\mathrm{o}}}$, the network model becomes a HMM along the chromosomes with the latent variables being the parental haplotypes ${\left\{H_{\mathrm{t}}\right\}}_{\mathrm{t}=1}^{{\mathrm{N}}_{\mathrm{t}}}$ and the parental origins ${\left\{X_{\mathrm{t}}^{\mathrm{o}}\right\}}_{\mathrm{t}=1,\dots ,{\mathrm{N}}_{\mathrm{t}}}^{\mathrm{o}=1,\dots ,{\mathrm{N}}_{\mathrm{o}}}$.