Figure 3.

Example of ${\text{Φ}}_P^{k,k^{\prime }}={\phi }_P^k\times {\phi }_P^{k^{\prime }}$ for an autotetraploid homology group with observed dosages $d_P^k=2$ and $d_P^{k^{\prime }}=2$ homologs sharing alleles. In this case, ${\phi }_P^k$ denotes a set of size six, containing all possible subsets of size two in ${\mathcal{P}}_k^4=\left\{P_k^1,P_k^2,P_k^3,P_k^4\right\}$. The same reasoning applies to ${\phi }_P^{k^{\prime }}$. The horizontal bars represent homologs forming a homology group and the dots represent allelic variations of a biallelic marker. The number below each homology group represents the number of homologs that share allelic variants ($w_P^{k,k^{\prime }}$). This defines three partitions: $w_P^{k,k^{\prime }}=2$, $w_P^{k,k^{\prime }}=1$ and $w_P^{k,k^{\prime }}=0$. Notice that, from a homology group within a specific partition, it is possible to obtain the same linkage phase configuration observed in another homology group within that partition by permuting the its homologs.