A branching process for homology distribution-based inference of polyploidy, speciation and loss

At generation j, for i + 1 ≤ j ≤ n , any two descendants of the two genes making up a i-pair with no more recent common ancestor is also called a i-pair (at generation j). In other words, for any two genes at generation j, they form an i-pair if their most recent common ancestor underwent replacement at generation i