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Moreover, the interleaving of formal and semantic rules along a single inheritance path presents a novel way to model derivational relations in a constrained manner.
An inheritance path of length ℓ involves ℓ transmissions.
We assume that ψ i, i+1) is not equal to zero if and only if the realized inheritance path at locus i + 1 is the same as the realized inheritance path at locus i, which basically means there are no recombination events along the inheritance path between these two loci.
For a particular site, these indicators for all the individuals, s j, is commonly referred to as the identity-by-descent (IBD) inheritance path.
An inheritance path is a graph with nodes being the alleles of individuals and directed edges between alleles that are inherited from parent to child.
As a descent graph is a realization of one particular inheritance pattern in a pedigree, for any two alleles, there is at most one inheritance path.
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Afterward, an "affected" individual was simulated to inherit two copies of the ancestral allele, generated through two independent inheritance paths.
The transition probabilities can then be theoretically derived based on the number and lengths of all inheritance paths.
The likelihood can be modeled using a hidden Markov model along the genome with inheritance paths as hidden states.
Thus, the hidden states for the haplotype HMM are the cross-product of the orientations and the inheritance paths.
This result is consistent with the fact that Bg-IBD is generated by long inheritance paths with many meioses.
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