NON-RECURSIVE ENUMERATION OF HETEROCHRONOUS TREES

P.F. Slade
2018 International Journal of Pure and Applied Mathematics  
The enumeration formula of a non-contemporaneous genealogy with total sample size n = n1 + n2 requires a nested sum-product. The set of ancestral patterns in the noncontemporaneous genealogy yields a multiplicity factor that translates from the set of ancestral patterns in the isochronous genealogy. A computation formula of the multiplicity factor proves to be non-recursive. Evaluation of small sample sizes demonstrates the emergent complexity. Extension to the enumeration formula in the
more » ... hronous genealogy with m samples of total size n = n1 + · · · + nm yields a non-recursive nested sum-product. These enumeration formulae measure sample spaces of Bayesian prior distributions of trees relevant to theoretical and computational phylogenetics.
doi:10.12732/ijpam.v117i1.17 fatcat:so4n7oryijarjbuqzh37rcsgoe