Enumeration of rooted binary perfect phylogenies

no code implementations • 19 Oct 2024 • Chloe E. Shiff, Noah A. Rosenberg

Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable lineages associated with the leaf.

On the number of genealogical ancestors tracing to the source groups of an admixed population

no code implementations • 22 Oct 2022 • Jazlyn A. Mooney, Lily Agranat-Tamir, Jonathan K. Pritchard, Noah A. Rosenberg

Using a mechanistic model of admixture, we characterize admixture genealogically: how many distinct ancestors from the source populations does the admixture represent?

A lattice structure for ancestral configurations arising from the relationship between gene trees and species trees

no code implementations • 19 Nov 2021 • Egor Lappo, Noah A. Rosenberg

To a given gene tree topology $G$ and species tree topology $S$ with leaves labeled bijectively from a fixed set $X$, one can associate a set of ancestral configurations, each of which encodes a set of gene lineages that can be found at a given node of the species tree.

Enumeration of binary trees compatible with a perfect phylogeny

no code implementations • 10 Aug 2021 • Julia A. Palacios, Anand Bhaskar, Filippo Disanto, Noah A. Rosenberg

Here, we investigate enumerative properties of the set of binary ranked and unranked tree shapes that are compatible with a perfect phylogeny, and hence, the binary ranked and unranked tree shapes conditioned on an observed pattern of mutations under the in? nitely-many-sites mutation model.