arXiv subjects

Lily Agranat-Tamir

Publications and source records attributed to Lily Agranat-Tamir.

3 recordsLinked to original sources

arXiv2026

Combinatorial comparison of general galled trees, time-consistent galled trees, and simplex time-consistent galled trees

Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted leaf-labeled phylogenetic networks in a variety of classes, finding that when the number of reticulations is fixed, the time-consistent galled trees are asymptotically less numerous than each of several network classes that had been previously examined. Here we provide enumerative results on two additional network classes: general galled trees and simplex time-consistent galled trees. We show that for a fixed number of galls, as the number of leaves goes to infinity, the asymptotic count of general galled trees is identical to that of time-consistent galled trees, whereas the count of simplex time-consistent galled trees is smaller. If the number of galls is not restricted, then the asymptotic approximations all differ: simplex time-consistent galled trees are less numerous than time-consistent galled trees, which are in turn less numerous than general galled trees. We also report a variety of additional results: recursions to count the studied networks with small numbers of leaves a fixed number of galls, as well as enumerative results for unlabeled networks in the classes that we investigate.

math.CO↗

arXiv2025

Enumerative combinatorics of unlabeled and labeled time-consistent galled trees

In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of unlabeled and labeled time-consistent galled trees. We present a new derivation via the symbolic method of the number of unlabeled time-consistent galled trees with a fixed number of leaves and a fixed number of galls. We also derive new generating functions and asymptotics for labeled time-consistent galled trees.

math.CO↗

arXiv2022

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

In genetically admixed populations, admixed individuals possess ancestry from multiple source groups. Studies of human genetic admixture frequently estimate ancestry components corresponding to fractions of individual genomes that trace to specific ancestral populations. However, the same numerical ancestry fraction can represent a wide array of admixture scenarios. Using a mechanistic model of admixture, we characterize admixture genealogically: how many distinct ancestors from the source populations does the admixture represent? We consider African Americans, for whom continent-level estimates produce a 75-85% value for African ancestry on average and 15-25% for European ancestry. Genetic studies together with key features of African-American demographic history suggest ranges for model parameters. Using the model, we infer that if genealogical lineages of a random African American born during 1960-1965 are traced back until they reach members of source populations, the expected number of genealogical lines terminating with African individuals is 314, and the expected number terminating in Europeans is 51. Across discrete generations, the peak number of African genealogical ancestors occurs for birth cohorts from the early 1700s. The probability exceeds 50% that at least one European ancestor was born more recently than 1835. Our genealogical perspective can contribute to further understanding the admixture processes that underlie admixed populations. For African Americans, the results provide insight both on how many of the ancestors of a typical African American might have been forcibly displaced in the Transatlantic Slave Trade and on how many separate European admixture events might exist in a typical African-American genealogy.

q-bio.PE↗