Lily Agranat-Tamir
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Lily Agranat-Tamir has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Noah A. Rosenberg
Department of Biology, Stanford University, Stanford, USA
3 shared publications - Jazlyn A. Mooney
Department of Quantitative and Computational Biology, University of Southern California , Los Angeles, CA 90089
2 shared publications - Bernhard Gittenberger
Technische Universität Wien
1 shared publication - Kennedy D. Agwamba
Center for Computational Biology, University of California, Berkeley , CA, USA
1 shared publication - Michael Fuchs
Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan
1 shared publication Noah A. Rosenberg
Department of Biology, Stanford University, Stanford, USA
1 shared publication
Latest Publications
- 1 June 2026
- Published by Elsevier in Theoretical Computer Science
- Vol. 1082
Enumerative combinatorics of unlabeled and labeled time-consistent galled trees
- 1 June 2026
- Published by Elsevier in Theoretical Computer Science
- Vol. 1082
Enumerative combinatorics of unlabeled and labeled time-consistent galled trees
- Open Access
- 10 February 2026
- Published by Taylor & Francis in The American Statistician
- Vol. 80 (3) , 1-10
Shared Ancestors and the Birthday Problem
- 10 February 2026
- Published by Taylor & Francis in The American Statistician
- Vol. 80 (3) , 1-10
Open AccessShared Ancestors and the Birthday Problem
- Open Access
- 22 March 2024
- Published by Springer Nature in Bulletin of Mathematical Biology
- Vol. 86 (5) , 1-35
Enumeration of Rooted Binary Unlabeled Galled Trees
Rooted binary galled trees generalize rooted binary trees to allow a restricted class of cycles, known as galls. We build upon the Wedderburn-Etherington enumeration of rooted binary unlabeled trees with n leaves to enumerate rooted binary unlabeled galled trees with n leaves, also enumerating rooted binary unlabeled galled trees with n leaves and g galls, $$0 \leqslant g \leqslant \lfloor \frac{n-1}{2} \rfloor $$ . The enumerations rely on a recursive decomposition that considers subtrees descended from the nodes of a gall, adopting a restriction on galls that amounts to considering only the rooted binary normal unlabeled galled trees in our enumeration. We write an implicit expression for the generating function encoding the numbers of trees for all n. We show that the number of rooted binary unlabeled galled trees grows with $$0.0779(4.8230^n)n^{-\frac{3}{2}}$$ , exceeding the growth $$0.3188(2.4833^n)n^{-\frac{3}{2}}$$ of the number of rooted binary unlabeled trees without galls. However, the growth of the number of galled trees with only one gall has the same exponential order 2.4833 as the number with no galls, exceeding it only in the subexponential term, $$0.3910n^{\frac{1}{2}}$$ compared to $$0.3188n^{-\frac{3}{2}}$$ . For a fixed number of leaves n, the number of galls g that produces the largest number of rooted binary unlabeled galled trees lies intermediate between the minimum of $$g=0$$ and the maximum of $$g=\lfloor \frac{n-1}{2} \rfloor $$ . We discuss implications in mathematical phylogenetics.- 22 March 2024
- Published by Springer Nature in Bulletin of Mathematical Biology
- Vol. 86 (5) , 1-35
Open AccessEnumeration of Rooted Binary Unlabeled Galled Trees
Rooted binary galled trees generalize rooted binary trees to allow a restricted class of cycles, known as galls. We build upon the Wedderburn-Etherington enumeration of rooted binary unlabeled trees with n leaves to enumerate rooted binary unlabeled galled trees with n leaves, also enumerating rooted binary unlabeled galled trees with n leaves and g galls, $$0 \leqslant g \leqslant \lfloor \frac{n-1}{2} \rfloor $$ . The enumerations rely on a recursive decomposition that considers subtrees descended from the nodes of a gall, adopting a restriction on galls that amounts to considering only the rooted binary normal unlabeled galled trees in our enumeration. We write an implicit expression for the generating function encoding the numbers of trees for all n. We show that the number of rooted binary unlabeled galled trees grows with $$0.0779(4.8230^n)n^{-\frac{3}{2}}$$ , exceeding the growth $$0.3188(2.4833^n)n^{-\frac{3}{2}}$$ of the number of rooted binary unlabeled trees without galls. However, the growth of the number of galled trees with only one gall has the same exponential order 2.4833 as the number with no galls, exceeding it only in the subexponential term, $$0.3910n^{\frac{1}{2}}$$ compared to $$0.3188n^{-\frac{3}{2}}$$ . For a fixed number of leaves n, the number of galls g that produces the largest number of rooted binary unlabeled galled trees lies intermediate between the minimum of $$g=0$$ and the maximum of $$g=\lfloor \frac{n-1}{2} \rfloor $$ . We discuss implications in mathematical phylogenetics. - Open Access
- 30 January 2024
- Published by Oxford University Press (OUP) in Genetics
- Vol. 226 (4)
Counting the genetic ancestors from source populations in members of an admixed population
In a genetically admixed population, admixed individuals possess genealogical and genetic ancestry from multiple source groups. Under a mechanistic model of admixture, we study the number of distinct ancestors from the source populations that the admixture represents. Combining a mechanistic admixture model with a recombination model that describes the probability that a genealogical ancestor is a genetic ancestor, for a member of a genetically admixed population, we count genetic ancestors from the source populations—those genealogical ancestors from the source populations who contribute to the genome of the modern admixed individual. We compare patterns in the numbers of genealogical and genetic ancestors across the generations. To illustrate the enumeration of genetic ancestors from source populations in an admixed group, we apply the model to the African-American population, extending recent results on the numbers of African and European genealogical ancestors that contribute to the pedigree of an African-American chosen at random, so that we also evaluate the numbers of African and European genetic ancestors who contribute to random African-American genomes. The model suggests that the autosomal genome of a random African-American born in the interval 1960–1965 contains genetic contributions from a mean of 162 African (standard deviation 47, interquartile range 127–192) and 32 European ancestors (standard deviation 14, interquartile range 21–43). The enumeration of genetic ancestors can potentially be performed in other diploid species in which admixture and recombination models can be specified.
- 30 January 2024
- Published by Oxford University Press (OUP) in Genetics
- Vol. 226 (4)
Open AccessCounting the genetic ancestors from source populations in members of an admixed population
In a genetically admixed population, admixed individuals possess genealogical and genetic ancestry from multiple source groups. Under a mechanistic model of admixture, we study the number of distinct ancestors from the source populations that the admixture represents. Combining a mechanistic admixture model with a recombination model that describes the probability that a genealogical ancestor is a genetic ancestor, for a member of a genetically admixed population, we count genetic ancestors from the source populations—those genealogical ancestors from the source populations who contribute to the genome of the modern admixed individual. We compare patterns in the numbers of genealogical and genetic ancestors across the generations. To illustrate the enumeration of genetic ancestors from source populations in an admixed group, we apply the model to the African-American population, extending recent results on the numbers of African and European genealogical ancestors that contribute to the pedigree of an African-American chosen at random, so that we also evaluate the numbers of African and European genetic ancestors who contribute to random African-American genomes. The model suggests that the autosomal genome of a random African-American born in the interval 1960–1965 contains genetic contributions from a mean of 162 African (standard deviation 47, interquartile range 127–192) and 32 European ancestors (standard deviation 14, interquartile range 21–43). The enumeration of genetic ancestors can potentially be performed in other diploid species in which admixture and recombination models can be specified.