Mailing address
Department of Biology
Stanford University
371 Jane Stanford Way
Stanford, CA 94305-5020 USA
Last modified 4-28-2024
Theory research in the lab
Theory research involves formulating and solving mathematical motivated by
consideration of biological scenarios, and interpreting the mathematical
results for their contributions to biology. Advances in our theoretical
work often focus on mathematical models, involving construction and
analysis of new models, derivation of new results about existing models,
development of new techniques for analyzing models, and model
comparisons. Progress can also come from mathematical analyses of
statistical methods, numerical studies and simulations, or introduction
of new theoretical principles.
X Liu, Z Ahsan, TK Martheswaran, NA
Rosenberg (2023) When is the allele-sharing dissimilarity between two
populations exceeded by the allele-sharing dissimilarity of a population
with itself? Statistical Applications in Genetics and Molecular
Biology 22: 2023004.
[Abstract]
[PDF]
ML Morrison, NA Rosenberg (2023) Mathematical bounds on
Shannon entropy given the abundance of the ith most abundant
taxon. Journal of Mathematical Biology 87: 76.
[Abstract]
[PDF]
[Supplement]
ML Morrison, N Alcala, NA Rosenberg (2022)
FSTruct: an FST-based tool for measuring ancestry
variation in inference of population structure. Molecular Ecology
Resources 22: 2614-2626.
[Abstract]
[PDF]
[Supplement]
N Alcala, NA Rosenberg (2022) Mathematical
constraints on
FST: multiallelic markers in arbitrarily many
populations. Philosophical Transactions of the Royal Society B:
Biological Sciences 377: 20200414.
[Abstract]
[PDF]
[Supplement]
SM Boca, L Huang, NA Rosenberg (2020) On the
heterozygosity of an admixed population. Journal of Mathematical
Biology 81: 1217-1250.
[Abstract]
IM Arbisser, NA Rosenberg
(2020) FST and the triangle inequality for
biallelic markers. Theoretical Population Biology 133:
117-129.
[Abstract]
NA Rosenberg, DM Zulman (2020) Measures of care fragmentation:
mathematical insights from population genetics.
Health Services Research 55: 318-327.
[Abstract]
JTL Kang, NA Rosenberg (2019) Mathematical
properties of linkage disequilibrium statistics defined by
normalization of the coefficient
D=pAB-pApB.
Human Heredity 84: 127-143. [Abstract]
[PDF]
N Alcala, NA Rosenberg
(2019) G'ST, Jost's D,
and FST are similarly constrained by allele
frequencies: a mathematical, simulation, and empirical
study. Molecular Ecology 28: 1624-1636.
[Abstract]
[PDF]
[Supplement]
AJ Aw, NA Rosenberg (2018) Bounding measures of
genetic similarity and diversity using majorization. Journal of
Mathematical Biology 77: 711-737.
[Abstract]
[PDF]
N Alcala, NA Rosenberg (2017) Mathematical
constraints
on FST: biallelic markers in arbitrarily many
populations.
Genetics 206: 1581-1600.
[Abstract]
[PDF]
[File
S1]
[File
S2]
NR Garud, NA Rosenberg (2015) Enhancing the mathematical
properties of new haplotype homozygosity statistics for the detection of
selective sweeps. Theoretical Population Biology 102: 94-101.
[Abstract]
[PDF]
MD Edge, NA Rosenberg (2014) Upper bounds
on FST in terms of the frequency of the most
frequent allele and total homozygosity: the case of a specified number
of alleles. Theoretical Population Biology 97: 20-34.
[Abstract]
[PDF]
M Jakobsson, MD Edge, NA Rosenberg (2013) The
relationship between FST and the frequency of the
most frequent allele.
Genetics 193: 515-528.
[Abstract]
[PDF]
SB Reddy, NA Rosenberg (2012) Refining the relationship
between homozygosity and the frequency of the most frequent
allele. Journal of Mathematical Biology 64: 87-108.
[Abstract]
[PDF]
SM Boca, NA Rosenberg (2011) Mathematical properties of
Fst between admixed populations and their parental
source populations. Theoretical Population Biology 80: 208-216.
[Abstract]
[PDF]
NA Rosenberg, M Jakobsson (2008) The relationship
between homozygosity and the frequency of the most frequent
allele. Genetics 179: 2027-2036. [Abstract] [PDF]
JM VanLiere, NA Rosenberg (2008) Mathematical
properties of the r2 measure of linkage disequilibrium.
Theoretical Population Biology 74: 130-137. [Abstract] [PDF]
The strict upper bound
on the value of
FST at a locus given the frequency of the most
frequent
allele. See Jakobsson,
Edge, and Rosenberg (2013) for details.
JA Mooney, L Agranat-Tamir, JK Pritchard, NA
Rosenberg (2023) On the number of genealogical ancestors tracing to
the source groups of an admixed population. Genetics
224: iyad079.
[Abstract]
[PDF]
[Supplement]
J Kim, MD Edge, A Goldberg, NA Rosenberg
(2021) Skin deep: the decoupling of genetic admixture levels from
phenotypes that differed between source populations. American
Journal of Physical Anthropology 175: 406-421 (2021).
[Abstract]
SM Boca, L Huang, NA Rosenberg (2020) On the
heterozygosity of an admixed population. Journal of Mathematical
Biology 81: 1217-1250.
[Abstract]
A Goldberg, A Rastogi, NA Rosenberg (2020)
Assortative mating by population of origin in a mechanistic model of
admixture. Theoretical Population Biology 134: 129-146.
[Abstract]
J Kim, F Disanto, NM Kopelman, NA
Rosenberg (2019) Mathematical and simulation-based analysis of the
behavior of admixed taxa in the neighbor-joining
algorithm. Bulletin of Mathematical Biology 81: 452-493.
[Abstract]
[PDF]
[Supplement]
NA Rosenberg (2016) Admixture models and the breeding systems of
H. S. Jennings: a GENETICS connection. Genetics 202:
9-13.
[PDF]
A Goldberg, NA Rosenberg (2015) Beyond 2/3 and 1/3: the
complex signatures of sex-biased admixture on the X
chromosome. Genetics 201: 263-279.
[Abstract]
[PDF]
EO Buzbas, NA Rosenberg (2015) AABC: approximate
approximate Bayesian computation for inference in population-genetic
models.
Theoretical Population Biology 99: 31-42.
[Abstract]
[PDF]
A Goldberg, P Verdu, NA Rosenberg (2014)
Autosomal admixture levels are informative about sex bias in admixed
populations.
Genetics 198: 1209-1229.
[Abstract]
[PDF]
NM Kopelman, L Stone, O Gascuel, NA Rosenberg (2013) The
behavior of admixed populations in neighbor-joining inference of
population trees. Pacific Symposium on Biocomputing 18:
273-284. [Abstract]
[PDF]
SM Boca, NA Rosenberg (2011) Mathematical properties of
Fst between admixed populations and their parental
source populations. Theoretical Population Biology 80: 208-216.
[Abstract]
[PDF]
A neighbor-joining tree illustrating the interior placement of
admixed populations in relation to populations from source
regions. See Kopelman,
Stone, Gascuel, and Rosenberg (2013) for details.
M DeGiorgio, NA Rosenberg (2013) Geographic sampling
scheme as a determinant of the major axis of genetic variation in
principal components analysis. Molecular Biology and Evolution
30:
480-488. [Abstract]
[PDF]
NA Rosenberg (2011) A population-genetic perspective on the
similarities and differences among worldwide human populations. Human
Biology 83: 659-684.
[Abstract]
[PDF]
M DeGiorgio, JH Degnan, NA Rosenberg (2011)
Coalescence-time distributions in a serial founder model of human
evolutionary history. Genetics 189: 579-593.
[Abstract]
[PDF]
ZA Szpiech, NA Rosenberg (2011) On the size
distribution of private microsatellite alleles. Theoretical
Population Biology 80: 100-113.
[Abstract]
[PDF]
C Wang, ZA Szpiech, JH Degnan,
M Jakobsson, TJ Pemberton, JA Hardy, AB Singleton, NA
Rosenberg (2010) Comparing spatial maps of human population-genetic
variation using Procrustes analysis. Statistical Applications in
Genetics and Molecular Biology 9: 13.
[Abstract]
[PDF]
DJ Cotter, AL Severson, S Carmi, NA Rosenberg
(2022) Limiting distribution of X-chromosomal coalescence times under
first-cousin consanguineous mating. Theoretical Population
Biology 147: 1-15.
[Abstract]
DJ Cotter, AL Severson, NA Rosenberg
The effect of consanguinity on coalescence times on the X
chromosome.
Theoretical Population Biology 140: 32-43 (2021).
[Abstract]
AL Severson, S Carmi, NA Rosenberg (2021) Variance
and limiting distribution of coalescence times in a diploid model of a
consanguineous population. Theoretical Population Biology
139: 50-65. [Abstract]
J Kim, MD Edge, BFB Algee-Hewitt, JZ Li, NA
Rosenberg (2018) Statistical detection of relatives typed with
disjoint forensic and biomedical loci. Cell 175: 848-858.
[Abstract]
[PDF]
[Supplement]
NA Rosenberg, TJ Pemberton, JZ Li, JW Belmont (2013) Runs
of homozygosity and parental relatedness. Genetics in Medicine
15: 753-754. [PDF]
ZA Szpiech, J Xu, TJ Pemberton, W Peng, S
Zöllner, NA Rosenberg, JZ Li (2013) Long runs of homozygosity
are enriched for deleterious variation. American Journal of Human
Genetics 93: 90-102.
[Abstract]
[PDF]
[Supplement]
[Data]
TJ Pemberton, F-Y Li, EK Hanson, NU Mehta, S Choi, J Ballantyne,
JW Belmont, NA Rosenberg, C Tyler-Smith, PI Patel (2012) Impact of
restricted marital practices on genetic variation in an endogamous
Gujarati group. American Journal of Physical Anthropology 149:
92-103. [Abstract]
[PDF]
[Supplement
(.docx)]
[Data]
M DeGiorgio*, I Jankovic*, NA Rosenberg (2010)
Unbiased estimation of gene diversity in samples containing related
individuals: exact variance and arbitrary ploidy. Genetics
186: 1367-1387. [Abstract]
[PDF]
TJ Pemberton, C Wang, JZ Li, NA Rosenberg
(2010) Inference of unexpected genetic relatedness among individuals
in HapMap Phase III. American Journal of Human Genetics 87:
457-464.
[Abstract]
[PDF]
[Supplement]
The 203 configurations of identity and nonidentity possible among
the six alleles at a locus in three diploid
individuals. The figure is inspired by the work
of Degiorgio, Jankovic,
and Rosenberg (2010).
M Doboli, H-K Hwang, NA Rosenberg (2024) Periodic behavior of
the minimal Colijn-Plazzotta rank for trees with a fixed number of leaves.
In C. Mailler, S. Wild, eds. Proceedings of the 35th International
Conference on Probabilistic, Combinatorial and Asymptotic Methods for the
Analysis of Algorithms (AofA 2024). Leibniz International Proceedings
in Informatics (LIPIcs) 302: 18. Schloss Dagstuhl
Leibniz-Zentrum für Informatik.
[Abstract]
[PDF]
L Agranat-Tamir, S Mathur, NA Rosenberg (2024)
Enumeration of rooted binary unlabeled galled trees.
Bulletin of Mathematical Biology 86: 45.
[Abstract]
[PDF]
E Lappo, NA Rosenberg (2024) A lattice structure for
ancestral configurations arising from the relationship between gene trees
and species trees. Discrete Applied Mathematics 343: 65-81.
[Abstract]
[PDF]
ARP Maranca, NA Rosenberg (2024) Bijections between the
multifurcating unlabeled rooted trees and the positive
integers. Advances in Applied Mathematics 153: 102612.
[Abstract]
[PDF].
F Disanto, M Fuchs, C-Y Huang, AR Paningbatan, NA
Rosenberg (2024) The distributions under two species-tree models of
the total number of ancestral configurations for matching gene trees and
species trees. Advances in Applied Mathematics 152: 102594.
[Abstract]
MC King, NA Rosenberg (2023) A mathematical
connection between single-elimination sports tournaments and
evolutionary trees. Mathematics Magazine 96: 484-497.
[Abstract]
[PDF]
S Mathur, NA Rosenberg (2023) All galls are divided into
three or more parts: recursive enumeration of labeled histories for
galled trees. Algorithms for Molecular Biology 18:1.
[Abstract]
[PDF]
F Disanto, M Fuchs, AR Paningbatan, NA Rosenberg (2022)
The distributions under two species-tree models of the number of root
ancestral configurations for matching gene trees and species
trees. Annals of Applied Probability 32: 4426-4458.
[Abstract]
[PDF]
JA Palacios, A Bhaskar, F Disanto, NA Rosenberg
(2022)
Enumeration of binary trees compatible with a perfect
phylogeny. Journal of Mathematical Biology 84: 54.
[Abstract]
[PDF]
MC King, NA Rosenberg (2021) A simple derivation of the
mean of the Sackin index of tree balance under the uniform model on
rooted binary labeled trees. Mathematical Biosciences 342:
108688.
[PDF]
E Alimpiev, NA Rosenberg Enumeration of coalescent
histories for caterpillar species trees
and p-pseudocaterpillar gene trees. Advances in
Applied
Mathematics 131: 102265 (2021).
[Abstract]
[PDF]
NA Rosenberg (2021) On the Colijn-Plazzotta numbering
scheme for unlabeled binary rooted trees. Discrete Applied
Mathematics 291:
88-98. [Abstract]
[PDF]
J Kim, NA Rosenberg, JA Palacios (2020) Distance
metrics for ranked evolutionary trees. Proceedings of the
National Academy of Sciences 117: 28876-28886.
[Abstract]
[PDF]
[Supplement]
ZM Himwich, NA Rosenberg (2020) Roadblocked monotonic
paths and the enumeration of coalescent histories for non-matching
caterpillar gene trees and species trees. Advances in Applied
Mathematics 113: 101939.
[Abstract]
F Disanto, NA Rosenberg (2019) Enumeration of compact
coalescent histories for matching gene trees and species
trees. Journal of Mathematical Biology 78: 155-188.
[Abstract]
[PDF]
F Disanto, NA Rosenberg (2019) On the number of
non-equivalent ancestral configurations for matching gene trees and
species trees. Bulletin of Mathematical Biology 81: 384-407.
[Abstract]
[PDF]
NA Rosenberg (2019) Enumeration of lonely pairs of gene trees
and species trees by means of antipodal cherries. Advances in
Applied Mathematics 102:
1-17. [Abstract]
[PDF]
F Disanto, NA Rosenberg (2017) Enumeration of ancestral
configurations for matching gene trees and species trees. Journal of
Computational Biology 24: 831-850.
[Abstract]
[PDF]
F Disanto, NA Rosenberg (2016) Asymptotic properties of
the number of matching coalescent histories for caterpillar-like
families of species trees.
IEEE/ACM Transactions on Computational Biology and Bioinformatics
13: 913-925.
[Abstract]
[PDF]
F Disanto, NA Rosenberg (2015) Coalescent histories for
lodgepole species trees. Journal of Computational Biology 22:
918-929.
[Abstract]
[PDF]
F Disanto, NA Rosenberg (2014) On the number of ranked
species trees producing anomalous ranked gene trees. IEEE/ACM
Transactions on Computational Biology and Bioinformatics 11:
1229-1238.
[Abstract]
[PDF]
CV Than, NA Rosenberg (2014) Mean deep coalescence cost
under exchangeable probability distributions. Discrete Applied
Mathematics 174: 11-26.
[Abstract]
[PDF]
NA Rosenberg (2013) Coalescent histories for
caterpillar-like families. IEEE/ACM Transactions on Computational
Biology and Bioinformatics 10:
1253-1262. [Abstract]
[PDF]
NA Rosenberg (2013) Discordance of species trees with their most
likely gene trees: a unifying principle. Molecular Biology and
Evolution 30: 2709-2713.
[Abstract]
[Full-text
at journal website]
[PDF]
CV Than, NA Rosenberg (2013) Mathematical properties of
the deep coalescence cost. IEEE/ACM Transactions on Computational
Biology and Bioinformatics 10: 61-72.
[Abstract]
[PDF]
JH Degnan, NA Rosenberg, T Stadler (2012) A
characterization
of the set of species trees that produce anomalous ranked gene trees.
IEEE/ACM Transactions on Computational Biology and Bioinformatics
9: 1558-1568.
[Abstract]
[PDF]
JH Degnan, NA Rosenberg, T Stadler (2012) The probability
distribution of ranked gene trees on a species tree.
Mathematical Biosciences 235:
45-55. [Abstract]
[PDF]
NA Rosenberg, JH Degnan (2010) Coalescent histories
for discordant gene trees and species trees. Theoretical Population
Biology 77:
145-151. [Abstract]
[PDF]
A gene tree that disagrees with
the species tree can have as many or more coalescent histories than a
matching gene tree. See
Rosenberg & Degnan
(2010) for details.
E Lappo, NA Rosenberg (2022) Approximations to the
expectations and variances of ratios of tree properties under the
coalescent. G3: Genes, Genomes, Genetics 12: jkac205.
[Abstract]
[PDF]
DJ Cotter, AL Severson, S Carmi, NA Rosenberg
(2022) Limiting distribution of X-chromosomal coalescence times under
first-cousin consanguineous mating. Theoretical Population
Biology 147: 1-15.
[Abstract]
RS Mehta, M Steel, NA Rosenberg (2022) The probability of
joint monophyly of samples of gene lineages for all species in an
arbitrary species tree. Journal of Computational Biology 27:
679-703.
[Abstract]
E Alimpiev, NA Rosenberg (2022) A compendium of
covariances and correlation coefficients of coalescent tree
properties. Theoretical Population Biology 143: 1-13.
[Abstract]
[PDF]
DJ Cotter, AL Severson, NA Rosenberg
The effect of consanguinity on coalescence times on the X
chromosome.
Theoretical Population Biology 140: 32-43 (2021).
[Abstract]
AL Severson, S Carmi, NA Rosenberg (2021) Variance
and limiting distribution of coalescence times in a diploid model of a
consanguineous population. Theoretical Population Biology
139: 50-65. [Abstract]
N Alcala, A Goldberg, U Ramakrishnan, NA Rosenberg
(2019) Coalescent theory of migration network motifs. Molecular
Biology and Evolution 36: 2358-2374.
[Abstract]
[PDF]
[Supplement]
AL Severson, S Carmi, NA Rosenberg (2019)
The effect of consanguinity on between-individual identity-by-descent
sharing. Genetics 212: 305-316.
[Abstract]
[PDF]
IM Arbisser, EM Jewett, NA Rosenberg (2018) On
the joint distribution of tree height and tree length under the
coalescent. Theoretical Population Biology 122: 46-56.
[Abstract]
[PDF]
RS Mehta, D Bryant, NA Rosenberg (2016) The probability
of monophyly of a sample of gene lineages on a species
tree. Proceedings of the National Academy of Sciences USA 113:
8002-8009.
[Abstract]
[PDF]
[Supplement]
[Software]
EM Jewett, NA Rosenberg (2014) Theory and
applications of a deterministic approximation to the coalescent
model. Theoretical Population Biology 93: 14-29.
[Abstract]
[PDF]
L Huang, EO Buzbas, NA Rosenberg (2013) Genotype
imputation in a coalescent model with infinitely-many-sites mutation.
Theoretical Population Biology 87: 62-74.
[Abstract]
[PDF]
EM Jewett*, M Zawistowski*, NA Rosenberg, S Zöllner
(2012) A coalescent model for genotype imputation.
Genetics 191:
1239-1255. [Abstract]
[PDF]
D Bryant, R Bouckaert, J Felsenstein, NA Rosenberg, A
RoyChoudhury (2012) Inferring species trees directly from biallelic
genetic markers: bypassing gene trees in a full coalescent analysis.
Molecular Biology and Evolution 29: 1917-1932.
[Abstract]
[PDF]
[Supplement]
JH Degnan, NA Rosenberg, T Stadler (2012) The
probability
distribution of ranked gene trees on a species tree.
Mathematical Biosciences 235:
45-55. [Abstract]
[PDF]
M DeGiorgio, JH Degnan, NA Rosenberg (2011)
Coalescence-time distributions in a serial founder model of human
evolutionary history. Genetics 189: 579-593.
[Abstract]
[PDF]
ZA Szpiech, NA Rosenberg (2011) On the size distribution
of private microsatellite alleles. Theoretical Population
Biology 80: 100-113.
[Abstract]
[PDF]
NA Rosenberg, M Nordborg (2002) Genealogical trees,
coalescent theory, and the analysis of genetic polymorphisms.
Nature Reviews Genetics 3:
380-390. [Abstract]
[PDF]
LH Uricchio, T Warnow, NA Rosenberg (2016) An analytical
upper bound on the number of loci required for all splits of a species
tree to appear in a set of gene trees. BMC Bioinformatics 17:
417.
[Abstract]
[PDF]
M DeGiorgio, NA Rosenberg (2016) Consistency and
inconsistency of consensus methods for inferring species trees from gene
trees in the presence of ancestral population structure.
Theoretical Population Biology 110: 12-24.
[Abstract]
[PDF]
D Bryant, R Bouckaert, J Felsenstein, NA Rosenberg, A
RoyChoudhury (2012) Inferring species trees directly from biallelic
genetic markers: bypassing gene trees in a full coalescent analysis.
Molecular Biology and Evolution 29: 1917-1932.
[Abstract]
[PDF]
[Supplement]
LJ Helmkamp, EM Jewett, NA Rosenberg (2012)
Improvements to a class of distance matrix methods for inferring species
trees from gene trees. Journal of Computational Biology 19:
632-649.
[Abstract]
[PDF]
EM Jewett, NA Rosenberg (2012) iGLASS: an improvement to
the GLASS method for estimating species trees from gene
trees. Journal of Computational Biology 19: 293-315.
[Abstract]
[PDF]
CV Than, NA Rosenberg (2011) Consistency properties
of species tree inference by minimizing deep coalescences.
Journal of Computational Biology 18: 1-15.
[Abstract]
[PDF]
JH Degnan, M DeGiorgio, D Bryant, NA Rosenberg
(2009) Properties of consensus methods for inferring species trees
from gene trees. Systematic Biology 58: 35-54.
[Abstract]
[PDF]
JH Degnan, NA Rosenberg (2009) Gene tree discordance,
phylogenetic inference and the multispecies coalescent. Trends in
Ecology and Evolution 24:
332-340. [Abstract]
[PDF]
[Supplement]
An inductive proof that all species tree topologies with five or
more taxa have anomalous gene trees. See Degnan &
Rosenberg (2006) and Rosenberg
(2013) for details.