











Noah A Rosenberg
+1 650 721 2599 (office phone)
+1 650 724 5122 (lab phone)
+1 650 724 5114 (fax)
Mailing address
Department of Biology
Stanford University
371 Serra Mall
Stanford, CA 943055020 USA
Last modified 1012019 


We are a mathematical, theoretical, and computational lab in genetics
and evolution. Research in the lab addresses problems in evolutionary
biology and human genetics through a combination of mathematical
modeling, computer simulations, development of statistical methods, and
inference from populationgenetic data.
Read more...
RECENT NEWS
1012019 — A
new study by Rohan
Mehta computes probabilities under the coalescent model of
reciprocal monophyly for sets of gene lineages from three and four
species. The computation extends an earlier computation that permitted
only two sets of lineages
[141]. The study appears in a
special issue of Theoretical Population Biology celebrating
Marc Feldman's 75th birthday.
9232019 — Nicolas Alcala studies the coalescent
theory of all possible symmetric migration models involving at most
four demes. His paper
examines coalescent quantities such as the time to the most recent
common ancestor under the models, determining how these quantities
relate to network properties such as the mean number of edges per
vertex and the density of edges. The study introduces a network
perspective for coalescent models — applying it to empirical
examples on tigers and birds of genus Sholicola in India. PhD
graduate Amy Goldberg also
contributed to the project.
992019 — A
new paper led by Rohan
Mehta examines the behavior of the F_{ST} measure of
genetic differentiation on haplotypic data. The study illustrates how
incrementing the length of the haplotype window tends to
decrease F_{ST} — but sometimes increases it. The
work is closely related to several of the lab's papers
on F_{ST}
[102]
[121]
[149]
[165]. Check out
the video
abstract drawn and narrated by coauthor Alison Feder.
582019 — In a collaboration with
the Stanford Conservation
Program, we have developed a stochastic population occupancy model
to examine two decades of occupancy data from the campus populations
of the California redlegged frog (Rana draytonii). The model
seeks to explain population declines of R. draytonii in
campus creeks and suggests conservation management approaches for
reversing these
declines. The study was led
by Nicolas Alcala.
522019 — A
new study led by Alissa
Severson examines the relationship between runs of homozygosity
and identitybydescent tracts. The paper determines for a diploid
coalescent model the time to the most recent common ancestor, both for
two haplotypes in the same individual and for two haplotypes in
different individuals. The work provides theory that builds on
empirical observations in an earlier study
[144].
4292019 — Nicolas Alcala has a
new study of
mathematical bounds on three populationgenetic
statistics: G_{ST}', Jost's D,
and F_{ST}. He shows that for biallelic markers whose
mean frequency across a set of populations is fixed, these three
statistics achieve their maximal values at the same configuration of
allele frequencies across populations. The results extend
Nicolas's earlier
work on F_{ST} bounds as well as that of two
other studies from the lab concerning bounds
on F_{ST}
[102]
[121].
3262019 — Filippo Disanto reports
a study of the
enumeration of compact coalescent histories for matching gene
trees and species trees. Compact coalescent histories represent a
combinatorial structure that collapses standard coalescent histories
into a smaller number of equivalence classes. The study extends the
lab's work on enumeration of
coalescent histories to a new structure.
332019 — A
new paper discusses
challenges of interpreting differences in polygenic scores across
populations. The paper builds from the models developed by
Ph.D. graduate Doc Edge for
analyzing the relationship between the magnitude of genetic and
phenotypic differences among populations [129]
[132].
1232019 — Two papers from the lab appear in a special
issue of Bulletin of Mathematical Biology on Algebraic
Methods in Phylogenetics.
 Jaehee Kim, Filippo Disanto, and Naama Kopelman
report a study of the properties
of the neighborjoining algorithm when applied to data from admixed
populations. The study shows that tree properties conjectured by
Kopelman et
al. [99] do
not necessarily hold for every distance matrix, but they do hold much more
frequently than in a null model without an admixed taxon.
 Filippo
Disanto examines the
number of nonequivalent ancestral configurations for matching gene trees
and species trees. Nonequivalent ancestral configurations at
first appear to be less numerous than ancestral configurations without
applying the equivalence relation — studied previously by Filippo
[152]. Here, Filippo
shows that asymptotic growth for nonequivalent configurations is also
exponential.
This pair of studies extends the lab's work
on theory of admixture and
combinatorics of evolutionary
trees.
10312018 — Congratulations to Ilana Arbisser on
defending her thesis "Mathematical investigations into
fundamental population genetics statistics and models." Ilana's
thesis examines the
joint distribution of the height and length of coalescent trees, the
relationship of the populationgenetic
statistic F_{ST} to the triangle inequality, and
the state space of a discretestate coalescent model with
recombination and migration. Dr. Arbisser's wise words about making
hard decisions, such as square root transformation vs. Cailliez
constant in multidimensional scaling: "it's important to consider
what choices we're making and the consequences of those choices."
Congrats Ilana!
10182018 — The lab examines the potential for
determining that relatives genotyped with nonoverlapping marker sets
are in fact relatives. This analysis demonstrates that people typed
with microsatellites used in forensic genetics can be connected to
close relatives typed with singlenucleotide polymorphisms used in
biomedical, genealogical, personalgenomic, and populationgenetic
studies. Lead author is Jaehee Kim with former lab
members Doc Edge and
Bridget
AlgeeHewitt also contributing.
[CNN]
[Nature]
[New
Scientist]
[Science]
[Scientific
American]
[Stanford
Report]
[Wired]
9142018 — A
new study characterizes all (gene
tree, species tree) pairs with exactly one coalescent history. The
characterization of these "lonely" pairs relies on the way in which the
taxa contained in cherries of the gene tree are placed with respect to the
root of the species tree.
8302018 — Rohan Mehta has defended his PhD
thesis "Mathematical modeling of genetic and cultural
traits." Rohan's thesis studies a variety of mathematical
modeling problems in diverse areas of population genetics and
evolutionary biology. He examines combinatorial and probabilistic
aspects of genealogical lineages along the branches of species
trees, mathematical properties of F_{ST} statistics in
relation to homozygosities and haploypes, and a geneculture
coevolutionary model of healthrelated behaviors. Congrats Rohan!
8302018 — Three articles from the lab have recently
appeared.

Alan Aw reports
a study in the Journal
of Mathematical Biology, on the bounds on
homozygosity and entropy statistics that measure genetic diversity in terms
of the frequency of the most frequent allele. Alan uses the theory of
majorization to obtain the bounds, generalizing previous
mathematical results from the lab
[52]
[87].
 Amy
Goldberg
and Lawrence
Uricchio report an overview of the literature on natural
selection in human populations in an Oxford
Bibliographies article.
 A commentary on Anthony
Edwards's 2003 essay of multivariate classification of individuals
into populations on the basis of genetic markers appears in a new book
edited by Rasmus Winther about Edwards's career and
contributions. Among other topics, the commentary discusses the
influence of Edwards's model on a phenotypic model from the lab
[129].
7182018 — Ilana
Arbisser reports a
mathematical investigation of the relationship between two of the most
frequently used features of gene genealogies, the height and length of
coalescent trees. The study also includes simulations describing the
effect of population growth and population subdivision on the
relationship between tree height and tree length. PhD
graduate Ethan Jewett contributed to the project.
7112018 — Check out
the Stanford XTree Project!
The lab visualizes concepts in phylogenetics using photos of trees on
the Stanford campus.
5302018 — We congratulate Jonathan Kang on
the defense of his PhD thesis "Analysis and application of linkage
disequilibrium in population and statistical genetics." In his
thesis, Jonathan focuses on three questions concerning linkage
disequilibrium (LD) and genomic sharing: the identification of optimal
subsamples to prioritize for sequencing in order to enhance LDbased
imputation, the relationship of runs of homozygosity to consanguinity
in Jewish populations, and mathematical properties of measures of
LD. Congrats to Jon!
9142017 — The lab reports
a study of consanguinity and
runs of homozygosity in Jewish populations. PhD student Jonathan
Kang compares runs of homozygosity in contemporary Jewish
populations to estimates of consanguinity measured in the 1950s from
interviews with mothers in maternity wards. The study finds that the
demographic consanguinity rates predict the fraction of the genome
that resides in long runs of homozygosity. PhD
graduates Amy Goldberg
and Doc Edge contributed to the study.
982017 — Filippo Disanto reports
a study of the
number of ancestral configurations possessed by matching gene trees
and species trees. Ancestral configurations represent a
combinatorial structure useful in producing probability formulas for
gene trees given species trees, and they are hence connected
to coalescent histories. Filippo's work is the latest in his
series of combinatorial enumerations of structures that arise in the
study of gene trees and species trees
[123]
[135]
[142].
8212017 — A new study from the lab shows that in the
admixed population of Cape Verde, genetic admixture is correlated with
a measure of linguistic admixture evaluated by tabulating words
of Portuguese and African origin in individuals' speech in the Cape
Verde Kriolu lnaguage. The analyses suggest a mechanism of
cotransmission of genetic and linguistic admixture during the descent
of a creolespeaking admixed population. We congratulate lab alumni Paul
Verdu*, Ethan Jewett*,
and Trevor
Pemberton on the study.
852017 — Olga Kamneva reports a phylogenetic
study of 20
worldwide species of strawberries (Fragaria) on the basis of
nextgeneration sequencing data assembled via a bioinformatics
pipeline designed specifically for polyploids of mixed ploidy. The
study suggests new hypotheses for the diploid progenitors of polyploid
species of Fragaria.
762017 — Nicolas Alcala has
obtained mathematical bounds on populationgenetic
statistic F_{ST} in the case of a biallelic marker
whose mean frequency across a set of populations is fixed. His bounds
provide an explanation of a frequently observed dependence
of F_{ST} on the number of populations under
consideration. Nicolas's paper
expands on two earlier studies from the lab concerning bounds
on F_{ST}
[102]
[121].
5302017 — Recent PhD graduate Doc
Edge reports in a
new study that on the basis of
correlations between genotypes at neighboring markers, profiles
containing nonoverlapping sets of genetic markers can be
connected to the same individual. This "recordmatching" is demonstrated
using genomic and forensic genetic markers, and it has implications for
forensic genetics and genomic
privacy. Postdoc Bridget
AlgeeHewitt and former
postdoc Trevor
Pemberton contributed to the project.
[Stanford
Report news story]
582017 —
Congratulations to
Amy
Goldberg on the defense of her thesis "Mathematical and
statistical approaches to elucidate recent human evolutionary
history." Amy's thesis considers mechanistic mathematical models of
admixture, including the effect of sexbiased admixture on autosomes and
on the X chromosome, and the inference from ancient autosomes and X
chromosomes of sexbiased migration during prehistoric admixture events in
Europe. She also examines the human population size history of South
America on the basis of the density and location of archaeological
sites. Congratulations Amy!
4242017 — We congratulate
Amy
Goldberg on receiving the 2017 Sherwood Washburn Prize from
the American Association of Physical Anthropologists! This prize
recognizes the best student presentation at the AAPA annual
meeting. Amy spoke about her work on the contrast between Neolithic
and Bronze Age migrations in Europe in their levels of male and female
migration. [Read the paper]
3152017
—
Amy
Goldberg reports
that two ancient migration events in Europe involved different
proportions of male and female migrants, the earlier Neolithic
migration from Anatolia having similar numbers of males and females
and the later PonticCaspian migration having a greater proportion of
males. The result, relying on comparisons of ancient DNA patterns from
the X chromosome and the autosomes, builds on Amy's earlier work on
sex bias in genetic admixture models
[122]
[133].
[Science
news story]
3102017 — A
new simulation
study by postdoc alum Olga Kamneva evaluates the behavior
of several methods for inferring species networks when the
evolutionary process includes hybridization. The paper provides
muchneeded information on the comparative performance of the
various approaches.
2272017 — Postdoc alum Olga Kamneva reports
in PLoS Computational Biology a
study
of the relationship between genome composition of microbes and the
cooccurrence of microbes in the environment. She finds that comparisons of
microbial genomes can contribute to predictions about whether microbes
are associated ecologically. Congrats Olga!
2222017 — We wish several members of the lab well in
their new positions.
 Nicolas Alcala — Postdoc with Matthieu Foll, International
Agency for Research on Cancer, World Health Organization, Lyon.
 Filippo Disanto — Junior faculty, Department of
Mathematics, University of Pisa (sponsored by the Rita Levi Montalcini
researcher program).
 Doc Edge — Postdoc with Graham Coop, Department of
Evolution and Ecology, University of California, Davis.
 Olga Kamneva — Bioinformatics Scientist, Affymetrix, Inc.
11142016 — Postdoc
Lawrence
Uricchio has reported an upper
bound on the size of gene tree sets required before all splits of a
species tree appear in a gene tree set with a specified probability. His
upper bound depends on a single parameter — the shortest internal
branch in the species tree. The computation extends the lab's work on
methods for species tree inference from gene trees.
10142016 — Recent PhD
graduate Doc Edge has
devised a general mathematical model to understand how genotypic
differences between populations contribute to phenotypic differences
between populations. He uses the model to analyze the relationship of
genetics to "health disparities," concluding that health disparities
that all trend in the same direction are incompatible with neutral
genetic explanations. The work extends a simpler model of Doc's
[129], allowing for
diploidy, genetic drift, and general distributions of allele
frequencies.
1072016 — Postdoc Filippo Disanto continues the
lab's work on coalescent histories with
a study of the number
of coalescent histories for matching gene trees in caterpillarlike
families of species trees. Filippo's work solves an open problem from
earlier work in the lab
[111], showing that the
number of coalescent histories is asymptotic to a constant multiple of
the Catalan numbers. He uses clever iterative enumerations and
techniques of analytic combinatorics to obtain the result. See also
[41],
[68], and
[135] for related
work.
7272016 — We are pleased to announce that the
software MONOPHYLER is now available.
MONOPHYLER computes probabilities
that sets of lineages are monophyletic, both for general species trees and
for trees of small size. MONOPHYLER
is reported by PhD student Rohan Mehta. The software encodes
formulas from Rohan's
recent Proceedings of the National
Academy of Sciences paper.
7222016 — We congratulate PhD
student Doc Edge on his thesis
defense, "Pick up the pieces: combining information from multiple
genetic loci." Doc's thesis examines several problems in the
mathematical modeling of the genotypetophenotype relationship in
structured populations, mathematical properties of
the F_{st} measure of genetic differentiation, and
populationgenetic aspects of forensic DNA testing and genetic association
studies. Doc has been recognized with the
Samuel Karlin Prize in Mathematical Biology, awarded by the Department of
Biology. Congratulations Doc!
7192016 — PhD student Rohan Mehta reports a
computation of the probability that a set of gene lineages on an
arbitrary species tree. The work generalizes earlier studies from the lab
that considered trees of
only two
or three species. Rohan
illustrates the new formula with an application in maize.
The study is a contribution to
the Comparative Phylogeography volume of the "In the Light of Evolution"
special issue series of Proceedings of the National Academy of
Sciences USA.
6272016 — We congratulate biology MS student Brian
Donovan on the completion of his PhD in science education "An
experimental exploration of how textbased instruction in school biology
affects belief in genetic essentialism of race in adolescent
populations." Brian defended his PhD in the Graduate School of
Education on May 26. He is continuing his studies as a postdoctoral fellow
at the Biological Sciences Curriculum Study in Colorado Springs.
6172016 — The lab reports
a study examining
the predicted distribution of gene tree shape under a birthdeath
model of species divergence. The work suggests that gene trees are
expected to be more imbalanced than species trees, potentially
providing part of the explanation for an excess of imbalance
observed in inferred phylogenies.
6152016 — Congratulations
to Amy
Goldberg
and Jaehee Kim, who have received fellowships for
20162017 from the Stanford Center for Computational, Evolutionary, and
Human Genomics!
5122016 — Lab
alumnus Mike
DeGiorgio reports on the consistency properties of species
tree inference methods in a model with ancestral population
structure. By introducing a model that includes population
subdivision in ancestral species,
his paper
introduces a new direction for studying consistency in species
tree inference. The work is related to several recent papers
from the lab on consistency of species tree methods
([85],
[88],
[89],
[97],
[109])
4222016 — Several projects from the lab have been in
the news:
452016 — We congratulate PhD
student Amy Goldberg
on the publication of
her Nature article
entitled "Postinvasion demography of prehistoric humans in South
America." In this work, Amy and her colleagues use the locations and
dates of South American archaeological sites to estimate the time
trajectory of the human population size history of the
continent. Read the news
story here.
442016 — Lab
members Bridget
AlgeeHewitt, Doc
Edge, and Jaehee Kim report that forensic genetic
markers selected for their use in individual identification possess
a surprising level of information about genetic ancestry. Moreover, their
study finds that a general correlation holds for genetic
markers between their information about individual identity and
ancestry information. The result makes use of theory from the lab on the
connection between measures of genetic diversity and genetic
differentiation ([102],
[121]).
152016 — The lab helps celebrate the centennial of the
journal Genetics!
When PhD
student Amy Goldberg
develops a model for sexbiased admixture on the Xchromosome, a
curious mathematical sequence leads to an unexpected connection deep
in the Genetics archive.
Read about the oscillatory functions and
coupled recursions encountered in this scholarly adventure — with a
surprise appearance of the Fibonacci numbers.
Past news items
SELECTED RECENT PUBLICATIONS
IM Arbisser, EM Jewett, NA Rosenberg (2018) On
the joint distribution of tree height and tree length under the
coalescent. Theoretical Population Biology 122: 4656.
[Abstract]
[PDF]
N Alcala, NA Rosenberg (2017) Mathematical
constraints on F_{ST}: biallelic markers in
arbitrarily many populations.
Genetics 206: 15811600.
[Abstract]
[PDF]
[File
S1]
[File
S2]
MD Edge, BFB AlgeeHewitt, TJ Pemberton, JZ
Li, NA Rosenberg (2017) Linkage disequilibrium matches forensic
genetic records to disjoint genomic marker sets.
Proceedings of the National Academy of Sciences USA 114:
56715676.
[Abstract]
[PDF]
[Supplement]
JTL Kang, A Goldberg, MD Edge, DM Behar, NA
Rosenberg (2016) Consanguinity rates predict long runs of
homozygosity in Jewish populations. Human Heredity 82:
87102. [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 113:
80028009.
[Abstract]
[PDF]
[Supplement]
[Software]
F Disanto, NA Rosenberg (2015) Coalescent histories for
lodgepole species trees. Journal of Computational Biology 22:
918929. [Abstract]
[PDF]
A Goldberg, NA Rosenberg (2015) Beyond 2/3 and 1/3: the
complex signatures of sexbiased admixture on the X
chromosome. Genetics 201: 263279.
[Abstract]
[PDF]
NA Rosenberg, JTL Kang (2015) Genetic diversity and
societally important disparities. Genetics 201: 112.
[Abstract]
[PDF]
[Supplement]
