Rosenberg lab at Stanford University

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 population-genetic data. Read more...


  • 8-4-2020Alyssa Fortier and Jaehee Kim examine the use of ancestry inference as a step to improve relatedness profiling in forensic genetics. By reducing the potential for misspecification of allele frequencies in likelihooid calculations, inference of the genetic ancestry of the forensic sample can avoid a false positive inference of relatedness.

  • 7-29-2020Amy Goldberg and Ananya Rastogi report a study of "Assortative mating by population of origin in a mechanistic model of admixture." This work analyzes a model in which individuals mate assortatively in a setting with two ancestral populations and an admixed populaton. The study builds on several previous models from the lab. [82] [122] [133]

  • 6-11-2020Rohan Mehta reports an article entitled "Modelling anti-vaccine sentiment as a cultural pathogen." The paper describes a coupled contagion: the spread of an anti-vaccine sentiment, and the spread of the disease against which the vaccine protects. The dynamics illustrate how spread of sentiment against a vaccine generates and magnifies outbreaks of the associated disease. [Stanford Report]

  • 5-29-2020 — The long-awaited 50th anniversary special issue of Theoretical Population Biology has been published. The special issue contains commentaries on major research areas developed in TPB, commentaries on historic papers, biograpical commentaries, and research articles — including a study by Ilana Arbisser on FST and the triangle inequality. [Stanford Report]

  • 4-24-2020 — Using a combination of coalescent theory and simulation, Kim et al. study the probability under a birth-death process that species trees lie in the "anomaly zone," the region of the parameter space in which species trees can disagree with the gene tree they are most likely to produce. The work buils on earlier studies of the anomaly zone [30] [47], ranked gene trees [85] [97], and joint simulation of species trees and gene trees [140].

  • 3-20-2020 — A new study examines the mathematical connections between homozygosity and heterozygosity statistics and measures of health care fragmentation in health services research. The study relies on results from related studies in the lab [87] [158].

  • 3-10-2020 — PhD graduate Jonathan Kang reports a new study of five measures of linkage disequilibrium. Jonathan computes mathematical bounds on linkage disequilibrium measures in relation to the allele frequencies at a pair of loci, analyzing the implications of these bounds in human genetic data. The study builds on an earlier analysis of the r2 measure [51].

  • 1-9-2020 — A paper by Zoe Himwich, recent Stanford graduate in mathematics, studies coalescent histories for non-matching caterpillar gene trees and species trees. This study in enumerative combinatorics identifies new connections to the Catalan numbers, Dyck paths, and roadblocked monotonic paths not crossing the diagonal of a square lattice. The paper builds on two earlier studies of coalescent histories for caterpillar-like tree families [111] [142].

  • 12-9-2019Gili Greenbaum introduces a new network-based approach to inference of population structure. The method relies on detection of "communities" in genetic distance matrices and can be used to produce a new way of displaying population structure — a "population structure tree."

  • 12-8-2019 — The work of lab alumnus Brian Donovan is featured on the front page of the New York Times.

  • 11-1-2019Gili Greenbaum reports a study of dynamics of the spatial boundary between Neanderthals and Modern Humans before Modern Humans spread rapidly out of Africa. The question is not "why did Modern Humans replace Neanderthals so quickly?" Rather, Gili asks "why did Modern Humans not replace Neanderthals for so long?" The proposed answer lies in the dynamics of infectious disease. [Haaretz] [Stanford Report]

  • 10-1-2019 — 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.

  • 9-23-2019Nicolas 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.

  • 9-9-2019 — A new paper led by Rohan Mehta examines the behavior of the FST measure of genetic differentiation on haplotypic data. The study illustrates how incrementing the length of the haplotype window tends to decrease FST — but sometimes increases it. The work is closely related to several of the lab's papers on FST [102] [121] [149] [165]. Check out the video abstract drawn and narrated by co-author Alison Feder.

  • 5-8-2019 — 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 red-legged 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.

  • 5-2-2019 — A new study led by Alissa Severson examines the relationship between runs of homozygosity and identity-by-descent 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].

  • 4-29-2019Nicolas Alcala has a new study of mathematical bounds on three population-genetic statistics: GST', Jost's D, and FST. 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 FST bounds as well as that of two other studies from the lab concerning bounds on FST [102] [121].

  • 3-26-2019Filippo 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.

  • 3-3-2019 — 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].

  • 1-23-2019 — 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 neighbor-joining 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.

  • 10-31-2018 — 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 population-genetic statistic FST to the triangle inequality, and the state space of a discrete-state 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!

  • 10-18-2018 — 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 single-nucleotide polymorphisms used in biomedical, genealogical, personal-genomic, and population-genetic studies. Lead author is Jaehee Kim with former lab members Doc Edge and Bridget Algee-Hewitt also contributing. [CNN] [Nature] [New Scientist] [Science] [Scientific American] [Stanford Report] [Wired]

  • 9-14-2018 — 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.

  • 8-30-2018Rohan 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 FST statistics in relation to homozygosities and haploypes, and a gene-culture coevolutionary model of health-related behaviors. Congrats Rohan!

  • 8-30-2018 — 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].

  • 7-18-2018Ilana 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.

  • 7-11-2018 — Check out the Stanford X-Tree Project! The lab visualizes concepts in phylogenetics using photos of trees on the Stanford campus.

  • 5-30-2018 — 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 LD-based imputation, the relationship of runs of homozygosity to consanguinity in Jewish populations, and mathematical properties of measures of LD. Congrats to Jon!

  • 9-14-2017 — 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.

  • 9-8-2017Filippo 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].

  • 8-21-2017 — 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 creole-speaking admixed population. We congratulate lab alumni Paul Verdu*, Ethan Jewett*, and Trevor Pemberton on the study.

  • 8-5-2017Olga Kamneva reports a phylogenetic study of 20 worldwide species of strawberries (Fragaria) on the basis of next-generation 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.

  • 7-6-2017Nicolas Alcala has obtained mathematical bounds on population-genetic statistic FST 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 FST on the number of populations under consideration. Nicolas's paper expands on two earlier studies from the lab concerning bounds on FST [102] [121].

  • 5-30-2017 — 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 "record-matching" is demonstrated using genomic and forensic genetic markers, and it has implications for forensic genetics and genomic privacy. Postdoc Bridget Algee-Hewitt and former postdoc Trevor Pemberton contributed to the project. [Stanford Report news story]

  • 5-8-2017 — 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 sex-biased admixture on autosomes and on the X chromosome, and the inference from ancient autosomes and X chromosomes of sex-biased 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!

  • 4-24-2017 — 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]

  • 3-15-2017Amy 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 Pontic-Caspian 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]

  • 3-10-2017 — 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 much-needed information on the comparative performance of the various approaches.

  • 2-27-2017 — Postdoc alum Olga Kamneva reports in PLoS Computational Biology a study of the relationship between genome composition of microbes and the co-occurrence of microbes in the environment. She finds that comparisons of microbial genomes can contribute to predictions about whether microbes are associated ecologically. Congrats Olga!

  • 2-22-2017 — 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.

  • Past news items


    AL Severson, S Carmi, NA Rosenberg (2019) The effect of consanguinity on between-individual identity-by-descent sharing. Genetics 212: 305-316. [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]

    AJ Aw, NA Rosenberg (2018) Bounding measures of genetic similarity and diversity using majorization. Journal of Mathematical Biology 77: 711-737. [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]

    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]

    MD Edge, BFB Algee-Hewitt, 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: 5671-5676. [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: 87-102. [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: 8002-8009. [Abstract] [PDF] [Supplement] [Software]

    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]

    NA Rosenberg, JTL Kang (2015) Genetic diversity and societally important disparities. Genetics 201: 1-12. [Abstract] [PDF] [Supplement]