# A Spatial Framework for Understanding Population Structure and Admixture.

A Spatial Framework for Understanding Population Structure and Admixture.
Gideon Bradburd, Peter L. Ralph, Graham Coop
doi: http://dx.doi.org/10.1101/013474

Geographic patterns of genetic variation within modern populations, produced by complex histories of migration, can be difficult to infer and visually summarize. A general consequence of geographically limited dispersal is that samples from nearby locations tend to be more closely related than samples from distant locations, and so genetic covariance often recapitulates geographic proximity. We use genome-wide polymorphism data to build “geogenetic maps”, which, when applied to stationary populations, produces a map of the geographic positions of the populations, but with distances distorted to reflect historical rates of gene flow. In the underlying model, allele frequency covariance is a decreasing function of geogenetic distance, and nonlocal gene flow such as admixture can be identified as anomalously strong covariance over long distances. This admixture is explicitly co-estimated and depicted as arrows, from the source of admixture to the recipient, on the geogenetic map. We demonstrate the utility of this method on a circum-Tibetan sampling of the greenish warbler (Phylloscopus trochiloides), in which we find evidence for gene flow between the adjacent, terminal populations of the ring species. We also analyze a global sampling of human populations, for which we largely recover the geography of the sampling, with support for significant histories of admixture in many samples. This new tool for understanding and visualizing patterns of population structure is implemented in a Bayesian framework in the program SpaceMix.

# Scaling probabilistic models of genetic variation to millions of humans

Scaling probabilistic models of genetic variation to millions of humans

Prem Gopalan, Wei Hao, David M. Blei, John D. Storey
doi: http://dx.doi.org/10.1101/013227

A major goal of population genetics is to quantitatively understand variation of genetic polymorphisms among individuals. Researchers have developed sophisticated statistical methods to capture the complex population structure that underlies observed genotypes in humans. The number of humans that have been densely genotyped across the genome has grown significantly in recent years. In aggregate about 1M individuals have been densely genotyped to date, and if we could analyze this data then we would have a nearly complete picture of human genetic variation. Existing state-of-the-art methods, however, cannot scale to data of this size. To this end, we have developed TeraStructure. TeraStructure is a new algorithm to fit Bayesian models of genetic variation in human populations on tera-sample-sized data sets (1012 observed genotypes, e.g., 1M individuals at 1M SNPs). It is a principled approach to approximate Bayesian inference that iterates between subsampling locations of the genome and updating an estimate of the latent population structure. On real and simulated data sets of up to 10K individuals, TeraStructure is twice as fast as existing methods and recovers the latent population structure with equal accuracy. On genomic data simulated at the tera-sample-size scales, TeraStructure continues to be accurate and is the only method that can complete its analysis.

# A new FST-based method to uncover local adaptation using environmental variables

A new $F_{\text{ST}}$-based method to uncover local adaptation using environmental variables
Pierre de Villemereuil, Oscar E. Gaggiotti
Comments: 18 pages, 5 figures, Supplementary Information at the end of the document
Subjects: Populations and Evolution (q-bio.PE)

Genome-scan methods are used for screening genome-wide patterns of DNA polymorphism to detect signatures of positive selection. There are two main types of methods: (i) “outlier” detection methods based on $F_{\text{ST}}$ that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables. In this article, we present a new $F_{\text{ST}}$-based genome scan method, BayeScEnv, which incorporates environmental information in the form of “environmental differentiation”. It is based on the F model but as opposed to existing approaches it considers two locus-specific effects, one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection. Simulation studies showed that our method has a much lower false positive rate than an existing $F_{\text{ST}}$-based method, BayeScan, under a wide range of demographic scenarios. Although it had lower power, it leads to a better compromise between power and false positive rate. We apply our method to Human and Salmon datasets and show that it can be used successfully to study local adaptation. The method was developped in C++ and is avaible at this http URL

# Visualizing spatial population structure with estimated effective migration surfaces

Visualizing spatial population structure with estimated effective migration surfaces
Desislava Petkova, John Novembre, Matthew Stephens
doi: http://dx.doi.org/10.1101/011809

Genetic data often exhibit patterns that are broadly consistent with “isolation by distance” – a phenomenon where genetic similarity tends to decay with geographic distance. In a heterogeneous habitat, decay may occur more quickly in some regions than others: for example, barriers to gene flow can accelerate the genetic differentiation between groups located close in space. We use the concept of “effective migration” to model the relationship between genetics and geography: in this paradigm, effective migration is low in regions where genetic similarity decays quickly. We present a method to quantify and visualize variation in effective migration across the habitat, which can be used to identify potential barriers to gene flow, from geographically indexed large-scale genetic data. Our approach uses a population genetic model to relate underlying migration rates to expected pairwise genetic dissimilarities, and estimates migration rates by matching these expectations to the observed dissimilarities. We illustrate the potential and limitations of our method using simulations and data from elephant, human, and Arabidopsis thaliana populations. The resulting visualizations highlight important features of the spatial population structure that are difficult to discern using existing methods for summarizing genetic variation such as principal components analysis.

# Demographic inference using genetic data from a single individual: separating population size variation

Demographic inference using genetic data from a single individual: separating population size variation from population structure
Olivier Mazet, Willy Rodríguez, Lounès Chikhi
doi: http://dx.doi.org/10.1101/011866

The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in genetic information will likely help biologists and anthropologists to reconstruct the demographic history of populations, it also represents new challenges. Recent work has shown that structured populations generate signals of population size change. As a consequence it is often difficult to determine whether demographic events such as expansions or contractions (bottlenecks) inferred from genetic data are real or due to the fact that populations are structured in nature. Given that few inferential methods allow us to account for that structure, and that genomic data will necessarily increase the precision of parameter estimates, it is important to develop new approaches. In the present study we analyse two demographic models. The first is a model of instantaneous population size change whereas the second is the classical symmetric island model. We (i) re-derive the distribution of coalescence times under the two models for a sample of size two, (ii) use a maximum likelihood approach to estimate the parameters of these models (iii) validate this estimation procedure under a wide array of parameter combinations, (iv) implement and validate a model choice procedure by using a Kolmogorov-Smirnov test. Altogether we show that it is possible to estimate parameters under several models and perform efficient model choice using genetic data from a single diploid individual.

# A Hidden Markov Model for Investigating Recent Positive Selection through Haplotype Structure

A Hidden Markov Model for Investigating Recent Positive Selection through Haplotype Structure

Hua Chen, Jody Hey, Montgomery Slatkin
doi: http://dx.doi.org/10.1101/011247

Recent positive selection can increase the frequency of an advantageous mutant rapidly enough that a relatively long ancestral haplotype will be remained intact around it. We present a hidden Markov model (HMM) to identify such haplotype structures. With HMM identified haplotype structures, a population genetic model for the extent of ancestral haplotypes is then adopted for parameter inference of the selection intensity and the allele age. Simulations show that this method can detect selection under a wide range of conditions and has higher power than the existing frequency spectrum-based method. In addition, it provides good estimate of the selection coefficients and allele ages for strong selection. The method analyzes large data sets in a reasonable amount of running time. This method is applied to HapMap III data for a genome scan, and identifies a list of candidate regions putatively under recent positive selection. It is also applied to several genes known to be under recent positive selection, including the LCT, KITLG and TYRP1 genes in Northern Europeans, and OCA2 in East Asians, to estimate their allele ages and selection coefficients.

# Estimating the Relative Rate of Recombination to Mutation in Bacteria from Single-Locus Variants using Composite Likelihood Methods

Estimating the Relative Rate of Recombination to Mutation in Bacteria from Single-Locus Variants using Composite Likelihood Methods

Paul Fearnhead, Shoukai Yu, Patrick Biggs, Barbara Holland, Nigel French
(Submitted on 5 Nov 2014)

A number of studies have suggested using comparisons between DNA sequences of closely related bacterial isolates to estimate the relative rate of recombination to mutation for that bacterial species. We consider such an approach which uses single locus variants: pairs of isolates whose DNA differ at a single gene locus. One way of deriving point estimates for the relative rate of recombination to mutation from such data is to use composite likelihood methods. We extend recent work in this area so as to be able to construct confidence intervals for our estimates, without needing to resort to computationally-intensive bootstrap procedures, and to develop a test for whether the relative rate varies across loci. Both our test and method for constructing confidence intervals are obtained by modelling the dependence structure in the data, and then applying asymptotic theory regarding the distribution of estimators obtained using a composite likelihood. We applied these methods to multi-locus sequence typing (MLST) data from eight bacteria, finding strong evidence for considerable rate variation in three of these: Bacillus cereus, Enterococcus faecium and Klebsiella pneumoniae.