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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.04849">arXiv:2108.04849</a> <span> [<a href="https://arxiv.org/pdf/2108.04849">pdf</a>, <a href="https://arxiv.org/format/2108.04849">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Enumeration of binary trees compatible with a perfect phylogeny </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Palacios%2C+J+A">Julia A. Palacios</a>, <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Disanto%2C+F">Filippo Disanto</a>, <a href="/search/q-bio?searchtype=author&query=Rosenberg%2C+N+A">Noah A. Rosenberg</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.04849v1-abstract-short" style="display: inline;"> Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy--a rooted, binary, timed tree, with tips corresponding to individual sequences. Under the infinitely-many-sites mutation model, mutations are randomly superimposed along the branches of the genealogy, so that every m… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.04849v1-abstract-full').style.display = 'inline'; document.getElementById('2108.04849v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.04849v1-abstract-full" style="display: none;"> Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy--a rooted, binary, timed tree, with tips corresponding to individual sequences. Under the infinitely-many-sites mutation model, mutations are randomly superimposed along the branches of the genealogy, so that every mutation occurs at a chromosomal site that has not previously mutated; if a mutation occurs at an interior branch, then all individuals descending from that branch carry the mutation. The implication is that observed patterns of molecular variation from this model impose combinatorial constraints on the hidden state space of genealogies. In particular, observed molecular variation can be represented in the form of a perfect phylogeny, a tree structure that fully encodes the mutational differences among sequences. For a sample of n sequences, a perfect phylogeny might not possess n distinct leaves, and hence might be compatible with many possible binary tree structures that could describe the evolutionary relationships among the n sequences. Here, we investigate enumerative properties of the set of binary ranked and unranked tree shapes that are compatible with a perfect phylogeny, and hence, the binary ranked and unranked tree shapes conditioned on an observed pattern of mutations under the infinitely-many-sites mutation model. We provide a recursive enumeration of these shapes. We consider both perfect phylogenies that can be represented as binary and those that are multifurcating. The results have implications for computational aspects of the statistical inference of evolutionary parameters that underlie sets of molecular sequences. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.04849v1-abstract-full').style.display = 'none'; document.getElementById('2108.04849v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages, 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.13337">arXiv:2004.13337</a> <span> [<a href="https://arxiv.org/pdf/2004.13337">pdf</a>, <a href="https://arxiv.org/format/2004.13337">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2020.109988">10.1016/j.chaos.2020.109988 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Investigating the dynamics of COVID-19 pandemic in India under lockdown </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Pai%2C+C">Chintamani Pai</a>, <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Ankush Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Rawoot%2C+V">Vaibhav Rawoot</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.13337v1-abstract-short" style="display: inline;"> In this paper, we investigate the ongoing dynamics of COVID-19 in India after its emergence in Wuhan, China in December 2019. We discuss the effect of nationwide lockdown implemented in India on March 25, 2020 to prevent the spread of COVID-19. Susceptible-Exposed-Infectious-Recovered (SEIR) model is used to forecast active COVID-19 cases in India considering the effect of nationwide lockdown and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.13337v1-abstract-full').style.display = 'inline'; document.getElementById('2004.13337v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.13337v1-abstract-full" style="display: none;"> In this paper, we investigate the ongoing dynamics of COVID-19 in India after its emergence in Wuhan, China in December 2019. We discuss the effect of nationwide lockdown implemented in India on March 25, 2020 to prevent the spread of COVID-19. Susceptible-Exposed-Infectious-Recovered (SEIR) model is used to forecast active COVID-19 cases in India considering the effect of nationwide lockdown and possible inflation in the active cases after its removal on May 3, 2020. Our model predicts that with the ongoing lockdown, the peak of active infected cases around 43,000 will occur in the mid of May, 2020. We also predict a 7$\%$ to 21$\%$ increase in the peak value of active infected cases for a variety of hypothetical scenarios reflecting a relative relaxation in the control strategies implemented by the government in the post-lockdown period. For India, it is an important decision to come up with a non-pharmaceutical control strategy such as nationwide lockdown for 40 days to prolong the higher phases of COVID-19 and to avoid severe load on its public health-care system. As the ongoing COVID-19 outbreak remains a global threat, it is a challenge for all the countries to come up with effective public health and administrative strategies to battle against COVID-19 and sustain their economies. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.13337v1-abstract-full').style.display = 'none'; document.getElementById('2004.13337v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 5 figures, 1 table</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1809.03968">arXiv:1809.03968</a> <span> [<a href="https://arxiv.org/pdf/1809.03968">pdf</a>, <a href="https://arxiv.org/ps/1809.03968">ps</a>, <a href="https://arxiv.org/format/1809.03968">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Subcellular Processes">q-bio.SC</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.98.032413">10.1103/PhysRevE.98.032413 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Braichenko%2C+S">Svitlana Braichenko</a>, <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Atul Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Dasmahapatra%2C+S">Srinandan Dasmahapatra</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1809.03968v2-abstract-short" style="display: inline;"> Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.03968v2-abstract-full').style.display = 'inline'; document.getElementById('1809.03968v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1809.03968v2-abstract-full" style="display: none;"> Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.03968v2-abstract-full').style.display = 'none'; document.getElementById('1809.03968v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.05035">arXiv:1712.05035</a> <span> [<a href="https://arxiv.org/pdf/1712.05035">pdf</a>, <a href="https://arxiv.org/format/1712.05035">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> </div> </div> <p class="title is-5 mathjax"> Geometry of the sample frequency spectrum and the perils of demographic inference </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Rosen%2C+Z">Zvi Rosen</a>, <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Roch%2C+S">Sebastien Roch</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.05035v1-abstract-short" style="display: inline;"> The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05035v1-abstract-full').style.display = 'inline'; document.getElementById('1712.05035v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.05035v1-abstract-full" style="display: none;"> The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to 0 or diverge to infinity, and show undesirable sensitivity of the inferred demography to perturbations in the data. The goal of this paper is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographic histories and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model with sample size 4, and generalize our intuition to arbitrary sample sizes n using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only k(n) epochs, where k(n) is between n/2 and 2n-1. The set of expected SFS for piecewise-constant demographies with fewer than k(n) epochs is open and non-convex, which causes the above phenomena for inference from data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05035v1-abstract-full').style.display = 'none'; document.getElementById('1712.05035v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 92D10; 14P10; 52A20; 62P10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1610.07306">arXiv:1610.07306</a> <span> [<a href="https://arxiv.org/pdf/1610.07306">pdf</a>, <a href="https://arxiv.org/format/1610.07306">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Methodology">stat.ME</span> </div> </div> <p class="title is-5 mathjax"> Novel probabilistic models of spatial genetic ancestry with applications to stratification correction in genome-wide association studies </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Javanmard%2C+A">Adel Javanmard</a>, <a href="/search/q-bio?searchtype=author&query=Courtade%2C+T+A">Thomas A. Courtade</a>, <a href="/search/q-bio?searchtype=author&query=Tse%2C+D">David Tse</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1610.07306v2-abstract-short" style="display: inline;"> Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.07306v2-abstract-full').style.display = 'inline'; document.getElementById('1610.07306v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1610.07306v2-abstract-full" style="display: none;"> Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure. Our algorithm, Geographic Ancestry Positioning (GAP), relates local genetic distances between samples to their spatial distances, and can be used for visually discerning population structure as well as accurately inferring the spatial origin of individuals on a two-dimensional continuum. On both simulated and several real datasets from diverse human populations, GAP exhibits substantially lower error in reconstructing spatial ancestry coordinates compared to PCA. Our spatial inference algorithm can also be effectively applied to the problem of population stratification in genome-wide association studies (GWAS), where hidden population structure can create fictitious associations when population ancestry is correlated with both the genotype and the trait. We develop an association test that uses the ancestry coordinates inferred by GAP to accurately account for ancestry-induced correlations in GWAS. Based on simulations and analysis of a dataset of 10 metabolic traits measured in a Northern Finland cohort, which is known to exhibit significant population structure, we find that our method has superior power to current approaches. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.07306v2-abstract-full').style.display = 'none'; document.getElementById('1610.07306v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Supplementary information included to the main text</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1310.1068">arXiv:1310.1068</a> <span> [<a href="https://arxiv.org/pdf/1310.1068">pdf</a>, <a href="https://arxiv.org/ps/1310.1068">ps</a>, <a href="https://arxiv.org/format/1310.1068">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Methodology">stat.ME</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1214/14-AOAS764">10.1214/14-AOAS764 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A novel spectral method for inferring general diploid selection from time series genetic data </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Steinr%C3%BCcken%2C+M">Matthias Steinr眉cken</a>, <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1310.1068v2-abstract-short" style="display: inline;"> The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of nonneutral models for the population allele frequency dynamics, given the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.1068v2-abstract-full').style.display = 'inline'; document.getElementById('1310.1068v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1310.1068v2-abstract-full" style="display: none;"> The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of nonneutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote advantage form of balancing selection may have been acting on these loci. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.1068v2-abstract-full').style.display = 'none'; document.getElementById('1310.1068v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 January, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published in at http://dx.doi.org/10.1214/14-AOAS764 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IMS-AOAS-AOAS764 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annals of Applied Statistics 2014, Vol. 8, No. 4, 2203-2222 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1309.5056">arXiv:1309.5056</a> <span> [<a href="https://arxiv.org/pdf/1309.5056">pdf</a>, <a href="https://arxiv.org/ps/1309.5056">ps</a>, <a href="https://arxiv.org/format/1309.5056">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistics Theory">math.ST</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1214/14-AOS1264">10.1214/14-AOS1264 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Descartes' rule of signs and the identifiability of population demographic models from genomic variation data </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1309.5056v3-abstract-short" style="display: inline;"> The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has be… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1309.5056v3-abstract-full').style.display = 'inline'; document.getElementById('1309.5056v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1309.5056v3-abstract-full" style="display: none;"> The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1309.5056v3-abstract-full').style.display = 'none'; document.getElementById('1309.5056v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published in at http://dx.doi.org/10.1214/14-AOS1264 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IMS-AOS-AOS1264 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annals of Statistics 2014, Vol. 42, No. 6, 2469-2493 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1308.0091">arXiv:1308.0091</a> <span> [<a href="https://arxiv.org/pdf/1308.0091">pdf</a>, <a href="https://arxiv.org/format/1308.0091">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1073/pnas.1322709111">10.1073/pnas.1322709111 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Distortion of genealogical properties when the sample is very large </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Clark%2C+A+G">Andrew G. Clark</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1308.0091v1-abstract-short" style="display: inline;"> Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large sample sizes call for carefully re-examining the theoretical foundation underlying commonly-used analytical tools. Here, we study the accuracy of the coalescent, a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.0091v1-abstract-full').style.display = 'inline'; document.getElementById('1308.0091v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1308.0091v1-abstract-full" style="display: none;"> Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large sample sizes call for carefully re-examining the theoretical foundation underlying commonly-used analytical tools. Here, we study the accuracy of the coalescent, a central model for studying the ancestry of a sample of individuals. The coalescent arises as a limit of a large class of random mating models and it is an accurate approximation to the original model provided that the population size is sufficiently larger than the sample size. We develop a method for performing exact computation in the discrete-time Wright-Fisher (DTWF) model and compare several key genealogical quantities of interest with the coalescent predictions. For realistic demographic scenarios, we find that there are a significant number of multiple- and simultaneous-merger events under the DTWF model, which are absent in the coalescent by construction. Furthermore, for large sample sizes, there are noticeable differences in the expected number of rare variants between the coalescent and the DTWF model. To balance the tradeoff between accuracy and computational efficiency, we propose a hybrid algorithm that utilizes the DTWF model for the recent past and the coalescent for the more distant past. Our results demonstrate that the hybrid method with only a handful of generations of the DTWF model leads to a frequency spectrum that is quite close to the prediction of the full DTWF model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.0091v1-abstract-full').style.display = 'none'; document.getElementById('1308.0091v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, 2 tables, 14 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proc. Natl. Acad. Sci. U.S.A., Vol. 111, No. 6 (2014) 2385-2390 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1109.2386">arXiv:1109.2386</a> <span> [<a href="https://arxiv.org/pdf/1109.2386">pdf</a>, <a href="https://arxiv.org/format/1109.2386">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1239/aap/1339878718">10.1239/aap/1339878718 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Approximate sampling formulae for general finite-alleles models of mutation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Kamm%2C+J+A">John A. Kamm</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1109.2386v3-abstract-short" style="display: inline;"> Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.2386v3-abstract-full').style.display = 'inline'; document.getElementById('1109.2386v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1109.2386v3-abstract-full" style="display: none;"> Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn construction related to the coalescent is used to derive approximate closed-form sampling formulas for an arbitrary irreducible recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively. It is demonstrated empirically that the formulas derived here are highly accurate when the per-base mutation rate is low, which holds for many biological organisms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.2386v3-abstract-full').style.display = 'none'; document.getElementById('1109.2386v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 July, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 September, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Advances in Applied Probability, Vol. 44, No. 2 (2012), 408-428 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1107.4700">arXiv:1107.4700</a> <span> [<a href="https://arxiv.org/pdf/1107.4700">pdf</a>, <a href="https://arxiv.org/format/1107.4700">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Populations and Evolution">q-bio.PE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1239/aap/1339878717">10.1239/aap/1339878717 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/q-bio?searchtype=author&query=Bhaskar%2C+A">Anand Bhaskar</a>, <a href="/search/q-bio?searchtype=author&query=Song%2C+Y+S">Yun S. Song</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1107.4700v2-abstract-short" style="display: inline;"> Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1107.4700v2-abstract-full').style.display = 'inline'; document.getElementById('1107.4700v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1107.4700v2-abstract-full" style="display: none;"> Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1107.4700v2-abstract-full').style.display = 'none'; document.getElementById('1107.4700v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 July, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Advances in Applied Probability, Vol. 44, No. 2 (2012), 391-407 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 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