Finite-site Model Research Articles

Improved inference of population histories by integrating genomic and epigenomic data.

With the availability of high-quality full genome polymorphism (SNPs) data, it becomes feasible to study the past demographic and selective history of populations in exquisite detail. However, such inferences still suffer from a lack of statistical resolution for recent, for example bottlenecks, events, and/or for populations with small nucleotide diversity. Additional heritable (epi)genetic markers, such as indels, transposable elements, microsatellites, or cytosine methylation, may provide further, yet untapped, information on the recent past population history. We extend the Sequential Markovian Coalescent (SMC) framework to jointly use SNPs and other hyper-mutable markers. We are able to (1) improve the accuracy of demographic inference in recent times, (2) uncover past demographic events hidden to SNP-based inference methods, and (3) infer the hyper-mutable marker mutation rates under a finite site model. As a proof of principle, we focus on demographic inference in Arabidopsis thaliana using DNA methylation diversity data from 10 European natural accessions. We demonstrate that segregating single methylated polymorphisms (SMPs) satisfy the modeling assumptions of the SMC framework, while differentially methylated regions (DMRs) are not suitable as their length exceeds that of the genomic distance between two recombination events. Combining SNPs and SMPs while accounting for site- and region-level epimutation processes, we provide new estimates of the glacial age bottleneck and post-glacial population expansion of the European A. thaliana population. Our SMC framework readily accounts for a wide range of heritable genomic markers, thus paving the way for next-generation inference of evolutionary history by combining information from several genetic and epigenetic markers.

Single-Cell Analysis Based Dissection of Clonality in Myelofibrosis

Introduction Large-scale sequencing studies have unraveled the mutational landscape of myelofibrosis (MF), demonstrating clonal heterogeneity and importance of genetically defined subgroups in disease prognosis and progression. In order to elucidate the genetics of MF progression and its molecular drivers during JAK inhibition therapy, we performed in-depth genetic studies on longitudinal blood samples from 15 MF patients covering a disease span of 3 to 5 years after initiation of ruxolitinib. Methods Sequential samples from 15 MF patients (PMF n=8; post-ET/PV-MF n=7) accounting for a total of 42 time points representing 58.5 years of ruxolitinib treatment were investigated by whole-exome sequencing (WES). Additionally, we performed targeted deep sequencing of patient-specific mutations in flow-sorted cell fractions to study clonal repartition within the hematopoietic differentiation tree. Finally, we genotyped more than 5000 Lin-CD34+ progenitor cells using a single-cell multiplexed qPCR approach on a micro-fluidic platform (Fluidigm) to infer MF phylogeny. Results WES identified a median of 14 non-silent somatic mutations per patient at initiation of ruxolitinib treatment (=baseline WES; Figure 1A). When comparing mutations between first and last investigated time points, the majority of baseline mutations (162/201=81%) could be detected also at a later disease stage. A total of 39 mutations were lost and 80 new mutations were detected at the last time point. All patients showed at least one gained/ lost mutation in sequential samples. We noted frequent acquisition of mutations in genes of the RAS/RTK pathways in one third of patients. Two patients with a JAK2 V617F mutation achieved a molecular remission at a level of persisting residual disease of 1x10-3 with ruxolitinib therapy. In one of them, a total of 13 mutations were detected at baseline. In the second sample, taken three years later, a completely different set of mutations was identified and at the last time point, four years after initiation of therapy, none of the mutations were detected. This likely represents genetic drift during neutral evolution as a consequence of a rapid expansion after JAK inhibition. All other 13 patients showed only a modest - if any - decrease of 10-20% JAK2/CALR allele burden which was often accompanied with the expansion of JAK2/CALR-wildtype clones due to positive selection and/or freed clonal space under treatment. However, in some patients with durable response to ruxolitinib, we noted opposing dynamics of clones questioning a common origin. The three patients who progressed to leukemia showed a higher number of mutations at baseline and all of them acquired mutations in KRAS or NRAS over time. As one example, MPN18 harbored mutations in ASXL1, ETV6, and SRSF2 at baseline. Thereafter, and in addition to other driver genes (IDH2,KRAS) a second JAK2 Mutation at codon R867 was acquired, which has been reported to confer treatment resistance to JAK Inhibitors (Marty, Blood 2014). Mutation analysis in flow-sorted cell fractions showed a higher allelic mutation load in the myeloid compared to the lymphoid compartment with only few mutations being detected at low allele frequency in lymphocytes. Interestingly, some patients showed evidence of differential expansion among different myeloid cell lineages (Figure 1B). Next, we sorted 480 CD34+ single-cells per sample from 12 time points from 8 patients which allowed identification of subclones at ≥2% frequency based on priori power calculations. Sorting errors (e.g.cell doublets, empty wells)determined the mean cell sorting failure rate to be 12.5%. We employed a heuristic search algorithm to select a phylogenetic tree with Maximum Likelihood under a finite site model of evolution. Loss of heterozygosity (LOH) events were found in 7/8 patients and were not restricted to the JAK2 locus. In some patients, LOH of JAK2 occurred independently in two subclones, a phenomenon of convergent evolution (Figure 1C). We also noted cases with multiple 9pUPDs, of which one got selected during therapy. LOH events gave rise to both, a mutant homozygous but also reversion to a wildtype genotype. Conclusions Comprehensive serial genotyping of MF patients treated with ruxolitinib revealed heterogeneous patterns of clonal composition and evolution. Our data support LOH as a major determination factor for clonal diversification in MF. EM, KY, and MF contributed equally Figure 1 Disclosures Zenz: Abbvie: Consultancy, Honoraria, Other: Travel support; Roche: Consultancy, Other: Travel support; Janssen: Consultancy; Takeda: Consultancy; Gilead: Honoraria. Bullinger:Pfizer: Honoraria; Astellas: Honoraria; Amgen: Honoraria; Abbvie: Honoraria; Bayer: Other: Financing of scientific research; Seattle Genetics: Honoraria; Sanofi: Honoraria; Novartis: Honoraria; Menarini: Honoraria; Jazz Pharmaceuticals: Honoraria; Janssen: Honoraria; Hexal: Honoraria; Gilead: Honoraria; Daiichi Sankyo: Honoraria; Celgene: Honoraria; Bristol-Myers Squibb: Honoraria. Le Coutre:Novartis: Honoraria, Speakers Bureau; Pfizer: Honoraria, Speakers Bureau; Bristol-Myers Squibb: Honoraria, Speakers Bureau; Incyte: Honoraria, Speakers Bureau. Ogawa:Kan Research Laboratory, Inc.: Consultancy; Asahi Genomics: Equity Ownership; Qiagen Corporation: Patents & Royalties; RegCell Corporation: Equity Ownership; ChordiaTherapeutics, Inc.: Consultancy, Equity Ownership; Dainippon-Sumitomo Pharmaceutical, Inc.: Research Funding. Damm:Novartis: Research Funding; AbbVie: Other: Travel support.

SiCloneFit: Bayesian inference of population structure, genotype, and phylogeny of tumor clones from single-cell genome sequencing data.

Accumulation and selection of somatic mutations in a Darwinian framework result in intra-tumor heterogeneity (ITH) that poses significant challenges to the diagnosis and clinical therapy of cancer. Identification of the tumor cell populations (clones) and reconstruction of their evolutionary relationship can elucidate this heterogeneity. Recently developed single-cell DNA sequencing (SCS) technologies promise to resolve ITH to a single-cell level. However, technical errors in SCS data sets, including false-positives (FP) and false-negatives (FN) due to allelic dropout, and cell doublets, significantly complicate these tasks. Here, we propose a nonparametric Bayesian method that reconstructs the clonal populations as clusters of single cells, genotypes of each clone, and the evolutionary relationship between the clones. It employs a tree-structured Chinese restaurant process as the prior on the number and composition of clonal populations. The evolution of the clonal populations is modeled by a clonal phylogeny and a finite-site model of evolution to account for potential mutation recurrence and losses. We probabilistically account for FP and FN errors, and cell doublets are modeled by employing a Beta-binomial distribution. We develop a Gibbs sampling algorithm comprising partial reversible-jump and partial Metropolis-Hastings updates to explore the joint posterior space of all parameters. The performance of our method on synthetic and experimental data sets suggests that joint reconstruction of tumor clones and clonal phylogeny under a finite-site model of evolution leads to more accurate inferences. Our method is the first to enable this joint reconstruction in a fully Bayesian framework, thus providing measures of support of the inferences it makes.

CoMuS: simulating coalescent histories and polymorphic data from multiple species.

The simultaneous analysis of intra- and interspecies variation is challenging mainly because our knowledge about patterns of polymorphisms where both intra- and interspecies samples coexist is limited. In this study, we present CoMuS (Coalescent of Multiple Species), a multispecies coalescent software that can simulate intra- and interspecies polymorphisms. CoMuS supports a variety of speciation models and demographic scenarios related to the history of each species. In CoMuS, speciation can be accompanied by either instant or gradual isolation between sister species. Sampling may also occur in the past, and thus, we can study simultaneously extinct and extant species. Our software supports both the infinite- and the finite-site model, with substitution rate heterogeneity among sites and a user-defined proportion of invariable sites. We demonstrate the usage of CoMuS in various applications: species delimitation, software testing, model selection and parameter inference involving present-day and ancestral samples, comparison between gradual and instantaneous isolation models, estimation of speciation time between human and chimpanzee using both intra- and interspecies variation. We expect that CoMuS will be particularly useful for studies where species have been separated recently from their common ancestor and phenomena such as incomplete lineage sorting or introgression still occur.

New Software for the Fast Estimation of Population Recombination Rates (FastEPRR) in the Genomic Era

Genetic recombination is a very important evolutionary mechanism that mixes parental haplotypes and produces new raw material for organismal evolution. As a result, information on recombination rates is critical for biological research. In this paper, we introduce a new extremely fast open-source software package (FastEPRR) that uses machine learning to estimate recombination rate (=) from intraspecific DNA polymorphism data. When and the number of sampled diploid individuals is large enough (), the variance of remains slightly smaller than that of . The new estimate (calculated by averaging and ) has the smallest variance of all cases. When estimating , the finite-site model was employed to analyze cases with a high rate of recurrent mutations, and an additional method is proposed to consider the effect of variable recombination rates within windows. Simulations encompassing a wide range of parameters demonstrate that different evolutionary factors, such as demography and selection, may not increase the false positive rate of recombination hotspots. Overall, accuracy of FastEPRR is similar to the well-known method, LDhat, but requires far less computation time. Genetic maps for each human population (YRI, CEU, and CHB) extracted from the 1000 Genomes OMNI data set were obtained in less than 3 d using just a single CPU core. The Pearson Pairwise correlation coefficient between the and maps is very high, ranging between 0.929 and 0.987 at a 5-Mb scale. Considering that sample sizes for these kinds of data are increasing dramatically with advances in next-generation sequencing technologies, FastEPRR (freely available at http://www.picb.ac.cn/evolgen/) is expected to become a widely used tool for establishing genetic maps and studying recombination hotspots in the population genomic era.

The link between segregation and phylogenetic diversity

We derive an invertible transform linking two widely used measures of species diversity: phylogenetic diversity and the expected proportions of segregating (non-constant) sites. We assume a bi-allelic (two-state), symmetric, finite site model of substitution. Like the Hadamard transform of Hendy and Penny, the transform can be expressed independently of the underlying phylogeny. Our results bridge work on diversity from two quite distinct scientific communities.

DISCERNING BETWEEN RECURRENT GENE FLOW AND RECENT DIVERGENCE UNDER A FINITE-SITE MUTATION MODEL APPLIED TO NORTH ATLANTIC AND MEDITERRANEAN SEA FIN WHALE (BALAENOPTERA PHYSALUS) POPULATIONS

Genetic divergence among conspecific subpopulations can be due to either low recurrent gene flow or recent divergence and no gene flow. Here we present a modification of an earlier method developed by Nielsen and Wakeley (2001), which accommodates a finite-site mutation model, to assess which of the two models of divergence is most likely given the observed data. We apply the method to nucleotide sequence data collected from the variable part of the mitochondrial control region in fin whales (Balaenoptera physalus) from the Atlantic coast off Spain and the Mediterranean Sea. Our estimations strongly favor a model of recurrent gene flow over a model of recent divergence and zero gene flow. We estimated the migration rate at two females per generation. While the estimated rate is high by evolutionary standards, exchange rates of this order of magnitude is low from an ecological and conservation perspective and entirely consistent with the current paucity of fin whale sightings in the Strait of Gibraltar today. Intensive commercial shore-based whaling during the 1920s removed substantial numbers of fin whales in the Strait of Gibraltar and this local population has seemingly since failed to recover.

DISCERNING BETWEEN RECURRENT GENE FLOW AND RECENT DIVERGENCE UNDER A FINITE-SITE MUTATION MODEL APPLIED TO NORTH ATLANTIC AND MEDITERRANEAN SEA FIN WHALE (BALAENOPTERA PHYSALUS) POPULATIONS

Genetic divergence among conspecific subpopulations can be due to either low recurrent gene flow or recent divergence and no gene flow. Here we present a modification of an earlier method developed by Nielsen and Wakeley (2001), which accommodates a finite-site mutation model, to assess which of the two models of divergence is most likely given the observed data. We apply the method to nucleotide sequence data collected from the variable part of the mitochondrial control region in fin whales (Balaenoptera physalus) from the Atlantic coast off Spain and the Mediterranean Sea. Our estimations strongly favor a model of recurrent gene flow over a model of recent divergence and zero gene flow. We estimated the migration rate at two females per generation. While the estimated rate is high by evolutionary standards, exchange rates of this order of magnitude is low from an ecological and conservation perspective and entirely consistent with the current paucity of fin whale sightings in the Strait of Gibraltar today. Intensive commercial shore-based whaling during the 1920s removed substantial numbers of fin whales in the Strait of Gibraltar and this local population has seemingly since failed to recover.

Antigenic drift of viruses within a host: a finite site model with demographic stochasticity.

We theoretically study the antigenic drift of viruses within an infected host, as observed in human immunodeficiency virus (HIV) and equine infectious anemia virus (EIAV) infections, assuming that a finite number of antigen-determining sites at the viral envelop gene are responsible for the specific immune response. The pattern of antigen evolution becomes more complex than that predicted from the previous one-dimensional antigen space models. If the viral growth rate is sufficiently large, the demographic stochasticity for the fate of a new antigen mutant can be neglected. The high dimensionality in the way a virus escapes the immune defense in genotype space could then causes a rapid increase in the antigenic diversity and the total viral density, until finally the whole antigen genotypes are used up. The viral population is then driven to extinction in a host by the enhanced immune response to all genotypes. In contrast, if the viral growth rate is moderate or small so that only a small fraction of new antigen mutants can survive during the initial endangered period of random extinction, the viral antigenic diversity and the total density remain bounded, thereby enabling them to persist for a prolonged period by shifting the dominant antigen types. The phylogenetic pattern of antigen divergence is well characterized by the mean number of surviving antigen mutants from an antigen genotype. The substitution rate at antigen-determining sites increases as the efficiency of host immune response increases.

Estimation of the amount of DNA polymorphism when the neutral mutation rate varies among sites.

Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (pi), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, theta is often used as a measure of the amount of DNA polymorphism, where theta = 4Nmu, N is the effective population size and mu is the neutral mutation rate per site per generation. It is known that theta estimated from pi, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating theta under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.

The Amount of Genetic Variation at the DNA Level Maintained in a Finite Population

Abstract The amount of DNA polymorphism can be estimated either from the average number of pairwise nucleotide differences per site (π) or from the proportion of segregating (polymorphic) site (s) among a sample of DNA sequences. Under a number of assumptions, including panmictic population and neutrality, it is known that the expectations of π and s are given by E(π) =θ and E(s) = a1(n)θ, where θ= 4Nv, a1(n) = 1 + 1/2 +…+ 1/(n‐1), N is the effective population size, v is the mutation rate per site per generation, and n is the sample size. Therefore, θ can be estimated by π or s/a1(n). These assumptions, however, are not always correct. In this paper, using a simple non‐random sampling model, I have examined the effect of non‐random sampling on the estimates of the amount of DNA polymorphism. The results indicate that the effect of non‐random sampling on the proportion of segregating site is substantially large whereas the effect of non‐random sampling on the average number of nucleotide differences per site is negligibly small unless non‐randomness is extremely large. Using a finite site model with and without rate variation, I have also examined the effect of rate variation among sites on the estimates of the amount of DNA polymorphism. The results indicate that if the neutral mutation rate varies among sites substantially, the estimates of θ based on the infinite site model are substantially underestimated. New methods for estimating θ are also presented.

The distribution of nucleotide site differences between two finite sequences

A simple method to obtain the distribution of site differences between two randomly chosen cistrons in a finite population is shown. It is assumed that the number of sites and the number of alleles at each site are finite and that no recombination occurs between sites. The mean and variance of the percent difference and the number of site differences between the two sequences are shown to be simple functions of two variables. The differences between a finite-site model an infinite-site model are discussed. The results are applied to the β-globin polymorphism in man.