Simple models of genomic variation in human SNP density

<p>Abstract</p> <p>Background</p> <p>Descriptive hierarchical Poisson models and population-genetic coalescent mixture models are used to describe the observed variation in single-nucleotide polymorphism (SNP) density from samples of size two across the human genome.</p> <p>Results</p> <p>Using empirical estimates of recombination rate across the human genome and the observed SNP density distribution, we produce a maximum likelihood estimate of the genomic heterogeneity in the scaled mutation rate <it>θ</it>. Such models produce significantly better fits to the observed SNP density distribution than those that ignore the empirically observed recombinational heterogeneities.</p> <p>Conclusion</p> <p>Accounting for mutational and recombinational heterogeneities can allow for empirically sound null distributions in genome scans for "outliers", when the alternative hypotheses include fundamentally historical and unobserved phenomena.</p

Duality and perfect probability spaces

Abstract. Given probability spaces (Xi, Ai,Pi),i =1,2,let M(P1,P2)denote the set of all probabilities on the product space with marginals P1 and P2 and let h be a measurable function on (X1 × X2, A1 ⊗A2). Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubinˇstein (1958) for the case of compact metric spaces are concerned with the validity of the duality sup { hdP:P∈M(P1,P2)

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Transcriptome characterization and polymorphism detection between subspecies of big sagebrush (Artemisia tridentata)

<p>Abstract</p> <p>Background</p> <p>Big sagebrush (<it>Artemisia tridentata</it>) is one of the most widely distributed and ecologically important shrub species in western North America. This species serves as a critical habitat and food resource for many animals and invertebrates. Habitat loss due to a combination of disturbances followed by establishment of invasive plant species is a serious threat to big sagebrush ecosystem sustainability. Lack of genomic data has limited our understanding of the evolutionary history and ecological adaptation in this species. Here, we report on the sequencing of expressed sequence tags (ESTs) and detection of single nucleotide polymorphism (SNP) and simple sequence repeat (SSR) markers in subspecies of big sagebrush.</p> <p>Results</p> <p>cDNA of <it>A. tridentata </it>sspp. <it>tridentata </it>and <it>vaseyana </it>were normalized and sequenced using the 454 GS FLX Titanium pyrosequencing technology. Assembly of the reads resulted in 20,357 contig consensus sequences in ssp. <it>tridentata </it>and 20,250 contigs in ssp. <it>vaseyana</it>. A BLASTx search against the non-redundant (NR) protein database using 29,541 consensus sequences obtained from a combined assembly resulted in 21,436 sequences with significant blast alignments (≤ 1e^-15). A total of 20,952 SNPs and 119 polymorphic SSRs were detected between the two subspecies. SNPs were validated through various methods including sequence capture. Validation of SNPs in different individuals uncovered a high level of nucleotide variation in EST sequences. EST sequences of a third, tetraploid subspecies (ssp. <it>wyomingensis</it>) obtained by Illumina sequencing were mapped to the consensus sequences of the combined 454 EST assembly. Approximately one-third of the SNPs between sspp. <it>tridentata </it>and <it>vaseyana </it>identified in the combined assembly were also polymorphic within the two geographically distant ssp. <it>wyomingensis </it>samples.</p> <p>Conclusion</p> <p>We have produced a large EST dataset for <it>Artemisia tridentata</it>, which contains a large sample of the big sagebrush leaf transcriptome. SNP mapping among the three subspecies suggest the origin of ssp. <it>wyomingensis </it>via mixed ancestry. A large number of SNP and SSR markers provide the foundation for future research to address questions in big sagebrush evolution, ecological genetics, and conservation using genomic approaches.</p

Does Sex Speed Up Evolutionary Rate and Increase Biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity

Ancestral population genomics

Borrowing both from population genetics and phylogenetics, the field of population genomics emerged as full genomes of several closely related species were available. Providing we can properly model sequence evolution within populations undergoing speciation events, this resource enables us to estimate key population genetics parameters such as ancestral population sizes and split times. Furthermore we can enhance our understanding of the recombination process and investigate various selective forces. With the advent of resequencing technologies, genome-wide patterns of diversity in extant populations have now come to complement this picture, offering an increasing power to study more recent genetic history