Sean O’Rourke

RAD Capture (Rapture): Flexible and Efficient Sequence-Based Genotyping

Massively parallel sequencing has revolutionized many areas of biology, but sequencing large amounts of DNA in many individuals is cost-prohibitive and unnecessary for many studies. Genomic complexity reduction techniques such as sequence capture and restriction enzyme-based methods enable the analysis of many more individuals per unit cost. Despite their utility, current complexity reduction methods have limitations, especially when large numbers of individuals are analyzed. Here we develop a much improved restriction site-associated DNA (RAD) sequencing protocol and a new method called Rapture (RAD capture). The new RAD protocol improves versatility by separating RAD tag isolation and sequencing library preparation into two distinct steps. This protocol also recovers more unique (nonclonal) RAD fragments, which improves both standard RAD and Rapture analysis. Rapture then uses an in-solution capture of chosen RAD tags to target sequencing reads to desired loci. Rapture combines the benefits of both RAD and sequence capture, i.e., very inexpensive and rapid library preparation for many individuals as well as high specificity in the number and location of genomic loci analyzed. Our results demonstrate that Rapture is a rapid and flexible technology capable of analyzing a very large number of individuals with minimal sequencing and library preparation cost. The methods presented here should improve the efficiency of genetic analysis for many aspects of agricultural, environmental, and biomedical science.

Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

AbstractWe study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble.We begin by considering an n×n matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let xk denote eigenvalue number k. Under the condition that both k and n−k tend to infinity as n→∞, we show that xk is normally distributed in the limit.We also consider the joint limit distribution of eigenvalues n

The evolutionary basis of premature migration in Pacific salmon highlights the utility of genomics for informing conservation

(x_{k_{1}},ldots,x_{k_{m}})

Products of Independent Elliptic Random Matrices

nfrom the GOE or GSE where k1, n−km and ki+1−ki, 1≤i≤m−1, tend to infinity with n. The result in each case is an m-dimensional normal distribution.Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.

Spectra of nearly Hermitian random matrices

Accounting for specific alleles can be necessary to prevent the loss of significant biodiversity and ecosystem services. The delineation of conservation units (CUs) is a challenging issue that has profound implications for minimizing the loss of biodiversity and ecosystem services. CU delineation typically seeks to prioritize evolutionary significance, and genetic methods play a pivotal role in the delineation process by quantifying overall differentiation between populations. Although CUs that primarily reflect overall genetic differentiation do protect adaptive differences between distant populations, they do not necessarily protect adaptive variation within highly connected populations. Advances in genomic methodology facilitate the characterization of adaptive genetic variation, but the potential utility of this information for CU delineation is unclear. We use genomic methods to investigate the evolutionary basis of premature migration in Pacific salmon, a complex behavioral and physiological phenotype that exists within highly connected populations and has experienced severe declines. Strikingly, we find that premature migration is associated with the same single locus across multiple populations in each of two different species. Patterns of variation at this locus suggest that the premature migration alleles arose from a single evolutionary event within each species and were subsequently spread to distant populations through straying and positive selection. Our results reveal that complex adaptive variation can depend on rare mutational events at a single locus, demonstrate that CUs reflecting overall genetic differentiation can fail to protect evolutionarily significant variation that has substantial ecological and societal benefits, and suggest that a supplemental framework for protecting specific adaptive variation will sometimes be necessary to prevent the loss of significant biodiversity and ecosystem services.

Low-Degree Factors of Random Polynomials

For fixed

The Elliptic Law

m > 1

On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-identically Distributed Entries

m>1, we study the product of