Hypernatural Numbers as Ultrafilters

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers

These aren’t the loci you’re looking for: Principles of effective SNP filtering for molecular ecologists

Sequencing reduced‐representation libraries of restriction site‐associated DNA (RADseq) to identify single nucleotide polymorphisms (SNPs) is quickly becoming a standard methodology for molecular ecologists. Because of the scale of RADseq data sets, putative loci cannot be assessed individually, making the process of filtering noise and correctly identifying biologically meaningful signal more difficult. Artefacts introduced during library preparation and/or bioinformatic processing of SNP data can create patterns that are incorrectly interpreted as indicative of population structure or natural selection. Therefore, it is crucial to carefully consider types of errors that may be introduced during laboratory work and data processing, and how to minimize, detect and remove these errors. Here, we discuss issues inherent to RADseq methodologies that can result in artefacts during library preparation and locus reconstruction resulting in erroneous SNP calls and, ultimately, genotyping error. Further, we describe steps that can be implemented to create a rigorously filtered data set consisting of markers accurately representing independent loci and compare the effect of different combinations of filters on four RAD data sets. At last, we stress the importance of publishing raw sequence data along with final filtered data sets in addition to detailed documentation of filtering steps and quality control measures

Selection and sex-biased dispersal in a coastal shark: The influence of philopatry on adaptive variation

Sex-biased dispersal is expected to homogenize nuclear genetic variation relative to variation in genetic material inherited through the philopatric sex. When site fidelity occurs across a heterogeneous environment, local selective regimes may alter this pattern. We assessed spatial patterns of variation in nuclear-encoded, single nucleotide polymorphisms (SNPs) and sequences of the mitochondrial control region in bonnethead sharks (Sphyrna tiburo), a species thought to exhibit female philopatry, collected from summer habitats used for gestation. Geographic patterns of mtDNA haplotypes and putatively neutral SNPs confirmed female philopatry and male-mediated gene flow along the northeastern coast of the Gulf of Mexico. A total of 30 outlier SNP loci were identified; alleles at over half of these loci exhibited signatures of latitude-associated selection. Our results indicate that in species with sex-biased dispersal, philopatry can facilitate sorting of locally adaptive variation, with the dispersing sex facilitating movement of potentially adaptive variation among locations and environments

Conservative extensions of models of arithmetic

We give two characterizations of conservative extensions of models of arithmetic, in terms of the existence and uniqueness of certain amalgàmations with other models. We also establish a connection between conservativity and some combinatorial properties of ultrafilter mappings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46061/1/153_2005_Article_BF02021128.pd