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

Next-Generation Phylogeography: A Targeted Approach for Multilocus Sequencing of Non-Model Organisms

The field of phylogeography has long since realized the need and utility of incorporating nuclear DNA (nDNA) sequences into analyses. However, the use of nDNA sequence data, at the population level, has been hindered by technical laboratory difficulty, sequencing costs, and problematic analytical methods dealing with genotypic sequence data, especially in non-model organisms. Here, we present a method utilizing the 454 GS-FLX Titanium pyrosequencing platform with the capacity to simultaneously sequence two species of sea star (Meridiastra calcar and Parvulastra exigua) at five different nDNA loci across 16 different populations of 20 individuals each per species. We compare results from 3 populations with traditional Sanger sequencing based methods, and demonstrate that this next-generation sequencing platform is more time and cost effective and more sensitive to rare variants than Sanger based sequencing. A crucial advantage is that the high coverage of clonally amplified sequences simplifies haplotype determination, even in highly polymorphic species. This targeted next-generation approach can greatly increase the use of nDNA sequence loci in phylogeographic and population genetic studies by mitigating many of the time, cost, and analytical issues associated with highly polymorphic, diploid sequence markers

Ocean sprawl facilitates dispersal and connectivity of protected species

Highly connected networks generally improve resilience in complex systems. We present a novel application of this paradigm and investigated the potential for anthropogenic structures in the ocean to enhance connectivity of a protected species threatened by human pressures and climate change. Biophysical dispersal models of a protected coral species simulated potential connectivity between oil and gas installations across the North Sea but also metapopulation outcomes for naturally occurring corals downstream. Network analyses illustrated how just a single generation of virtual larvae released from these installations could create a highly connected anthropogenic system, with larvae becoming competent to settle over a range of natural deep-sea, shelf and fjord coral ecosystems including a marine protected area. These results provide the first study showing that a system of anthropogenic structures can have international conservation significance by creating ecologically connected networks and by acting as stepping stones for cross-border interconnection to natural populations