Efficient Forward Simulation of Fisher-Wright Populations with Stochastic Population Size and Neutral Single Step Mutations in Haplotypes

In both population genetics and forensic genetics it is important to know how haplotypes are distributed in a population. Simulation of population dynamics helps facilitating research on the distribution of haplotypes. In forensic genetics, the haplotypes can for example consist of lineage markers such as short tandem repeat loci on the Y chromosome (Y-STR). A dominating model for describing population dynamics is the simple, yet powerful, Fisher-Wright model. We describe an efficient algorithm for exact forward simulation of exact Fisher-Wright populations (and not approximative such as the coalescent model). The efficiency comes from convenient data structures by changing the traditional view from individuals to haplotypes. The algorithm is implemented in the open-source R package 'fwsim' and is able to simulate very large populations. We focus on a haploid model and assume stochastic population size with flexible growth specification, no selection, a neutral single step mutation process, and self-reproducing individuals. These assumptions make the algorithm ideal for studying lineage markers such as Y-STR.Comment: 17 pages, 6 figure

Lattice Interferometer for Ultra-Cold Atoms

We demonstrate an atomic interferometer based on ultra-cold atoms released from an optical lattice. This technique yields a large improvement in signal to noise over a related interferometer previously demonstrated. The interferometer involves diffraction of the atoms using a pulsed optical lattice. For short pulses a simple analytical theory predicts the expected signal. We investigate the interferometer for both short pulses and longer pulses where the analytical theory break down. Longer pulses can improve the precision and signal size. For specific pulse lengths we observe a coherent signal at times that differs greatly from what is expected from the short pulse model. The interferometric signal also reveals information about the dynamics of the atoms in the lattice. We investigate the application of the interferometer for a measurement of $h/m_A$ that together with other well known constants constitutes a measurement of the fine structure constant