Effects of directional epistasis on molecular evolution

Forward population genetic simulations are used to explore the evolution of a sequence of nucleotide sites subject to reversible mutation under selection, mutation, and drift. Three selection schemes are studied: synergistic, antagonistic, and multiplicative interactions among sites. Their respective effects on the level of nucleotide diversity, the pattern of linkage disequilibrium, and the allele frequency spectrum are determined. Surprisingly, none of these aspects are affected by directional epistasis when the overall strength of selection is held constant (where the equilibrium allele frequencies are equal). The equilibrium mean fitness does differ with selection regime, and is relatively higher with synergistic interactions while lower with antagonistic epistasis. These findings legitimate the application of many population genetic models assuming multiplicative selection when there are actually epistatic interactions among sites, and have important implications on the evolution of recombination

Asymmetric sequential Landau-Zener dynamics of Bose condensed atoms in a cavity

We explore the asymmetric sequential Landau-Zener (LZ) dynamics in an ensemble of interacting Bose condensed two-level atoms coupled with a cavity field. Assuming the couplings between all atoms and the cavity field are identical, the interplay between atom-atom interaction and detuning may lead to a series of LZ transitions. Unlike the conventional sequential LZ transitions, which are symmetric to the zero detuning, the LZ transitions of Bose condensed atoms in a cavity field are asymmetric and sensitively depend on the photon number distribution of the cavity. In LZ processes involving single excitation numbers, both the variance of the relative atom number and the step slope of the sequential population ladder are asymmetric, and the asymmetry become more significant for smaller excitation numbers. Furthermore, in LZ processes involving multiple excitation numbers, there may appear asymmetric population ladders with decreasing step heights. During a dynamical LZ process, due to the atom-cavity coupling, the cavity field shows dynamical collapse and revivals. In comparison with the symmetric LZ transitions in a classical field, the asymmetric LZ transitions in a cavity field originate from the photon-number-dependent Rabi frequency. The asymmetric sequential LZ dynamics of Bose condensed atoms in a cavity field may open up a new way to explore the fundamental many-body physics in coupled atom-photon systems.Comment: 14 pages, 6 figure