Speciation in multidimensional evolutionary space.

Adaptive dynamics in two-dimensional phenotype space is investigated by computer simulation. The model assumes Lotka-Voltera-type competition and a stochastic mutation process. The carrying capacity has a single maximum in the origin of the strategy space and the competition coefficient decreases with strategy difference. Evolutionary branching, an asexual analog of adaptive speciation, is observed with suitable parameters. The branching at the singular point, which is a fixed point of the directional evolution, may occur into two or three, but not more, directions. Further branchings may occur after the initial separation. The probability of three-branching is studied as a function of several parameters. We conclude that the two-way branching is the predominant mode of adaptive speciation.

Transitions in the horizontal transport of vertically vibrated granular layers.

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.