BackgroundOn rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial “uphill” mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the evolutionary process determine the probability that evolution will take any specific path among a variety of competing possible trajectories. Understanding this evolutionary choice is essential if we are to understand the outcomes and predictability of adaptation on rugged landscapes.ResultsWe present a simple model to analyze the probability that evolution will eschew immediately uphill paths in favor of crossing fitness valleys or plateaus that lead to higher fitness but less accessible genotypes. We calculate how this probability depends on the population size, mutation rates, and relevant selection pressures, and compare our analytical results to Wright-Fisher simulations.ConclusionWe find that the probability of valley crossing depends nonmonotonically on population size: intermediate size populations are most likely to follow a “greedy” strategy of acquiring immediately beneficial mutations even if they lead to evolutionary dead ends, while larger and smaller populations are more likely to cross fitness valleys to reach distant advantageous genotypes. We explicitly identify the boundaries between these different regimes in terms of the relevant evolutionary parameters. Above a certain threshold population size, we show that the probability that the population finds the more distant peak depends only on a single simple combination of the relevant parameters.
An axisymmetric fully ionized plasma rotates around its axis when a charge separation between magnetic surfaces is produced from DC fields or RF waves. On each magnetic surface both electrons and ions obey the isorotation law and perform an azimuthal E cross B rotation at the same angular velocity. When Coulomb collisions are taken into account such a flow displays no Ohmic current short circuiting of the charge separation and thus no linear dissipation. A nonlinear Ohmic response appears when inertial effects are considered, providing a dissipative relaxation of the charge separation between the magnetic surfaces. This nonlinear conductivity results from an interplay between Coriolis, centrifugal and electron-ion collisional friction forces. This phenomena is identified, described and analyzed. In addition, both the quality factor of angular momentum storage as well as the efficiency of wave driven angular momentum generation are calculated and shown to be independent of the details of the charge separation processes.
In a rotating magnetized plasma cylinder with shear, cross-field current can arise from inertial mechanisms and from the cross-field viscosity. Considering these mechanisms, it is possible to calculate the irreducible radial current draw in a cylindrical geometry as a function of the rotation frequency. The resulting expressions raise novel possibilities for tailoring the electric field profile by controlling the density and temperature profiles of a plasma.
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