8 research outputs found
Genetic Algorithms in Time-Dependent Environments
The influence of time-dependent fitnesses on the infinite population dynamics
of simple genetic algorithms (without crossover) is analyzed. Based on general
arguments, a schematic phase diagram is constructed that allows one to
characterize the asymptotic states in dependence on the mutation rate and the
time scale of changes. Furthermore, the notion of regular changes is raised for
which the population can be shown to converge towards a generalized
quasispecies. Based on this, error thresholds and an optimal mutation rate are
approximately calculated for a generational genetic algorithm with a moving
needle-in-the-haystack landscape. The so found phase diagram is fully
consistent with our general considerations.Comment: 24 pages, 14 figures, submitted to the 2nd EvoNet Summerschoo
On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3
Phases and phase transitions in pure and doped spin-Peierls system CuGeO_3
are considered on the basis of a Landau-theory. In particular we discuss the
critical behaviour, the soliton width and the low temperature specific heat of
the incommensurate phase. We show, that dilution leads always to the
destruction of long range order in this phase, which is replaced by an
algebraic decay of correlations if the disorder is weak.Comment: 4 pages revtex, no figure
Genetic Algorithms in Time-Dependent Environments
The inuence of time-dependent tnesses on the in nite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies
Dynamic Fitness Landscapes in Molecular Evolution
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates of the molecules. In general, therefore, molecular evolution takes place in a dynamic rather than a static tness landscape. We incorporate dynamic replication and decay rates into the standard quasispecies theory of molecular evolution, and show that for periodic time-dependencies, a system of evolving molecules enters a limit cycle for t ! 1. For fast periodic changes, we show that molecules adapt to the timeaveraged tness landscape, whereas for slow changes they track the variations in the landscape arbitrarily closely. We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement. We also discuss landscapes with arbitrary time dependencies, and show that very fast changes again lead to a system that adapts to the time-averaged landscape. Finally, we analyze the dynamics of a nite population of molecules in a dynamic landscape, and discuss its relation to the infinite population limit
Dynamic fitness landscapes in molecular evolution
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environmentâs resource composition lead to both non-constant replication and decay rates of the molecules. In general, therefore, molecular evolution takes place in a dynamic rather than a static fitness landscape. We incorporate dynamic replication and decay rates into the standard quasispecies theory of molecular evolution, and show that for periodic time-dependencies, a system of evolving molecules enters a limit cycle for t â â. For fast periodic changes, we show that molecules adapt to the timeaveraged fitness landscape, whereas for slow changes they track the variations in the landscape arbitrarily closely. We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement. We also discuss landscapes with arbitrary time dependencies, and show that very fast changes again lead to a system that adapts to the time-averaged landscape. Finally, we analyze the dynamics of