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Identification of a fitness function via a dynamical system generated by phenotypic evolution

100%

Karcz-Dulęba I.

2009

tom z. 169

87-94

Studies of a dynamical system model generated by a phenotypic evolution may be exploited to identify an unknown fitness function of a black-box" type. Depending on a fitness function itself and a standard deviation of mutation, the system converges either to stable fixed points or demonstrates a periodic and/or chaotic behavior. Stable fixed points locate fitness optima while the unstable behavior may indicate asymmetry of the function. A family of bimodal tent functions are analyzed with their parameters varied, in order to gain knowledge about their optima positions and heights, saddles widths and levels.

The Cantor set generated by a simple evolutionary model

100%

Karcz-Dulęba I.

2000

tom z. 10

29-36

Distributions of traits in a population provide important information about evolution of the population itself. In this paper an analysis of traits distributions in a phenotypic evolution is presented. A very simple model of evolution is under consideration - infinite populations evolve in one dimension space of a bimodal fitness function. The analysis of dynamic behavior of a population yields an interesting result concerning generation of the subsequent distributions. It appears that every normal distribution generates two offspring normal distributions. The evolutionary process initialized with a single normal distribution grows up to 2t normal distributions after t generations. The evolution of normal distributions is described equivalently by evolution of their parameters: means and variances. The evolution of distributions' means resembles fractals generated by an Iterated Function System (IFS). Equations describing the location of distrbutions' means in the next generation define contractive affine transformations. The defined iterative system maps the interval [0,1] into the Cantor set after infinite number of iterations.

Identification of cyclic and chaotic behavior in a dynamical system generated by phenotypic evolution

100%

Karcz-Dulęba I.

2006

tom z. 156

195-202

A discrete deterministic dynamical system generated by the expected value derived from the model of phenotypic evolution is considered. Depending on fitness functions and a standard deviation of mutation, the system converges not only to stable fixed points but also displays cyclic and chaotic behavior. To detect the phenomena an auto-correlation function, a phase space portrait and a power spectrum of trajectories of the system were exploited.