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Calculation Of The Crossing Time Through The Fitness Barrier In A Symmetric Multiplicative Landscape

Author

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  • DOKYOON KIM

    (Department of Physics, Pusan National University, Pusan, 609-735, Korea)

  • WONPYONG GILL

    (Department of Physics, Pusan National University, Pusan, 609-735, Korea)

Abstract

The crossing time through fitness barrier in a symmetric multiplicative landscape is systematically calculated for various mutation rates, fitness parameters, and sequence lengths by using a computer simulation. It is found that the crossing time scales as a power law in the mutation rate and the fitness parameter. It is also found that the crossing time increases exponentially as the sequence length increases. We have obtained the approximate formula, which decribes the asymptotic behavior of the crossing time in the long-crossing-time region, and the improved approximate formula with the correction factor, which nicely fit computer simulation results even below the long-crossing-time region. From the comparison between the approximate formula in the multiplicative landscape and the approximate formula in the sharply-peaked landscape, it is found that both landscapes have the same scaling effect of fitness parameter and mutation rate on the crossing time in the long-crossing-time region.

Suggested Citation

  • Dokyoon Kim & Wonpyong Gill, 2005. "Calculation Of The Crossing Time Through The Fitness Barrier In A Symmetric Multiplicative Landscape," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 85-97.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:01:n:s0129183105006942
    DOI: 10.1142/S0129183105006942
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