https://doi.org/10.1140/epjb/e2005-00335-8
Percolation of a bit-string model
Feza Gürsey Institute PO Box 6,
81220 Çengelköy, Istanbul, Turkey
Corresponding author: a taneri@gursey.gov.tr
Received:
8
March
2005
Revised:
2
August
2005
Published online:
28
October
2005
We investigate the effect of mutations on adaptability in a bit-string model of invading species in a random environment. The truncation-like fitness function depends on the Hamming distance between the optimal (wild)-type at each site and the invading species for a square lattice. We allow invasion if the relative fitness is above or equal to an adjustable threshold. We have also allowed for the decay and extinction of a species at a site that it has already invaded. We find that the invading species always percolates through regions of arbitrary size, for all threshold values, with a time parameter which depends on the threshold and the size in the absence of decay. If decay is introduced then there is a critical value of the threshold variable beyond which the invading species is confined. Radius of gyration and average population of a colony of mutants have a power-law dependence with time and relevant fractal dimensions are calculated for percolation.
PACS: 02.60.Lj – Ordinary and partial differential equations; boundary value problems / 05.10.Ln – Monte Carlo methods / 05.45.Df – Fractals
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005