Percolation of a bit-string model

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.