Boundary spatiotemporal correlations in a self-organized critical model of punctuated equilibrium
In a semi-infinite geometry, a one-dimensional, M-component model of biological evolution realizes microscopically an inhomogeneous branching process for M-->infinity. This implies a size distribution exponent tau(')=7/4 for avalanches starting at a free, "dissipative" end of the evolutionary chain. A bulklike behavior with tau(')=3/2 is restored by "conservative" boundary conditions. These are such as to strictly fix to its critical, bulk value the average number of species directly involved in an evolutionary avalanche by the mutating species located at the chain end. A two-site correlation function exponent tau(')(R)=4 is also calculated exactly in the "dissipative" case, when one of the points is at the border. Together with accurate numerical determinations of the time recurrence exponent tau(')(first), these results show also that, no matter whether dissipation is present or not, boundary avalanches have the same space and time fractal dimensions as those in the bulk, and their distribution exponents obey the basic scaling laws holding there.
Montevecchi
E
Laboratorium voor Vaste Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
Stella
AL