Boundary spatiotemporal correlations in a self-organized critical model ofpunctuated equilibrium

In a semi-infinite geometry, a one-dimensional, M-component model of biolog ical 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" boundar y conditions. These are such as to strictly fix to its critical, bulk value the average number of species directly involved in an evolutionary avalanc he by the mutating species located at the chain end. A two-site correlation function exponent tau(R)' = 4 is also calculated exactly in the "dissipati ve'' 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, b oundary 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.