BRANCHING-PROCESSES AND EVOLUTION AT THE ENDS OF A FOOD-CHAIN

In a critically self-organized model of punctuated equilibrium, bounda ries determine peculiar scaling of the size distribution of evolutiona ry avalanches. This is derived by an inhomogeneous generalization of s tandard branching processes, extending previous mean field description s and yielding nu = 1/2 together with tau' = 7/4, as distribution expo nent of avalanches starting from species at the ends of a food chain. For the nearest neighbor chain one obtains numerically tau' = 1.25 +/- 0.01, and tau(first) = 1.35 +/- 0.01 for the first return times of ac tivity, again distinct from bulk exponents.