Branching processes and evolution at the ends of a food chain

In a critically self-organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes, extending previous mean field descriptions and yielding nu = 1/2 together with tau' = 7/4, as distribution exponent 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 activity, again distinct from bulk exponents.