Branching Processes and Evolution at the Ends of a Food Chain

TL;DR

This paper models the scaling behavior of evolutionary avalanches at the ends of a food chain using an inhomogeneous branching process, revealing unique exponents for avalanches and first return times.

Contribution

It introduces a generalized branching process model to analyze boundary effects in punctuated equilibrium, extending previous mean field approaches.

Findings

Derived new scaling exponents $ u=1/2$ and $ au'=7/4$ for avalanches.

Numerical results show $ au'=1.25 \u00b1 0.01$ for the chain ends.

First return time exponent $ au'_{first}=1.35 \u00b1 0.01$ differs from bulk values.

Abstract

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 $\tau'=1.25 \pm 0.01$, and $\tau'_{first}=1.35 \pm 0.01$ for the first return times of activity, again distinct from bulk exponents.