Scaling and Zipf’s Law in Ecological Size Spectra

Size distributions in some ecosystems follow a power (Zipf-)law behavior spanning up to two ten decades. A model for the origins of this scaling behavior is presented. The model shows that the intrinsic dynamics of the system leads to a power law distribution, $N(m) ~ m^-alpha$, with $\alpha approximately 2$, in agreement with field data. We assume that each individual is eventually the predator of any smaller individual, thereby connecting all elements in the food web among themselves. We consider reproduction and death coming from predation and natural death. It is shown that the most important mechanism generating the exponent $N(m) ~ m^-alpha$ is predation.