Scaling in ecological size spectra

Size distributions in some ecosystems follow a power behavior spanning up to ten orders of magnitude. 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, $N(m)\sim m^{-\alpha },$ with $\alpha \approx 2$, in agreement with field data. We assume that each individual is eventually the predator of all smaller individual, thereby connecting all elements in the food web among themselves. We consider reproduction and death coming from predation and natural mortality. It is shown that the most important mechanism generating the exponent $\alpha \approx 2$ is predation