The Marine Size Spectrum

In the play "Pericles", Shakespeare described a discussion between a young
and an old fisherman: "Master, I wonder how the fishes in the sea live. Why,
as men do a-land; the great ones eat up the little ones". Using just this
Shakespearean principle, and basic assumptions about the scaling of the
metabolism of organisms with size, I will derive the marine size spectrum,
describing how many small fish there are compared to large ones.
Specifically, it is shown that if all organisms in the sea is sorted into
bins with an exponentially increasing width, the biomass in each bin is
roughly the same, from bacteria to whales. Adding more assumptions, one can
also derive the structure of individual fish species, and finally, through
dynamical simulations it is possible to elucidate aspects of the assembly
process of marine ecosystems.