Models of aquatic biomass size spectra and the common structure of their solutions

Abstract

Mathematical models of aquatic biomass body-size spectra are usually interpreted as single-valued functions of the body weight of organisms. Where these spectra are recognized as dependent on predator-prey energy transfers, it is shown that solutions of the models consist of a smoothly varying or linear part plus a neglected but not negligible part that is periodic in the logarithm of body weight. The models can also be interpreted as yielding multiple spectra, in which the spectrum for a given trophic position is replicated at regular intervals over the range of body weight. In either interpretation the models support empirical data exhibiting significant quasi-periodic departures from a smoothly varying or straight line, without implying a priori knowledge of underlying mechanisms. Under some conditions the biomass size spectrum in an ecosystem describable by a multiple spectra ecosystem model may be indistinguishable from one characterized by a single-valued spectrum.