Reanalysis of Models and an Improved Model of Biomass Size Spectra

Abstract

Our reanalysis aimed at understanding the regularity in empirical biomass size spectra (BSS) suggests that the construction of BSS depends of the size interval and size scales used and different definitions of BSS in literature are therefore very different. Existing empirical models of BSS can be fitted perfectly to the observed data, but the biological basis of the fitted parameters is not explained and comparison and interpretation of the findings is therefore difficult. Parameters of mechanistic models of BSS have a biological background and are interpretable. Discrete mechanistic models based on L indeman's trophic chain theory assume a constant ratio of size (or body mass) in two adjacent trophic levels. However, this biomass ratio is not comparable with that in two adjacent (logarithmic) size intervals in the measured biomass size spectra. The continuous model by T hiebaux and D ickie (1992) is based on the discrete model by B oudreau et al. (1991). We show how the validity of the transformation of a discrete form into a continous form depends on the size ranges of prey and predator population. The model by P latt and D enman (1977) does not represent a continuous formulation due to the use of normalized biomass defined in logarithmic size intervals. We suggest to eliminate the use of trophic levels and normalized biomass. On the basis of the reanalysis we formulate and improved continuous model based on the model by S ilvert and P latt (1978). The model is based on Eulerian strategy which appears more adequate for the problem than the previously used Lagrangian strategy. The model appears to be able to demonstrate the regularity in observed BSS.