Reanalysis of models and an improved model of biomass size spectra

Our reanalysis aimed at understanding the regularity in empirical biomass s ize spectra (BSS) suggests that the construction of BSS depends of the size interval and size scales used and different definitions of BSS in literatu re are therefore very different. Existing empirical models of BSS can be fitted perfectly to the observed da ta, but the biological basis of the fitted parameters is not explained and comparison and interpretation of the findings is therefore difficult. Param eters of mechanistic models of BSS have a biological background and are int erpretable. Discrete mechanistic models based on LINDEMAN's trophic chain t heory assume a-constant ratio of size (or body mass) in two adjacent trophi c levels. However, this biomass ratio is not comparable with that in two ad jacent (logarithmic) size intervals in the measured biomass size spectra. T he continuous model by THIEBAUX and DICKIE (1992) is based on the discrete model by BOUDREAU et al. (1991). We show how the validity of the transforma tion of a discrete form into a continous form depends on the size ranges of prey and predator population. The model by PLATT and DENMAN (1977) does no t represent a continuous formulation due to the use of normalized biomass d efined in logarithmic size intervals. We suggest to eliminate the use of tr ophic levels and normalized biomass. On the basis of the reanalysis we formulate and improved continuous model b ased on the model by SILVERT and PLATT (1978). The model is based on Euleri an 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.