Size Dependence of Biomass Spectra and Population Density I. The Effects of Size Scales and Size Intervals

Empirical biomass spectra in which biomass is measured in logarithmically equal body size intervals are different from those measured in linearly equal size intervals. Moreover, the scales of body size used by different authors may differ, e.g., length, volume, equivalent-sphere diameter and body mass. The discrete models derived to explain the regularity of the empirical spectra are dependent on the choice of size-scales and size-intervals. Hence, evaluating the effect of size scales and intervals on biomass spectra is helpful for understanding the size-structures of ecosystems. In the present contribution, we analyse the relationships between the size measures used frequently in expressing the empirical data and discuss the difference between the biomass spectra organized in logarithmically equal size intervals and those in linearly equal size intervals. On this basis, we present the distribution function of biomass spectral density and transformation to different size scales. After defining the effect of size intervals on the distribution functions of biomass spectral density, we give an example of the calculation of this effect by assuming that the distribution function of biomass spectral density is an allometric relationship. Finally, we explore the influence of size intervals on the validity of three discrete models developed by Kerr, Sheldon and co-workers and Borgman.