POPULATION-DYNAMICS THEORY OF PLANKTON BASED ON BIOMASS SPECTRA

Here we construct a fundamental mathematical theory of population dyna mics in the context of the normalized spectra of abundance and biomass of plankton. The theory begins with the distribution function of abun dance as a function of individual body weight and growth rate, and the law of the conservation of mass. The basic governing equations for po pulation growth and biomass production are then deduced without empiri cal assumptions. The governing equations represent the fundamental mas s balance between the biomass flux iron small to large sizes due to in dividual growth and the sum of sources and sinks such as birth, natura l death and predation. The slope of the normalized biomass spectrum at steady state is proved to be approximately equal to the ratio of the intrinsic rate of increase in abundance to individual weight-specific growth rate. We demonstrate that measurements of biomass spectra in na ture can be used to estimate population-dynamics parameters of individ ual growth rate and the intrinsic rate of increase. We further apply t his population dynamics theory to data collected by an Optical Plankto n Counter in the California Current region during June and July, 1993. These data cover a range in the marine biomass spectrum from 10(0) to 10(4) mu g C individual body weight.