Size-spectra dynamics from stochastic predation and growth of individuals

Authored by Richard Law, Michael J Plank, Alex James, Julia L Blanchard

Date Published: 2009

DOI: 10.1890/07-1900.1

Sponsors: European Union United Kingdom Natural Environment Research Council (NERC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

In aquatic ecosystems, where organisms typically feed and grow by eating smaller individuals, a characteristic size spectrum emerges, such that large organisms are much more rare than small ones. Here, a stochastic individual-based model for the dynamics of size spectra is described, based on birth, growth, and death of individuals, using simple assumptions about feeding behavior. It is shown that the deterministic limit derived from the stochastic process is a partial differential equation previously used to describe the dynamics of size spectra. The equation has two classes of dynamics in the long term. The. first is a steady state. A derivation under simple mass-balance assumptions shows that, at steady state, the linear size spectrum relating log abundance to log mass has a slope of approximately -1, similar to that often observed in natural size spectra. The second class of dynamics, not previously described, is a traveling-wave solution in which waves move along the size spectrum from small to large body size. Traveling waves become more likely when predators prefer prey much smaller than themselves and when they are specialized in the range of prey body sizes consumed. Wavelength depends on the size of prey relative to the size of predator, and wave speed depends on how fast mass moves through the spectrum.

Tags

Model plankton Body-size Food webs Indicators Marine ecosystems Fish community Species abundance Structured energy-flow Biomass spectra