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.
| Original language | English |
|---|---|
| Pages (from-to) | 802-811 |
| Number of pages | 10 |
| Journal | Ecology |
| Volume | 90 |
| Issue number | 3 |
| Publication status | Published - Mar 2009 |
Keywords
- aquatic ecosystems
- food web
- individual-based model
- partial differential equation
- power function
- predator-prey dynamics
- predator-prey mass ratio
- size spectrum
- size-dependent predation
- traveling wave
- STRUCTURED ENERGY-FLOW
- BODY-SIZE
- MARINE ECOSYSTEMS
- SPECIES ABUNDANCE
- BIOMASS SPECTRA
- FISH COMMUNITY
- FOOD WEBS
- MODEL
- INDICATORS
- PLANKTON