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Size-spectra dynamics from stochastic predation and growth of individuals

journal contribution
posted on 2023-05-18, 10:04 authored by Law, R, Plank, MJ, James, A, Julia BlanchardJulia Blanchard
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.

History

Publication title

Ecology

Volume

90

Pagination

802-811

ISSN

0012-9658

Department/School

Institute for Marine and Antarctic Studies

Publisher

Ecological Soc Amer

Place of publication

1707 H St Nw, Ste 400, Washington, USA, Dc, 20006-3915

Rights statement

Copyright 2009 Ecological Society of America

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the biological sciences

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