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Updated: Jul 13, 2026
07:41
Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
Published on: July 30, 2019
Bounding biomass in the Fisher equation.
Daniel A Birch1, Yue-Kin Tsang, William R Young
1Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0213, USA. dbirch@ucsd.edu
Summary
This study models plankton dispersal in ocean currents using the Fisher-Kolmogorov-Petrovskii-Piskunov equation. It identifies a survival-extinction transition and characterizes the steady state biomass and productivity.
Area of Science:
- Mathematical Biology
- Oceanography
- Fluid Dynamics
Background:
- Plankton dispersal is crucial for marine ecosystems.
- Ocean currents significantly influence plankton distribution and survival.
- Mathematical models are essential for understanding these complex interactions.
Purpose of the Study:
- To model plankton dispersal using the Fisher-Kolmogorov-Petrovskii-Piskunov equation with variable growth and advection.
- To analyze the survival-extinction transition in plankton populations.
- To characterize the statistical steady state of biomass and productivity.
Main Methods:
- Utilized the Fisher-Kolmogorov-Petrovskii-Piskunov equation.
- Employed variational arguments to constrain parameter space and derive bounds.
- Performed simulations to delimit the transition and validate results.
- Analyzed the behavior of the velocity field in the limit of zero-decorrelation time.
Main Results:
- Identified a survival-extinction transition for negative average growth rates.
- Characterized the statistical steady state with integral constraints and bounds on biomass/productivity.
- Demonstrated that the velocity field acts as eddy diffusion, enhancing dispersal.
- Showcased the predictive power of a one-dimensional model for biomass, productivity, and extinction.
Conclusions:
- The Fisher-Kolmogorov-Petrovskii-Piskunov equation effectively models plankton dynamics under advection.
- Variational methods provide robust predictions for plankton survival and steady-state properties.
- Eddy diffusivity significantly impacts plankton distribution and transition dynamics.
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