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Structured model conserving biomass for the size-spectrum evolution in aquatic ecosystems.

L Kanzler1, B Perthame2, B Sarels3

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Summary
This summary is machine-generated.

Mathematical modeling reveals how predation shapes aquatic ecosystems. Our study shows models can predict ecosystem stability and the cascade effect, crucial for understanding environmental changes.

Keywords:
Aquatic ecosystemCascade-effectConvergence to equilibriumPredator–preySize-spectrum model

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Oceanography

Background:

  • Mathematical modeling is vital for understanding aquatic ecosystem dynamics and human impacts.
  • Predation drives size-spectrum evolution, influencing growth, death, and biomass.
  • Existing models require refinement to capture complex ecological interactions.

Purpose of the Study:

  • To formulate and analyze a mathematical model for aquatic ecosystem size-spectrum dynamics.
  • To investigate the role of predation, feeding preferences, and search efficiency.
  • To explore ecosystem stability and the emergence of size-spectrum gaps.

Main Methods:

  • Developed a deterministic, non-local, quadratic-type mathematical model based on binary interactions.
  • Analyzed the existence of solutions based on feeding preference functions and search exponents.
  • Investigated the stability of steady states, including trivial and non-trivial equilibria.
  • Utilized numerical simulations to complement analytical findings.

Main Results:

  • Demonstrated the existence of solutions, influenced by feeding preference and search exponent parameters.
  • Identified a trivial steady state (extinct ecosystem) and non-trivial states with size-spectrum gaps (cascade effect).
  • Showed parameter-dependent convergence to the trivial steady state.
  • Numerical simulations confirmed convergence to non-trivial equilibria under specific parameter regimes.

Conclusions:

  • The developed model provides insights into size-spectrum dynamics and ecosystem stability.
  • Feeding preference and search efficiency are key parameters influencing ecosystem structure.
  • The model supports the understanding of ecological cascade effects and ecosystem resilience.