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Population dynamic regulators in an empirical predator-prey system.

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  • 1Computational Biology Unit, Dept. of Informatics, University of Bergen, PO Box 7803, 5020 Bergen, Norway.

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|June 23, 2021
PubMed
Summary

Capelin collapses in the Barents Sea may be driven by food availability and predator-prey timing mismatches. Mathematical modeling confirms the match-mismatch hypothesis and bottom-up effects regulate capelin population dynamics.

Keywords:
Barents sea capelinDelay differential equationsHopf bifurcationMatch-MismatchOptimization

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Area of Science:

  • Marine ecology
  • Population dynamics
  • Theoretical ecology

Background:

  • Capelin (Mallotus villosus) is a key forage fish in the Barents Sea, experiencing significant biomass declines.
  • Observed capelin collapses suggest regulation by food availability (bottom-up effect) or predator-prey timing (match-mismatch hypothesis).

Purpose of the Study:

  • To investigate the role of food availability and predator-prey timing in capelin population dynamics.
  • To mathematically model the capelin predator-prey system and analyze stability regimes.

Main Methods:

  • A predator-prey model with a single delay term (τ) was developed using coupled differential equations.
  • Theoretical conditions for system stability were derived, focusing on the delay parameter τ.
  • Unconstrained optimization fitted the model to empirical data, integrating theoretical and empirical findings.

Main Results:

  • Hopf bifurcation was identified in the predator-prey system when τ exceeds a critical value (τ*).
  • This critical value (τ*) signifies the time lag between prey availability and optimal predator growth.
  • Mathematical evidence supports the validity of the match-mismatch hypothesis and bottom-up effects for capelin.

Conclusions:

  • The study provides mathematical validation for the match-mismatch hypothesis in regulating capelin populations.
  • Bottom-up effects, influenced by prey availability timing, are crucial for Barents Sea capelin stability.
  • The derived critical delay time (τ*) offers insights into ecological thresholds for capelin population dynamics.