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This study develops individual-based models for population dynamics, revealing how internal fluctuations impact extinction risk and abundance distributions in common ecological models.

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Area of Science:

  • Mathematical Biology
  • Theoretical Ecology
  • Population Dynamics

Background:

  • Generalized logistic models are widely used in population dynamics.
  • Understanding the impact of internal fluctuations on these models is crucial.
  • Existing models like theta-logistic and Savageau models have limitations in parameter interpretation.

Purpose of the Study:

  • To construct individual-based models that yield generalized logistic models at the mean-field level.
  • To interpret model parameters in terms of individual interactions.
  • To analyze the effect of internal fluctuations on long-time population dynamics, extinction, and abundance distributions.

Main Methods:

  • Construction of individual-based models.
  • Application of WKB theory.
  • Utilizing the probability generating function formalism.
  • Verification through numerical simulations.

Main Results:

  • Derived individual-based models that reproduce generalized logistic dynamics.
  • Determined conditions for population extinction and calculated mean time to extinction.
  • Obtained analytical expressions for population abundance distributions when extinction does not occur.
  • Interpreted model parameters based on individual interaction mechanisms.

Conclusions:

  • Individual-based models provide a mechanistic basis for generalized logistic models.
  • Internal fluctuations significantly influence population extinction probabilities and long-term dynamics.
  • The theoretical framework offers insights into population persistence and abundance patterns.