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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
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An alternative delayed population growth difference equation model.

Sabrina H Streipert1, Gail S K Wolkowicz2

  • 1McMaster University, Hamilton, Ontario, Canada. streipes@mcmaster.ca.

Journal of Mathematical Biology
|August 7, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new delayed population growth model. Exceeding a critical delay threshold leads to population extinction, while shorter delays result in a stable population size that decreases with increased delay.

Keywords:
Beverton–Holt modelComponentwise monotonicityDelay difference equationDelayed Beverton–Holt/Pielou modelDiscretizationExtinction thresholdGlobal stabilityLogistic growthSingle species growth models

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Area of Science:

  • Population dynamics
  • Mathematical biology
  • Ecological modeling

Background:

  • Traditional population models often assume immediate growth responses.
  • Delayed responses in population growth can significantly alter dynamics.
  • Existing delayed logistic models do not fully account for mortality during the delay period.

Purpose of the Study:

  • To develop an alternative delayed population growth difference equation model.
  • To analyze the impact of growth delays on population dynamics.
  • To investigate the conditions for population survival and extinction.

Main Methods:

  • Modification of the Beverton-Holt recurrence relation.
  • Introduction of a delay specifically in the growth contribution.
  • Analysis of the delayed difference equation model to identify critical thresholds.
  • Application of contraction mapping and componentwise monotone map techniques to prove global asymptotic stability.

Main Results:

  • Identification of a critical delay threshold influencing population persistence.
  • Prediction of population extinction for delays exceeding the threshold.
  • Convergence to a positive, globally asymptotically stable equilibrium for sub-threshold delays.
  • Demonstration that equilibrium population size decreases as delay increases.

Conclusions:

  • The proposed model provides a more nuanced understanding of delayed population growth.
  • Delay duration is a critical factor determining population viability.
  • The model predicts a trade-off between delay and population size, with longer delays leading to smaller stable populations or extinction.