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Dispersal-induced growth in a time-periodic environment.

Guy Katriel1

  • 1Department of Mathematics, Braude College, Karmiel, Israel. katriel@braude.ac.il.

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Summary

Dispersal-induced growth (DIG) allows populations with fluctuating, extinction-prone growth rates to survive and grow exponentially when connected. This study mathematically explores DIG, identifying key factors and conditions for its occurrence.

Keywords:
Dispersal-induced growthFloquet theoryNonautonmous differential equations

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Isolated populations with time-varying growth rates often face extinction.
  • Dispersal can alter population dynamics, potentially preventing extinction.

Purpose of the Study:

  • To mathematically explore the phenomenon of dispersal-induced growth (DIG).
  • To identify critical factors and parameter conditions that generate DIG.
  • To understand how interconnectedness can rescue failing populations.

Main Methods:

  • Development of a deterministic mathematical model.
  • Inclusion of periodic variation in population growth rates.
  • Analysis of model parameters to characterize DIG conditions.

Main Results:

  • Demonstrated that dispersal can enable populations, individually doomed to extinction, to achieve exponential growth.
  • Identified specific mathematical conditions and parameters crucial for the DIG effect.
  • Quantified the relationship between dispersal rates, growth rate variability, and population persistence.

Conclusions:

  • Dispersal-induced growth is a mathematically supported phenomenon.
  • Periodic fluctuations in growth rates, combined with dispersal, are key drivers of DIG.
  • The study provides a framework for understanding population rescue through metapopulation dynamics.