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Related Experiment Videos

Stochasticity, invasions, and branching random walks.

Mark Kot1, Jan Medlock, Timothy Reluga

  • 1Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA 98195-2420, USA. kot@amath.washington.edu

Theoretical Population Biology
|October 7, 2004
PubMed
Summary

This study connects mathematical models to simulations of individual organisms. It finds that random variations can cause extinction but do not slow down invasion speeds.

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Area of Science:

  • Mathematical Biology
  • Ecology
  • Population Dynamics

Background:

  • Deterministic integrodifference equations model population dynamics.
  • Stochastic, individual-based simulations offer alternative perspectives.
  • Linking these approaches is crucial for comprehensive ecological understanding.

Purpose of the Study:

  • To bridge deterministic mathematical models with stochastic simulations.
  • To analyze invasion speeds in ecological models.
  • To investigate the impact of demographic stochasticity on invasion dynamics.

Main Methods:

  • Utilizing branching random walks to connect integrodifference equations and individual-based models.
  • Applying standard methods to calculate invasion speeds.

Related Experiment Videos

  • Analyzing density-independent branching random walks.

    • Main Results:

    • Invasion speeds were determined for both average population densities and the furthest-advancing individuals.
    • Demographic stochasticity, in density-independent scenarios, can lead to population extinction.
    • Stochasticity does not impede the overall asymptotic invasion speed or prevent accelerating invasions.

    Conclusions:

    • Branching random walks effectively link deterministic and stochastic ecological models.
    • Demographic stochasticity introduces extinction risk but does not alter asymptotic invasion rates.
    • Invasions can continue to accelerate even with random individual variations.