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Related Experiment Videos

Persistence, spread and the drift paradox.

E Pachepsky1, F Lutscher, R M Nisbet

  • 1Department of Ecology, Evolution and Marine Biology, University of California Santa Barbara, Santa Barbara, CA 93106, USA. pachepsk@lifesci.ucsb.edu

Theoretical Population Biology
|January 15, 2005
PubMed
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Population persistence in flowing environments depends on growth rate versus downstream drift. If growth doesn't outpace drift, a minimum habitat size is needed for survival, impacting spread dynamics.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Aquatic insect populations in streams face downstream drift, posing a challenge to their persistence in upstream reaches, known as the drift paradox.
  • Understanding population dynamics in environments with unidirectional flow (rivers, marine currents, wind-affected areas) is crucial for ecological modeling.
  • Previous research has proposed various mechanisms to explain the persistence of populations against directional flow.

Purpose of the Study:

  • To derive conditions for population persistence and spread in a one-dimensional medium with unidirectional flow.
  • To investigate the relationship between population persistence and the ability to spread against or with the flow.
  • To evaluate proposed ecological mechanisms for resolving the drift paradox using a two-phase model.

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Main Methods:

  • Development of a two-phase mathematical model incorporating immobile and dispersing individuals.
  • Analysis of population dynamics considering advection, diffusion, and reproduction in the stationary phase.
  • Calculation of invasion front propagation rates upstream and downstream.

Main Results:

  • Population persistence is guaranteed at low densities if local growth rate exceeds the rate of entry into drift.
  • Persistence may require a critical domain size when growth rate does not exceed drift rate.
  • Persistence and spread are interconnected; inability to advance upstream implies inability to persist in finite domains.
  • Residence in the immobile state consistently enhances population persistence.

Conclusions:

  • The study provides conditions for population persistence and spread in flowing environments, offering insights into the drift paradox.
  • The findings highlight the critical role of the balance between reproduction and dispersal in maintaining populations against flow.
  • The model suggests that the ability to move upstream is essential for long-term persistence in certain flowing habitats.