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Fast migration and emergent population dynamics.

Michael Khasin1, Evgeniy Khain, Leonard M Sander

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA.

Physical Review Letters
|February 2, 2013
PubMed
Summary
This summary is machine-generated.

Fast migration in population networks does not always lead to a well-mixed system. New global dynamics can emerge, requiring case-by-case analysis for population dynamics on networks.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Population dynamics are often studied in networks of interconnected patches.
  • Patches may have identical local dynamics but vary in carrying capacities.
  • Fast migration is often assumed to create a 'well-mixed' system where global dynamics mirror local ones.

Purpose of the Study:

  • To investigate if fast migration in population networks guarantees that the total population dynamics resemble those of individual patches.
  • To identify conditions under which the well-mixed assumption holds for population dynamics on networks.

Main Methods:

  • Mathematical modeling of population dynamics on a network of patches.
  • Analysis of system behavior under conditions of rapid migration between patches.
  • Derivation of general conditions for emergent global population dynamics.

Main Results:

  • The assumption that fast migration leads to a well-mixed system is generally false.
  • New and distinct global population dynamics can emerge in such systems.
  • A specific general condition is identified for the total population dynamics to match constituent patch dynamics.

Conclusions:

  • Fast migration does not automatically simplify population dynamics to a well-mixed state.
  • Emergent global dynamics in population networks necessitate individual case analysis.
  • A derived condition provides a criterion for when global dynamics will mirror local dynamics.