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Evolutionary dynamics on degree-heterogeneous graphs.

T Antal1, S Redner, V Sood

  • 1Center of Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|May 23, 2006
PubMed
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Investigating species evolution on complex networks, this study reveals fixation probability depends on evolutionary dynamics. Voter model dynamics favor fitter species on high-degree nodes, while invasion dynamics favor them on low-degree nodes.

Area of Science:

  • Evolutionary dynamics on complex networks
  • Population genetics
  • Mathematical modeling of biological systems

Background:

  • Understanding species evolution requires considering population structure and interaction dynamics.
  • Degree-heterogeneous graphs, representing real-world networks, significantly influence evolutionary outcomes.
  • Previous models often simplify network topology or evolutionary mechanisms.

Purpose of the Study:

  • To investigate the fixation probability of a fitter species on degree-heterogeneous graphs.
  • To compare the effects of two distinct evolutionary dynamics: voter model and invasion process.
  • To analyze how node degree influences the success of a fitter mutant.

Main Methods:

  • Simulated the evolution of two competing species on degree-heterogeneous graphs.

Related Experiment Videos

  • Implemented voter model dynamics: death and replacement by a neighbor's offspring.
  • Implemented invasion process dynamics: offspring replaces a random neighbor.

    • Main Results:

    • Fixation probability is highly dependent on the specific evolutionary dynamics employed.
    • For voter model dynamics, fixation probability is proportional to the node's degree (k).
    • For invasion process dynamics, fixation probability is inversely proportional to the node's degree (1/k).

    Conclusions:

    • The local network environment (node degree) critically shapes evolutionary trajectories.
    • Voter model dynamics promote fitter species in highly connected regions.
    • Invasion process dynamics favor fitter species in less connected regions.