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Agnieszka Czaplicka1, Krzysztof Suchecki1, Borja Miñano2

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Tournament selection models reveal that limited information available to new nodes restricts the emergence of new hierarchy levels in growing systems. The absolute information amount, not relative, governs this hierarchical development.

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Area of Science:

  • Complex Systems
  • Evolutionary Dynamics
  • Network Science

Background:

  • Growing multilevel systems often exhibit hierarchical structures.
  • Tournament selection is a mechanism influencing system evolution and node attachment.
  • Limited information availability impacts decision-making in evolving systems.

Purpose of the Study:

  • To model and analyze the emergence of hierarchy levels in growing systems under tournament selection.
  • To compare two distinct tournament selection models: constant tournament (CT) and proportional tournament (PT).
  • To investigate the role of information availability in shaping system hierarchy.

Main Methods:

  • Development of analytical models based on rate equations.
  • Numerical simulations to validate analytical findings.
  • Comparative analysis of CT and PT models.

Main Results:

  • In the CT model, hierarchy levels emerge, but their appearance time increases exponentially; the first level grows logarithmically, and the last level shows quasi-log-periodic oscillations.
  • In the PT model, the first two levels grow linearly, while higher levels emerge rarely or not at all.
  • Both models demonstrate that limited information availability constrains the formation of new hierarchy levels.

Conclusions:

  • Tournament dynamics, constrained by information availability, limit the emergence of new hierarchy levels.
  • The absolute quantity of information, rather than its relative proportion, is the key factor governing hierarchical emergence.
  • These findings have implications for understanding organizational structures and evolutionary processes in complex adaptive systems.