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Active-to-absorbing-state phase transition in an evolving population with mutation.

Niladri Sarkar1

  • 1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
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Summary

This study explores the active to absorbing phase transition (AAPT) in a species and its mutant. Mutation significantly impacts species survival, linking the model to directed percolation universality.

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Area of Science:

  • Theoretical physics
  • Mathematical biology
  • Ecology

Background:

  • The active to absorbing phase transition (AAPT) is a critical phenomenon observed in various systems.
  • Understanding the role of mutation in species dynamics is crucial for evolutionary biology.
  • The directed percolation universality class describes critical behavior in systems with quenched disorder.

Purpose of the Study:

  • To investigate the AAPT in a two-component model of a species and its mutant.
  • To analyze the critical scaling behavior and dynamic scaling near the AAPT.
  • To determine the influence of mutation on species extinction or survival.

Main Methods:

  • Development of a simple two-component model system.
  • Analysis of critical scaling and weak dynamic scaling.
  • Comparison with the directed percolation universality class.

Main Results:

  • The model exhibits nontrivial critical scaling behavior near the AAPT.
  • Weak dynamic scaling is observed, indicating the significance of mutation.
  • The model's behavior aligns with the directed percolation universality class.

Conclusions:

  • Mutation plays a significant role in the AAPT of species.
  • The model provides insights into how mutations affect species survival and extinction.
  • This model serves as a foundation for further research on mutation's ecological impact.