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Mutations01:39

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Mutations are changes in the sequence of DNA. These changes can occur spontaneously or they can be induced by exposure to environmental factors. Mutations can be characterized in a number of different ways: whether and how they alter the amino acid sequence of the protein, whether they occur over a small or large area of DNA, and whether they occur in somatic cells or germline cells.
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In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).
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Metapopulation model for rock-paper-scissors game: Mutation affects paradoxical impacts.

Takashi Nagatani1, Genki Ichinose2, Kei-Ichi Tainaka3

  • 1Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.

Journal of Theoretical Biology
|April 9, 2018
PubMed
Summary

Mutation in the rock-paper-scissors (RPS) game can lead to three distinct population phases: stable coexistence of three species, two species, or a single species. Varying the mutation rate drives these phase transitions and can cause unique paradoxes in different patches.

Keywords:
BiodiversityBiological controlCondition of coexistenceMetapopulation modelMultiple paradoxesMutationRandom walkRock–paper–scissors gameSpatially heterogeneous mutation

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Area of Science:

  • Ecology
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • The rock-paper-scissors (RPS) game illustrates cyclic dominance, a fundamental concept for understanding biodiversity and species coexistence.
  • Three species (Rock, Paper, Scissors) can stably coexist in nature through this game's dynamics.

Purpose of the Study:

  • To investigate the impact of mutation on species coexistence within a metapopulation model of the RPS game.
  • To analyze how mutation rates influence population dynamics and lead to different stable phases.

Main Methods:

  • Developed a metapopulation model for the RPS game incorporating mutation (R to S) across spatially separated patches.
  • Utilized reaction-diffusion equations combining reaction (RPS dynamics) and migration (random walk) terms.
  • Solved the model equations analytically and numerically.

Main Results:

  • Mutation can induce three distinct population phases: stable coexistence of three species, stable coexistence of two species, or a single-species phase.
  • Phase transitions between these states are controlled by varying the mutation rate.
  • Mutation introduces patch-specific paradoxes, altering conditions for species coexistence depending on the metapopulation structure.

Conclusions:

  • Mutation is a critical factor in determining the stability and coexistence patterns of species in cyclic dominance systems.
  • Metapopulation structure significantly influences how mutation affects biodiversity outcomes.
  • The study highlights the complex and context-dependent effects of mutation on ecological dynamics.