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Following the Dynamics of Structural Variants in Experimentally Evolved Populations
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Bernoulli and binomial proliferation on evolutionary graphs.

Fernando Alcalde Cuesta1, Gustavo Guerberoff2, Álvaro Lozano Rojo3

  • 1Instituto de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela E-15782, Spain.

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|October 31, 2021
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Summary
This summary is machine-generated.

This study introduces novel random proliferation models on graphs, enhancing the Moran model by allowing rapid mutant particle spread. These models offer a more realistic approach to studying population dynamics and evolution.

Keywords:
Critical probabilityEvolutionary models on graphsProliferation modelsRandom waves

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Area of Science:

  • Mathematical Biology
  • Graph Theory
  • Evolutionary Dynamics

Background:

  • The Moran model on graphs is a foundational tool for studying evolutionary processes.
  • Existing models often limit particle interactions and spread dynamics.

Purpose of the Study:

  • To introduce and analyze novel random proliferation models on graphs.
  • To extend the capabilities of the Moran model for more realistic simulations.
  • To investigate the dynamics of competing particle types on a graph.

Main Methods:

  • Development of two random proliferation models: Bernoulli and binomial proliferation.
  • Analysis of particle proliferation dynamics on graph structures.
  • Introduction of critical parameters by comparing with the Moran process fixation probability.
  • Analytical solutions for specific model cases.
  • Incorporation of density-dependent mechanisms for dynamic parameter updates.

Main Results:

  • Type-1 particles exhibit enhanced proliferation capabilities compared to the standard Moran model.
  • Introduction of critical parameters to characterize proliferation dynamics.
  • Analytical solutions derived for particular scenarios.
  • Density-dependent mechanisms enable the observation of fluctuating waves of type-1 particles.
  • Models demonstrate adaptability to complex and realistic evolutionary situations.

Conclusions:

  • The proposed random proliferation models offer a more flexible and realistic framework for studying evolutionary dynamics on graphs.
  • These models capture complex phenomena like fluctuating population waves.
  • The models can be adapted for a wider range of biological and ecological simulations.