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Related Experiment Video

Updated: Oct 15, 2025

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

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.

Journal of Theoretical Biology

|October 31, 2021

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 probability Evolutionary models on graphs Proliferation models Random 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.