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Related Experiment Video

Updated: Jun 14, 2025

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Published on: February 3, 2023

Error-induced extinction in a multi-type critical birth-death process.

Meritxell Brunet Guasch¹, P L Krapivsky^2,3, Tibor Antal⁴

¹School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, UK. xell.brunetguasch@ed.ac.uk.

Journal of Mathematical Biology

|September 2, 2024

Summary

This summary is machine-generated.

Extreme mutation rates can cause error-induced extinction (EEX) in cell populations. This study models EEX using birth-death processes, revealing distinct extinction patterns for different cell types.

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Area of Science:

Mathematical Biology
Population Dynamics
Theoretical Ecology

Background:

Extreme mutation rates can lead to error-induced extinction (EEX) in microbial and cancer cell populations.
Understanding extinction dynamics is crucial for predicting population viability under high mutation pressures.

Purpose of the Study:

To investigate critical birth-death processes as a model for EEX in growing populations with multiple cell types.
To derive and analyze the large-time asymptotic behavior of these n-type processes.

Main Methods:

Modeling EEX using an n-type critical birth-death process.
Analyzing the process as a Yule process until a specific cell type appears, triggering criticality.
Deriving large-time asymptotic results for the mass function and survival probability.

Main Results:

The mass function for cell type k exhibits an algebraic, stationary tail for k < n, contrasting with exponential tails for type 1.
The exponents governing these algebraic tails are identified.
The asymptotic survival probability also follows these algebraic tails.

Conclusions:

The study reveals distinct extinction dynamics for different cell types within a population under high mutation rates.
The derived mathematical framework provides insights into EEX phenomena and can be applied to biological populations facing intolerable mutation rates.