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Updated: Jun 15, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

A stochastic version of the Eigen model.

¹Departamento de Física, Facultad de Ciencias, Universidad de Burgos, Plaza Misael Bañuelos s/n, 09001 Burgos, Spain. fmusso@ubu.es

Bulletin of Mathematical Biology

|March 17, 2010

Summary

This summary is machine-generated.

We present a new stochastic model that replicates the Eigen model in simplified limits. This evolutionary computation model explores competition dynamics and master sequence concentrations.

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Last Updated: Jun 15, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

Evolutionary Biology
Theoretical Biology
Computational Biology

Background:

The Eigen model provides a foundational framework for understanding molecular evolution and self-replication.
Existing models often operate in deterministic or continuous-time regimes, potentially limiting their applicability to real-world stochastic systems.

Purpose of the Study:

To develop a discrete-time stochastic model that bridges the gap between the Eigen model and more complex biological realities.
To analyze the behavior of this new model, particularly concerning master sequence concentrations under varying population sizes.

Main Methods:

Formulation of a discrete-time stochastic model based on fecundity-driven competition with uniform viability.
Explicit derivation of the Markov matrix for a two-species scenario.
Numerical computation of master sequence concentrations and derivation of the master equation.
Application of the Van Kampen expansion for theoretical analysis.

Main Results:

The proposed stochastic model reproduces the Eigen model in deterministic and continuous-time limits.
Numerical simulations provide insights into master sequence concentrations for different population sizes in the two-species case.
The master equation and Van Kampen expansion offer a theoretical framework for analyzing the model's dynamics.

Conclusions:

The developed stochastic discrete-time model offers a more nuanced approach to evolutionary dynamics than the original Eigen model.
The findings are relevant for understanding molecular evolution, particularly in systems with discrete populations and stochastic fluctuations.
The study highlights the importance of considering stochasticity and discrete time in evolutionary modeling, with implications for extending the analysis to multi-species systems.