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Studying Age-dependent Genomic Instability using the S. cerevisiae Chronological Lifespan Model

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Published on: September 29, 2011

Trait Substitution Sequence process and Canonical Equation for age-structured populations.

Sylvie Méléard¹, Viet Chi Tran

¹CMAP, Ecole Polytechnique, Palaiseau Cedex, France. Sylvie.Meleard@polytechnique.edu

Journal of Mathematical Biology

|August 1, 2008

Summary

This study introduces novel stochastic models for age-structured populations, incorporating mutation and selection. These models extend adaptive dynamics and canonical equations, offering new insights into evolutionary processes.

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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Published on: February 3, 2023

Area of Science:

Evolutionary biology
Mathematical modeling
Population dynamics

Background:

Existing models for population evolution often lack age structure.
Adaptive Dynamics and Canonical Equations provide frameworks for evolutionary modeling.
Integrating age structure is crucial for capturing life history nuances like senescence.

Purpose of the Study:

To develop a stochastic model for trait and age-structured populations under mutation and selection.
To generalize existing evolutionary process models (Trait Substitution Sequence, Canonical Equation) by incorporating age structure.
To explore the impact of age structure on evolutionary approximations and population behavior.

Main Methods:

Formulation of a continuous-time, discrete individual-centered population process.
Derivation of a jump process under large population and rare mutation limits.
Development of an age-dependent ordinary differential equation (ODE) under small mutation assumptions, generalizing the Canonical Equation and based on ecological PDEs.

Main Results:

A novel jump process generalizing the Trait Substitution Sequence for age-structured populations.
An age-dependent ODE extending the Canonical Equation, incorporating an establishment probability.
Demonstration of how age structure enriches population modeling with life history features like senescence.

Conclusions:

The developed evolutionary approximations offer a new framework for studying age-structured populations.
The inclusion of age structure provides a more realistic representation of evolutionary dynamics.
The study highlights the importance of age-specific demographic processes in shaping evolutionary trajectories.