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Dynamics of Concentration in a Population Model Structured by Age and a Phenotypical Trait

Dynamics of Concentration in a Population Model Structured by Age and a Phenotypical Trait We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behavior of the solution to a renewal type equation, and then to derive properties that illustrate the adaptive dynamics of such a population. We begin with a simplified model by discarding the effect of mutations, which allows us to introduce the main ideas and state the full result. Then we discuss the general model and its limitations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Dynamics of Concentration in a Population Model Structured by Age and a Phenotypical Trait

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References (44)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-017-0151-0
Publisher site
See Article on Publisher Site

Abstract

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behavior of the solution to a renewal type equation, and then to derive properties that illustrate the adaptive dynamics of such a population. We begin with a simplified model by discarding the effect of mutations, which allows us to introduce the main ideas and state the full result. Then we discuss the general model and its limitations.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 18, 2017

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