Vogels, A. A. (2011). The fundamentals and theoretical concepts of modeling age structured populations. Retrieved from http://scholar.acadiau.ca/islandora/object/theses:195

The fundamentals and theoretical concepts of modeling age structured populations.

Author

Vogels, Angela Adrianne

Call Number

LE3 .A278 2011

Date

2011

Supervisor

Karsten, Richard
Teismann, Holger

Degree Grantor

Acadia University

Degree Name

Master of Science

Degree Level

Masters

Discipline

Mathematics and Statistics

Affiliation

Mathematics & Statistics

Abstract

There are populations of single species that exhibit uctuations and oscillations in their growth such that it is necessary to use structured dynamic models in order to accurately capture such behaviours. Speci cally, we examine age-structured mod- els. In this thesis, two time-continuous, age-structured models are considered of the partial di erential equation and delay di erential equation types as well as a time-continuous, age discrete model in the form of a system of ordinary di erential equations. For each type of age-structured model, common concepts used in demog- raphy are discussed such as Lotka`s r, stable age distribution and reproductive value. These are asymptotic quantities that are formally de ned for linear models. In this work, the relevance of these demographic quantities are further extended to nonlinear models where analogous quantities such as the population`s xed point and the zero growth reproductive value are shown to play important roles in the discussion of the dynamics of nonlinear models.

Rights

The author grants permission to the University Librarian at Acadia University to reproduce, loan or distribute copies of my thesis in microform, paper or electronic formats on a non-profit basis. The author retains the copyright of the thesis.