Date of Award

8-2001

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Thomas G. Hallam

Committee Members

Lou Gross, Suzanne Lenhart, Steven Bartell

Abstract

Individual-based models have been used to study the population dynamics of semelparous and iteroparous organisms. The rst model, developed for sockeye salmon ( On-corhynchus nerka), was based on the physiology of the individual and incorporated into a population model via a McKendrick-von Foerster type partial di
erential equation. Cycles of population abundance historically found in the Fraser River system were recreated through model simulations. Explanations for the appearance of the cycling were investigated and tested. The results showed that density- and size-dependent mortality were not necessary for cycling to appear, however their inclusion or exclusion in combination with the type of schooling could alter the character of the periodic cycling. The use of sequential design of experiments as a method for sensitivity analysis of the model allowed for a thorough investigation of the parameter space. The approach combined standard and non-standard designs and used reverse methodology to screen for insignificant factors. The resulting sequence of designs isolated the sensitive parameters and allowed for realistic model output.

The second individual-based model was used to study iteroparous reproduction strategies and population dynamics. Two population models were formulated, a set of continuous partial differential equations of the McKendrick-von Foerster type and aset of discrete matrix equations. The asymptotic relationship between the two types of models was evaluated. It was found that a lack of convergence to the steady-state age distribution can occur in discrete event reproduction models and that convergence depends on whether the ratio between the maximum age and the length of the reproductive period is rational.

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Mathematics Commons

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