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A multiple age class population model with delayed recruitment

University of British Columbia

An exploited single-species population model with a density dependent reproductive function is constructed, in which recruitment to the adult breeding population may occur in one of several possible age classes. The parent is assumed capable of giving birth only once. It is also assumed that all density dependence is concentrated in the first year of life. A linearized stability analysis of the multiply-delayed difference equation model is carried out and a sufficient condition for stability is derived for the general case, while necessary and sufficient conditions are found in specific examples. Some indication of the complicated bifurcation structure of the model is given by a series of computer simulation plots. Finally, the method of Lagrange multipliers is used to find the optimal equilibrium escapement level for the original exploited population model.

Text

2010-03-23

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http://hdl.handle.net/2429/22417

Mathematics

University of British Columbia

Graduate