Date on Master's Thesis/Doctoral Dissertation

5-2012

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Committee Chair

Li, Bingtuan

Author's Keywords

Integrodifference model; Perennial; Seed bank; Spreading seed; Structured; Traveling waves

Subject

Plant propagation--Mathematical models

Abstract

We formulate an integro-difference model to predict the growth and spatial spread of a perennial plant population with an age-structured seed bank. We allow the seeds in the bank to be of any age, producing an infinite system of equations. The production of new seed can be density-dependent and so the function describing this growth is allowed to be non-monotone. The functions describing the seed bank are linear. We develop properties about the non-spatial model, including the existence of a positive steady-state and conditions under which solutions converge to this steady-state. We also show that when the origin is unstable, the system has a spreading speed and that this spreading speed is characterized as the slowest speed of a class of traveling wave solutions. We conduct numerical simulations of a truncated version of this model which show that both the perennial term and the seed bank can have a stabilising effect on the population. On the other hand, traveling wave solutions may exhibit different patterns of fluctuations including periodic oscillations and chaotic tails.

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