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University of Nebraska - Lincoln
Department of Mathematics: Dissertations, Theses, and Student Research
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Full-Text Articles in Population Biology
Spectral Properties Of A Non-Compact Operator In Ecology, Matthew Reichenbach
Spectral Properties Of A Non-Compact Operator In Ecology, Matthew Reichenbach
Department of Mathematics: Dissertations, Theses, and Student Research
Ecologists have used integral projection models (IPMs) to study fish and other animals which continue to grow throughout their lives. Such animals cannot shrink, since they have bony skeletons; a mathematical consequence of this is that the kernel of the integral projection operator T is unbounded, and the operator is not compact. A priori, it is unclear whether these IPMs have an asymptotic growth rate λ, or a stable-stage distribution ψ. In the case of a compact operator, these quantities are its spectral radius and the associated eigenvector, respectively. Under biologically reasonable assumptions, we prove that the non-compact operators in …
Modeling And Analysis Of Biological Populations, Joan Lubben
Modeling And Analysis Of Biological Populations, Joan Lubben
Department of Mathematics: Dissertations, Theses, and Student Research
Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.
(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …