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Applications of statistical mechanics and nonlinear science to ecological phenomena


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/9797

Applications of statistical mechanics and nonlinear science to ecological phenomena

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Title: Applications of statistical mechanics and nonlinear science to ecological phenomena
Author: Gonzalez-Palacio, Luis Felipe
Advisor(s): Kenkre, Vasudev (Nitant)
Committee Member(s): Kenkre, Vasudev (Nitant)
Dunlap, David
Parmenter, Robert
Department: University of New Mexico. Dept. of Physics & Astronomy
Subject: Peromyscus
animal diffusion
home range
LC Subject(s): Ecology--Mathematical models.
Epidemiology--Statistical methods.
Reaction-diffusion equations--Numerical solutions.
Peromyscus maniculatus--New Mexico--Valles Caldera National Preserve--Geographical distribution--Mathematical models.
Peromyscus maniculatus--Wyoming--Geographical distribution--Mathematical models.
Hantaviruses--Geographical distribution--Mathematical models.
Degree Level: Masters
Abstract: The application of techniques widely used in physics to explain biological phenomena has become a very successful endeavor in the past few decades. Such techniques include, but are not limited to, kinetic equations and nonlinear dynamics. We present an overview of some current topics of interest in ecology that use such techniques to explain and predict a wide array of phenomena. Several successful models are reviewed. We present the results of our analyses of two datasets of repeated sessions of mark-recaptures of the deer mouse, Peromyscus maniculatus (Rodentia: Muridae), the host and reservoir of Sin Nombre virus (Bunyaviridae: Hantavirus). The first dataset corresponds to a three-year period of mark-recaptures in the Valles Caldera National Preserve, New Mexico. The second one corresponds to a four-year period of mark-recaptures in the Wyoming grassland. We study the displacements of the recaptured rodents from a web distribution of traps on the landscape (New Mexico), and a square grid (Wyoming). From the displacements we extract the diffusion constant of the motion of the rodents. In New Mexico, the short-time behavior (1 day) shows the motion to be approximately diffusive and the diffusion constant to be 320 ± 40 m2/day. In Wyoming, the average diffusion constant for the deer mice was 105 ± 10 m2/day. The long-time behavior is capable, in principle, of providing an estimation of the extent of the rodent home ranges. However, the datasets analyzed were not sufficiently detailed to yield a value for the home ranges, and the focus of the thesis is on the diffusion constants rather than on the home ranges.
Graduation Date: July 2009
URI: http://hdl.handle.net/1928/9797

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