Analysis and extension of the coalescing colony model of invasive species spread

Graduation Date

2015

Document Type

Thesis

Program

Other

Program

Thesis (M.S.)--Humboldt State University, Environmental Systems: Mathematical Modeling, 2015

Committee Chair Name

Christopher Dugaw

Committee Chair Affiliation

HSU Faculty or Staff

Keywords

Integro-differential equations, Population ecology, Invasive species, Mathematical modeling, Numerical methods, Humboldt State University -- Theses -- Mathematical Modeling, Coalescing colony model

Abstract

The need to accurately predict the spread rates of invasive species has produced a variety of mathematical models with highly varied results. Early models of range expansion based on Fisher's (1937) reaction-diffusion equations predicted linear spread rates. Somewhat more recently, integro-difference equation models were shown to predict continually increasing spread rates when offspring dispersal distances were leptokurtically distributed (Kot et al., 1996). This thesis examines and then expands on the coalescing colony model (CCM) originally proposed by Shigesada and Kawasaki (1997). The Adapted CCM developed here relaxes with two of the main assumptions made by Shigesada and Kawasaki (1997) in their original formulation of the CCM, namely that offspring travel a constant distance from the main body of the invasion, and that they originate only at the perimeter of the invasion front. To test and develop this model I have created computer simulations of spreading invasions, and a numerically implemented solution to the equations which comprise the Adapted CCM. Additionally, I have developed versions of the mathematical and simulation models in which either the offspring production rate or the diffusive growth rate decays as the invasion progresses spatially. These additions may eventually provide the basis for a more comprehensive model incorporating species range limits. For all parameter values considered spread rates were less than that predicted by Shigesada's (1997) CCM, but did asymptotically approach a constant value as t →∞. The results of this research appear to indicate that lognormally distributed offspring migration distances will have an effect on an invasion's rate of spread when the coefficient of variation is low ( 2). Continually accelerating spread rates, such as those predicted under certain conditions with integro-difference equation models (Kot et al., 1996), were not observed.

https://scholarworks.calstate.edu/concern/theses/qn59q638k

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