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.
Recommended Citation
Miltz, Benjamin, "Analysis and extension of the coalescing colony model of invasive species spread" (2015). Cal Poly Humboldt theses and projects. 1172.
https://digitalcommons.humboldt.edu/etd/1172
https://scholarworks.calstate.edu/concern/theses/qn59q638k