Rs. Cantrell et al., SPATIALLY EXPLICIT MODELS FOR THE POPULATION-DYNAMICS OF A SPECIES COLONIZING AN ISLAND, Mathematical biosciences, 136(1), 1996, pp. 65-107
We construct reaction-diffusion models for the population dynamics of
a species colonizing an island from a source population on a continent
. We view the source population as inducing a density or flux of immig
rants onto the island and interpret colonization as succeeding if the
population on the island is predicted to persist even when immigration
from the continent is stopped. To capture the observation that a suff
iciently large population or density must be attained for colonization
to succeed, we assume Allee (i.e., bistable) dynamics rather than log
istic dynamics for the colonizing population. We consider the cases of
colonization in both the absence and presence of a competitor. We use
reaction-diffusion theory, especially comparison methods and sub- and
supersolutions, to determine how parameters such as the distance from
the continent to the island and the dispersal, birth and mortality ra
tes, carrying capacity, and minimum viable population density of the c
olonizing species affect the outcome of the attempted colonization. In
the case of colonization in the presence of a competitor we consider
a number of scenarios involving different types and strengths of compe
tition. Our analysis permits us to draw conclusions about the characte
ristics of a species that make it a good colonizer.