Mathematical Biosciences and Engineering (MBE)

The implications of model formulation when transitioning from spatial to landscape ecology
Pages: 27 - 60, Issue 1, January 2012

doi:10.3934/mbe.2012.9.27      Abstract        References        Full text (395.8K)           Related Articles

Robert Stephen Cantrell - Department of Mathematics, The University of Miami, Coral Gables, FL 33124, United States (email)
Chris Cosner - Department of Mathematics, The University of Miami, Coral Gables, FL 33124, United States (email)
William F. Fagan - Department of Biology, The University of Maryland, College Park, MD 20742, United States (email)

1 A. Berman and J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.       
2 K. J. Brown, C. Cosner and J. Fleckinger, Principal eigenvalues for problems with indefinite weight function on $\mathbbR^n$, Proceedings of the American Mathematical Society, 109 (1990), 147-155.       
3 R. S. Cantrell and C. Cosner, "Spatial Ecology via Reaction-Diffusion Equations," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003.       
4 C. Cosner, Reaction-diffusion equations and ecological modeling, in "Tutorials in Mathematical Biosciences. IV" (ed. A. Friedman), Lecture Notes in Mathematics, 1922, Springer, Berlin,(2008), 77-115.       
5 W. F. Fagan and F. Lutscher, Average dispersal success: Linking home range, dispersal, and metapopulation dynamics to refuge design, Ecological Applications, 16 (2006), 820-828.
6 I. Hanski, Predictive and practical metapopualtion models: The incidence function approach, in "Spatial Ecology" (eds. D. Tilman and P. Kareiva), Princton University Press, Princeton, NJ, (1997), 21-45.
7 I. Hanski, "Metapopulation Ecology," Oxford University Press, Oxford, UK, 1999.
8 I. Hanski and O. Ovaskainen, The metapopulation capacity of a fragmented landscape, Nature, 404 (2000), 755-758.
9 R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bulletin of the Entomological Society of America, 15 (1969), 237-240.
10 F. Lutscher and M. A. Lewis, Spatially-explicit matrix models, Journal of Mathematical Biology, 48 (2004), 293-324.       
11 O. Ovaskainen and I. Hanski, Spatially structured metapopulation models: Global and local assessment of metapopulation capacity, Theoretical Population Biology, 60 (2001), 281-304.
12 R. Van Kirk and M. A. Lewis, Integro-difference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137.

Go to top