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Nonlinear stochastic Markov processes and modeling uncertainty in populations
The implications of model formulation when transitioning from spatial to landscape ecology
1. | Department of Mathematics, The University of Miami, Coral Gables, FL 33124, United States, United States |
2. | Department of Biology, The University of Maryland, College Park, MD 20742, United States |
References:
[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.
doi: 10.2307/2048374. |
[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.
doi: 10.1890/1051-0761(2006)016[0820:ADSLHR]2.0.CO;2. |
[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.
doi: 10.1038/35008063. |
[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.
doi: 10.1007/s00285-003-0234-6. |
[11] |
O. Ovaskainen and I. Hanski, Spatially structured metapopulation models: Global and local assessment of metapopulation capacity, Theoretical Population Biology, 60 (2001), 281-304.
doi: 10.1006/tpbi.2001.1548. |
[12] |
R. Van Kirk and M. A. Lewis, Integro-difference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137. |
show all references
References:
[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.
doi: 10.2307/2048374. |
[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.
doi: 10.1890/1051-0761(2006)016[0820:ADSLHR]2.0.CO;2. |
[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.
doi: 10.1038/35008063. |
[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.
doi: 10.1007/s00285-003-0234-6. |
[11] |
O. Ovaskainen and I. Hanski, Spatially structured metapopulation models: Global and local assessment of metapopulation capacity, Theoretical Population Biology, 60 (2001), 281-304.
doi: 10.1006/tpbi.2001.1548. |
[12] |
R. Van Kirk and M. A. Lewis, Integro-difference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137. |
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