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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 YorkLondon, 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), 147155. doi: 10.2307/2048374. 
[3] 
R. S. Cantrell and C. Cosner, "Spatial Ecology via ReactionDiffusion Equations," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003. 
[4] 
C. Cosner, Reactiondiffusion equations and ecological modeling, in "Tutorials in Mathematical Biosciences. IV" (ed. A. Friedman), Lecture Notes in Mathematics, 1922, Springer, Berlin,(2008), 77115. 
[5] 
W. F. Fagan and F. Lutscher, Average dispersal success: Linking home range, dispersal, and metapopulation dynamics to refuge design, Ecological Applications, 16 (2006), 820828. doi: 10.1890/10510761(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), 2145. 
[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), 755758. 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), 237240. 
[10] 
F. Lutscher and M. A. Lewis, Spatiallyexplicit matrix models, Journal of Mathematical Biology, 48 (2004), 293324. doi: 10.1007/s0028500302346. 
[11] 
O. Ovaskainen and I. Hanski, Spatially structured metapopulation models: Global and local assessment of metapopulation capacity, Theoretical Population Biology, 60 (2001), 281304. doi: 10.1006/tpbi.2001.1548. 
[12] 
R. Van Kirk and M. A. Lewis, Integrodifference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107137. 
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 YorkLondon, 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), 147155. doi: 10.2307/2048374. 
[3] 
R. S. Cantrell and C. Cosner, "Spatial Ecology via ReactionDiffusion Equations," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003. 
[4] 
C. Cosner, Reactiondiffusion equations and ecological modeling, in "Tutorials in Mathematical Biosciences. IV" (ed. A. Friedman), Lecture Notes in Mathematics, 1922, Springer, Berlin,(2008), 77115. 
[5] 
W. F. Fagan and F. Lutscher, Average dispersal success: Linking home range, dispersal, and metapopulation dynamics to refuge design, Ecological Applications, 16 (2006), 820828. doi: 10.1890/10510761(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), 2145. 
[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), 755758. 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), 237240. 
[10] 
F. Lutscher and M. A. Lewis, Spatiallyexplicit matrix models, Journal of Mathematical Biology, 48 (2004), 293324. doi: 10.1007/s0028500302346. 
[11] 
O. Ovaskainen and I. Hanski, Spatially structured metapopulation models: Global and local assessment of metapopulation capacity, Theoretical Population Biology, 60 (2001), 281304. doi: 10.1006/tpbi.2001.1548. 
[12] 
R. Van Kirk and M. A. Lewis, Integrodifference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107137. 
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