Patch-size and isolation effects in the Fisher-Kolmogorov equation

Journal of Mathematical Biology

Volumn 57, Issue 4, 2008, Pages 521-535

  Artiles, W ^a   Carvalho, P G S ^a   Kraenkel, R A ^a  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

Critical patch size; Fisher Kolmogorov equation; Isolation; Population dynamics

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIRD; ECOSYSTEM; PHYSIOLOGY; POPULATION DENSITY; POPULATION DYNAMICS; SOUTH AMERICA; TREE;

ALGORITHMS; ANIMALS; BIRDS; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION DYNAMICS; SOUTH AMERICA; TREES;

AVES;

EID: 47649119598     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0174-2     Document Type: Article

References (26)

1. D. Andow P. Kareiva S. Levin A. Okubo 1990 Spread of invading organisms Landsc. Ecol. 4 177 188
2. R. Bainbridge 1957 The size, shape and density of marine phytoplankton concentrations Biol. Rev. Camb. Phil. Soc. 32 91 115
3. M. Ballard V.M. Kenkre M.N. Kupperman 2004 Periodically varying externally imposed environmental effects in population biology Phys. Rev. E 70 031912
4. H. Berestycki F. Hamel 2006 Fronts and invasions in general domains C. R. Acad. Sci. Paris, Ser. I 343 711 716
5. R.S. Cantrell C. Cosner 1998 On the effects of spatial heterogeneity on the persistence of interacting species J. Math. Biol. 37 103 145
6. R.S. Cantrell C. Cosner 1991 The effects of spatial heterogeneity on population dynamics J. Math. Biol. 29 315 338
7. R.S. Cantrell C. Cosner 1994 Insular biogeographic theory and diffusion models in population dynamics Theor. Pop. Biol. 45 177 202
8. R.S. Cantrell C. Cosner W.F. Fagan 1998 Competitive reversals inside ecological reserves: the role of external habitat degradation J. Math. Biol. 37 491 533
9. L. Fahrig 2003 Effects of habitat fragmentation on biodiversity Ann. Rev. Ecol. Syst. 34 487 515
10. G. Ferraz 2007 A large scale deforestation experiment: effects of patch area and isolation on amazon birds Science 315 238 241
11. Fife P.C.: Mathematical Aspects of reacting and Diffusing Systems. Lecture Notes in Biomath., vol. 28. Springer, Berlin (1979)
12. V.M. Kenkre M.N. Kuperman 2003 Applicability of Fisher equation to bacterial population dynamics Phys. Rev. E 67 051921
13. H. Kierstaed I.B. Slobodkin 1953 The size of water masses containing plankton bloom J. Marine Research 12 141 147
14. J. Latore P. Gould M.A. Mortimer 1998 Spatial Dynamics and Critical Patch Size of Annual Plant Populations J. Theo. Biol. 180 277 285
15. A.L. Lin 2004 Localization and extinction of bacterial populations under inhomogeneous growth conditions Bioph. J. 87 75 80
16. D. Ludwig D.G. Aronson H.F. Weinberger 1979 Spatial patterning of the spruce bud-worm J. Math. Biol. 8 217 258
17. MacArthur R.H., Wilson E.O.: Theory of Island Biogeography. Princeton University Press, Princeton (1967)
18. A.P. Martin 2000 On filament width in oceanic plankton distributions J. Plankton Res. 22 597 602
19. T. Neicu A. Pradhan D.A. Larochelle A. Kudrolli 2000 Extinction transition in bacterial colonies under forced convection Phys. Rev. E 62 1059 1062
20. Okubo, A., Levin, S.A. (eds.) Diffusion and Ecological Problems, Chap. 9. Springer, Berlin (2001)
21. S.W. Pacala J. Roughgarden 1982 Spatial heterogeneity and interspecific competition Theor. Pop. Biol. 21 91 113
22. N. Perry 2005 Experimental validation of a critical domain size in reaction-diffusion systems with Escherichia coli populations J. R. Soc. Interface 2 379 387
23. B.C. Sanchez R.R. Parmenter 2002 Patterns of shrub-dwelling arthropod diversity across a desert shrubland-grassland ecotone: a test of island biogeographic theory J. Arid. Environ. 50 247 265
24. J. Skellam 1951 Random dispersal in theoretical populations Biometrika 38 196 218
25. Shigesada N., Kawasaki K.: Biological Invasions: Theory and Practice. Oxford University Press, Oxford (1997)
26. P.C. Stouffer R.O. Bierregaard Jr R. Strong T.E. Lovejoy 2006 Long-term landscape change and bird abundance in Amazonian rainforest fragments Conserv. Biol. 20 1212 1223