Coexistence of competitors in deterministic and stochastic patchy environments

References

• Ackleh , A. S. , Allen , L. J.S. and Carter , J. 2007 . Establishing a beachhead: A stochastic population model with an Allee effect applied to species invasion . Theor. Popul. Biol. , 71 : 290 – 300 .
   PubMed Web of Science ®Google Scholar
• Adler , F. and Mosquera , J. 2000 . Is space necessary? Interference competition and limits to biodiversity . Ecology , 81 : 3226 – 3232 .
   Web of Science ®Google Scholar
• Amarasekare , P. and Possingham , H. 2001 . Patch dynamics and metapopulation theory: The case of successional species . J Theor. Biol. , 209 : 333 – 344 .
   PubMed Web of Science ®Google Scholar
• Andersonb , R. M. and May , R. M. 1991 . Infectious Diseases of Humans: Dynamics and Control , Oxford : Oxford University Press .
   Google Scholar
• Grenfell , B. and Harwood , J. 1997 . (Meta)population dynamics of infectious disease . Trends Ecol. Evol. , 12 : 395 – 404 .
   PubMed Web of Science ®Google Scholar
• Hanski , I. 1983 . Coexistence of competitors in patchy environment . Ecology , 64 : 493 – 500 .
   Web of Science ®Google Scholar
• Hanski , I. 1998 . Metapopulation dynamics . Nature , 365 : 41 – 49 .
   Google Scholar
• Hanski , I. and Ranta , E. 1983 . Coexistence in a patchy environment: Three species of Daphnia in Rock Pools . J. Animal Ecol. , 52 : 263 – 279 .
   Web of Science ®Google Scholar
• Hassell , M. P. , Comins , H. N. and May , R. M. 1991 . Spatial structure and chaos in insect population dynamics . Nature , 353 : 255 – 258 .
   Web of Science ®Google Scholar
• Hastings , A. 1980 . Disturbance, coexistence, history and competition for space . Theor. Popul. Biol. , 18 : 363 – 373 .
   Web of Science ®Google Scholar
• Holt , R. D. 1997 . “ From metapopulation dynamics to community structure: Some consequences of spatial heterogeneity ” . In Metapopulation Biology: Ecology, Genetics and Evolution , Edited by: Hanski , I. and Gilpin , M. 149 – 165 . New York : Academic Press .
   Google Scholar
• Horn , H. S. and MacArthur , R. 1972 . Competition among fugitive species in a harlequin environment . Ecology , 53 : 749 – 752 .
   Web of Science ®Google Scholar
• Jiang , J. F. , Qiu , Z. P. , Wu , J. H. and Zhu , H. P. 2009 . Threshold conditions for West Nile virus outbreaks . Bull. Math. Biol. , 71 : 627 – 647 .
   PubMed Web of Science ®Google Scholar
• Kareiva , P. 1987 . Habitat fragmentation and the stability of predator-prey interactions . Nature , 326 : 388 – 390 .
   Web of Science ®Google Scholar
• Levin , S. A. 1974 . Dispersion and population interactions . Am. Nat. , 108 : 207 – 225 .
   Web of Science ®Google Scholar
• Levins , R. 1969 . Some demographic and genetic consequences of environmental heterogeneity for biological control . Bull. Entomol. Soc. Amer. , 15 : 237 – 240 .
   Google Scholar
• Lv , Q. , Schneider , M. K. and Pitchford , J. W. 2008 . Individualism in plant populations: Using stochastic differential equations to model individual neighbour-dependent plant growth . Theor. Popul. Biol. , 74 : 74 – 83 .
   PubMed Web of Science ®Google Scholar
• May , R. M. 1973 . Stability in randomly fluctuating versus determinist environments . Am. Nat. , 107 : 621 – 650 .
   Web of Science ®Google Scholar
• McCormack , R. and Allen , L. J.S. 2005 . Disease emergence in deterministic and stochastic models for host and pathogen . Appl. Math. Comput. , 168 : 1281 – 1305 .
   Web of Science ®Google Scholar
• Mosquera , J. and Adler , F. R. 1998 . Evolution of virulence: A unified framework for coinfection and superinfection . J. Theor. Biol. , 195 : 293 – 313 .
   Google Scholar
• Nee , S. and May , R. M. 1992 . Dynamics of metapopulations: Habitat destruction and competitive coexistence . J. Animal Ecol. , 61 : 37 – 40 .
   Web of Science ®Google Scholar
• Nee , S. , May , R. and Hassell , M. 1997 . “ Two-species metapopulation models ” . In Metapopulation Biology: Ecology, Genetics and Evolution , Edited by: Hanski , I. and Gilpin , M. 123 – 147 . New York : Academic Press .
   Google Scholar
• Neuhauser , C. 2001 . Mathematical challenges in spatial ecology . Notices Amer. Math. Soc. , 48 : 1304 – 1314 .
   Google Scholar
• Nowak , M. A. and May , R. M. 1992 . Evolutionary games and spatial chaos . Nature , 359 : 826 – 829 .
   Web of Science ®Google Scholar
• Ovaskainen , O. and Cornell , S. J. 2006 . Space and stochasticity in population . PNAS , 103 : 12781 – 12786 .
   PubMed Web of Science ®Google Scholar
• Rohrbach , T. “ Metapopulations and patch dynamics: Animal dispersal in heterogeneous landscapes ” . Available at http://crssa.rutgers.edu/courses/lse/Web_Patch/final/Tanya/Rohrbach_Final.htm
   Google Scholar
• Smith , H. L. 1995 . “ Monotone dynamical systems: An introduction to theory of competitive and cooperative systems ” . Providence, RI : AMS . Mathematical Surveys and Monographs, Vol. 41
   Google Scholar
• Takac , P. 1992 . Domains of attraction of generic-limit sets for strongly monotone discrete-time semigroups . J. Reine Angew. Math. , 423 : 101 – 173 .
   Web of Science ®Google Scholar
• Thieme , H. R. 1993 . Persistence under relaxed point-dissipativity with an application to an epidemic model . SIAM J. Math. Anal. , 24 : 407 – 435 .
   Web of Science ®Google Scholar
• Tilman , D. 1994 . Competition and biodiversity in spatially structured habitats . Ecology , 75 : 2 – 16 .
   Web of Science ®Google Scholar
• Tilman , D. and Kareiva , P. 1997 . Spatial Ecology: the Role of Spare in Population Dynamics and Interspecies Interactions , Princeton, NJ : Princeton University Press .
   Google Scholar
• Varughese , M. M. and Fatti , L. P. 2008 . Incorporating environmental stochasticity within a biological population model . Theor. Popul. Biol. , 74 : 115 – 129 .
   PubMed Web of Science ®Google Scholar
• Wang , Y. and Jiang , J. 2001 . The general properties of discrete time competitive dynamical systems . J. Differential Equations , 176 : 470 – 493 .
   Web of Science ®Google Scholar
• Wang , W. D. and Zhao , X. Q. 2004 . An epidemic model in a patchy environment . Math. Biosci. , 190 : 97 – 112 .
   PubMed Web of Science ®Google Scholar
• Xu , D. , Feng , Z. , Allen , L. J.S. and Swihart , R. K. 2006 . A Spatially structure metapopulation model with patch dynamics . J. Theor. Biol. , 239 : 469 – 481 .
   PubMed Web of Science ®Google Scholar
• Zhao , X. Q. 2003 . Dynamical Systems in Population Biology , New York : Springer .
   Google Scholar