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Original Articles

On several conjectures from evolution of dispersal

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Pages 117-130 | Received 24 Jun 2010, Accepted 30 Sep 2010, Published online: 24 Jan 2011

References

  • Belgacem , F. and Cosner , C. 1995 . The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment . Can. Appl. Math. Q. , 3 : 379 – 397 .
  • Bezuglyy , A. and Lou , Y. 2010 . Reaction-diffusion models with large advection coefficients . Appl. Anal. , 89 : 983 – 1004 .
  • R.S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Series in Mathematical and Computational Biology, John Wiley and Sons, Chichester, UK, 2003
  • Cantrell , R. S. , Cosner , C. and Lou , Y. 2006 . Movement towards better environments and the evolution of rapid diffusion . Math. Biosci. , 204 : 199 – 214 .
  • Cantrell , R. S. , Cosner , C. , DeAngelis , D. L. and Padrón , V. 2007 . The ideal free distribution as an evolutionarily stable strategy . J. Biol. Dyn. , 1 : 249 – 271 .
  • Cantrell , R. S. , Cosner , C. and Lou , Y. 2007 . Advection mediated coexistence of competing species . Proc. R. Soc. Edinb. , 137A : 497 – 518 .
  • Cantrell , R. S. , Cosner , C. and Lou , Y. 2008 . Approximating the ideal free distribution via reaction-diffusion-advection equations . J. Diff. Eqs , 245 : 3687 – 3703 .
  • Cantrell , R. S. , Cosner , C. and Lou , Y. 2009 . Evolution of dispersal in heterogeneous landscape, Spatial Ecology, Spatial Ecology Mathematical and Computational Biology Series , Edited by: Cantrell , R. S. , Cosner , C. and Ruan , S. 213 – 229 . Boca Raton , FL : Chapman Hall/CRC Press .
  • Cantrell , R. S. , Cosner , C. and Lou , Y. 2010 . Evolution of dispersal and ideal free distribution . Math. Biosci. Eng. , 7 : 17 – 36 .
  • Chen , X. F. and Lou , Y. 2008 . Principal eigenvalue and eigenfunction of elliptic operator with large convection and its application to a competition model . Indiana Univ. Math. J. , 57 : 627 – 658 .
  • Chen , X. F. , Hambrock , R. and Lou , Y. 2008 . Evolution of conditional dispersal: A reaction-diffusion-advection model . J. Math. Biol. , 57 : 361 – 386 .
  • Cosner , C. 2005 . A dynamic model for the ideal-free distribution as a partial differential equation . Theor. Popul. Biol. , 67 : 101 – 108 .
  • Cosner , C. and Lou , Y. 2003 . Does movement toward better environments always benefit a population? . J. Math. Anal. Appl. , 277 : 489 – 503 .
  • Dancer , E. N. 1995 . “ Positivity of maps and applications ” . In Topological Nonlinear Analysis , Edited by: Matzeu , M. and Vignoli , A. 303 – 340 . Boston : Birkhauser . Prog. Nonlinear Diff. Eqs Appl. 15
  • Dieckmann , U. 1997 . Can adaptive dynamics invade? . Trends Ecol. Evol. , 12 : 128 – 131 .
  • Diekmann , O. 2003 . A beginner's guide to adaptive dynamics . Banach Cent. Publ. , 63 : 47 – 86 .
  • Dieckmann , U. and Law , R. 1996 . The dynamical theory of coevolution: A derivation from stochastic ecological processes . J. Math. Biol. , 34 : 579 – 612 .
  • Dieckmann , U. , O'Hara , B. and Weisser , W. 1999 . The evolutionary ecology of dispersal . Trends Ecol. Evol. , 14 : 88 – 90 .
  • Dockery , J. , Hutson , V. , Mischaikow , K. and Pernarowski , M. 1998 . The evolution of slow dispersal rates: A reaction-diffusion model . J. Math. Biol. , 37 : 61 – 83 .
  • Geritz , S. A.H. , Kisdi , E. , Meszena , G. and Metz , J. A.J. 1998 . Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree . Evol. Ecol. , 12 : 35 – 57 .
  • Gilbarg , D. and Trudinger , N. 1983 . Elliptic Partial Differential Equation of Second Order , 2 , Berlin : Springer-Verlag .
  • Hambrock , R. and Lou , Y. 2009 . The evolution of conditional dispersal strategy in spatially heterogeneous habitats . Bull. Math. Biol. , 71 : 1793 – 1817 .
  • Hanski , I. 1999 . Metapopulation Ecology , Oxford : Oxford University Press .
  • Hastings , A. 1983 . Can spatial variation alone lead to selection for dispersal? . Theor. Popul. Biol. , 24 : 244 – 251 .
  • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer, Berlin, 1981
  • P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes Mathematics Series 247, Longman Scientific & Technical, John Wiley & Sons, New York, 1991
  • Holt , R. D. 1985 . Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution . Theor. Popul. Biol. , 28 : 181 – 208 .
  • Holt , R. D. and McPeek , M. A. 1996 . Chaotic population dynamics favors the evolution of dispersal . Am. Nat. , 148 : 709 – 718 .
  • Hsu , S. , Smith , H. and Waltman , P. 1996 . Competitive exclusion and coexistence for competitive systems on ordered Banach spaces . Trans. Am. Math. Soc. , 348 : 4083 – 4094 .
  • Hutson , V. , Mischaikow , K. and Poláčik , P. 2001 . The evolution of dispersal rates in a heterogeneous time-periodic environment . J. Math. Biol. , 43 : 501 – 533 .
  • Hutson , V. , Martinez , S. , Mischaikow , K. and Vickers , G. T. 2003 . The evolution of dispersal . J. Math. Biol. , 47 : 483 – 517 .
  • Kao , C. Y. , Lou , Y. and Shen , W. X. 2010 . Random dispersal vs non-local dispersal . Discrete Contin. Dyn. Syst. Ser. A. , 26 : 551 – 596 .
  • Kirkland , S. , Li , C.-K. and Schreiber , S. J. 2006 . On the evolution of dispersal in patchy environments . SIAM J. Appl. Math. , 66 : 1366 – 1382 .
  • Lam , K. Y. 2011 . Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model . J. Diff. Eqs. , 250 : 161 – 181 .
  • K.Y. Lam, Limiting profiles of semilinear elliptic equations with large advection in population dynamics II, preprint
  • Lam , K. Y. and Ni , W. M. 2010 . Limiting profiles of semilinear elliptic equations with large advection in population dynamics . Discrete Contin. Dyn. Syst. Ser. A , 28 : 1051 – 1067 .
  • Matano , H. 1984 . Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems . J. Fac. Sci. Univ. Tokyo , 30 : 645 – 673 .
  • McPeek , M. A. and Holt , R. D. 1992 . The evolution of dispersal in spatially and temporally varying environments . Am. Nat. , 140 : 1010 – 1027 .
  • Padrón , V. and Trevisan , M. C. 2006 . Environmentally induced dispersal under heterogeneous logistic growth . Math. Biosci. , 199 : 160 – 174 .
  • Protter , M. H. and Weinberger , H. F. 1984 . Maximum Principles in Differential Equations , 2 , Berlin : Springer-Verlag .
  • H. Smith, Monotone Dynamical Systems, Mathematical Surveys and Monographs 41, American Mathematical Society, Providence, RI, 1995
  • Wang , X. F. 2000 . Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemotaxis and dynamics . SIAM J. Math. Anal. , 31 : 535 – 560 .
  • Wang , X. F. and Wu , Y. P. 2002 . Qualitative analysis on a chemotactic diffusion model for two species competing for a limited resource . Q. Appl. Math. , LX : 505 – 531 .
  • Cosner , C. , Davila , J. and Martinez , S. Evolutionary stability of ideal free nonlocal dispersal . J. Biol. Dyn. , submitted
  • Xu , D. and Feng , Z. 2009 . A metapopulation model with local competitions . Discrete Contin. Dyn. Syst. Ser. B , 12 : 495 – 510 .