References
- Cantrell , RS and Cosner , C . 2003 . “ Spatial Ecology via Reaction-Diffusion Equations ” . In Series in Mathematical and Computational Biology , Chichester, , UK : John Wiley and Sons .
- Okubo , A and Levin , SA . 2001 . “ Diffusion and Ecological Problems: Modern Perspectives ” . In Interdisciplinary Applied Mathematics, , 2nd , Vol. 14 , Berlin : Springer .
- Shigesada , N and Kawasaki , K . 1997 . Biological Invasions: Theory and Practice, Oxford Series in Ecology and Evolution , Oxford, New York, Tokyo : Oxford University Press .
- Skellam , JG . 1951 . Random dispersal in theoretical populations . Biometrika , 38 : 196 – 218 .
- 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 .
- Hastings , A . 1983 . Can spatial variation alone lead to selection for dispersal? . Theoret. Popul. Biol. , 33 : 311 – 314 .
- Kirkland , S , Li , C-K and Schreiber , SJ . 2006 . On the evolution of dispersal in patchy environments . SIAM J. Appl. Math. , 66 : 1366 – 1382 .
- McPeek , MA and Holt , RD . 1992 . The evolution of dispersal in spatially and temporally varying environments . Amer. Nat. , 140 : 1010 – 1027 .
- Holt , RD and McPeek , MA . 1996 . Chaotic population dynamics favours the evolution of dispersal . Amer. Nat. , 148 : 709 – 718 .
- 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 .
- Clobert , J , Danchin , E , Dhondt , AA and Nichols , JD . 2001 . Dispersal , Oxford : Oxford University Press .
- Holyoak , M , Leibol , MA and Holt , RD . 2005 . Metacommunities: Spatial Dynamics and Ecological Communities , Chicago : Chicago University Press .
- Abrams , PA . 2007 . Habitat choice in predator-prey systems: Spatial instability due to interacting adaptive movements . Amer. Nat. , 169 : 581 – 594 .
- Amarasekare , P . 2008 . Spatial dynamics of foodwebs . Annu. Rev. Ecol. Evol. Syst. , 39 : 479 – 500 .
- Koelle , K and Vandermeer , J . 2005 . Dispersal-induced desynchronization: From metapopulations to metacommunities . Ecol. Lett. , 8 : 167 – 175 .
- Belgacem , F and Cosner , C . 1995 . The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment . Can. Appl. Math. Quart. , 3 : 379 – 397 .
- Cosner , C and Lou , Y . 2003 . Does movement toward better environments always benefit a population? . J. Math. Anal. Appl. , 277 : 489 – 503 .
- Cantrell , RS , Cosner , C and Lou , Y . 2006 . Movement towards better environments and the evolution of rapid diffusion . Math. Biosci. , 204 : 199 – 214 .
- Cantrell , RS , Cosner , C and Lou , Y . 2007 . Advection mediated coexistence of competing species . Proc. R. Soc. Edinb. , 137A : 497 – 518 .
- Chen , XF , Hambrock , R and Lou , Y . 2008 . Evolution of conditional dispersal: A reaction–diffusion–advection model . J. Math. Biol. , 57 : 361 – 386 .
- Hambrock , R and Lou , Y . 2009 . The evolution of conditional dispersal strategy in spatially heterogeneous habitats . Bull. Math. Biol. , 71 : 1793 – 1817 .
- Y. Lou, Some challenging mathematical problems in evolution of dispersal and population dynamics, pp. 171–205 in A. Friedman, ed., Tutorials in Mathematical Bioscience Vol. IV: Evolution and Ecology, Lecture Notes in Mathematics, Vol. 1922, Springer, Berlin, 2007.
- Lam , KY . 2009 . Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model, preprint ,
- Friedman , A . 1969 . Partial Differential Equations , New York : Holt, Rinehart, and Winston .
- Protter , MH and Weinberger , HF . 1984 . Maximum Principles in Differential Equations, , 2nd , Berlin : Springer-Verlag .
- Chen , XF 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 .
- Lam , KY and Ni , WM . 2009 . preprint
- Pao , CV . 1992 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
- Hess , P . 1991 . Periodic Parabolic Boundary Value Problems and Positivity , Harlow, , UK : Longman Scientific & Technical .
- Gilbarg , D and Trudinger , N . 1983 . Elliptic Partial Differential Equation of Second Order, , 2nd , Berlin : Springer-Verlag .
- Dancer , EN and Hess , P . 1991 . Stability of fixed points for order-preserving discrete-time dynamical systems . J. Reine Angew. Math. , 419 : 125 – 139 .
- Hsu , S , Smith , H and Waltman , P . 1996 . Competitive exclusion and coexistence for competitive systems on ordered Banach spaces . Trans. Amer. Math. Soc. , 348 : 4083 – 4094 .
- Smith , H . 1995 . Monotone Dynamical Systems, Mathematical Surveys and Monographs, 41. , Providence, , Rhode Island, USA : American Mathematical Society .