References
- Fisher , RA . 1937 . The advance of advantageous genes . Ann. Eugenics , 7 : 355 – 369 .
- Skellam , JG . 1951 . Random dispersal in theoretical populations . Biometrika , 38 : 196 – 218 .
- Cantrell , RS and Cosner , C . 2003 . “ Spatial Ecology via Reaction–Diffusion Equations, Series ” . In Mathematical and Computational Biology , New York : Wiley .
- Kot , M . 2001 . Elements of Mathematical Ecology , Cambridge : Cambridge University Press .
- Weinberger , HF . 1982 . Long-time behavior of a class of biological models . SIAM J. Math. Anal. , 13 : 353 – 396 .
- Hastings , A , Cuddington , K , Davies , KF , Dugaw , CJ , Elmendorf , A , Freestone , A , Harrison , S , Holland , M , Lambrinos , J , Malvadkar , U , Melbourne , BA , Moore , K , Taylor , C and Thomson , D . 2005 . The spatial spread of invasions: new developments in theory and evidence . Ecol. Lett. , 8 : 91 – 101 .
- Shigesada , N , Kawasaki , K and Teramoto , E . 1986 . Traveling periodic waves in heterogeneous environments . Theor. Popul. Biol. , 30 : 143 – 160 .
- Kinezaki , N , Kawasaki , K , Takasu , F and Shigesada , N . 2003 . Modeling biological invasions into periodically fragmented environments . Theor. Pop. Biol. , 64 : 291 – 302 .
- Kinezaki , N , Kawasaki , K and Shigesada , N . 2006 . Spatial dynamics of invasion in sinusoidally varying environments . Popul. Ecol. , 48 : 263 – 270 .
- Lutscher , F , Lewis , MA and McCauley , E . 2006 . The effects of heterogeneity on population persistence and invasion in rivers . Bull. Math. Biol. , 68 ( 8 ) : 2129 – 2160 .
- Weinberger , HF . 2002 . On spreading speeds and travelling waves for growth and migration models in a periodic habitat . J. Math. Biol. , 45 : 511 – 548 .
- Berestycki , H , Hamel , F and Roques , L . 2005 . Analysis of the periodically fragmented environment model. I. Species persistence . J. Math. Biol. , 51 : 75 – 113 .
- Holmes , MH . 1995 . “ Introduction to Perturbation Methods ” . In Texts in Applied Mathematics, Vol. 20 , New York : Springer Verlag .
- Powell , J and Zimmermann , NE . 2004 . Multiscale analysis of active seed dispersal contributed to resolving Reid's paradox . Ecology , 85 ( 2 ) : 490 – 506 .
- Othmer , HG . 1983 . A continuum model for coupled cells . J. Math. Biol. , 17 : 351 – 369 .
- Dewhirst , S and Lutscher , F . 2009 . Dispersal in heterogeneous habitats: Thresholds, spatial scales and approximate rates of spread . Ecology , 90 ( 5 ) : 1338 – 1345 .
- Turchin , P . 1998 . Quantitative Analysis of Movement , Sunderland, MS : Sinauer Association .
- Hutson , V , Martinez , S , Mischaikow , K and Vickers , GT . 2003 . The evolution of dispersal . J. Math. Biol. , 46 : 483 – 517 .
- Lutscher , F , Pachepsky , E and Lewis , MA . 2005 . The effect of dispersal patterns on stream populations . SIAM Rev. , 47 ( 4 ) : 749 – 772 .
- Medlock , J and Kot , M . 2003 . Spreading diseases: Integro-differential equations new and old . Math. Biosci. , 184 : 201 – 222 .
- Mollison , D . 1991 . Dependence of epidemic and population velocities on basic parameters . Math. Biosci. , 107 : 255 – 287 .
- Engel , KJ and Nagel , R . 2000 . One-parameter Semigroups for Linear Evolution Equations , New York : Springer .
- van Kirk , RW and Lewis , MA . 1997 . Integrodifference models for persistence in fragmented habitats . Bull. Math. Biol. , 59 ( 1 ) : 107 – 137 .
- Fagan , WF and Lutscher , F . 2006 . The average dispersal success approximation: A bridge linking home range size, natal dispersal, and metapopulation dynamics to critical patch size and reserve design . Ecol. Appl. , 16 ( 2 ) : 820 – 828 .
- Botsford , LW , Hastings , A and Gaines , SD . 2001 . Dependence of sustainability on the configuration of marine reserves and larval dispersal distance . Ecol. Lett. , 4 : 144 – 150 .
- Lui , R . 1989 . Biological growth and spread modeled by systems of recursions. I. Mathematical theory . Math. Biosci. , 93 : 269 – 295 .
- Neubert , MG and Caswell , H . 2000 . Demography and dispersal: Calculation and sensitivity analysis of invasion speeds for structured populations . Ecology , 81 ( 6 ) : 1613 – 1628 .
- Aronson , DG . 1983 . “ The role of diffusion in mathematical population biology: Skellam revisited ” . In Mathematics in Biology and Medicine , Edited by: Levin , SA . Vol. 57 , 2 – 6 . Berlin : Springer . Lecture Notes on Biomathematics
- 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 .
- Lutscher , F , Pachepsky , E and Lewis , MA . 2005 . The effect of dispersal patterns on stream populations . SIAM Appl. Math. , 65 ( 4 ) : 1305 – 1327 .