H. Berestycki and F. Hamel, Front propagation in periodic excitable media. Communications on Pure and Applied Mathematics,55 (2002), 949–1032.
H. Berestycki, N. Nadirashvili and F. Hamel, The speed of propagation for KPP type problems. I: Periodic framework. Journal of the European Mathematical Society,7 (2005), 173–214.
F. van den Bosch, R. Hengeveld and J.A.J. Metz, Analyzing the velocity of animal range expansion. J. Biogeography,19 (1992), 135–150.
M. Bramson, Convergence of solutions of the Kolmogorov equation to traveling waves. Mem. Am. Math. Soc.,285 (1983), 1–190.
S.R. Broadbent and D.G. Kendall, The random walk of Trichostrongylus retortaeformis. Biometrics,9 (1953), 460–466
J.S. Clark, Why trees migrate so fast: confronting theory with dispersal biology and the paleorecord. Am. Nat.,152 (1998), 204–224.
S.P. Ellner, A. Sasaki, Y. Haraguchi and H. Matsuda, Speed of invasion in lattice population models: pair-edge approximation. J. Math. Biol.,36 (1998), 469–484.
R.A. Fisher, The wave of advance of advantageous genes. Annals of Eugenics. (Lond.),7 (1937), 355–369.
M.I. Freidlin, On wavefront propagation in periodic media. Stochastic Analysis Applications, (ed. M. Pinsky) Advances in Probability and Related Topics,7, M. Dekker, New-York, 1984, 147–166.
M.I. Freidlin, Limit theorems for large deviations and reaction-diffusion equations. Ann. Probab.,13 (1985), 639–675.
J. Gartner and M.I. Freidlin, On the propagation of concentration waves in periodic and random media. Soviet Math. Dokl.,20 (1979), 1282–1286.
A. Hastings, Models of spatial spread: Is the theory complete? Ecology,77 (1996), 1675–1679.
A. Hastings, K. Cuddington, K.F. Davies, C.J. Dugaw, S. Elmendorf, A. Freestone, S. Harrison, M. Holland, J. Lambrinos, U. Malvadkar, B.A. Melbourne, K. Moore, C. Taylor and D. Thomson, The spatial spread of invasions: new developments in theory and evidence. Ecology Letters,8 (2005), 91–101.
S.I. Higgins and D.M. Richardson, Predicting plant migration rates in a changing world: The Role of Long-Distance Dispersal. Am. Nat.,153 (1999), 464–475.
S.I. Higgins, D.M. Richardson and R.M. Cowling, Modeling invasive plant spread: The role of plant-environment interactions and model structure. Ecology,7 (1996), 2043–2054.
K. Kawasaki, F. Takasu, H. Caswell and N. Shigesada, How does stochasticity in colonization accelerate speeds of invasion in a cellular automaton model? Ecol. Res.,21 (2006), 334–345.
N. Kinezaki, K. Kawasaki and N. Shigesada, Spatial dynamics of invasion in sinusoidally varying environments. Population Ecology,48 (2006), 263–270.
N. Kinezaki, K. Kawasaki, F. Takasu and N. Shigesada, Modeling biological invasions into periodically fragmented environments. Theor. Popul. Biology,64 (2003), 291–302.
R.W. Van Kirk and M.A. Lewis, Integrodifference models for persistence in fragmented habitats. Bull. Math. Biology,59 (1997), 107–137.
M. Kot, M.A. Lewis and F. van den Driessche, Dispersal data and the spread of invading organisms. Ecology,77 (1996), 2027–2042.
M. Kot, J. Medlock, T. Reluga and D.B. Walton, Stochasticity, invasions, and branching random walks. Theor. Popul. Biology,66 (2004), 175–184.
M.A. Lewis and S. Pacala, Modeling and analysis of stochastic invasion processes. J. Math. Biol.,41 (2000), 387–429.
M.A. Lewis, M.G. Neubert, H. Caswell, J.S. Clark and K. Shea, A guide to calculating discrete-time invasion rates from data. In Conceptual ecology and invasion biology: Reciprocal approaches to nature (eds. M.W. Cadotte, S.M. McMahon and T. Fukami), Springer, 2006, 169–192.
F. Lutscher, M.A. Lewis and E. McCauley, Effects of heterogeneity on spread and persistence in rivers. Bull. Math. Biology,68 (2006), 2129–2160.
J.A.J. Metz, D. Mollison and F. van den Bosch, The dynamics of invasion waves. The Geometry of Ecological Interactions: Simplfying Spatial Complexity (eds. O. Dieckmann, R. Law and J.A.J. Metz), Cambridge University Press, 2000, 482–512.
D. Mollison, Spatial contact model for ecological and epidemic spread. J. Rol. Stat. Soc. B,39 (1977), 283–326
M.G. Neubert and H. Caswell, Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations. Ecology,81 (2000), 1613–1628.
M.G. Neubert, M. Kot and M.A. Lewis, Invasion speeds in fluctuating environments. Proc. R. Soc. Lond. B,267 (2000), 1603–1610.
A. Okubo, Diffusion and Ecological Problems: Mathematical Models. Springer-Verlag, New York, 1980.
A. Okubo and S.A. Levin, Diffusion and Ecological Problems: New Perspectives (second edition). Springer-Verlag, New York, 2001.
W.E. Ricker, Stock and recruitment. J. Fisheries Research Board of Canada,11 (1954), 559–623.
T.C. Robbins and M.A. Lewis, Modeling population spread in heterogeneous environments using integrodifference equations. preprint, 2006.
M.W. Shaw, Modeling stochastic processes in plant pathology. Annu. Rev. Phytopathol,32 (1994), 523–544.
N.Shigesada and K. Kawasaki, Biological Invasions; Theory and Practice. Oxford University Press, 1997.
N. Shigesada and K. Kawasaki, Invasion and species range expansion: effects of long-distance dispersal. Dispersal Ecology (eds. J.M. Bullock, R.E. Kenward and R.S. Hails), Blackwell, Oxford, 2002, 350–373.
N. Shigesada, K. Kawasaki and Y. Takeda, Modeling stratified diffusion in biological invasions. Am. Nat.,146 (1995), 229–251.
N. Shigesada, K. Kawasaki and E. Teramoto, Traveling periodic waves in heterogeneous environments. Theor. Popul. Biology,30 (1986), 143–160.
J.G. Skellam, Random dispersal in theoretical populations. Biometrika,38 (1951), 196–218.
M. Slatkin, Gene flow and selection in a cline. Genetics,75 (1973), 733–756.
F. Takasu, N. Yamamoto, K. Kawasaki, T. Togashi, Y. Kishi and N. Shigesada, Modeling the expansion of an introduced tree disease. Biological Invasions,2 (2000), 141–150.
R.R. Veit and M.A. Lewis, Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. Am. Nat.,148 (1996), 255–274.
H.F. Weinberger, Long-time behavior of a class of biological models. SIAM J. Math. Anal.,13 (1982), 353–396.
H.F. Weinberger, On spreading speeds and traveling waves for growth and migration models in a periodic habitat. J. Math. Biol.,45 (2002), 511–548.
E.J. Williamson, The distribution of larvae of randomly moving insect. Austral. J. Biol. Sci.,14 (1961), 598–604.
E.J. Williamson and S. Harrison, The Biotic and abiotic limits to the spread of exotica revegetation species in oak woodland and serpentine habitats. Ecol. Appl.,12 (2002), 40–51.
K.A. With, The landscape ecology of invasive spread. Cons. Biol.,16 (2002), 1192–1203.
J. Xin, Front propagation in heterogeneous media. SIAM Review,42 (2000), 161–230.