Erratum to Integrodifference equations, Allee effects, and invasions (J Math Biol, (2002), 44, (150-168), 10.1007/s002850100116);Integrodifference equations, Allee effects, and invasions

Journal of Mathematical Biology

Volumn 44, Issue 2, 2002, Pages 150-168

  Wang, Mei Hui ^a   Kot, Mark ^b   Neubert, Michael G ^c  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

^c WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

Allee effects; Integrodifference equations; Invasion models; Traveling waves

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOLOGY; MATHEMATICAL COMPUTING; POPULATION DENSITY; POPULATION DYNAMICS;

ANIMALS; ECOLOGY; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; POPULATION DENSITY; POPULATION DYNAMICS;

EID: 0036483294     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-013-0643-0     Document Type: Erratum

References (61)

1. Allee, W.C.: The Social Life of Animals. W. W. Norton and Co., New York 1938
2. Allen, E.J., Allen, L.J.S., Gilliam, X.: Dispersal and competition models for plants. J. Math. Biol. 34, 445-481 (1996)
3. Andersen, M.: Properties of some density-dependent integrodifference- equation population models. Math. Biosci. 104, 135-157 (1991)
4. Anselone, P.M., Sloan, I.H.: Numerical solutions of integral equations on the half line II: the Wiener-Hopf case. J. Integ. Eqs. Appl. 1, 203-225 (1988)
5. Apostol, T.M.: Mathematical Analysis. Addition-Wesley Publishing Company, Inc. 1974
6. Atkinson, K.: The numerical solution of integral equations on the half-line. SIAM J. Numer. Anal. 6, 375-397 (1969)
7. Brewster, C.C., Allen, J.C.: Spatiotemporal model for studying insect dynamics in large-scale cropping systems. Environ. Entomol. 26, 473-482 (1997)
8. Brewster, C.C., Allen, J.C., Schuster, D.J., Stansly, P.A.: Simulating the dynamics of Bemisia argentifoli (Homoptera: Aleyrodidae) in an organic cropping system with a spatiotemporal model. Environ. Entomol. 26, 603-616 (1997)
9. Britton, N.F.: Reaction-Diffusion Equations and their Applications to Biology. Academic Press, London 1986
10. Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resource. John Wiley and Sons, New York 1990
11. Clark, J.S.: Why trees migrate so fast: confronting theory with dispersal biology and the paleorecord. Am. Nat. 152, 204-224 (1998)
12. Cruickshank, I., Gurney, W.S.C., Veitch, A.R.: The characteristics of epidemics and invasions with thresholds. Theor. Pop. Biol. 56, 279-292 (1999)
13. Drake, J.A., Mooney, H.A., di Castri, F., Groves, R.H., Kruger, F.J., Rejmanek, M., Williamson, M.: Biological Invasions: A Global Perspective. John Wiley and Sons, Chichester, UK 1989
14. Friedman, A.: Foundations of Modern Analysis. Holt, Rinehart, and Winston, Inc., New York 1970
15. Gohberg, I.C., Fel'dman, I.A.: Convolution Equations and Projection methods for their solution. American Mathematical Society, Providence, Rhode Island 1974
16. Gruntfest, Y., Arditi, R., Dombrovsky, Y.: A fragmented population in a varying environment. J. Theor. Biol. 185, 539-547 (1997)
17. Groom, M.J.: Allee effects limit population viability of an annual plant. Am. Nat. 151, 487-496 (1998)
18. Hardin, D.P., Takac, P., Webb, G.F.: A comparison of dispersal strategies for survival of spatially heterogeneous populations. SIAM J. Appl. Math. 48, 1396-1423 (1988a)
19. Hardin, D.P., Takac, P., Webb, G.F.: Asymptotic properties of a continuous-space discrete-time population model in a random environment. J. Math. Biol. 26, 361-374 (1988b)
20. Hardin, D.P., Takac, P., Webb, G.F.: Dispersion population models discrete in time and continuous in space. J. Math. Biol. 28, 1-20 (1990)
21. Hart, D.R., Gardner, R.H.: A spatial model for the spread of invading organisms subject to competition. J. Math. Biol. 35, 935-948 (1997)
22. Hastings, A., Higgins, K.: Persistence of transients in spatially structured ecological models. Science 263, 1133-1136 (1994)
23. Hengeveld, R.: Dynamics of Biological Invasions. Chapman and Hall, London, UK 1990
24. Hochstadt, H.: Integral Equations. John Wiley and Sons, Inc. New York 1973
25. Hoog, F.D., Sloan I.H.: The finite-section approximation for integral equations on the half-line. J. Austral. Math. Soc. Ser. B 28, 415-434 (1987)
26. Hopf, F.A., Hopf, F.W.: The role of the Allee effect in species packing. Theor. Pop. Biol. 27, 27-50 (1985)
27. Hopper K.R., Roush, R.T.: Mate finding, dispersal, number released, and the success of biological control introductions. Ecol. Entomol. 18, 321-331 (1993)
28. Hosono, Y.: The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model. Bull. Math. Biol. 60, 435-448 (1998)
29. Keener, J., Sneyd, J.: Mathematical Physiology. Springer-Verlag, New York 1998
30. Kot, M.: Diffusion-driven period-doubling bifurcations. Biosystems 22, 279-287 (1989)
31. Kot, M.: Discrete-time traveling waves: ecological examples. J. Math. Biol. 30, 413-436 (1992)
32. Kot, M., Schaffer, W.M.: Discrete-time growth-dispersal models. Math. Biosci. 80, 109-136 (1986)
33. Kot, M., Lewis, M.A., van den Driessche, P.: Dispersal data and the spread of invading organisms. Ecology 77, 2027-2042 (1996)
34. Kunin, W.E.: Sex and the single mustard: population density and pollinator behavior effects on seed-set. Ecology 74, 2145-2160 (1993)
35. Kuussaari, M., Saccheri, I., Camara, M., Hanski, I.: Allee effect and population dynamics in the Glanville fritillary butterfly. Oikos 82, 384-392 (1998)
36. Lamont, B.B., Klinkhamer, P.G.L., Witkowski, E.T.F.: Population fragmentation may reduce fertility to zero in Banksia goodii - a demonstration of the Allee effect. Oecologia 94, 446-450 (1993)
37. Latore, J., Gould, P., Mortimer, A.M.: Spatial dynamics and critical patch size of annual plant populations. J. Theor. Biol. 190, 277-285 (1998)
38. Lewis, M.A., Kareiva, P.: Allee dynamics and the spread of invading organisms. Theor. Pop. Biol. 43, 141-158 (1993)
39. Lewis, M.A., van den Driessche, P.: Waves of extinction from sterile insect release. Math. Biosci. 116, 221-247 (1993)
40. Lui, R.: A nonlinear integral operator arising from a model in population genetics, I. Monotone initial data. SIAM J. Math. Anal. 13, 913-937 (1982a)
41. Lui, R.: A nonlinear integral operator arising from a model in population genetics, II. Initial data with compact support. SIAM J. Math. Anal. 13, 938-953 (1982b)
42. Lui, R.: Existence and stability of traveling wave solutions of a nonlinear integral operator. J. Math. Biol. 16, 199-220 (1983)
43. McCarthy, M.A.: The Allee effect, finding mates and theoretical models. Ecol. Model. 103, 99-102 (1997)
44. Mollison, D.: Dependence of epidemics and population velocities on basic parameters. Math. Biosc. 107, 255-287 (1991)
45. Mooney, H.A., Drake, J.A.: Ecology of Biological Invasions of North America and Hawaii. Springer-Verlag, New York (1986)
46. Neubert, M.G., Kot, M., Lewis, M.A.: Dispersal and pattern formation in a discrete-time predator-prey model. Theor. Pop. Biol. 48, 7-43 (1995)
47. Neubert, M.G.: A simple population model with qualitatively uncertain dynamics. J. Theor. Biol. 189, 399-411 (1997)
48. Neubert, M.G., Kot, M., Lewis, M.A.: Invasion speeds in fluctuating environments. Proc. R. Soc. Lond. B 267, 1603-1610 and 267, 2568-2569 (2000)
49. Neubert, M.G., Caswell, H.: Dispersal and demography: calculation and sensitivity analysis of invasion speeds for stage-structured populations. Ecology. 81, 1613-1628 (2000)
50. Pipkin, A.C.: A Course on Integral Equations. Springer-Verlag, New York 1991
51. Press, W.H., Flannery B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge 1986
52. Ruiz, G.M., Fofonoff, P.W., Carlton, J.T., Wonham, M.J., Hines, A.H.: Invasion of coastal marine communities in north America: apparent patterns, processes, and biases. Anim. Rev. Ecol. Syst. 31, 481-531 (2000)
53. Shigesada, N., Kawasaki, K.: Biological Invasions: Theory and Practice. Oxford University Press, Oxford, UK 1997
54. Sloan, I.H., Spence, A.: Integral Equations on the half-line: a modified finite-section approximation. Math. Comp. 47, 589-595 (1986)
55. van den Bosch, F., Metz, J.A.J., Diekmann, O.: The velocity of population spatial expansion. J. Math. Biol. 28, 529-565 (1990)
56. Van Kirk, R.W., Lewis, M.A.: Integrodifference models for persistence in fragmented habitats. Bull. Math. Biol. 59, 107-138 (1997)
57. Veit, R.R., Lewis, M.A.: Dispersal, population growth, and the Allee effect, Dynamics of the House Finch invasion of eastern North America. Am. Nat. 148, 255-274 (1996)
58. Wang, M.H., Kot, M.: Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 173, 83-97 (2001)
59. Weinberger, H.F.: Asymptotic behavior of a model of population genetics. In, Chadam, J. (ed.), Nonlinear Partial Differential Equations and Applications. Lecture Notes in Mathematics 648, 47-98 (1978)
60. Weinberger, H.F.: Long-time behavior of a class of biological models. SIAM J. Math. Anal. 13, 353-396 (1982)
61. Wheeden, R.L., Zygmund, A.: Measure and Integral: An Introduction to Real Analysis. Marcel Dekker, Inc. New York 1977