Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts

Journal of Mathematical Biology

Volumn 36, Issue 6, 1998, Pages 515-549

  Edelstein Keshet, Leah ^a   Watmough, James ^b   Grunbaum, Daniel ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Locust swarms; Swarm migration; Travelling band solutions

Indexed keywords

EID: 0141576240     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050112     Document Type: Article

References (41)

1. Albrecht, F. O. 1967, Polymorphism Phasaire et Biologie des Acridiens Migrateurs, Masson et Cie, Paris
2. Alt, W. 1980, Biased random walk models for chemotaxis and related diffusion approximation, J. Math. Biol. 9: 147-177
3. Alt, W. 1985, Degenerate diffusion equations with drift functional modelling aggregation, Nonlinear Analysis, Theory, Methods and Applications 9: 811-836
4. Aoki, K. 1987, Gene-culture waves of advance, J. Math. Biol. 25: 453-464
5. Bertsch, M., Gurtin, M. E., Hilhorst, D. and Peletier, L. 1984, On interacting populations that disperse to avoid crowding: The effect of a sedentary colony, J. Math. Biol. 19: 1-12
6. Bertsch, M., Gurtin, M. E. Hilhorst, D. and Peletier, L. 1985, On interacting populations that disperse to avoid crowding: preservation of segregation, J. Math. Biol. 23: 1-13
7. Cohen, D. S. and Murray, J. D. 1981, A generalized diffusion model for growth and dispersal in a population, J. Math. Biol. 12: 237-249
8. Conley, C. and Fife, P. 1982, Critical manifolds, travelling waves, and an example from population genetics, J. Math. Biol. 14: 159-176
9. Dunbar, S. R. 1983, Travelling wave solutions of diffusive Lotka-Volterra equations, J. Math. Biol. 17: 11-32
10. Edelstein-Keshet, L. 1988, Mathematical Models in Biology, McGraw Hill (formerly Random House), New York
11. Ellis, P. E. 1953, The gregarious behaviour of marching Locusta migratoria migratorioides (R. F.) hoppers, J. exp. Biol. 30: 214-233
12. Ermentrout, G. B. and Rinzel, J. 1981, Waves in a simple, excitable or oscillatory reaction-diffusion model, J. Math. Biol. 11: 269-294
13. Fisher, R. 1937, The wave of advance of advantageous genes, Ann. Eugen. London 7: 355-369
14. Greenberg, J. and Alt, W. 1987, Stability results for a diffusion equation with functional drift approximating a chemotaxis model, Trans AMS 300: 235-258
15. Grunbaum, D. 1994, Translating stochastic density-dependent individual behavior to a continuum model of animal swarming, J. Math. Biol. 33: 139-161
16. Grunbaum, D. 1997, Advection-diffusion equations for generalized tactic searching behaviors, J. Math. Biol., in press
17. Gueron, S. and Liron, N. 1989, A model of herd grazing as a travelling wave, chemotaxis and stability, J. Math. Biol. 27: 595-608
18. Heiland, I. S. 1983, Diffusion models for the dispersal of insects near an attractive center, J. Math. Biol. 18: 103-122
19. Kawasaki, K. 1978, Diffusion and the formation of spatial distribution, Mathematical Sciences 16(183): 47-52
20. Keller, E. F. and Odell, G. M. 1975, Necessary and sufficient conditions for chemotactic bands, Math. Biosci. 27: 309-317
21. Keller, E. F. and Segel, L. A. 1971, Traveling bands of chemotactic bacteria: a theoretical analysis, J. theor Biol. 30: 235-248
22. Kennedy, J. S. 1951, The migration of the desert locust (Schistocerca gregaria Forsk.), Phil. Trans. R. Soc. Lond. B. 235: 163-290
23. Ludwig, D., Aronson, D. G., and Weinberger, H. F. 1979, Spatial patterning of the spruce budworm, J. Math B. 8: 217-258
24. Mogilner, A. 1995, Modelling Spatio-Angular Patterns in Cell Biology, Ph.D. thesis, University of British Columbia, Vancouver, BC
25. Mogilner, A. and Edelstein-Keshet, L. 1997, A non-local model for a swarm, Submitted for publication
26. Mogilner, A., Edelstein-Keshet, L., and Ermentrout, G. B. 1996, Selecting a common direction: II. Peak-like solutions representing total alignment of cell clusters, J. Math. Biol. 34: 811-842
27. Mogilner, A. and Gueron, S. 1997, Pattern formation in a system with positive and negative chemotaxis, J. Math. Biol., in press
28. Murray, J. D. 1989, Mathematical Biology, Springer Verlag, New York
29. Nagai, T. and Ikeda, T. 1991, Travelling waves in a chemotactic model, J. Math. Biol. 30: 169-184
30. Novick-Cohen, A. and Segel, L. A. 1984, A gradually slowing travelling band of chemotactic bacteria, J. Math. Biol. 19: 125-132
31. Ochoa, F. L. 1984, A generalized reaction diffusion model for spatial structure formed by mobile cells, Biosystems, 17: 35-50
32. Odell, G. M. 1980, Biological Waves, in L. A. Segel (ed.), Mathematical Models in Molecular and Cellular Biology, Chapt. 6.7, pp 523-567, Cambridge University Press
33. Odell, G. M. and Keller, E. F. 1976, Traveling bands of chemotactic bacteria revisited, J. theor Biol. 56: 243-247
34. Okubo, A. 1980, Diffusion and Ecological Problems: Mathematical Models, Springer Verlag, New York
35. Othmer, H. G., Dunbar, S. R. and Alt, W. 1988, Models of dispersal in biological systems, J. Math. Biol. 26: 263-298
36. Pfistner, B. 1989, A one-dimensional model for the swarming behaviour of Myxobacteria, in W. Alt and G. Hoffmann (eds.), Biological Motion, pp 556-563, Springer Verlag
37. Rainey, R. C. 1989, Migration and Meteorology: Flight behaviour and the atmospheric environment of locusts and other migrant pests, Oxford Science, Oxford
38. Skellam, J. G. 1951, Random dispersal in theoretical populations, Biometrica 38: 196-218
39. Uvarov, B. P. 1928, Locusts and Grasshoppers, Imperial Bureau of Entomology, London
40. Waloff, Z. 1962, Flight activity of different phases of the desert locust in relation to plague dynamics, in F. O. Albrecht (ed.), Physiologie, Comportement et Ecologie des Acridiens en Rapport avec la Phase, pp 201-211, Centre National de la Recherche Scientifique, Paris
41. Waloff, Z. 1972, Observations on the airspeeds of freely flying locusts, Anim. Behav. 20: 367-372