The effects of density-dependent dispersal on the spatiotemporal dynamics of cyclic populations

Journal of Theoretical Biology

Volumn 254, Issue 2, 2008, Pages 264-274

  Smith, Matthew J ^a,b,c   Sherratt, Jonathan A ^b   Lambin, Xavier ^c  

^a MICROSOFT RESEARCH   (United States)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

AUTO; Invasion; Lambda omega; Landscape obstacle; Larch budmoth; Numerical continuation; Predator prey; Wave train

Indexed keywords

COMPARATIVE STUDY; DENSITY DEPENDENCE; DISPERSAL; MOTH; POPULATION CYCLE; POPULATION DISTRIBUTION; TROPHIC INTERACTION;

ARTICLE; DIFFUSION; LANDSCAPE; POPULATION CYCLE; POPULATION DENSITY DEPENDENCE; POPULATION DISPERSAL; POPULATION DYNAMICS; POPULATION MODEL; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; SPECTRAL SENSITIVITY;

ANIMAL MIGRATION; ANIMALS; ECOSYSTEM; MODELS, BIOLOGICAL; MODELS, STATISTICAL; POPULATION DENSITY; POPULATION DYNAMICS; PREDATORY BEHAVIOR; TIME;

ANIMALIA; ZEIRAPHERA DINIANA;

EID: 50149087095     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2008.05.034     Document Type: Article

References (66)

1. Amarasekare P. Interactions between local dynamics and dispersal: insights from single species models. Theor. Popul. Biol. 53 (1998) 44-59
2. Ashwin P., Bartuccelli M.V., Bridges T.J., and Gourley S.A. Travelling fronts for the KPP equation with spatio-temporal delay. Z. Angew. Math. Phys. 53 (2002) 103-122
3. Auchmuty J.F.G., and Nicolis G. Bifurcation analysis of reaction-diffusion equations 3. Chemical oscillations. Bull. Math. Biol. 38 (1976) 325-350
4. Baltensweiler W., Benz G., Bovey P., and Delucchi V. Dynamics of Larch bud moth populations. Annu. Rev. Entomol. 22 (1977) 79-100
5. Berryman A. Population cycles: causes and analysis. In: Berryman A. (Ed). Population Cycles: The Case for Trophic Interactions vol. 1 (2002), Oxford University Press, Oxford 3-28
6. Best A.S., Johs K., Munkemuller T., and Travis J.M.J. Which species will successfully track climate change? The influence of intraspecific competition and density dependent dispersal on range shifting dynamics. Oikos 116 (2007) 1531-1539
7. Bjørnstad O.N., Peltonen M., Liebhold A.M., and Baltensweiler W. Waves of Larch budmoth outbreaks in the European Alps. Science 298 (2002) 1020-1023
8. Bowler D.E., and Benton T.G. Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics. Biol. Rev. 80 (2005) 205-225
9. Brandt M.J., and Lambin X. Movement patterns of a specialist predator, the weasel Mustela nivalis exploiting asynchronous cyclic field vole Microtus agrestis populations. Acta Theriol. 52 (2007) 13-25
10. Cantrell R.S., Cosner C., and Fagan W.F. Competitive reversals inside ecological reserves: the role of external habitat degradation. J. Math. Biol. 37 (1998) 491-533
11. Codling E.A., Plank M.J., and Benhamou S. Random walk models in biology (review). J. R. Soc. Interface 5 (2008) 813-834
12. Denno R.F., and Peterson M.A. Density dependent disperal and its consequences for population dynamics. In: Cappucccino N., and Price P.W. (Eds). Population Dynamics: New Approaches and Synthesis (1995), Academic Press, New York 113-130
13. Doedel E., Keller H.B., and Kernevez J.P. Numerical analysis and control of bifurcation problems (I): bifurcation in finite dimensions. Int. J. Bifurcat. Chaos 1 (1991) 493-520
14. Doedel E., Keller H.B., and Kernevez J.P. Numerical analysis and control of bifurcation problems (II): bifurcation on infinite dimensions. Int. J. Bifurcat. Chaos 1 (1991) 723-745
15. Doedel E.J. AUTO: a program for the automatic bifurcation analysis of autonomous systems. Congr. Numer. 30 (1981) 265-284
16. Drover J.D., and Ermentrout B. Nonlinear coupling near a degenerate Hopf (Bautin) bifurcation. SIAM J. Appl. Math. 63 (2003) 1627-1647
17. Ermentrout B., Chen X.F., and Chen Z.X. Transition fronts and localized structures in bistable reaction-diffusion equations. Physica D 108 (1997) 147-167
18. Garvie M.R. Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB. Bull. Math. Biol. 69 (2007) 931-956
19. Giraudoux P., Delattre P., Habert M., Quere J.P., Deblay S., Defaut R., Duhamel R., Moissenet M.F., Salvi D., and Truchetet D. Population dynamics of fossorial water vole (Arvicola terrestris scherman): a land use and landscape perspective. Agric. Ecosyst. Environ. 66 (1997) 47-60
20. Hagan P.S. Spiral waves in reaction-diffusion equations. SIAM J. Appl. Math. 42 (1982) 762-786
21. Hauzy C., Hulot F.D., Gins A., and Loreau M. Intra- and interspecific density dependent dispersal in an aquatic prey-predator system. J. Anim. Ecol. 76 (2007) 552-558
22. Huu T.N., Auger P., Lett C., and Marva M. Emergence of global behaviour in a host-parasitoid model with density dependent dispersal in a chain of patches. Ecol. Complexity 5 (2008) 9-21
23. Ims R.A., and Andreassen H.P. Density dependent dispersal and spatial population dynamics. Proc. R. Soc. B-Biol. Sci. 272 (2005) 913-918
24. Ims R.A., and Hjermann D.O. Condition-dependent dispersal. In: Clobert J., et al. (Ed). Dispersal (2001), Oxford University Press, Oxford 203-216
25. Johnson D.M., Bjørnstad O.N., and Liebhold A.M. Landscape geometry and travelling waves in the Larch budmoth. Ecol. Lett. 7 (2004) 967-974
26. Johnson D.M., Bjørnstad O.N., and Liebhold A.M. Landscape mosaic induces traveling waves of insect outbreaks. Oecologia 148 (2006) 51-60
27. Johst K., and Brandl R. The effect of dispersal on local population dynamics. Ecol. Modelling 104 (1997) 87-101
28. Kopell N., and Howard L.N. Plane-wave solutions to reaction-diffusion equations. Stud. Appl. Math. 52 (1973) 291-328
29. Kuussaari M., Nieminen M., and Hanski I. An experimental study of migration in the Glanville fritillary butterfly Melitaea cinxia. J. Anim. Ecol. 65 (1996) 791-801
30. Lambin X., Elston D.A., Petty S.J., and MacKinnon J.L. Spatial asynchrony and periodic travelling waves in cyclic populations of field voles. Proc. R. Soc. London Ser. B-Biol. Sci. 265 (1998) 1491-1496
31. Lambin X., Aars J., and Piertney S.B. Dispersal, intraspecific competition, kin competition and kin facilitation: a review of the empirical evidence. In: Clobert J., et al. (Ed). Dispersal (2001), Oxford University Press, Oxford 110-122
32. Lutscher F. Density dependent dispersal in integrodifference equations. J. Math. Biol. 56 (2008) 499-524
33. Mackinnon J.L., Petty S.J., Elston D.A., Thomas C.J., Sherratt T.N., and Lambin X. Scale invariant spatio-temporal patterns of field vole density. J. Anim. Ecol. 70 (2001) 101-111
34. Massey F.P., Smith M.J., Lambin X., and Hartley S.E. Are silica defences in grasses driving vole population cycles?. Biol. Lett. 13 (2008) 1234 Published online 15/05/08, doi:10.1098/rsbl.2008.0106
35. Matthysen E. Density dependent dispersal in birds and mammals. Ecography 28 (2005) 403-416
36. Moss R., Elston D.A., and Watson A. Spatial asynchrony and demographic travelling waves during red grouse population cycles. Ecology 81 (2000) 981-989
37. Murray J.D. Multi-Species Waves and Practical Applications, Mathematical Biology II: Spatial Models and Biomedical Applications vol. II (2003), Springer, Berlin pp. 1-67
38. Murray J.D., Stanley E.A., and Brown D.L. On the spread of rabies among foxes. Proc. R. Soc. B-Biol. Sci. 229 (1986) 111-150
39. Pearce I.G., Chaplain M.A.J., Schofield P.G., Anderson A.R.A., and Hubbard S.F. Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications. J. Theor. Biol. 241 (2006) 876-886
40. Peltonen M., Liebhold A.M., Bjørnstad O.N., and Williams D.W. Spatial synchrony in forest insect outbreaks: roles of regional stochasticity and dispersal. Ecology 83 (2002) 3120-3129
41. Petrovskii S.V., and Malchow H. A minimal model of pattern formation in a prey-predator system. Math. Comput. Modelling 29 (1999) 49-63
42. Rademacher J.D.M., Sandstede B., and Scheel A. Computing absolute and essential spectra using continuation. Physica D 229 (2007) 166-183
43. Ranta E., and Kaitala V. Travelling waves in vole population dynamics. Nature 390 (1997) 456
44. Rosenzweig M.L., and MacArthur R.H. Graphical representation and stability conditions of predator-prey interaction. Am. Nat. 97 (1963) 209-223
45. Rouquette J.R., and Thompson D.J. Patterns of movement and dispersal in an endangered damselfly and the consequences for its management. J. Appl. Ecol. 44 (2007) 692-701
46. Royama T., MacKinnon W.E., Kettela E.G., Carter N.E., and Hartling L.K. Analysis of spruce budworm outbreak cycles in New Brunswick, Canada, since 1952. Ecology 86 (2005) 1212-1224
47. Russell C.A., Smith D.L., Childs J.E., and Real L.A. Predictive spatial dynamics and strategic planning for racoon rabies emergence in Ohio. Plos Biol. 3 (2005) 382-388
48. Saether B.-E., Engen S., and Lande R. Finite metapopulation models with density dependent migration and stochastic local dynamics. Proc. R. Soc. B-Biol. Sci. 266 (1999) 113-118
49. Sandstede B. Stability of travelling waves. In: Fiedler B. (Ed). Handbook of Dynamical Systems II (2002), North-Holland, Amsterdam 983-1055
50. Sandstede B., and Scheel A. Absolute and convective instabilities of waves on unbounded and large bounded domains. Physica D 145 (2000) 233-277
51. Schwartz M.K., Mills L.S., McKelvey K.S., Ruggiero L.F., and Allendorf F.W. DNA reveals high dispersal synchronizing the population dynamics of Canada lynx. Nature 415 (2002) 520-522
52. Sherratt J.A. On the evolution of periodic plane-waves in reaction-diffusion systems of lambda-omega type. SIAM J. Appl. Math. 54 (1994) 1374-1385
53. Sherratt J.A. Periodic travelling waves in cyclic predator-prey systems. Ecol. Lett. 4 (2001) 30-37
54. Sherratt J.A. Periodic travelling wave selection by Dirichlet boundary conditions in oscillatory reaction-diffusion systems. SIAM J. Appl. Math. 63 (2003) 1520-1538
55. Sherratt J.A., and Smith M.J. Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models. J. R. Soc. Interface 5 (2008) 483-505
56. Sherratt J.A., Eagan B.T., and Lewis M.A. Oscillations and chaos behind predator-prey invasion: mathematical artefact or ecological reality. Philos. Trans. R. Soc. B-Biol. Sci. 352 (1997) 21-38
57. Sherratt J.A., Lambin X., and Sherratt T.N. The effects of the size and shape of landscape features on the formation of traveling waves in cyclic populations. Am. Nat. 162 (2003) 503-513
58. Smith J.E., and Batzli G.O. Dispersal and mortality of prairie voles (Microtus ochrogaster) in fragmented landscapes: a field experiment. Oikos 112 (2006) 209-217
59. Smith M.J., and Sherratt J.A. The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems. Physica D 236 (2007) 90-103
60. Sutherland W.J., Gill J.A., and Norriss K. Density dependent dispersal in animals: concepts, evidence, mechanisms and consequences. In: Bullock J.M., et al. (Ed). Dispersal Ecology (2002), Blackwell, Oxford 113-133
61. Tenow O., Nilssen A.C., Bylund H., and Hogstad O. Waves and synchrony in Epirrita autumnata/Operophtera brumata outbreaks. I. Lagged synchrony: regionally, locally and among species. J. Anim. Ecol. 76 (2007) 258-268
62. Tuckerman L.S., and Barkley D. Bifurcation-analysis of the Eckhaus instability. Physica D 46 (1990) 57-86
63. Turchin P. Complex Population Dynamics: A Theoretical/Empirical Synthesis (2003), Princeton University Press, Princeton
64. Webb S.D., and Sherratt J.A. Oscillatory reaction-diffusion equations with temporally varying parameters. Math. Comp. Modelling 39 (2004) 45-60
65. Ydenberg R. Nomadic predators and geographical synchrony in microtine population cycles. Oikos 50 (1987) 270-272
66. Ylikarjula J., Alaja S., Laakso J., and Tesar D. Effects of patch number and dispersal patterns on population dynamics and synchrony. J. Theor. Biol. 207 (2000) 377-387