Monarch butterfly spatially discrete advection model

Mathematical Biosciences

Volumn 190, Issue 2, 2004, Pages 183-202

  Yakubu, Abdul Aziz ^a   Sáenz, Roberto ^b   Stein, Julie ^c   Jones, Laura E ^d  

^a HOWARD UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT EL PASO   (United States)

^c NEW COLLEGE OF FLORIDA   (United States)

^d Cornell University ^*  (United States)

Author keywords

Compensatory dynamics; Contest competition; Fecundity function; Metapopulation; Migration; Monarch butterfly; Overcompensatory dynamics; Scramble competition

Indexed keywords

POPULATION STATISTICS;

MONARCH BUTTERFLY; POPULATION CYCLES;

BIODIVERSITY;

BUTTERFLY; CONTEST COMPETITION; FECUNDITY; INTRASPECIFIC COMPETITION; MIGRATION; POPULATION CYCLE; SCRAMBLE COMPETITION;

ARTICLE; BREEDING; BUTTERFLY; CANADA; DIAPAUSE; FERTILITY; INTRASPECIFIC COMPETITION; MATHEMATICAL COMPUTING; METAPOPULATION; MEXICO; NONHUMAN; POPULATION DYNAMICS; POPULATION MIGRATION; POPULATION MODEL; REPRODUCTIVE PROCEDURES; SURVIVAL TIME; UNITED STATES;

ANIMAL MIGRATION; ANIMALS; BUTTERFLIES; MODELS, BIOLOGICAL; POPULATION DYNAMICS;

DANAUS PLEXIPPUS; PAPILIONOIDEA;

EID: 3242738611     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2004.03.002     Document Type: Article

References (60)

1. Allen J.C., Schaffer W.M., Rosko D. Chaos reduces species extinction by amplifying local population noice. Nature (London). 364:1993;229
2. Allen L.J.S. Persistence, extinction, and critical patch number for island populations. J. Math. Biol. 4(6):1987;617
3. Barker J.F., Herman W.S. On the neuroendocrinology of reproduction in the Monarch butterfly. J. Exp. Zool. 183:1973;1
4. Begon M., Harper J.L., Townsend C.R. Ecology: individuals, populations and communities. 1996;Blackwell Science, Oxford
5. Brauer F., Castillo-Chávez C. Mathematical Models in Population Biology and Epidemiology. 2001;Springer, New York
6. Brower L.P. New perspectives on the migration biology of the Monarch butterfly Danaus plexippus L. Rankin M.A. Migration: Mechanisms and Adaptive Significance. 1985;748 University of Texas, Austin, TX
7. Castillo-Chavez C., Yakubu A.-A. Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments. Castillo-Chavez C., Blower S., van den Driessche P., Kirschner D., Yakubu A.-A. Mathematical Approaches For Emerging and Reemerging Infectious Diseases: An Introduction. 2002;Springer, Berlin
8. Comins H.N., Hassell M.P., May R.M. The spatial dynamics of host-parasitoid systems. J. Anim. Ecol. 61:1992;735
9. Day J.R., Possingham H.P. A stochastic metapopulation model with variability in patch size and position. Theor. Popul. Biol. 48:1995;333
10. Den Boer P.J. On the survival of populations in a heterogeneous and variable environment. Oecologia. 50:1981;39
11. Franke J.E., Yakubu A.-A. Extinction and persistence of species in discrete competitive systems with a safe refuge. J. Math. Anal. Appl. 23:1996;746
12. Fujita K. Systems analysis of an acarine predator-prey system 11: interactions in discontinuous environment. Res. Popul. Ecol. 25:1983;387
13. Gillman M., Hails R. An Introduction to Ecological Modelling: Putting Practice into Theory. 1997;Blackwell Science, Oxford
14. Gilpin M., Hanski I. Metapopulation dynamics: Empirical and Theoretical Investigations. 1991;Academic Press, New York
15. Gurney W.S.C., Nisbet R.M. Predator-prey fluctuations in patchy environments. J. Anim. Ecol. 47:1978;85
16. Hanski I., Gilpin M. Metapopulation Biology: Ecology, Genetics, and Evolution. 1997;Academic Press, New York
17. Hanski I., Pöyra J., Pakkala T., Kuussaari M. Multiple equilibria in metapopulation dynamics. Nature. 377:1995;618
18. Hastings A. Dynamics of a single species in a spatially varying environment - the stabilizing role of high dispersal rates. J. Math. Biol. 16:1982;49
19. Herman W.S. The endocrine basis of reproductive inactivity in Monarch butterflies overwintering in central California. J. Insect Physiol. 19:1997;1883
20. Hilborn R. The effect of spatial heterogeneity on the persistence of predator-prey interactions. Theor. Popul. Biol. 8:1975;346
21. Iwasa Y., Roughgarden J. Intraspecific competition among metapopulations with space-limited subpopulations. Theor. Popul. Biol. 30:1986;194
22. Karieva P. Population dynamics in spatially complex environments: theory and data. Philos. Trans. R. Soc. London B. 330:1990;175
23. Kindlmann P., Dixon A.F.G., Dostalkova I. Role of aging and temperature in shaping reaction norms and fecundity functions in insects. J. Evol. Biol. 14:2001;835
24. Kishimoto K. Coexistence of any number of species in the Lotka-Volterra competitive system over two patches. Theor. Popul. Biol. 38:1990;149
25. Knight A. Spring remigration of the Monarch butterfly in north-central Florida: estimating population parameters using mark-recapture. Biol. J. Linnean Soc. 68:1999;531
26. Li T.-Y., Yorke J.A. Period three implies chaos. Am. Math. Month. 82:1975;985
27. Lorenz E.N. The problem of deducing the climate from the governing equations. Tellus. 16:1964;1
28. Levin S.A. Dispersion and population interactions. Am. Nat. 108:1974;207
29. S.B. Malcolm, B.J. Cockrell, L.P. Brower, Spring recolonization of eastern North America by the Monarch butterfly: successive brood or sweep migration? Biology and Conservation of the Monarch Butterfly. Natural History Museum of Los Angeles County, 1993
30. May R.M. Biological populations obeying difference equations: stable points, stable cycles, and chaos. J. Theor. Biol. 51:1975;511
31. May R.M. Simple mathematical models with very complicated dynamics. Nature. 261:1975;459
32. May R.M., Oster G.F. Bifurcations and dynamic complexity in simple ecological models. Am. Nat. 110:1976;573
33. Monarch Lab, UMN. Available from
34. Nee S., May R.M. Dynamics of metapopulations: habitat destruction and competitive coexistence. J. Anim. Ecol. 61:1992;37
35. Nachman G. Temporal and spatial dynamics of an acrine predator-prey system. J. Anim. Ecol. 50:1981;435
36. Nicholson A.J. Compensatory reactions of populations to stresses, and their evolutionary significance. Aust. J. Zool. 2:1954;1
37. Nusse H.E., Yorke J.A. Dynamics: Numerical Explorations. 1998;Springer, New York
38. Oberhauser K. Fecundity, lifespan, and egg mass in butterflies: effects of male-derived nutrients and female size. Funct. Ecol. 11(2):1997;166
39. Okubo A., Levin S. Diffusion and Ecological Problems: Modern Perspectives. 2001;Springer, Berlin
40. Pielou E.C. Modeling Ecology. 1977;John Wiley and Sons, New York. p. 385
41. Reeve J.D. Environmental variability migration and persistence in host-parasitoid systems. Am. Nat. 132:1988;810
42. Ricker W.E. Stock and recruitment. J. Fish. Res. Bd. Canada. 11(5):1954;559
43. Roff D.A. The evolution of life histories. 1992;Chapman and Hall, New York
44. Rowe L., Ludwig D. Size and timing of metamorphosis in complex life cycles: time constraints and variation. Ecology. 72(2):1991;413
45. Sabelis M.W., Diekmann O. Overall population stability despite local extinction: the stabilizing influence of prey dispersal from predator-invaded patches. Theor. Pop. Biol. 34:1988;169
46. R. Sáenz, J. Stein, Intraspecific competition in the population of Danaus plexippus (L.), MTBI Department of Biological Statistics and Computational Biology Cornell University Technical Reports, 2002
47. Smith H.L. Cooperative systems of differential equations with concave nonlinearities. Nonlinear Anal. Theory Methods Appl. 10(10):1986;1037
48. Swengel A.B. Population fluctuations of the Monarch in the fourth of July butterfly count 1977-1994. Am. Midl. Nat. 134:1995;205
49. Tilman D., Karieva P. Spatial Ecology. 1997;Princeton University, Princeton, NJ
50. Urquhart F.A. The Monarch Butterfly: International Traveler. 1987;Nelson-Hall, Chicago, IL
51. Urquhart F.A. The Monarch Butterfly. 1960;University of Toronto, Canada
52. Vance R.R. The effects of dispersal on population stability in one-species population-growth models. Am. Nat. 123(2):1984;230
53. Walton R.K. Monarch migration project, fall 1996. Peregrine Observer. 19:1997;31
54. Walton R.K., Brower L.P. Monitoring the fall migration of the Monarch butterfly Danaus plexippus (Nymphalidae: Danainae) in eastern North America: 1991-1994. J. Lepidopterists' Soc. 50:1996;1
55. Walton R.K. Tracking North American Monarchs. Part I. East Am. Butterflies. 1(3):1993;11
56. Yakubu A.-A., Castillo-Chavez C. Interplay between local dynamics and dispersal in discrete-time metapopulation models. J. Theor. Biol. 218:2002;273
57. Yakubu A.-A. Discrete-time metapopulation dynamics and unidirectional dispersal. J. Diff. Equat. Appl. 9(7):2003;633
58. Yakubu A.-A. Prey dominance in discrete predator-prey systems with a prey refuge. Math. Biosci. 144:1997;155
59. Yamaguti M. Chaos with special reference to mathematical ecology. Math. Sci. 16(183):1978;5
60. Yodzis P. Introduction to Theoretical Ecology. 1989;Harper & Rowe, New York