The role of prey taxis in biological control: A spatial theoretical model

American Naturalist

Volumn 162, Issue 1, 2003, Pages 61-76

  Sapoukhina, Natalia ^a,b   Tyutyunov, Yuri ^a   Arditi, Roger ^b  

^a SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

^b CEMAGREF   (France)

Author keywords

Predator prey model; Reaction diffusion advection; Spatial heterogeneity; Trophic function

Indexed keywords

BIOLOGICAL CONTROL; ECOLOGICAL MODELING; POPULATION DYNAMICS; PREDATOR-PREY INTERACTION; SPATIAL ANALYSIS; TAXIS;

ANIMAL; ARTICLE; BIOLOGICAL PEST CONTROL; COMPUTER SIMULATION; POPULATION DYNAMICS; PREDATION; THEORETICAL MODEL;

ANIMALS; COMPUTER SIMULATION; MODELS, THEORETICAL; PEST CONTROL, BIOLOGICAL; POPULATION DYNAMICS; PREDATORY BEHAVIOR;

ANIMALIA;

EID: 0038505662     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/375297     Document Type: Article

References (88)

1. Arditi, R., and A. A. Berryman. 1991. The biological control paradox. Trends in Ecology & Evolution 6:32.
2. Arditi, R., and L. R. Ginzburg. 1989. Coupling in predator-prey dynamics: ratio-dependence. Journal of Theoretical Biology 139:311-326.
3. Arditi, R., and H. Saïah. 1992. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 73:1544-1551.
4. Arditi, R., Y. Tyutyunov, A. Morgulis, V. Govorukhin, and I. Senina. 2001. Directed movement of predators and the emergence of density-dependence in predator-prey models. Theoretical Population Biology 59:207-221.
5. Basset, A., D. L. DeAngelis, and E. Diffendorfer. 1997. The effect of functional response on stability of a grazer population on a landscape. Ecological Modelling 101:153-162.
6. Beddington, J. R. 1975. Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology 45:331-340.
7. Beddington, J. R., C. A. Free, and J. H. Lawton. 1975. Dynamic complexity in predator-prey models framed in difference equation. Nature 225:58-60.
8. _. 1978. Characteristics of successful natural enemies in models of biological control of insect pest. Nature 273:513-519.
9. Berezovskaya, F. S., and G. P. Karev. 1999. Bifurcations of running waves in population models with taxis. Uspekhi Fizicheskikh Nauk 9:1011-1024. (In Russian.)
10. Berezovskaya, F. S., N. V. Davydova, A. S. Isaev, G. P. Karev, and R. G. Khlebopros. 1999. Migration waves and the spatial dynamics of phytophagous insects. Siberian Ecological Journal 4:347-357. (In Russian.)
11. Berg, H. C., and D. A. Brown. 1972. Chemotaxis in Escheria coli analyzed by three-dimensional tracking. Nature 239:500-504.
12. Berryman, A. A. 1999. The theoretical foundations of biological control. Pages 3-21 in B. A. Hawkins and H. V. Cornell, eds. Theoretical approaches to biological control. Cambridge University Press, Cambridge.
13. Bohannan, B. J. M., and R. E. Lenski. 1997. Effect of resource enrichment on a chemostat community of bacteria and bacteriophage. Ecology 78:2303-2315.
14. _. 1999. Effect of prey heterogeneity on the response of a model food chain to resource enrichment. American Naturalist 153:73-82.
15. Bondarenko, N. V., and B. P. Asiakin. 1975. The behavior of predator Aphidoletes aphidimyza Rond. and of the other aphidophagous in dependence on prey population density. Pages 8-15 in V. P. Pristavkin, ed. Insect behavior as a basis for elaboration of measures against agricultural and forest's pests. Naukova Dumka, Kiev. (In Russian.)
16. Briggs, C. F., W. W. Murdoch, and R. M Nisbet. 1999. Recent developments in theory for biological control of insect pests by parasitoids. Pages 22-42 in B. A. Hawkins and H. V. Cornell, eds. Theoretical approaches to biological control. Cambridge University Press, Cambridge.
17. Chesson, P. L., and W. W. Murdoch. 1986. Aggregation of risk: relationships among host-parasitoid models. American Naturalist 127:696-715.
18. Cosner, C., D. L. DeAngelis, J. S. Ault, and D. B. Olson. 1999. Effects of spatial grouping on the functional response of predators. Theoretical Population Biology 56:65-75.
19. Crawley, M. J. 1997. Plant-herbivore dynamics. Pages 463-465 in M. J. Crawley, ed. Plant ecology. Blackwell Scientific, Oxford.
20. Cuddington, K. M., and P. Yodzis. 2000. Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model. Theoretical Population Biology 58:259-278.
21. Czárán, T. 1998. Spatiotemporal models of population and community dynamics. Chapman & Hall, London.
22. DeAngelis, D. L., R. A. Goldstein, and R. V. O'Neill. 1975. A model for trophic interaction. Ecology 56:881-892.
23. Dixon, A. F. G. 2000. Insect predator-prey dynamics: ladybird beetles and biological control. Cambridge University Press, Cambridge.
24. Edelstein-Keshet, L. 1988. Mathematical models in biology. McGraw-Hill, New York.
25. Ferran, A., L. Giuge, R. Tourniaire, J. Gambier, and D. Fournier. 1998. An artificial non-flying mutation to improve the efficiency of the ladybird Harmonia axyridis in the biological control of aphids. Biocontrol 43:53-64.
26. Fisher, R. A. 1937. The wave of advance of advantageous genes. Annals of Eugenics 7:355-369.
27. Flierl, G., D. Grünbaum, S. Levin, and D. Olson. 1999. From individuals to aggregations: the interplay between behavior and physics. Journal of Theoretical Biology 196:397-454.
28. Free, C. A., J. R. Beddington, and J. H. Lawton. 1977. On the inadequacy of simple models of mutual interference for parasitism and predation. Journal of Animal Ecology 36:375-389.
29. Gause, G. F. 1935. Experimental demonstrations of Volterra's periodic oscillations in the numbers of animals. Journal of Experimental Biology 12:44-48.
30. Godfray, H. C. J. 1994. Parasitoids, behavioral and evolutionary ecology. Princeton University Press, Princeton, N.J.
31. Govorukhin, V. N., A. B. Morgulis, I. N. Senina, and Y. V. Tyutyunov. 1999. Modelling of active migrations of spatially dispersed populations. Obozrenie Prikladnoy i Promyshlennoy Matematiki 6:271-295. (In Russian.)
32. Govorukhin, V. N., A. B. Morgulis, and Y. V. Tyutyunov. 2000. Slow taxis in a predator-prey model. Doklady Mathematics 61:420-422. (Translated from Doklady Akademii Nauk 372:730-732.)
33. Grünbaum, D. 1997. Advection-diffusion equations for generalized tactic searching behaviours. Journal of Mathematical Biology 38:169-194.
34. _. 1998. Using spatially explicit model to characterize performance in heterogeneous landscape. American Naturalist 151:97-115.
35. Gurianova, T. M. 1984. The behavioral mechanisms of hosts parasitoid-entomophagous interactions and regulation of insects abundance. Pages 42-48 in B. P. Manteifel, ed. Insect behavior. Nauka, Moscow. (In Russian.)
36. Hassell, M. P. 1976. The dynamics of competition and predation. Edward Arnold, London.
37. _. 1978. The dynamics of arthropod predator-prey systems. Princeton University Press, Princeton, N.J.
38. Hassell, M. P., and R. M. Anderson. 1989. Predator-prey and host-pathogen interactions. Pages 147-196 in J. M. Cherrett, ed. Ecological concepts: the contribution of ecology to an understanding of the natural world. Blackwell Scientific, Oxford.
39. Hassell, M. P., and H. C. J. Godfray. 1992. The population biology of insect parasitoids. Pages 265-292 in M. J. Crawley, ed. Natural enemies: the population biology of predators, parasites and diseases. Blackwell Scientific, Oxford.
40. Hassell, M. P., and R. M. May. 1973. Stability in insect host-parasite models. Journal of Animal Ecology 42:693-726.
41. _. 1974. Aggregation in predators and insect parasites and its effect on stability. Journal of Animal Ecology 43:567-594.
42. Hassell, M. P., and G. C. Varley. 1969. New inductive population model for insect parasites and its bearing on biological control. Nature 223:1133-1137.
43. Hastings, A. 1990. Spatial heterogeneity and ecological models. Ecology 71:426-428.
44. Hawkins, B. A., M. B. Thomas, and M. E. Hochberg. 1993. Refuge theory and biological control. Science (Washington, D.C.) 262:1429-1432.
45. Haydon, D. T., and A. L. Lloyd. 1999. On the origins of the Lotka-Volterra equations. Bulletin of the Ecological Society of America 3:205-206.
46. Holling, C. S. 1959. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Canadian Entomologist 91:293-320.
47. Huston, M. A. 1994. Biological diversity: the coexistence of species on changing landscapes. Cambridge University Press, Cambridge.
48. Ives, A. R., P. Kareiva, and R. Perry. 1993. Response of a predator to variation in prey density at three hierarchical scales: lady beetles feeding on aphids. Ecology 74:1929-1938.
49. Izhevsky, S. S. 1990. Introduction and use of entomophagous insects. Agropromizdat, Moscow. (In Russian.)
50. Jansen, V. A. A., and A. M. de Roos. 2000. The role of space in reducing predator-prey cycles. Pages 183-201 in U. Dieckmann, R. Law, and J. A. J. Metz, eds. The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge.
51. Kareiva, P. 1982. Experimental and mathematical analyses of herbivore movement: quantifying the influence of plant spacing and quality on foraging discrimination. Ecological Monographs 52:261-282.
52. _. 1987. Habitat fragmentation and the stability of predator-prey interactions. Nature 326:388-390.
53. Kareiva, P., and G. Odell. 1987. Swarms of predators exhibit "preytaxis" if individual predators use area-restricted search. American Naturalist 130:233-270.
54. Keller, E., and L. A. Segel. 1971. Travelling bands of chemotactic bacteria: a theoretical analysis. Journal of Theoretical Biology 30:235-248.
55. Kindlmann, P., and A. F. G. Dixon. 1993. Optimal foraging in ladybird beetles (Coleoptera: Coccinellidae) and its consequences for their use in biological control. European Journal of Entomology 90:443-450.
56. Kolmogorov, A. N., I. G. Petrovsky, and N. S. Piskunov. 1937. Research of a diffusion equation, joint with increase of substance amount, and application to a biological problem. Moscow University Bulletin of Mathematics Series A 6:1-26. (In Russian.)
57. Kuznetsov, Y. A. 1998. Elements of applied bifurcation theory. Springer, New York.
58. Levin, S. A. 1977. A more functional response to predator-prey stability. American Naturalist 108:207-228.
59. Levin, S. A., and L. A. Segel. 1976. Hypothesis for origin of planktonic patchiness. Nature 259:659.
60. Luck, R. F. 1990. Evaluation of natural enemies for biological control: a behavioral approach. Trends in Ecology & Evolution 5:196-199.
61. Luckinbill, L. S. 1973. Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology 54:1320-1327.
62. Lynch, L. D., R. G. Bowers, M. Begon, and D. J. Thompson. 1998. A dynamics refuge model and population regulation by insect parasitoids. Journal of Animal Ecology 67:270-279.
63. Malchow, H. 2000. Motion instabilities in prey-predator systems. Journal of Theoretical Biology 204:639-647.
64. May, R. M. 1978. Host-parasitoid systems in patchy environments: a phenomenological model. Journal of Animal Ecology 47:833-844.
65. McFarland, D. J. 1985. Animal behavior: psychobiology, ethology and evolution. Pitman, London.
66. Mimura, M., and K. Kawasaki. 1980. Spatial segregation in competitive interaction-diffusion equations. Journal of Mathematical Biology 9:49-64.
67. Mimura, M., and J. D. Murray. 1978. On a diffusive prey-predator model which exhibits patchiness. Journal of Theoretical Biology 75:249-252.
68. Mimura, M., and M. Yamaguti. 1982. Pattern formation in interacting and diffusive systems in population biology. Advances in Biophysics 15:19-65.
69. Murdoch, W., and A. Stewart-Oaten. 1989. Aggregation by parasitoids and predators: effects on equilibrium and stability. American Naturalist 134:288-310.
70. Murdoch, W., J. Chesson, and P. L. Chesson. 1985. Biological control in theory and practice. American Naturalist 140:41-58.
71. Murray, J. D. 1993. Mathematical biology. Springer, New York.
72. Nechols, J. R., and J. J. Obrycki. 1989. Comparative behavioral and ecological studies in relation to biological control: an overview. Journal of the Kansas Entomological Society 62:146-147.
73. Okubo, A. 1980. Diffusion and ecological problems: mathematical models. Biomathematics. Vol. 10. Springer, Berlin.
74. Okubo, A., and H. C. Chiang. 1974. An analysis of the kinematics of swarming of Anarete pritchardi Kim (Diptera: Cecidomyiidae). Researches on Population Ecology (Kyoto) 16:1-42.
75. Okubo, A., H. C. Chiang, and C. C. Ebbesmeyer. 1977. Acceleration field of individual midges, Anarete pritchardi (Diptera: Cecidomyiidae), within a swarm. Canadian Entomologist 109:149-156.
76. Parrish, J. K., and P. Turchin. 1997. Individual decisions, traffic rules, and emergent pattern: a Lagrangian analysis. Pages 126-142 in J. K. Parrish, W. M. Hamner, and C. T. Prewitt, eds. Animal aggregations: three-dimensional measurement and modelling. Cambridge University Press, Cambridge.
77. Petrovskii, S. V., and H. Malchow. 1999. A minimal model of pattern formation in a prey-predator system. Mathematical and Computer Modelling 29:49-63.
78. _. 2001. Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theoretical Population Biology 59:157-174.
79. Poggiale, J. C., J. Michalski, and R. Arditi. 1998. Emergence of donor control in patchy predator-prey systems. Bulletin of Mathematical Biology 60:1149-1166.
80. Rotheray, G. E. 1979. The biology and host searching behavioral of a cynipid parasite of aphidophagous syrphid larvae. Ecological Entomology 4:75-82.
81. Sapoukhina, N. Y. 2002. Modeling spatial dynamics of trophic communities with application to biological control. Ph.D. thesis. Institut National Agronomique Paris-Grignon, Paris.
82. Sapoukhina, N. Y., and Y. V. Tyutyunov. 2000. The effect of insects migrations on success of natural enemies at the biological control of pests. Pages 36-57 in G. A. Ougolnitsky, ed. Computer simulation: ecology. Higher School Book, Moscow. (In Russian.)
83. Svirezhev, Y. M., and D. O. Logofet. 1983. Stability of biological communities. Mir, Moscow.
84. Turchin, P. 1998. Quantitative analysis of movement. Sinauer, Sunderland, Mass.
85. Tyutyunov, Y. V., N. Y. Sapoukhina, A. B. Morgulis, and V. N. Govorukhin. 2001. Mathematical model of active migrations as feeding strategy in trophic communities. Zhurnal Obshchei Biologii 62:253-262. (In Russian.)
86. Viktorov, G. A. 1975. The role of behavior in regulation of insect population density. Pages 26-33 in V. P. Pristavkin, ed. Insect behavior as a basis for elaboration of measures against agricultural and forest's pests. Naukova Dumka, Kiev. (In Russian.)
87. Waage, J. K., and N. J. Mills. 1992. Biological control. Pages 412-430 in M. J. Crawley, ed. Natural enemies: the population biology of predators, parasites and diseases. Blackwell Scientific, Oxford.
88. Winder, L., C. J. Alexander, J. M. Holland, C. Woolley, and J. N. Perry. 2001. Modelling the dynamic spatio-temporal response of predators to transient prey patches in the field. Ecology Letters 4:568-576.