Predator-Prey Dynamics in Spatially Structured Populations: Manipulating Dispersal in a Coccinellid-Aphid Interaction

  • Peter Kareiva
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 54)

Abstract

Naturalists have long recognized that populations change not only as a result of birth and death, but also as a result of individual movement (Elton 1949). Only within the last decade, however, have mathematical ecologists given much attention to dispersal. Nonetheless, because theoretical advances have proceeded so rapidly, mathematical investigations of dispersal’s involvement in population dynamics have raced far ahead of empirical studies (see Levin 1978 for a review of the theory). Consequently, whereas there is a plethora of models connecting dispersal and interspecific interactions, none of these models have been tested in the field. The dearth of empirical work addressing theory in this area is especially evident in the literature on predator-prey systems; Huffaker’s (1958) classic “orange-andmites” experiment, which was published a quarter of a century ago, is still the key inspiration for most models of predator-prey interactions in patchy environments (cf Maynard Smith 1974, Hilborn 1975, Gurney and Nisbet 1978, Hassell 1980). Much more exploratory empirical work is clearly needed, both for evaluating existing models and indicating new theoretical avenues.

Keywords

Biomass Convection Prep Editing Stake 

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Literature Cited

  1. Banks, H.T. and Daniel, P.L. (1982). Estimation of variable coefficients in parabolic distributed systems. Lefschetz Cent. Dyn. Syst. Report#82–22.Google Scholar
  2. Banks, H.T., Daniel, P.L. and Kareiva, P. (1983). Estimation of temporally and spatially varying coefficients in models for insect dispersal. LCDS Report 83–14, June 1983, Brown University.Google Scholar
  3. Banks, H.T., Crowley, S.M. and Kunisch, K. (1981). Cubic spline approximation techniques for parameter estimation in distributed systems. LCDS Tech. Rep. 81–25, Brown University, Providence, RI.Google Scholar
  4. Banks, H.T. and Kareiva, P. (1983). Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models. J. Math. Biol. in press.Google Scholar
  5. Chesson, P. (1978). Predator-prey theory and variability. Ann. Rev. Ecol. Syst. 9: 323–347Google Scholar
  6. Dempster, J. (1957). The population dynamics of the Moroccan locust in Cyprus. Anti-Locust Bull. 27: 1–59.Google Scholar
  7. Elton, C. (1949). Population interspersion: an essay on animal community patterns. J. Ecol. 37: 1–23.Google Scholar
  8. Evans, E.W. (1980). Lifeways of the predatory stinkbugs: feeding and reproductive patterns of a generalist and specialist (Pentatomidae: Podisus maculiventris and Perillus circumcinctus). Ph.D. Diss., Cornell University, Ithaca, NY, USA. 147 pp.Google Scholar
  9. Gurney, W.S.C. and Nisbet, R.M. (1978). Predator-prey fluctuations in patchy environments. J. Aním. Ecol. 47: 85–102.Google Scholar
  10. Hämäläinen, M., Markkula, M. and Raij, T. (1975). Fecundity and larval voracity of four ladybird species (Coleoptera, Coccinellidae). Ann. Ent. Fenn. 41: 124–127.Google Scholar
  11. Hassell, M.P. (1978). The dynamics of arthropod predator-prey systems. Princeton University Press, Princeton, New Jersey, USA.Google Scholar
  12. Hassell, M.P. (1980). Some consequences of habitat heterogeneity for population dynamics. Oikos 35: 150–160.CrossRefGoogle Scholar
  13. Hassell, M.P. and May, R.M. (1974). Aggregation of predators and insect parasites and its effect on stability. J. Anim. Ecol. 43: 567–594.Google Scholar
  14. Hastings, A. (1978). Spatial heterogeneity and the stability of predator-prey systems: predator-mediated coexistence. Theor. Pop. Biol. 14: 380–395.Google Scholar
  15. Hilborn, R. (1975). The effect of spatial heterogeneity on the persistence of predator-prey interactions. Theor. Pop. Biol. 8: 346–355.Google Scholar
  16. Huffaker, C.B. (1958). Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27: 343–383.Google Scholar
  17. Kareiva, P. (1982). Experimental and mathematical analyses of herbivore movement• quantifying the influence of plant spacing and quality on foraging discrimination. Ecol. Monog. 52: 261–282.Google Scholar
  18. Kareiva, P. (1983). Local movement in herbivorous insects: applying a passive diffusion model to mark-recapture field experiments. Oecologia 57: 322–327.CrossRefGoogle Scholar
  19. Kareiva, P. and Shigesada, N. (1983). Analyzing insect movement as a correlated random walk. Oecologia 56: 234–238.CrossRefGoogle Scholar
  20. Kidd, N.A.C. (1982). Predator.avoidance as a result of aggregation in the grey pine aphid, Schizolachnus pineti. J. Anim. Ecol. 51: 397–412.Google Scholar
  21. Levin, S.A. (1974). Dispersion and population interactions. Am. Nat. 108: 207–228.Google Scholar
  22. Levin, S.A. (1976a). Population dynamic models in heterogeneous environments. Ann. Rev. Ecol. Systematics 7: 287–310.Google Scholar
  23. Levin, S.A. (1976b). Spatial patterning and the structure of ecological communities In: Some Mathematical Questions in Biology, 7. Lectures on Mathematics in the Life Sciences. Levin, S.A. (ed.). Vol. 8, 1–35, Providence, R.I. Amer. Math. Soc.Google Scholar
  24. Levin, S.A. (1978). Population models and community structure in heterogeneous environments. In: Mathematical Association of America Study in Mathematical Biology II: Populations and Communities, Levin, S.A. (ed.), pp. 439–476., Math. Assoc. Amer. Washington.Google Scholar
  25. Levin, S.A. (1981). The role of theoretical ecology in the description and understanding of populations in heterogeneous environments. Amer. Zool. 21: 865–875.Google Scholar
  26. Levin, S.A. and Segel, L.A. (1976). Hypothesis for origin of planktonic patchiness. Nature 259: 659.CrossRefGoogle Scholar
  27. May, R.M. (1978). Host-parasitoid systems in patchy environments: a phenomenological model. J. Anim. Ecol. 47: 833–843.Google Scholar
  28. Maynard Smith, J. (1974). Models in Ecology, Cambridge University Press.Google Scholar
  29. Messina, F. (1982a). Comparative biology of the goldenrod leaf beetles, Trirhabda virgata Leconte and T. borealis Blake (Coleoptera: Chrysomelidae). Coleop. Bull. 36: 255–269.Google Scholar
  30. Messina, F. (1982b). Food plant choices of two goldenrod beetles: relation to plant quality. Oecología 55: 342–354.CrossRefGoogle Scholar
  31. Nicholson, A.J. and Bailey, V.A. (1935). The balance of animal populations. Part I. Proc. Zool. Soc. Lond. 3: 551–598.Google Scholar
  32. Obrycki, J., Nechols, J. and Tauber, M. (1982). Establishment of a European lady beetle in New York State. New York Food and Life Science Bull. 94: 1–3.Google Scholar
  33. Okubo, A. (1980). Diffusion and ecological problems: mathematical models. Springer-Verlag, New York, NY, USA.Google Scholar
  34. Richards, W.R. (1972). Review of Solidago-inhabiting aphids in Canada with descriptions of three new species (Homoptera: Aphididae). Can. Entom. 104: 1–34.Google Scholar
  35. Roitberg, B.D., Nyers, J.H. and Frazer, B.D. (1979). The influence of predators on the movement of apterous pea aphids between plants. J. Anim. Ecol. 48: 111–122.Google Scholar
  36. Segel, L.A. and Jackson, J.L. (1972). Dissipative structure: an explanation and an ecological example. J. Theor. Biol. 37: 545–549.Google Scholar
  37. Segel, L.A. and Levin, S.A. (1976). Application of nonlinear stability theory to the study of the effects of diffusion on predator-prey interactions. In: Topics in Statistical Mechanics and Biophysics: A Memorial to Julius Jackson. AIP Conf. Proc. No. 27:123–152. Piccirelli, R.A. (ed.). New York: Amer. Inst. Physics.Google Scholar
  38. Tsubaki, Y. and Shiotsu, Y. (1982). Group feeding as a strategy for exploiting food resources in the burnet moth Pryeria sinica. Oecologia 55: 12–20.Google Scholar
  39. Way, M.J. and Banks, C.J. (1967). Intra-specific mechanisms in relation to the natural regulation of numbers of Aphis fabae Scop. Ann. Appl. Biol. 59: 189–205.Google Scholar
  40. Way, M.J. and Cammell, M. (1970). Aggregation behavior in relation to food utilization by aphids. In: Animal Populations in Relation to their Food Resources, A. Watson (ed.), pp. 229–247. Blackwell Scientific Publications, Oxford.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Peter Kareiva
    • 1
  1. 1.Division of Biology and MedicineBrown UniversityProvidenceUSA

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