Effects of Predator and Prey Dispersal on Success or Failure of Biological Control

  • Sanyi TangEmail author
  • Robert A. Cheke
  • Yanni Xiao
Original Article


Biological control, defined as the reduction of pest populations by natural enemies, is often a component of integrated pest management strategies. Augmentation of natural enemy numbers by planned releases is a common biological control method, the successes and failures of which have been extensively reviewed. The effectiveness of biological control is influenced by how populations of predators and prey (or hosts and parasitoids) disperse in patchy environments. Here, we address the question of whether such dispersal leads to beneficial or detrimental pest control outcomes by developing a simple predator-prey model with constant releases of natural enemies in a two-patch environment. Theoretical and numerical results for all possible cases indicate that population dispersal has significant effects on the persistence of pests. For some ranges of dispersal rates or parameter space, dispersal is beneficial for pest control measures but this is not so for other ranges when it is detrimental. Therefore, knowledge of pest and natural enemy dispersal is crucial for understanding the effectiveness of biological control in a patchy environment. Finally, the model is generalised for multi-patch systems.


Natural enemy Pest Biological control Dispersal 


  1. Amarasekare, P., 2008. Spatial dynamics of Foodwebs. Annu. Rev. Ecol. Evol. Syst. 39, 479–500. CrossRefGoogle Scholar
  2. Amarasekare, P., Nisbet, R.M., 2001. Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species. Am. Nat. 158, 572–584. CrossRefGoogle Scholar
  3. Beverton, R.J., Holt, S.J., 1956. The theory of fishing. In: Graham, M. (Ed.), Sea Fisheries; Their Investigation in the United Kingdom, pp. 372–441. Edward Arnold, London. Google Scholar
  4. Collier, T., Van Steenwyk, R., 2004. A critical evaluation of augmentative biological control. Biol. Control 31, 245–256. CrossRefGoogle Scholar
  5. Cooke, K., Van den Driessche, P., Zou, X., 1999. Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39, 332–352. zbMATHCrossRefMathSciNetGoogle Scholar
  6. Crowley, P.H., 1981. Dispersal and the stability of predator-prey interactions. Am. Nat. 118, 673–701. CrossRefMathSciNetGoogle Scholar
  7. DeBach, P., Rosen, D., 1991. Biological Control by Natural Enemies. Cambridge University Press, Cambridge. Google Scholar
  8. Dwyer, G., Hails, R., 2002. Manipulating your host: host-pathogen population dynamics, host dispersal and genetically modified baculoviruses. In: Bullock, J.M., Kenward, R.E., Hails, R. (Eds.), Dispersal Ecology, pp. 173–193. Blackwell, Oxford. Google Scholar
  9. Gompertz, B., 1925. On the nature of the function expressive of the law of human mortability. Philos. Trans. 115, 513–585. Google Scholar
  10. Greathead, D.J., 1992. Natural enemies of tropical locusts and grasshoppers: their impact and potential as biological control agents. In: Lomer, C.J., Prior, C. (Eds.), Biological Control of Locusts and Grasshoppers, pp. 105–121. C.A.B. International, Wallingford. Google Scholar
  11. Hanski, I., Gilpin, M.E., 1997. Metapopulation Dynamics: Ecology, Genetics and Evolution. Academic Press, San Diego. zbMATHGoogle Scholar
  12. Hassell, M.P., 1978. The Dynamics of Predator-Prey Systems. Princeton University Press, Princeton. zbMATHGoogle Scholar
  13. Hassell, M.P., 2000. The Spatial and Temporal Dynamics of Host-Parasitoid Intereactions. Oxford University Press, London. Google Scholar
  14. Hoffmann, M.P., Frodsham, A.C., 1993. Natural Enemies of Vegetable Insect Pests. Cooperative Extension. Cornell University, Ithaca. Google Scholar
  15. Holling, C.S., 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Can. 45, 3–60. Google Scholar
  16. Hopper, K.R., Roush, R.T., 1993. Mate finding, dispersal, number released, and the success of biological control introductions. Ecol. Entomol. 18, 321–331. CrossRefGoogle Scholar
  17. Huffaker, C.B., 1958. Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27, 343–383. Google Scholar
  18. Jansen, V.A.A., Sabelis, M.W., 1992. Prey dispersal and predator persistence. Exp. Appl. Acarol. 14, 215–231. CrossRefGoogle Scholar
  19. Kareiva, P., 1982. Experimental and mathematical analyses of herbivore movement: quantifying the influence of plant spacing and quality on foraging discrimination. Ecol. Monogr. 52(3), 261–282. CrossRefGoogle Scholar
  20. Levins, R., 1970. Extinction. Ann. NY Acad. Sci. 231, 123–138. CrossRefGoogle Scholar
  21. Lotka, A.J., 1920. Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc. 42, 1595–1599. CrossRefGoogle Scholar
  22. McDougall, S.L., Mills, N.J., 1997. Dispersal of Trichogramma platnery Nnagarkatti (Hym., Trichogrammatidae) from point-source releases in an apple orchard in California. J. Appl. Entomol. 121,205–209. CrossRefGoogle Scholar
  23. Neuenschwander, P., Herren, H.R., 1988. Biological Control of the Cassava Mealybug, Phenacoccus manihoti, by the Exotic Parasitoid Epidinocarsis lopezi in Africa. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 318, 319–333. CrossRefGoogle Scholar
  24. Nicholson, A.J., Bailey, V.A., 1935. The balance of animal populations. Part I. Proc. Zool. Soc. Lond. 3, 551–598. Google Scholar
  25. Parker, F.D., 1971. Management of pest populations by manipulating densities of both host and parasites through periodic releases. In: Huffaker, C.B. (Ed.), Biological Control. Plenum, New York. Google Scholar
  26. Pels, B., Sabelis, M.W., 1999. Local dynamics, overexploitation and predator dispersal in an acarine predator-prey system. Oikos 86, 573–583. CrossRefGoogle Scholar
  27. Saavedra, J.L.D., Torres, J.B., Ruiz, M.G., 1997. Dispersal and parasitism of Heliothis virescens eggs by Trichogramma pretiosum (Rriley) in cotton. J. Pest Manag. 43(2), 169–171. CrossRefGoogle Scholar
  28. Stein, S.J., Price, W.P., Craig, T.P., Itami, J.K., 1994. Dispersal of a galling sawfly: implications for studies of insect population dynamics. J. Anim. Ecol. 63, 666–676. CrossRefGoogle Scholar
  29. Stiling, P., Cornelissen, T., 2005. What makes a successful biological control agent? A meta-analysis of biological control agent performance. Biol. Control 34, 236–246. CrossRefGoogle Scholar
  30. Takafuji, A., 1976. The effect of the rate of successful dispersal of a Phytoseiid mite, Phytoseiulus persimilis ATHIAS-HENRIOT (Acarina: Phytoseiidae) on the persistence in the interactive system between the predator and its prey. Popul. Ecol. 18, 1438–3896. Google Scholar
  31. Tang, S.Y., Chen, L.S., 2004. Modelling and analysis of integrated pest management strategy. Discrete Contin. Dyn. Syst. B 4, 759–768. zbMATHCrossRefMathSciNetGoogle Scholar
  32. Tang, S.Y., Cheke, R.A., 2005. State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences. J. Math. Biol. 50, 257–292. zbMATHCrossRefMathSciNetGoogle Scholar
  33. Tang, S.Y., Cheke, R.A., 2008. Models for integrated pest control and their biological implications. Math. Biosci. 215, 115–125. zbMATHCrossRefMathSciNetGoogle Scholar
  34. Tang, S.Y., Xiao, Y.N., Chen, L.S., Cheke, R.A., 2005. Integrated pest management models and their dynamical behaviour. Bull. Math. Biol. 67, 115–135. CrossRefMathSciNetGoogle Scholar
  35. Van den Driesche, R.D., Bellows, T.S., 1996. Biological Control. Chapman & Hall, London. Google Scholar
  36. Van den Driessche, P., Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48. zbMATHCrossRefMathSciNetGoogle Scholar
  37. Van Lenteren, J.C., 1995. Integrated pest management in protected crops. In: Dent, D. (Ed.), Integrated Pest Management, pp. 311–320. Chapman & Hall, London. Google Scholar
  38. Van Lenteren, J.C., 2000. Measures of success in biological control of arthropods by augmentation of natural enemies. In: Wratten, S., Gurr, G. (Eds.), Measures of Success in Biological Control, pp. 77–89. Kluwer Academic, Dordrecht. Google Scholar
  39. Van Lenteren, J.C., Woets, J., 1988. Biological and integrated pest control in greenhouses. Annu. Rev. Entomol. 33, 239–250. CrossRefGoogle Scholar
  40. Volterra, V., 1931. Variations and fluctuations of a number of individuals in animal species living together. In: R.N. Chapman: Animal Ecology. McGraw Hill, New York. Translation. Google Scholar
  41. Wang, W.D., Zhao, X.Q., 2004. An epidemic model in a patchy environment. Math. Biosci. 190, 97–112. zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.Natural Resources InstituteUniversity of Greenwich at MedwayChathamUK
  3. 3.Department of Applied MathematicsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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