Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amarasekare, P., 2008. Spatial dynamics of Foodwebs. Annu. Rev. Ecol. Evol. Syst. 39, 479–500.
Amarasekare, P., Nisbet, R.M., 2001. Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species. Am. Nat. 158, 572–584.
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.
Collier, T., Van Steenwyk, R., 2004. A critical evaluation of augmentative biological control. Biol. Control 31, 245–256.
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.
Crowley, P.H., 1981. Dispersal and the stability of predator-prey interactions. Am. Nat. 118, 673–701.
DeBach, P., Rosen, D., 1991. Biological Control by Natural Enemies. Cambridge University Press, Cambridge.
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.
Gompertz, B., 1925. On the nature of the function expressive of the law of human mortability. Philos. Trans. 115, 513–585.
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.
Hanski, I., Gilpin, M.E., 1997. Metapopulation Dynamics: Ecology, Genetics and Evolution. Academic Press, San Diego.
Hassell, M.P., 1978. The Dynamics of Predator-Prey Systems. Princeton University Press, Princeton.
Hassell, M.P., 2000. The Spatial and Temporal Dynamics of Host-Parasitoid Intereactions. Oxford University Press, London.
Hoffmann, M.P., Frodsham, A.C., 1993. Natural Enemies of Vegetable Insect Pests. Cooperative Extension. Cornell University, Ithaca.
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.
Hopper, K.R., Roush, R.T., 1993. Mate finding, dispersal, number released, and the success of biological control introductions. Ecol. Entomol. 18, 321–331.
Huffaker, C.B., 1958. Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27, 343–383.
Jansen, V.A.A., Sabelis, M.W., 1992. Prey dispersal and predator persistence. Exp. Appl. Acarol. 14, 215–231.
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.
Levins, R., 1970. Extinction. Ann. NY Acad. Sci. 231, 123–138.
Lotka, A.J., 1920. Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc. 42, 1595–1599.
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.
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.
Nicholson, A.J., Bailey, V.A., 1935. The balance of animal populations. Part I. Proc. Zool. Soc. Lond. 3, 551–598.
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.
Pels, B., Sabelis, M.W., 1999. Local dynamics, overexploitation and predator dispersal in an acarine predator-prey system. Oikos 86, 573–583.
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.
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.
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.
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.
Tang, S.Y., Chen, L.S., 2004. Modelling and analysis of integrated pest management strategy. Discrete Contin. Dyn. Syst. B 4, 759–768.
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.
Tang, S.Y., Cheke, R.A., 2008. Models for integrated pest control and their biological implications. Math. Biosci. 215, 115–125.
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.
Van den Driesche, R.D., Bellows, T.S., 1996. Biological Control. Chapman & Hall, London.
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.
Van Lenteren, J.C., 1995. Integrated pest management in protected crops. In: Dent, D. (Ed.), Integrated Pest Management, pp. 311–320. Chapman & Hall, London.
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.
Van Lenteren, J.C., Woets, J., 1988. Biological and integrated pest control in greenhouses. Annu. Rev. Entomol. 33, 239–250.
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.
Wang, W.D., Zhao, X.Q., 2004. An epidemic model in a patchy environment. Math. Biosci. 190, 97–112.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tang, S., Cheke, R.A. & Xiao, Y. Effects of Predator and Prey Dispersal on Success or Failure of Biological Control. Bull. Math. Biol. 71, 2025–2047 (2009). https://doi.org/10.1007/s11538-009-9438-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-009-9438-2