Advertisement

Phase transition from environmental to dynamic determinism in mountain pine beetle attack

  • Peter White
  • James Powell
Article

Abstract

Mountain pine beetle outbreaks are responsible for widespread tree mortality in pine forests throughout western North America. Intensive outbreaks result in significant economic loss to the timber industry and massive changes to the forest habitat. Because of the time and space scales involved in a beetle outbreak, mathematical models are needed to study the evolution of an outbreak. In this paper we present a partial differential equation model of the flight phase of the mountain pine beetle which includes chemotactic responses and tree defense. We present a numerical method for integrating this model and use this method to investigate the relationship between emergence rate, forest demographic and patterns of beetle attack. In particular we look at how emergence rate affects the beetles' ability to successfully attack strong trees, which may be an indicator of an epidemic outbreak.

Keywords

Bark Beetle Partial Differential Equation Epidemic Outbreak Emergence Level Attack Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Borden, J. H., L. C. Ryker, L. J. Chong, H. D. Pierce, B. D. Johnston and A. C. Oehlschlager. (1987). Response of the mountain pine beetle,Dendroctonus ponderosae, to five semiochemicals in British Columbia lodgepole pine forests.Can. J. Forest. Res. 17, 118–128.Google Scholar
  2. Burden, R. L. and J. D. Faires. 1985.Numerical Analysis, 3rd ed. Boston: Prindle, Weber and Schmidt.Google Scholar
  3. Conn, J. E., J. D. Borden, B. E. Schott, L. M. Friskie, H. D. Pierce and A. C. Oehlschlager. 1983. Semiochemicals for the mountain pine beetle,Dendroctonus ponderosae, in British Columbia: field trapping studies.Can. J. Forest. Res. 13, 320–324.CrossRefGoogle Scholar
  4. Gara, R. I., D. R. Geiszler and W. R. Littke. 1984. Primary attraction of the mountain pine beetle to lodgepole pine in Oregon.Ann. Entomol. Soc. Am. 77, 333–334.Google Scholar
  5. Gear, C. W. 1971.Numerical Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs, NJ: Prentice-Hall.MATHGoogle Scholar
  6. Geiszler, D. R., V. F. Gallucci and R. I. Gara. 1980. Modeling the dynamics of mountain pine beetle aggregation in a lodgepole pine standOecologia 46 244–253.CrossRefGoogle Scholar
  7. Geiszler, D. R. and R. I. Gara. 1978. Mountain pine beetle attack dynamics in lodgepole pine. InTheory and Practice of Mountain Pine, Beetle Management in Lodgepole Pine Forests: Symp. Proc. A. A. Berryman, G. D. Amman and R. W. Stark (Eds). Pullman, WA: Washington State Univ.Google Scholar
  8. Hughes, P. R. 1973.Dendroctonus: production of pheromones and related compounds in response to host monoterpenes.Zeit. Angew. Ent. 73, 294–312.Google Scholar
  9. Hunt, D. W. A., J. H. Borden, B. S. Lindgren and G. Gries. 1989. The role of autoxidation of alpha pinene in the production of pheromones ofDendroctonus ponderosae.Can. J. Forest. Res. 19, 1275–1282.Google Scholar
  10. Hynum, B. G. and A. A. Berryman. 1980.Dendroctonus ponderosae (Coleoptera: Scolytidae): preaggregation landing and gallery initiation on lodgepole pine.Can. Entomol. 112, 185–191.Google Scholar
  11. McCambridge, W. F. 1967. Nature of induced attacks by the black hills beetle,Dendroctonus ponderosae (Coleoptera: Scolytidae).Ann. Entomol. Soc. Am 60, 920–928.Google Scholar
  12. Moeck, H. A. and C. S. Simmons. 1991. Primary attraction of mountain pine beetle to bolts of lodgepole pine.Can. Entomol. 123, 299–304.Google Scholar
  13. Nebeker, T. E., J. D. Hodges and C. A. Blanche. 1993. Host responses to bark beetle pathogen colonization. InBeetle-Pathogen Interactions in Conifer Forests, T. D. Schowalter and G. M. Filip (Eds). New York: Academic Press.Google Scholar
  14. Norris, D. M. and J. E. Baker. 1967. Feeding response of Scolytus to chemical stimuli in the bark of Ulmus.J. Insect Phys. 13, 955–962.CrossRefGoogle Scholar
  15. Pitman, G. B. 1971. Trans-verbenol and alpha-pinene: their utility in manipulation of the mountain pine beetle.J. Econ. Entomol. 64, 426–430.Google Scholar
  16. Pitman, G. B., J. P. Vite, G. W. Kinzer and A. F. Fentiman. 1968. Bark beetle attractants: trans-verbenol isolated fromDendroctonus.Nature 218, 168–169.CrossRefGoogle Scholar
  17. Powell, J. A. and J. D. Rose, 1996. Local consequences of a global model for mountain pine beetle mass attack.Dynamics Stability Syst.12.Google Scholar
  18. Powell, J., J. A. Logan and B. J. Bentz. 1995. Local projection of a global model of mountain pine beetle attacks.J. Theort Biol. 179, 243–260.CrossRefGoogle Scholar
  19. Press, W. H., W. T. Vetterling, S. A. Teukolsky and B. P. Flannery. 1992.Numerical Recipes in C, 2nd ed. London: Cambridge Univ. Press.MATHGoogle Scholar
  20. Prokopy, R. J. 1980. Epideictic pheromones influencing spacing patterns of phytophagous insects. InSemiochemicals: Their Role in Pest Control, D. A. Norlund, R. L. Jones and W. J. Lewis (Eds), New York: Wiley.Google Scholar
  21. Raffa K. F. 1988. Host orientation behavior ofDendroctonus ponderosae: integration of token stimuli and host defenses. InMechanism of Woody Plant Resistance to Insects and Pathogens, W. J. Mattson, J. Levieux and C. Bernard-Dagen (Eds), pp. 369–390. New York: Springer-Verlag.Google Scholar
  22. Raffa, K. F. and A. A. Berryman. 1979. Flight responses and host selection by bark beetles. InDispersal of Forest Insects: Evaluation, Theory and Management Implications, A. A. Berryman and L. Safranyik (Eds), pp. 213–233, Pullman, WA: Washington State University.Google Scholar
  23. Raffa, K. F., T. W. Phillips and S. M. Salom. 1993. Strategies and mechanisms of host colonization by bark beetles. InBeetle-Pathogen Interactions in Conifer Forests, T. D. Schowalter and G. M. Filip (Eds), pp. 103–120. New York: Academic Press.Google Scholar
  24. Raffa, K. F. and A. A. Berryman. 1982. Gustatory cues in the orientation ofDendroctonus ponderosae (Coleoptera: Scolytidae) to host trees.Can. Entomol. 114, 97–104.Google Scholar
  25. Raffa, K. F., T. W. Philips and S. M. Salom. 1993. Strategies and mechanisms of host colonization by bark beetles. InBeetle-Pathogen Interactions in Conifer Forests, T. D. Schowalter and G. M. Filip (Eds), pp. 103–120. New York: Academic Press.Google Scholar
  26. Rasmussen, L. A. 1974. Flight and attack behavior of mountain pine beetle in lodgepole pine of northern Utah and southern Idaho. Research Note INT-18, USDA Forest Service.Google Scholar
  27. Reid, R. W., H. S. Whitney and J. A. Watson. 1967. Reactions of lodgepole pine to attack byDendroctonus ponderosae hopkins and the blue stain fungi.Can. J. Botany 45, 1115–1116.CrossRefGoogle Scholar
  28. Renwick, J. A. A. and J. P. Vite. 1970. Systems of chemical communication inDendroctonus.Contrib. Boyce Thompson Inst. 23, 355–360.Google Scholar
  29. Roe, A. L and G. D. Amman. 1970. The mountain pine beetle in lodgepole pine forests. Research Paper INT-71, USDA Forest Service.Google Scholar
  30. Safranyik, L., R. Silversides, L. H. McMullen and D. A. Linton. 1989. An empirical approach to modeling the local dispersal of the mountain pine beetle (Dendroctonus ponderosae hopk.) in relation to sources of attraction, wind direction and speed.J. Appl. Entomol. 108, 498–511.CrossRefGoogle Scholar
  31. Schmitz, R. F. 1988. Understanding Scolytid problems in lodgepole pine forests: the need for an integrated approach. InIntegrated Control of Scolytid Bark Beetles. T. L. Payne and H. Saarenmaa (Eds). Blacksburg, VA: Virginia Polytechnic Institute and State University.Google Scholar
  32. Schonherr, J. 1976. Mountain pine beetle: visual behavior related to integrated control. InProceedings, XVI IUFRO World Congress, Oslo, Norway, pp. 449–452.Google Scholar
  33. Schowalter T. D. and G. M. Filip (Eds). 1993.Beetle-Pathogen Interactions in Conifer Forests. New York: Academic Press.Google Scholar
  34. Sheppard, R. F. 1966. Factors influencing the orientation and rates of activity ofDendroctonus ponderosae (Coleoptera: Scolytidae).Can. Entomol. 98, 507–518.CrossRefGoogle Scholar
  35. Smith, R. H. 1963. Toxicity of pine resin vapors to three species ofDendroctonus bark beetles.J. Econ. Entomol. 56, 827–831.Google Scholar
  36. Smith, R. H. 1966. Resin quality as a factor in the resistance of pines to bark beetles. InProceedings of the NATO and National Science Foundation, H. D. England, R. E. Gerhold, R. E. McDermot, E. J. Schreiner and J. A. Winieski (Eds), pp. 189–196. Oxford, England: Pergamon.Google Scholar
  37. Tkacz, B. M. and R. F. Schmitz. 1986. Association of an endemic mountain pine beetle population with lodgepole pine infected byArmillaria root disease in Utah. Research Note INT-353, USDA Forest Service.Google Scholar
  38. White, P. and J. Powell. 1996. Spatial invasion of pine beetles into lodgepole forests: a numerical approach. Unpublished manuscript.Google Scholar
  39. Wood, D. L. 1972. Selection and colonization of ponderosa pine by bark beetles.Symp. Roy. Entomol. Soc. London 6, 110–117.Google Scholar

Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Peter White
    • 1
  • James Powell
    • 1
  1. 1.Department of Mathematics and StatisticsUtah State UniversityLoganU.S.A.

Personalised recommendations