Skip to main content
SpringerLink
Log in

A Model for Mountain Pine Beetle Outbreaks in an Age-Structured Forest: Predicting Severity and Outbreak-Recovery Cycle Period

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations. Stability of fixed points is analyzed as a function of (thermally controlled) MPB population growth rates and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise analytical methods to predict outbreak severity and duration as well as outbreak return time. After incorporating a spatial aspect and controlling initial stand demographic variation, the model predicts cycle periods that fall within observed outbreak return time ranges. To assess future MPB impact on forests, we use climate model projected temperatures with our model-based approximation methods to predict potential severity of future outbreaks that reflect the effects of changing climate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Abatzoglou JT (2011) Development of gridded surface meteorological data for ecological applications and modelling. Int J Climatol. doi:10.1002/joc.3413

  • Abatzoglou JT, Brown TJ (2012) A comparison of statistical downscaling methods suited for wildfire applications. Int J Climatol. doi:10.1002/joc.2312

  • Alfaro RI, Campbell R, Vera P, Hawkes B, Shore TL (2004) Dendroecological reconstruction of mountain pine beetle outbreaks in the Chilcotin Plateau of British Columbia. In: Shore TL, Brooks JE, Stone JE (eds) Mountain pine beetle symposium: challenges and solutions. Natural Resources Canada, Information Report BC-X-399, Kelowna, British Columbia, pp 245–256

  • Amman G, Cole WE (1983) Mountain pine beetle dynamics in lodgepole pine forests: Part II population dynamics. U.S. Department of Agriculture, General Technical Report INT-145, Intermountain Forest and Range Experiment Station, Ogden, UT

  • Amman GD, Schmitz RF (1988) Mountain pine beetle–lodgepole pine interactions and strategies for reducing tree losses. Ambio 17:62–68

    Google Scholar 

  • Anderson RM, May RM (1979) Population biology of infectious diseases: Part I. Nature 280:361–362

    Article  Google Scholar 

  • Anderson RM, May RM (1979) Population biology of infectious diseases: Part II. Nature 280(5722):455–461

    Article  Google Scholar 

  • Anderson RM, May RM (1982) The logic of vaccination. New Scientist 96(1332):410–415

    Google Scholar 

  • Aukema BH, Carroll AL, Zhu J, Raffa KF, Sickley TA, Taylor SW (2006) Landscape level analysis of mountain pine beetle in British Columbia, Canada: spatiotemporal development and spatial synchrony within the present outbreak. Ecography 29(3):427–441

    Article  Google Scholar 

  • Axelson JN, Alfaro RI, Hawkes BC (2009) Influence of fire and mountain pine beetle on the dynamics of lodgepole pine stands in British Columbia, Canada. For Ecol Manag 257:1874–1882

    Article  Google Scholar 

  • Bentz BJ, Logan JA, Amman GD (1991) Temperature dependent development of the mountain pine beetle (Coleoptera: Scolytidae), and simulation of its phenology. Can Entomol 123(1083):1094

    Google Scholar 

  • Bentz BJ, Mullins DE (1999) Ecology of mountain pine beetle (Coleoptera: Scolytidae) cold hardening in the Intermountain west. Environ Entomol 28(4):577–587

    Article  Google Scholar 

  • Bentz BJ, Régnière J, Fettig CJ, Hansen EM, Hayes JL, Hicke JA, Seybold SJ et al (2010) Climate change and bark beetles of the western United States and Canada: direct and indirect effects. BioScience 60(8):602–613

    Article  Google Scholar 

  • Berryman AA, Dennis B, Raffa KF, Stenseth NC (1985) Evolution of optimal group attack, with particular reference to bark beetles (Coleoptera: Scolytidae). Ecology 898:903

    Google Scholar 

  • Bleiker KP, O’Brien MR, Smith GD, Carroll AL (2014) Characterisation of attacks made by the mountain pine beetle (Coleoptera: Curculionidae) during its endemic population phase. Can Entomol 146(03):271–284

    Article  Google Scholar 

  • Heath R, Alfaro RI (1990) Growth response in a Douglas-fir/lodgepole pine stand after thinning of lodgepole pine by the mountain pine beetle: A case study. J Entomol Soc B. C. 87:16–21

    Google Scholar 

  • Heavilin J, Powell J (2008) A novel method for fitting spatio-temporal models to data, with applications to the dynamics of mountain pine beetle. Nat Res Model 21:489–524

    Article  MATH  MathSciNet  Google Scholar 

  • Heavilin J, Powell JA, Logan JA (2007) Development and parametrization of a model for bark beetle disturbance in lodgepole forest. In: Miyanishi K, Johnson E (eds) Plant disturbance ecology. Academic Press, New York, pp 527–553

    Chapter  Google Scholar 

  • Hrinkevich K, Lewis KJ (2011) Northern range limit mountain pine beetle outbreak dynamics in mixed sub-boreal pine forests of British Columbia. Ecosphere 2(10):116. doi:10.1890/ES11-00150.1

    Article  Google Scholar 

  • Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc A 115(772):700–721. doi:10.1098/rspa.1927.0118

    Article  MATH  Google Scholar 

  • Kurz WA, Dymond CC, Stinson G, Rampley GJ, Neilson ET, Carroll AL, Ebata T, Safranyik L (2008) Mountain pine beetle and forest carbon feedback to climate change. Nature 452:0028–0836

    Article  Google Scholar 

  • Leslie PH (1945) The use of matrices in certain population mathematics. Biometrika 33(3):183–212

    Article  MATH  MathSciNet  Google Scholar 

  • Meddens AJH, Hicke JA, Ferguson CA (2012) Spatiotemporal patterns of observed bark beetle-caused tree mortality in British Columbia and the western United States. Ecol Appl 22(1876):1891

    Google Scholar 

  • Powell JA, Bentz BJ (2009) Connecting phenological predictions with population growth rates for an outbreak insect. Landsc Ecol 24:657–672

    Article  Google Scholar 

  • Powell JA, Bentz BJ (2014) Phenology and density-dependent dispersal predict patterns of mountain pine beetle (Dendroctonus ponderosae) impact. Ecol Model 273:173–185

    Article  Google Scholar 

  • Régnière J, Powell J, Bentz B, Nealis V (2012) Effects of temperature on development, survival and reproduction of insects: experimental design, data analysis and modeling. J Insect Physiol 58:634–647

    Article  Google Scholar 

  • Régnière J, Bentz B (2007) Modeling cold tolerance in the mountain pine beetle, Dendroctonus ponderosae. J Insect Physiol 53:559–572. doi:10.1016/j.jinsphys.2007.02.007

    Article  Google Scholar 

  • Safranyik L (2003) Mountain pine beetle epidemiology in lodgepole pine. In: Mountain pine beetle symposium: challenges and solutions. Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, Victoria BC V8Z 1M5, pp 33–40

  • Safranyik L, Shrimpton DM, Whitney HS (1975) An interpretation of the inter-action between lodgepole pine, the mountain pine beetle and its associated blue stain fungi in western Canada. In: Baumgartner, DM (ed) Management of lodgepole pine ecosystems: Proceeding of the Symposium on the Washington State University. Cooperative Extension Service, pp 406–428

  • Schmidt WC, Alexander RR (1985) Strategies for managing lodgepole pine. In: Baumgartner DM, Krebill RG, Arnott JT, and Weetman GF (ed) Lodgepole pine—the species and its management, Office of Conferences and Institutes, Cooperative Extension, Washington State University, Pullman, WA, pp 202–210

  • Sharpe PJH, Curry GL, DeMichele DW, Cole CL (1977) Distribution model of organism development times. J Theor Biol 66:21–38

    Article  Google Scholar 

  • Thomson AM, Calvin KV, Smith SJ, Kyle GP, Volke A, Patel P, Delgado-Arias S, Bond-Lamberty B, Wise MA, Clarke LE et al. (2011) RCP4.5: a pathway for stabilization of radiative forcing by 2100. Clim Change. doi:10.1007/s10584-011-0151-4

Download references

Acknowledgments

Funding was provided by the USDA Forest Service, Western Wildland Threat Assessment Center and National Science Foundation, DEB 0918756. The authors would like to thank Dr. Barbara Bentz, USDA-FS Rocky Mountain Research Station, as well as three anonymous reviewers, who read an earlier draft and provided much helpful commentary.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322-3900, USA

    Jacob P. Duncan, James A. Powell & Luis F. Gordillo

  2. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112-0090, USA

    Joseph Eason

Authors
  1. Jacob P. Duncan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James A. Powell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis F. Gordillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joseph Eason
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacob P. Duncan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duncan, J.P., Powell, J.A., Gordillo, L.F. et al. A Model for Mountain Pine Beetle Outbreaks in an Age-Structured Forest: Predicting Severity and Outbreak-Recovery Cycle Period. Bull Math Biol 77, 1256–1284 (2015). https://doi.org/10.1007/s11538-015-0085-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-015-0085-5

Keywords

Search

Navigation