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

Bulletin of Mathematical Biology volume 77, pages 1256–1284 (2015)Cite this article

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.

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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.

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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

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  1. Jacob P. Duncan
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  2. James A. Powell
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  3. Luis F. Gordillo
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  4. Joseph Eason
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Correspondence to Jacob P. Duncan.

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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

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

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