Skip to main content

Advertisement

Log in

Selection of Spatial-Temporal Lattice Models: Assessing the Impact of Climate Conditions on a Mountain Pine Beetle Outbreak

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript

Abstract

Insects are among the most significant indicators of a changing climate. Here we evaluate the impact of temperature, precipitation, and elevation on the tree-killing ability of an eruptive species of bark beetle in pine forests of British Columbia, Canada. We consider a spatial-temporal linear regression model and in particular, a new statistical method that simultaneously performs model selection and parameter estimation. This approach is penalized maximum likelihood estimation under a spatial-temporal adaptive Lasso penalty, paired with a computationally efficient algorithm to obtain approximate penalized maximum likelihood estimates. A simulation study shows that finite-sample properties of these estimates are sound. In a case study, we apply this approach to identify the appropriate components of a general class of landscape models which features the factors that propagate an outbreak. We interpret the results from ecological perspectives and compare our method with alternative model selection procedures.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aukema, B. H., Carroll, A. L., Zhu, J., Raffa, K. F., Sickley, T. A., and Taylor, S. W. (2006), “Landscape Level Analysis of Mountain Pine Beetle in British Columbia, Canada: Spatiotemporal Development and Spatial Synchrony Within the Present Outbreak,” Ecography, 29, 427–441.

    Article  Google Scholar 

  • Aukema, B. H., Carroll, A. L., Zheng, Y., Zhu, J., Raffa, K. F., Moore, R. D., and Stahl, K. (2008), “Movement of Outbreak Populations of Mountain Pine Beetle: Influences of Spatiotemporal Patterns and Climate,” Ecography, 31, 348–358.

    Article  Google Scholar 

  • Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton: Chapman and Hall.

    MATH  Google Scholar 

  • Battistia, A., Stastny, M., Buffo, E., and Larsson, S. (2006), “A Rapid Altitudinal Range Expansion in the Pine Processionary Moth Produced by the 2003 Climatic Anomaly,” Global Change Biology, 12, 662–671.

    Article  Google Scholar 

  • Bentz, B. J., Regnier, J., Fettig, C. J., Hansen, E. M., Hayes, J. L., Hicke, J. A., Kelsey, R. G., Negron, J. F., and Seybold, S. J. (2010), “Climate Change and Bark Beetles of the Western United States and Canada: Direct and Indirect Effects,” Bioscience, 60, 602–613.

    Article  Google Scholar 

  • Cressie, N. (1993), Statistics for Spatial Data, New York: Wiley, revised edition.

    Google Scholar 

  • De la Giroday, H.-M. C., Carroll, A. L., Lindgren, B. S., and Aukema, B. H. (2011), “Association of Landscape Features With Dispersing Mountain Pine Beetle Populations During a Range Expansion Event in Western Canada,” Landscape Ecology, 26, 1097–1110.

    Article  Google Scholar 

  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression” (with discussion), Annals of Statistics, 32, 407–499.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, H.-C., Hsu, N.-J., Theobald, D., and Breidt, F. J. (2010), “Spatial LASSO With Applications to GIS Model Selection,” Journal of Computational and Graphical Statistics, 19, 963–983.

    Article  MathSciNet  Google Scholar 

  • Jenkins, M. J., Hebertson, E. G., Page, W., and Jorgersen, C. A. (2008), “Bark Beetles, Fuels, Fire and Implications for Forest Management in the Intermountain West,” Forest Ecology and Management, 254, 16–34.

    Article  Google Scholar 

  • Kurz, W. A., Dymond, C. C., Stinson, G., Rampley, G. J., Neilson, E. T., Carroll, A. L., Ebata, T., and Safranyik, L. (2008), “Mountain Pine Beetle and Forest Carbon Feedback to Climate Change,” Nature, 452, 987–990.

    Article  Google Scholar 

  • Powell, J. A., Jenkins, J. L., Logan, J. A., and Bentz, B. J. (2000), “Seasonal Temperature Alone Can Synchronize Life Cycles,” Bulletin of Mathematical Biology, 62, 977–998.

    Article  Google Scholar 

  • Raffa, K. F., Aukema, B. H., Bentz, B. J., Carroll, A. L., Hicke, J. A., Turner, M. G., and Romme, W. H. (2008), “Cross-Scale Drivers of Natural Disturbances Prone to Anthropogenic Amplification: The Dynamics of Bark Beetle Eruptions,” Bioscience, 58, 501–518.

    Article  Google Scholar 

  • Reyes, P. E. (2010), “Selection of Spatial and Spatial-Temporal Linear Models for Lattice Data”. PhD thesis, University of Wisconsin-Madison.

  • Robertson, C., Nelson, T. A., Jelinski, D. E., Wulder, M. A., and Boots, B. (2009), “Spatial-Temporal Analysis of Species Range Expansion: The Case of the Mountain Pine Beetle Dendroctonus Ponderosae,” Journal of Biogeography, 36, 1446–1458.

    Article  Google Scholar 

  • Safranyik, L., Shrimpton, D. M., and Whitney, H. S. (1975), “An Interpretation of the Interaction Between Lodgepole Pine, the Mountain Pine Beetle and Its Associated Blue Stain Fungi in Western Canada,” in The Biology and Epidemiology of the Mountain Pine Beetle in Lodgepole Pine Forests, ed. D. M. Baumgartner, pp. 406–428. Management of Lodgepole Pine Ecosystems Symposium Proceedings, Washington State University Cooperative Extension Service, Pullman, Washington

    Google Scholar 

  • Safranyik, L., Carroll, A. L., Regniere, J., Langor, D. W., Riel, W. G., Shore, T. L., Peter, B., Cooke, B. J., and Nealis, V. G. S. W. T. (2010), “Potential for Range Expansion of Mountain Pine Beetle Into The Boreal Forest of North America,” The Canadian Entomologist, 142, 415–442.

    Article  Google Scholar 

  • Sambaraju, K. R., Carroll, A. L., Zhu, J., Stahl, K., Moore, R. D., and Aukema, B. H. (2011), “Climate Change Could Alter the Distribution of Mountain Pine Beetle Outbreaks in Western Canada,” Ecography, 35, 211–223.

    Article  Google Scholar 

  • Schabenberger, O., and Gotway, C. A. (2005), Statistical Methods for Spatial Data Analysis, Boca Raton: Chapman and Hall.

    MATH  Google Scholar 

  • Stahl, K., Moore, R. D., and McKendry, I. G. (2006), “Climatology of Winter Cold Spells in Relation to Mountain Pine Beetle Mortality in British Columbia, Canada,” Climate Research, 32, 13–23.

    Article  Google Scholar 

  • Stahl, K., Moore, R. D., Floyer, J. A., Asplin, M. G., and McKendry, I. G. (2006), “Comparison of Approaches for Spatial Interpolation of Daily Air Temperature in a Large Region With Complex Topography and Highly Variable Station Density,” Agricultural and Forest Metereology, 139, 224–236.

    Article  Google Scholar 

  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Venables, W. N., and Ripley, B. D. (2002), Modern Applied Statistics with S (4th ed.), Berlin: Springer.

    MATH  Google Scholar 

  • Wang, H., Li, G., and Tsai, C.-L. (2007a), “Regression Coefficients and Autoregressive Order Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 69, 63–78.

    MathSciNet  Google Scholar 

  • Wang, H., Li, R., and Tsai, C.-L. (2007b), “Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method,” Biometrika, 94, 553–568.

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng, Y., and Zhu, J. (2008), “Markov Chain Monte Carlo for Spatial-Temporal Autologistic Regression Model,” Journal of Computational and Graphical Statistics, 17, 123–127.

    Article  MathSciNet  Google Scholar 

  • Zhu, J., Huang, H.-C., and Reyes, P. (2010), “On Selection of Spatial Linear Models for Lattice Data,” Journal of the Royal Statistical Society, Series B, 72, 389–402.

    Article  MathSciNet  Google Scholar 

  • Zhu, J., Huang, H.-C., and Wu, J. (2005), “Modeling Spatial-Temporal Binary Data Using Markov Random Fields,” Journal of Agricultural, Biological, and Environmental Statistics, 10, 212–225.

    Article  Google Scholar 

  • Zhu, Z., and Liu, Y. (2009), “Estimating Spatial Covariance Using Penalized Likelihood With Weighted L 1 Penalty,” Journal of Nonparametric Statistics, 21, 925–942.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu, J., Zheng, Y., Carroll, A. L., and Aukema, B. H. (2008), “Autologistic Regression Analysis of Spatial-Temporal Binary Data via Monte Carlo Maximum Likelihood,” Journal of Agricultural, Biological, and Environmental Statistics, 13, 84–98.

    Article  MathSciNet  Google Scholar 

  • Zou, H. (2006), “The Adaptive LASSO and Its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.

    Article  MathSciNet  MATH  Google Scholar 

  • Zou, H., and Li, R. (2008), “One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models” (with discussion), Annals of Statistics, 36, 1509–1566.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Perla E. Reyes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reyes, P.E., Zhu, J. & Aukema, B.H. Selection of Spatial-Temporal Lattice Models: Assessing the Impact of Climate Conditions on a Mountain Pine Beetle Outbreak. JABES 17, 508–525 (2012). https://doi.org/10.1007/s13253-012-0103-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13253-012-0103-0

Key Words

Navigation