Landscape Ecology

, Volume 30, Issue 6, pp 1075–1093

Geographically variable response of Dendroctonus ponderosae to winter warming in the western United States

  • Aaron S. Weed
  • Barbara J. Bentz
  • Matthew P. Ayres
  • Thomas P. Holmes
Research Article

Abstract

Context

Milder winters have contributed to recent outbreaks of Dendroctonus ponderosae in Canada, but have not been evaluated as a factor permitting concurrent outbreaks across its large range (ca.1500 × 1500 km) in the western United States (US).

Objectives

We examined the trend in minimum air temperatures in D. ponderosae habitats across the western US and assessed whether warming winters explained the occurrence of outbreaks using physiological and population models.

Methods

We used climate data to analyze the history of minimum air temperatures and reconstruct physiological effects of cold on D. ponderosae. We evaluated relations between winter temperatures and beetle abundance using aerial detection survey data.

Results

Extreme winter temperatures have warmed by about 4 °C since 1960 across the western US. At the broadest scale, D. ponderosae population dynamics between 1997 and 2010 were unrelated to variation in minimum temperatures, but relations between cold and D. ponderosae dynamics varied among regions. In the 11 coldest ecoregions, lethal winter temperatures have become less frequent since the 1980s and beetle-caused tree mortality increased—consistent with the climatic release hypothesis. However, in the 12 warmer regions, recent epidemics cannot be attributed to warming winters because earlier winters were not cold enough to kill D. ponderosae.

Conclusions

There has been pronounced warming of winter temperatures throughout the western US, and this has reduced previous constraints on D. ponderosae abundance in some regions. However, other considerations are necessary to understand the broad extent of recent D. ponderosae epidemics in the western US.

Keywords

Climate change Demography Mountain pine beetle Process-based model Bark beetles Pinus Cold tolerance 

Supplementary material

10980_2015_170_MOESM1_ESM.docx (11.6 mb)
Supplementary material 1 (DOCX 11927 kb)

References

  1. Altwegg R, Dummermuth S, Anholt BR (2005) Winter weather affects asp viper Vipera aspis population dynamics through susceptible juveniles. Oikos 110:55–66CrossRefGoogle Scholar
  2. Altwegg R, Roulin A, Kestenholz M, Jenni L (2006) Demographic effects of extreme winter weather in the barn owl. Oecologia 149:44–51Google Scholar
  3. Alward R, Detling J, Milchunas D (1999) Grassland vegetation changes and nocturnal global warming. Science 283:229–231CrossRefPubMedGoogle Scholar
  4. Amman GD (1973) Population changes of the mountain pine beetle in relation to elevation. Environ Entomol 2:541–547CrossRefGoogle Scholar
  5. 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 29:427–441Google Scholar
  6. Aukema BH, Carroll AL, Zheng Y, Zhu J, Raffa KF, Dan Moore R, Stahl K, Taylor SW (2008) Movement of outbreak populations of mountain pine beetle: influences of spatiotemporal patterns and climate. Ecography 31:348–358Google Scholar
  7. 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 257:1874–1882CrossRefGoogle Scholar
  8. Bale JS, Masters GJ, Hodkinson ID, Awmack C, Bezemer TM, Brown VK, Butterfield J, Buse A, Coulson JC, Farrar J, Good J, Harrington R, Hartley S, Jones TH, Lindroth RL, Press MC, Symrnioudis I, Watt AD, Whittaker JB (2002) Herbivory in global climate change research: direct effects of rising temperature on insect herbivores. Global Change Biol 8:1–16Google Scholar
  9. Battisti A, Stastny M, Netherer S (2005) Expansion of geographic range in the pine processionary moth caused by increased winter temperatures. Ecol Appl 15:2084–2096CrossRefGoogle Scholar
  10. Bentz BJ, Mullins DE (1999) Ecology of mountain pine beetle (Coleoptera: Scolytidae) cold hardening in the Intermountain West. Environ Entomol 28:577–587CrossRefGoogle Scholar
  11. Bentz BJ, Logan JA, Vandygriff JC (2001) Latitudinal variation in Dendroctonus ponderosae (Coleoptera: Scolytidae) development time and adult size. Can Entomol 133:375–387CrossRefGoogle Scholar
  12. Bentz BJ, Régnière J, Fettig CJ, Hansen EM, Hayes JL, Hicke JA, Kelsey RG, Negrón JF, Seybold SJ  (2010) Climate change and bark beetles of the western United States and Canada: Direct and indirect effects. Bioscience 60:602–613Google Scholar
  13. Bentz B, Campbell E, Gibson K, Kegley S, Logan J, Six D (2011a) Mountain pine beetle in high-elevation five-needle white pine ecosystems. In: Keane RE, Tomback DF, Murray MP, Smith CM (eds) The future of high-elevation, five-needle white pines in Western North America: Proceedings of the High Five Symposium, June 28-30 2010, Missoula, MT, USDA Forest Service, Rocky Mountain Research Station Report RMRS-P-63. Fort Collins, CO, pp 78–84Google Scholar
  14. Bentz BJ, Bracewell RR, Mock KE, Pfrender ME (2011b) Genetic architecture and phenotypic plasticity of thermally-regulated traits in an eruptive species, Dendroctonus ponderosae. Evol Ecol 25:1269–1288Google Scholar
  15. Bentz BJ, Vandygriff JC, Jensen C, Coleman T, Maloney P, Smith S, Grady A, Schen-Langenheim G (2014) Mountain pine beetle voltinism and life history characteristics across latitudinal and elevational gradients in the western United States. For Sci 60:434–449Google Scholar
  16. Berryman AA (1976) Theoretical explanation of mountain pine beetle dynamics in lodgepole pine forests. Environ Entomol 5:1225–1233CrossRefGoogle Scholar
  17. Berryman AA (2003) On principles, laws and theory in population ecology. Oikos 103:695–701CrossRefGoogle Scholar
  18. Beyer HL (2012) Geospatial Modeling Environment (Version 0.7.1.0). Available from http://www.spatialecology.com/gme. Accessed March 2013
  19. Bolstad PV, Bentz BJ, Logan JA (1997) Modelling micro-habitat temperature for Dendroctonus ponderosae (Coleoptera: Scolytidae). Ecol Model 94:287–297CrossRefGoogle Scholar
  20. Bone C, White J, Wulder M, Robertson C, Nelson T (2013) Impact of forest fragmentation on patterns of mountain pine beetle-caused tree mortality. Forests 4:279–295Google Scholar
  21. Boone CK, Aukema BH, Bohlmann J, Carroll AL, Raffa KF (2011) Efficacy of tree defense physiology varies with bark beetle population density: a basis for positive feedback in eruptive species. Can J For Res 41:1174–1188Google Scholar
  22. Buckley LB, Kingsolver J (2012) Functional and phylogenetic approaches to forecasting species’ responses to climate change. Annu Rev Ecol Syst 43:205–226CrossRefGoogle Scholar
  23. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer Verlag, New YorkGoogle Scholar
  24. Campbell EM, Alfaro RI, Hawkes B (2007) Spatial distribution of mountain pine beetle outbreaks in relation to climate and stand characteristics: a dendroecological analysis. J Integr Plant Biol 49:168–178CrossRefGoogle Scholar
  25. Carroll AL, Taylor SW, Régnière J, Safranyik L (2004) Effect of climate change on range expansion by the mountain pine beetle in British Columbia. In: Shore TL, Brooks JE, Shore JE (eds), Proceedings of the mountain pine beetle symposium: challenges and solutions, 30-31 Oct. 2003, Kelowna, BC, Information Report BC-X-399, Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, pp 223–232Google Scholar
  26. Chapman TB, Veblen TT, Schoennagel T (2012) Spatiotemporal patterns of mountain pine beetle activity in the southern Rocky Mountains. Ecology 93:2175–2185CrossRefPubMedGoogle Scholar
  27. Chen H, Walton A (2011) Mountain pine beetle dispersal: spatiotemporal patterns and role in the spread and expansion of the present outbreak. Ecosphere 2:1–17CrossRefGoogle Scholar
  28. Christensen JH, Hewitson B, Busuioc A, Chen A, Gao X, Held R, Jones R, Kolli RK, Kwon WK, Laprise R, Rueda VM, Mearns L, Menendez CG, Raisanen J, Rinke A, Sarr A, Whetton P (2007) Regional climate projections. In: Solomon S, Qin SD, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds), Climate Change, 2007: The Physical Science Basis. Contribution of Working group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, pp 847–940Google Scholar
  29. Cole WE (1981) Some risks and causes of mortality in mountain pine-beetle populations - a long-term analysis. Res Popul Ecol 23:116–144CrossRefGoogle Scholar
  30. Coulson T, Catchpole EA, Albon SD, Morgan BJ, Pemberton JM, Clutton-Brock TH, Crawley MJ, Grenfell BT (2001) Age, sex, density, winter weather, and population crashes in Soay sheep. Science 292:1528–1531Google Scholar
  31. Crozier L (2004) Warmer winters drive butterfly range expansion by increasing survivorship. Ecology 85:231–241CrossRefGoogle Scholar
  32. Cudmore TJ, Bjorklund N, Carroll AL, Lindgren BS (2010) Climate change and range expansion of an aggressive bark beetle: evidence of higher beetle reproduction in naive host tree populations. J Appl Ecol 47:1036–1043Google Scholar
  33. Daly C, Widrlechner MP, Halbleib MD, Smith JI, Gibson WP (2012) Development of a new USDA plant hardiness zone map for the United States. J Appl Meteor Climatol 51:242–264Google Scholar
  34. de la Giroday H-MC, Carroll AL, Aukema BH (2012) Breach of the northern Rocky Mountain geoclimatic barrier: initiation of range expansion by the mountain pine beetle. J Biogeogr 39:1112–1123CrossRefGoogle Scholar
  35. Deutsch CA, Tewksbury JJ, Huey RB, Sheldon KS, Ghalambor CK, Haak DC, Martin PR (2008) Impacts of climate warming on terrestrial ectotherms across latitude. Proc Natl Acad Sci U S A 105:6668–6672Google Scholar
  36. Donat MG, Alexander LV, Yang H, Durre I, Vose R, Dunn RJH, Willett KM, Aguilar E, Brunet M, Caesar J, Hewitson B, Jack C, Tank AMGK, Kruger AC, Marengo J, Peterson TC, Renom M, Oria Rojas C, Rusticucci M, Salinger J, Elrayah AS, Sekele SS, Srivastava AK, Trewin B, Villarroel C, Vincent LA, Zhai P, Zhang X, Kitching S (2013) Updated analyses of temperature and precipitation extreme indices since the beginning of the twentieth century: the HadEX2 dataset. J Geophys Res-Atmos 118:2098–2118Google Scholar
  37. Edburg SL, Hicke JA, Brooks PD (2012) Cascading impacts of bark beetle-caused tree mortality on coupled biogeophysical and biogeochemical processes. Front Ecol Environ 10:416–424CrossRefGoogle Scholar
  38. Edgell DJ (1994) Extreme minimum winter temperatures in Ohio. Ohio J Sci 94:41–54Google Scholar
  39. Evenden JC, Gibson AL (1940) A destructive infestation in lodgepole pine stands by the mountain pine beetle. J Forestry 38:271–275Google Scholar
  40. Fettig CJ, Gibson KE, Munson AS, Negron JF (2014) Cultural practices for prevention and mitigation of mountain pine beetle infestations. For Sci. doi:10.5849/forsci.13-032
  41. Fischer EM, Beyerle U, Knutti R (2013) Robust spatially aggregated projections of climate extremes. Nat Clim Change 3:1033–1038CrossRefGoogle Scholar
  42. Frazier MR, Huey RB, Berrigan D (2006) Thermodynamics constrains the evolution of insect population growth rates: “warmer is better”. Am Nat 168:512–520CrossRefPubMedGoogle Scholar
  43. Friedenberg NA, Sarkar S, Kouchoukos N, Billings RF, Ayres MP (2008) Temperature extremes, density dependence, and southern pine beetle (Coleoptera: Curculionidae) population dynamics in east Texas. Environ Entomol 37:650–659Google Scholar
  44. Gayathri Samarasekera GDN, Bartell NV, Lindgren BS, Cooke JEK, Davis CS, James PMA, Coltman DW, Mock KE, Murray BW (2012) Spatial genetic structure of the mountain pine beetle (Dendroctonus ponderosae) outbreak in western Canada: historical patterns and contemporary dispersal. Mol Ecol 21:2931–2948Google Scholar
  45. Hicke JA, Logan JA, Powell J, Ojima DS (2006) Changing temperatures influence suitability for modeled mountain pine beetle (Dendroctonus ponderosae) outbreaks in the western United States. J Geophys Res 111:G02019Google Scholar
  46. Jenkins J, Powell JA, Logan JA, Bentz BJ  (2001) Low Seasonal Temperatures Promote Life Cycle Synchronization. Bull Math Biol 63:573–595Google Scholar
  47. Jepsen J, Hagen S, Ims R (2008) Climate change and outbreaks of the geometrids Operophtera brumata and Epirrita autumnata in subarctic birch forest: evidence of a recent outbreak range expansion. J Anim Ecol 77:257–264CrossRefPubMedGoogle Scholar
  48. Jung H-S, Choi Y, Oh J-H, Lim G-H (2002) Recent trends in temperature and precipitation over South Korea. Int J Climatol 22:1327–1337Google Scholar
  49. Keen FP, Furniss RL (1937) Effects of subzero temperatures on populations of western pine beetle Dendroctonus brevicomis Lee. J Econ Entomol 30:482–504CrossRefGoogle Scholar
  50. Kinloch BB (2003) White pine blister rust in North America: past and prognosis. Phytopathology 93:1044–1047CrossRefPubMedGoogle Scholar
  51. Lee RE (2010) A primer on insect cold-tolerance. In: Denlinger DL, Lee RE (eds) Low temperature biology of insects. Cambridge University Press, CambridgeK, pp 3–35CrossRefGoogle Scholar
  52. Lester JD, Irwin JT (2012) Metabolism and cold tolerance of overwintering adult mountain pine beetles (Dendroctonus ponderosae): evidence of facultative diapause? J Insect Physiol 58:808–815CrossRefPubMedGoogle Scholar
  53. Liebhold AM, Koenig W, Bjørnstad ON (2004) Spatial synchrony in population dynamics. Annu Rev Ecol Evol Syst 35:467–490CrossRefGoogle Scholar
  54. Logan JA, Powell JA (2001) Ghost forests, global warming, and the mountain pine beetle (Coleoptera:Scolytidae). Am Entomol 47:160–173CrossRefGoogle Scholar
  55. Logan JA, Macfarlane WW, Willcox L (2010) Whitebark pine vulnerability to climate-driven mountain pine beetle disturbance in the Greater Yellowstone Ecosystem. Ecol Appl 20:895–902CrossRefPubMedGoogle Scholar
  56. Luterbacher J, Dietrich D, Xoplaki E, Grosjean M, Wanner H (2004) European seasonal and annual temperature variability, trends, and extremes since 1500. Science 303:1499–1503Google Scholar
  57. Macias Fauria M, Johnson EA (2009) Large-scale climatic patterns and area affected by mountain pine beetle in British Columbia. Canada. J Geophys Res 114:G01012Google Scholar
  58. MacQuarrie CJK, Cooke BJ (2011) Density-dependent population dynamics of mountain pine beetle in thinned and unthinned stands. Can J For Res 41:1031–1046CrossRefGoogle Scholar
  59. Martinson SJ, Ylioja T, Sullivan BT, Billings RF, Ayres MP (2013) Alternate attractors in the population dynamics of a tree-killing bark beetle. Popul Ecol 55:95–106Google Scholar
  60. 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 22:1876–1891CrossRefPubMedGoogle Scholar
  61. Mock KE, Bentz BJ, O’Neill EM, Chong JP, Orwin J, Pfrender ME (2007) Landscape-scale genetic variation in a forest outbreak species, the mountain pine beetle (Dendroctonus ponderosae). Mol Ecol 16:553–568Google Scholar
  62. Mora C, Frazier AG, Longman RJ, Dacks RS, Walton MM, Tong EJ, Sanchez JJ, Kaiser LR, Stender YO, Anderson JM, Ambrosino CM, Fernandez-Silva I, Giuseffi LM, Giambelluca TW (2013) The projected timing of climate departure from recent variability. Nature 502:183–187Google Scholar
  63. Moran P (1953) The statistical analysis of the Canadian lynx cycle. 2. Synchronization and meteorology. Aust J Zool 1:291–298CrossRefGoogle Scholar
  64. Morris RF (1959) Single-factor analysis in population dynamics. Ecology 40:580–588CrossRefGoogle Scholar
  65. Økland B, Berryman AA (2004) Resource dynamic plays a key role in regional fluctuations of the spruce bark beetles Ips typographus. Agric For Entomol 6:141–146CrossRefGoogle Scholar
  66. Omernik JM (2004) Perspectives on the nature and definition of ecological regions. Environ Manag 34:S27–S38CrossRefGoogle Scholar
  67. Paradis A, Elkinton J, Hayhoe K (2008) Role of winter temperature and climate change on the survival and future range expansion of the hemlock woolly adelgid (Adelges tsugae) in eastern North America. Mitigation Adapt Strateg Glob Chang 13:541–554CrossRefGoogle Scholar
  68. Peet RK (2000) Forests and meadows of the Rocky Mountains. In: Barbour MG, Billings WD (eds) North American terrestrial vegetation. Cambridge University Press, New York, pp 75–122Google Scholar
  69. Powell JA, Bentz BJ (2009) Connecting phenological predictions with population growth rates for mountain pine beetle, an outbreak insect. Landscape Ecol 24:657–672CrossRefGoogle Scholar
  70. Powell JA, Bentz BJ (2014) Phenology and density-dependent dispersal predict patterns of mountain pine beetle (Dendroctonus ponderosae) impact. Ecol Model 273:173–185CrossRefGoogle Scholar
  71. Preisler HK, Hicke JA, Ager A, Hayes JL  (2012) Climate and weather influences on spatial temporal patterns of mountain pine beetle populations in Washington and Oregon. Ecology 93:2421–2434Google Scholar
  72. Raffa KF, Berryman AA (1986) A mechanistic computer model of mountain pine beetle populations interacting with lodgepole pine stands and its implications for forest managers. For Sci 32:789–805Google Scholar
  73. Raffa KF, Aukema BH, Bentz BJ, Carroll AL, Hicke JA, Turner MG, Romme WH (2008) Cross-scale drivers of natural disturbances prone to anthropogenic amplification: the dynamics of bark beetle eruptions. Bioscience 58:501–517Google Scholar
  74. Régnière J (1996) Generalized approach to landscape-wide seasonal forecasting with temperature-driven simulation models. Environ Entomol 25:869–881CrossRefGoogle Scholar
  75. Régnière J, Bentz BJ (2007) Modeling cold tolerance in the mountain pine beetle, Dendroctonus ponderosae. J Insect Physiol 53:559–572CrossRefPubMedGoogle Scholar
  76. Régnière J, St-Amant R (2007) BioSIM 9 user’s manual. Information Report LAU-X-129. Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, Quebec, CanadaGoogle Scholar
  77. Robinet C, Roques A (2010) Direct impacts of recent climate warming on insect populations. Integr Zool 5:132–142CrossRefPubMedGoogle Scholar
  78. Royama T (1992) Analytical population dynamics. Chapman & Hall, LondonCrossRefGoogle Scholar
  79. Ruefenacht B, Finco MV, Nelson MD, Czaplewsk R, Helmer EH, Blackard JA, Holden GR, Lister AJ, Salajanu D, Weyermann D, Winterberger K (2008) Conterminous U.S. and Alaska forest type mapping using forest inventory and analysis data. USDA Forest Service, Forest Inventory and Analysis, Arlington, VAGoogle Scholar
  80. Sæther BE, Engen S, Matthysen E (2002) Demographic characteristics and population dynamical patterns of solitary birds. Science 295:2070–2073CrossRefPubMedGoogle Scholar
  81. Safranyik L (1978) Effects of climate and weather on mountain pine beetle populations. In: Kibbee DL, Berryman AA, Amman GD, Stark RW (eds), Proceedings of Symposium on theory and practice of mountain pine beetle management in lodgepole pine forests, 25–27 April 1978, Pullman, Washington University of Idaho, Moscow, Idaho and USDA Forest Service, Odgen, UT, Washington State University, Pullman, Washington, pp 77–86Google Scholar
  82. Safranyik L, Carroll AL (2006) The biology and epidemiology of the mountain pine beetle in lodgepole pine forests. In: Safranyik L, Wilson WR (eds) The mountain pine beetle: a synthesis of biology, management, and impacts on lodgepole pine. Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, Victoria, pp 3–66Google Scholar
  83. Safranyik L, Linton DA (1991) Unseasonably low fall and winter temperatures affecting mountain pine beetle and pine engraver beetle populations and damage in the British Columbia Chilcotin Region. J Entomol Soc BC 88:17–21Google Scholar
  84. Safranyik L, Linton DA (1998) Mortality of mountain pine beetle larvae, Dendroctonus ponderosae (Coleoptera: Scolytidae) in logs of lodgepole pine (Pinus contorta var. latifolia) at constant low temperatures. J Entomol Soc B C 95:81–87Google Scholar
  85. Safranyik L, Carroll AL, Regniere J, Langor DW, Riel WG, Shore TL, Peter B, Cooke BJ, Nealis VG, Taylor SW (2010) Potential for range expansion of mountain pine beetle into the boreal forest of North America. Can Entomol 142:415–442Google Scholar
  86. Sambaraju KR, Carroll AL, Zhu J, Stahl K, Moore RD, Aukema BH (2012) Climate change could alter the distribution of mountain pine beetle outbreaks in western Canada. Ecography 35:211–223Google Scholar
  87. Somme L (1964) Effects of glycerol on cold-hardiness in insects. Can J Zool 42:87–101CrossRefGoogle Scholar
  88. Somme L (1982) Supercooling and winter survival in terrestrial arthropods. Comp Biochem Physiol 73:519–543CrossRefGoogle Scholar
  89. Taylor SW, Carroll AL (2004) Disturbance, forest age, and mountain pine beetle outbreak dynamics in BC: A historical perspective. In: Shore TL, Brooks JE, Stone JE (eds), Proceedings of the mountain pine beetle symposium: challenges and solutions, 30–31 Oct. 2003, Kelowna, BC, Information Report BC-X-399, Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, pp 67–94Google Scholar
  90. Thomas CD, Cameron A, Green RE, Bakkenes M, Beaumont LJ, Collingham YC, Erasmus BFN, De Siqueira MF, Grainger A, Hannah L, Hughes L, Huntley B, Van Jaarsveld AS, Midgley GF, Miles L, Ortega-Huerta MA, Peterson AT, Phillips OL, Williams SE (2004) Extinction risk from climate change. Nature 427:145–148Google Scholar
  91. Tran JK, Ylioja T, Billings RF, Régnière J, Ayres MP (2007) Impact of minimum winter temperatures on the population dynamics of Dendroctonus frontalis. Ecol Appl 17:882–899Google Scholar
  92. Valtonen A, Leinonen R, Pöyry J, Roininen H, Tuomela J, Ayres MP (2014) Is climate warming more consequential towards poles? The phenology of Lepidoptera in Finland. Global Change Biol 20:16–27Google Scholar
  93. Varley GC, Gradwell GR, Hassell MP (1973) Insect population ecology. Blackwell, OxfordGoogle Scholar
  94. Vose RS, Easterling DR, Gleason B (2005) Maximum and minimum temperature trends for the globe: an update through 2004. Geophys Res Lett. doi:10.1029/2005GL024379 Google Scholar
  95. Weed AS, Ayres MP, Hicke JA (2013) Consequences of climate change for biotic disturbances in North American forests. Ecol Monogr 83:441–470CrossRefGoogle Scholar
  96. Zuur A, Ieno EN, Walker N, Saveliev AA, Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht (outside the USA) 2015

Authors and Affiliations

  • Aaron S. Weed
    • 1
  • Barbara J. Bentz
    • 2
  • Matthew P. Ayres
    • 1
  • Thomas P. Holmes
    • 3
  1. 1.Department of Biological SciencesDartmouth CollegeHanoverUSA
  2. 2.USDA Forest ServiceRocky Mountain Research StationLoganUSA
  3. 3.USDA Forest ServiceSouthern Research StationResearch Triangle ParkUSA

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