Landscape Ecology

, Volume 32, Issue 12, pp 2365–2381 | Cite as

A Bayesian method for assessing multi-scale species-habitat relationships

  • Erica F. StuberEmail author
  • Lutz F. Gruber
  • Joseph J. Fontaine
Research Article



Scientists face several theoretical and methodological challenges in appropriately describing fundamental wildlife-habitat relationships in models. The spatial scales of habitat relationships are often unknown, and are expected to follow a multi-scale hierarchy. Typical frequentist or information theoretic approaches often suffer under collinearity in multi-scale studies, fail to converge when models are complex or represent an intractable computational burden when candidate model sets are large.


Our objective was to implement an automated, Bayesian method for inference on the spatial scales of habitat variables that best predict animal abundance.


We introduce Bayesian latent indicator scale selection (BLISS), a Bayesian method to select spatial scales of predictors using latent scale indicator variables that are estimated with reversible-jump Markov chain Monte Carlo sampling. BLISS does not suffer from collinearity, and substantially reduces computation time of studies. We present a simulation study to validate our method and apply our method to a case-study of land cover predictors for ring-necked pheasant (Phasianus colchicus) abundance in Nebraska, USA.


Our method returns accurate descriptions of the explanatory power of multiple spatial scales, and unbiased and precise parameter estimates under commonly encountered data limitations including spatial scale autocorrelation, effect size, and sample size. BLISS outperforms commonly used model selection methods including stepwise and AIC, and reduces runtime by 90%.


Given the pervasiveness of scale-dependency in ecology, and the implications of mismatches between the scales of analyses and ecological processes, identifying the spatial scales over which species are integrating habitat information is an important step in understanding species-habitat relationships. BLISS is a widely applicable method for identifying important spatial scales, propagating scale uncertainty, and testing hypotheses of scaling relationships.


Abundance Bayesian model selection Habitat selection Model uncertainty Spatial scale 



Funding for this project was received from Federal Aid in Wildlife Restoration projects W-98-R, administered by the Nebraska Game and Parks Commission. We would like to thank Chelsea Forehead, Caitlyn Gillespi, Anthony Jenniges, Amanda Lipinski, and Lindsey Messinger for their assistance in collecting the data presented here, Annie Madsen and Matthew Strassburg for assistance in conducting the literature review, and two anonymous reviewers for their valuable comments on earlier versions of this manuscript. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. The Nebraska Cooperative Fish and Wildlife Research Unit is supported by a cooperative agreement among the U.S. Geological Survey, the Nebraska Game and Parks Commission, the University of Nebraska, the U.S. Fish and Wildlife Service, and the Wildlife Management Institute. The authors declare no conflicts of interest.

Supplementary material

10980_2017_575_MOESM1_ESM.r (4 kb)
Supplementary material 1 (R 5 kb)
10980_2017_575_MOESM2_ESM.txt (2 kb)
Supplementary material 2 (TXT 2 kb)
10980_2017_575_MOESM3_ESM.7z (78 kb)
Supplementary material3 (7Z 78 kb)


  1. Akaike H (1998) Information theory and an extension of the maximum likelihood principle. In: Parzen E, Tanabe K, Kitagawa G (eds) Selected papers of Hirotugu Akaike. Springer, New York, pp 199–213CrossRefGoogle Scholar
  2. Anselin L, Griffith DA (1988) Do spatial effects really matter in regression analysis? Pap Reg Sci 65(1):11–34CrossRefGoogle Scholar
  3. Būhning-Gaese K (1997) Determinants of avian species richness at different spatial scales. J Biogeogr 24(1):49–60CrossRefGoogle Scholar
  4. Bini LM, Diniz JAF, Rangel TFLVB, Akre TSB, Albaladejo RG, Albuquerque FS, Aparicio A, Araújo MD, Baselga A, Beck J, Isabel Bellocq M, Böhning-Gaese K, Borges PAV, Castro-Parga I, Chey VK, Chown SL, De Marco Paulo Jr, Dobkin DS, Ferrer-Castán D, Field R, Filloy J, Fleishman E, Gómez JF, Hortal J, Iverson JB, Kerr JT, Daniel Kissling W, Kitching IJ, León-Cortés JL, Lobo JM, Montoya D, Morales-Castilla I, Moreno JC, Oberdorff T, Olalla-Tárraga MÁ, Pausas JG, Qian H, Rahbek C, RodrÍguez MÁ, Rueda M, Ruggiero A, Sackmann P, Sanders NJ, Terribile LC, Vetaas OR, Hawkins BA (2009) Coefficient shifts in geographical 565 ecology: an empirical evaluation of spatial and non-spatial regression. Ecography 32(2):193–204CrossRefGoogle Scholar
  5. Bishop A, Barenberg A, Volpe N, Riens J, Grosse R (2011) Nebraska land cover development. Rainwater Basin Joint Venture Report, Landcover Accuracy Assessment ReportGoogle Scholar
  6. Boyce MS (2006) Scale for resource selection functions. Divers Distrib 12(3):269–276CrossRefGoogle Scholar
  7. Chalfoun AD, Martin TE (2007) Assessments of habitat preferences and quality depend on spatial scale and metrics of fitness. J Appl Ecol 44(5):983–992CrossRefGoogle Scholar
  8. Chase JM, Myers JA (2011) Disentangling the importance of ecological niches from stochastic processes across scales. Philos Trans R Soc Lond 366(1576):2351–2363CrossRefGoogle Scholar
  9. Clifford P, Richardson S, Hémon D (1989) Assessing the significance of the correlation between two spatial processes. Biometrics 12:123–134CrossRefGoogle Scholar
  10. Coppeto SA, Kelt DA, Van Vuren DH, Wilson JA, Bigelow S (2006) Habitat associations of small mammals at two spatial scales in the northern Sierra Nevada. J Mammal 87(2):402–413CrossRefGoogle Scholar
  11. Cunningham RB, Lindenmayer DB, Crane M, Michael DR, Barton PS, Gibbons P, Okada S, Ikin K, Stein JAR (2014) The law of diminishing returns: woodland birds respond to native vegetation cover at multiple spatial scales and over time. Divers Distrib 20(1):59–71CrossRefGoogle Scholar
  12. Cushman SA, McGarigal K (2002) Hierarchical, multi-scale decomposition of species-environment relationships. Landscape Ecol 17(7):637–646CrossRefGoogle Scholar
  13. De Knegt HJ, van Langevelde FV, Coughenour MB, Skidmore AK, de Boer WF, Heitkönig IMA, Knox NM, van der Waal C, Prins HHT (2010) Spatial autocorrelation and the scaling of species-environment relationships. Ecology 91(8):2455–2465CrossRefPubMedGoogle Scholar
  14. Dungan JL, Perry JN, Dale MRT, Legendre P, Citron-Pousty S, Fortin M-J, Jakomulska A, Miriti M, Rosenberg MS (2002) A balanced view of scale in spatial statistical analysis. Ecography 25(5):626–640CrossRefGoogle Scholar
  15. Gelman A, Hwang J, Vehtari A (2014) Understanding predictive information criteria for Bayesian models. Stat Comput 24(6):997–1016CrossRefGoogle Scholar
  16. Godsill SJ (2001) On the relationship between Markov Chain Monte Carlo methods for model uncertainty. J Comput Graph Stat 10(2):1–19CrossRefGoogle Scholar
  17. Grand J, Cushman SA (2003) A multi-scale analysis of species-environment relationships: breeding birds in a pitch pine-scrub oak (Pinus rigidaQuercus ilicifolia) community. Biol Conserv 112(3):307–317CrossRefGoogle Scholar
  18. Gray TNE, Phan C, Long B (2010) Modelling species distribution at multiple spatial scales: gibbon habitat preferences in a fragmented landscape. Anim Conserv 13(3):324–332CrossRefGoogle Scholar
  19. Guillera-Arroita G, Lahoz-Monfort José JJ, MacKenzie DI, Wintle BA, McCarthy MA (2014) Ignoring imperfect detection in biological surveys is dangerous: a response to ‘fitting and interpreting occupancy models’. PLoS ONE 9(7):71CrossRefGoogle Scholar
  20. Guisan A, Thuiller W (2005) Predicting species distribution: offering more than simple habitat models. Ecol Lett 8(9):993–1009CrossRefGoogle Scholar
  21. Henebry GM (1995) Spatial model error analysis using autocorrelation indexes. Ecol Model 82(1):75–91CrossRefGoogle Scholar
  22. Holland JD, Bert DG, Fahrig L (2004) Determining the spatial scale of species’ response to habitat. BioScience 54(3):227–233CrossRefGoogle Scholar
  23. Hooten MB, Hobbs NT (2015) A guide to Bayesian model selection for ecologists. Ecol Monogr 85(1):3–28CrossRefGoogle Scholar
  24. Horne JK, Schneider DC (1995) Spatial variance in ecology. Oikos 12:18–26CrossRefGoogle Scholar
  25. Hurlbert AH, Jetz W (2007) Species richness, hotspots, and the scale dependence of range maps in ecology and conservation. Proc Natl Acad Sci 104(33):13384–13389CrossRefPubMedPubMedCentralGoogle Scholar
  26. Hutto RL, Pletschet SM, Hendricks P (1986) A fixed-radius point count method for nonbreeding and breeding season use. Auk 12:593–602Google Scholar
  27. Jackson HB, Fahrig L (2015) Are ecologists conducting research at the optimal scale? Glob Ecol Biogeogr 24(1):52–63CrossRefGoogle Scholar
  28. Johnson DS, Hoeting JA (2011) Bayesian multimodel inference for geostatistical regression models. PLoS ONE 6(11):e25677CrossRefPubMedPubMedCentralGoogle Scholar
  29. Jorgensen CF, Powell LA, Lusk JJ, Bishop AA, Fontaine JJ (2014) Assessing landscape constraints on species abundance: does the neighborhood limit species response to local habitat conservation programs? PLoS ONE 9(6):e99339CrossRefPubMedPubMedCentralGoogle Scholar
  30. Keitt TH, Bjornstad ON, Dixon PM, Citron-Pousty S (2002) Accounting for spatial pattern when modeling organism-environment interactions. Ecography 25(5):616–625CrossRefGoogle Scholar
  31. Kellner KF, Swihart RK (2014) Accounting for imperfect detection in ecology: a quantitative review. PLoS ONE 9(10):e111436CrossRefPubMedPubMedCentralGoogle Scholar
  32. Kirol CP, Beck JL, Huzurbazar SV, Holloran MJ, Miller SN (2015) Identifying greater Sage-Grouse source and sink habitats for conservation planning in an energy development landscape. Ecol Appl 25(4):968–990CrossRefPubMedGoogle Scholar
  33. Kuhn I (2007) Incorporating spatial autocorrelation may invert observed patterns. Divers Distrib 13(1):66–69Google Scholar
  34. Legendre P, Dale MRT, Fortin M-J, Gurevitch J, Hohn M, Myers D (2002) The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25(5):601–615CrossRefGoogle Scholar
  35. Lennon JJ (2000) Red-shifts and red herrings in geographical ecology. Ecography 23(1):101–113CrossRefGoogle Scholar
  36. Levin SA (1992) The problem of pattern and scale in ecology: the Robert H. MacArthur award lecture. Ecology 73(6):1943–1967CrossRefGoogle Scholar
  37. Mccarthy KP, Fletcher RJ Jr, Rota CT, Hutto RL (2012) Predicting species distributions from samples collected along roadsides. Conserv Biol 26(1):68–77CrossRefPubMedGoogle Scholar
  38. Nams VO (2005) Using animal movement paths to measure response to spatial scale. Oecologia 143(2):179–188CrossRefPubMedGoogle Scholar
  39. O’Hara RB, Sillanpää MJ (2009) A review of Bayesian variable selection methods: what, how and which. Bayesian Anal 4(1):85–117CrossRefGoogle Scholar
  40. Overmars KP, De Koning GHJ, Veldkamp A (2003) Spatial autocorrelation in multi-scale land use models. Ecol Model 164(2):257–270CrossRefGoogle Scholar
  41. Pearson RG, Dawson TP, Liu C (2004) Modelling species distributions in Britain: a hierarchical integration of climate and land-cover data. Ecography 27(3):285–298CrossRefGoogle Scholar
  42. Plummer M (2003) JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd international workshop on distributed statistical computing, vol 124, p 125Google Scholar
  43. Plummer M (2013) rjags: Bayesian graphical models using MCMC. R package version 3Google Scholar
  44. Pope SE, Fahrig L, Gray Merriam H (2000) Landscape complementation and metapopulation effects on leopard frog populations. Ecology 81(9):2498–2508CrossRefGoogle Scholar
  45. Robbins CS, Bystrak D, Geissler PH (1986) The breeding bird survey: its first fifteen years, 1965–1979. Report, DTIC DocumentGoogle Scholar
  46. Robinson WS (1950) Ecological correlations and the behavior of individuals. Am Sociol Rev 15(3):351–357CrossRefGoogle Scholar
  47. Royle JA (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60(1):108–115CrossRefPubMedGoogle Scholar
  48. Saab V (1999) Importance of spatial scale to habitat use by breeding birds in riparian forests: a hierarchical analysis. Ecol Appl 9(1):135–151CrossRefGoogle Scholar
  49. Sandel B, Smith AB (2009) Scale as a lurking factor: incorporating scale-dependence in experimental ecology. Oikos 118(9):1284–1291CrossRefGoogle Scholar
  50. Schwartz MW, Iverson LR, Prasad AM, Matthews SN, O’Connor RJ (2006) Predicting extinctions as a result of climate change. Ecology 87(7):1611–1615CrossRefPubMedGoogle Scholar
  51. Steffan-Dewenter I, Münzenberg U, Bürger C, Thies C, Tscharntke T (2002) Scale-dependent effects of landscape context on three pollinator guilds. Ecology 83(5):1421–1432CrossRefGoogle Scholar
  52. Tenan S, O’Hara RB, Hendriks I, Tavecchia G (2014) Bayesian model selection: the steepest mountain to climb. Ecol Model 283:62–69CrossRefGoogle Scholar
  53. Thornton DH, Fletcher RJ (2014) Body size and spatial scales in avian response to landscapes: a meta-analysis. Ecography 37(5):454–463Google Scholar
  54. Turner MG, O’Neill RV, Gardner RH, Mine BT (1989) Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecol 3(3–4):153–162CrossRefGoogle Scholar
  55. Urban DL, Robert VO, Shugart HH Jr (1987) A hierarchical perspective can help scientists understand spatial patterns. BioScience 37(2):119–127CrossRefGoogle Scholar
  56. van Langevelde F (2000) Scale of habitat connectivity and colonization in fragmented nuthatch populations. Ecography 23:614–622CrossRefGoogle Scholar
  57. Watanabe S (2013) A widely applicable Bayesian information criterion. J Mach Learn Res 14:867–897Google Scholar
  58. Wheatley M, Johnson C (2009) Factors limiting our understanding of ecological scale. Ecol Complex 6(2):150–159CrossRefGoogle Scholar
  59. Williams BK, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic Press, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Erica F. Stuber
    • 1
    Email author
  • Lutz F. Gruber
    • 1
  • Joseph J. Fontaine
    • 2
  1. 1.Nebraska Cooperative Fish and Wildlife Research Unit, School of Natural ResourcesUniversity of Nebraska-LincolnLincolnUSA
  2. 2.U.S. Geological Survey Nebraska Cooperative Fish and Wildlife Research Unit, School of Natural ResourcesUniversity of Nebraska-LincolnLincolnUSA

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