Population Ecology

, Volume 58, Issue 1, pp 31–44 | Cite as

Bayesian data analysis in population ecology: motivations, methods, and benefits

  • Robert M. DorazioEmail author
Special feature: Review Bayesian, Fisherian, error, and evidential statistical approaches for population ecology


During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.


Frequentist inference Hierarchical modeling Missing data Occupancy model Spatial analysis State-space modeling 



I thank Dr. Yukihiko Toquenaga for inviting me to present this article in a plenary symposium of the 30th Annual Meeting of the Society of Population Ecology in Tsukuba, Japan. I am also grateful to the Society and to the University of Tsukuba for providing funding for my travel expenses and publication costs. Chris Wikle and two anonymous referees kindly provided suggestions that improved an earlier draft of this article. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Supplementary material

10144_2015_503_MOESM1_ESM.pdf (176 kb)
Supplementary material 1 (PDF 176 kb)


  1. Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc 53:370–418CrossRefGoogle Scholar
  2. Berger JO (2006) The case for objective Bayesian analysis. Bayesian Anal 1:385–402CrossRefGoogle Scholar
  3. Box GEP (1980) Sampling and Bayes inference in scientific modelling and robustness (with discussion). J Royal Statist Soc Ser A 143:383–430CrossRefGoogle Scholar
  4. Box GEP, Tiao GC (1973) Bayesian inference in statistical analysis. Addison-Wesley, ReadingGoogle Scholar
  5. Brooks S, Gelman A, Jones GL, Meng XL (eds) (2011) Handbook of Markov chain Monte Carlo. Chapman & Hall / CRC, Boca Raton, FloridaGoogle Scholar
  6. Buckland ST, Newman KB, Fernández C, Thomas L, Harwood J (2007) Embedding population dynamics models in inference. Stat Sci 22:44–58CrossRefGoogle Scholar
  7. Clark JS (2007) Models for ecological data: an introduction. Princeton University Press, PrincetonGoogle Scholar
  8. Diggle PJ, Tawn JA, Moyeed RA (1998) Model-based geostatistics (with discussion). Journal of the Royal Statistical Society. C (Applied Statistics) 47:299–350CrossRefGoogle Scholar
  9. Dorazio RM, Taylor Rodríguez D (2012) A Gibbs sampler for Bayesian analysis of site-occupancy data. Methods Ecol Evol 3:1093–1098CrossRefGoogle Scholar
  10. Draper D (1996) Utility, sensitivity analysis, and cross-validation in Bayesian model-checking. Stat Sinica 6:760–767Google Scholar
  11. Efron B (2005) Bayesians, frequentists, and scientists. J Am Stat Assoc 100:1–5CrossRefGoogle Scholar
  12. Flegal JM, Jones GL (2010) Batch means and spectral variance estimators in Markov chain Monte Carlo. Ann Stat 38:1034–1070CrossRefGoogle Scholar
  13. Flegal JM, Jones GL (2011) Implementing MCMC: estimating with confidence. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo, Chapman & Hall / CRC. Florida, Boca Raton, pp 175–197Google Scholar
  14. Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409CrossRefGoogle Scholar
  15. Gelman A (2011) Induction and deduction in Bayesian data analysis. Rational Markets Morals 2:67–78Google Scholar
  16. Gelman A, Shirley K (2011) Inference from simulations and monitoring convergence. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo, Chapman & Hall / CRC. Florida, Boca Raton, pp 163–174Google Scholar
  17. Gelman A, Meng XL, Stern H (1996) Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Stat Sinica 6:733–807Google Scholar
  18. Geyer CJ (2011) Introduction to Markov chain Monte Carlo. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo, Chapman & Hall / CRC. Florida, Boca Raton, pp 3–48Google Scholar
  19. Hobert JP (2011) The data augmentation algorithm: theory and methodology. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo. Chapman & Hall / CRC, Boca Raton, Florida, pp 253–293Google Scholar
  20. Hooten MB, Hobbs NT (2015) A guide to Bayesian model selection for ecologists. Ecol Monogr 85:3–28CrossRefGoogle Scholar
  21. Hooten MB, Wikle CK (2007) A hierarchical bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasion collared-dove. Environ Ecol Stat 15:59–70CrossRefGoogle Scholar
  22. Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, New YorkGoogle Scholar
  23. Johnson DS, Conn PB, Hooten MB, Ray JC, Pond BA (2013) Spatial occupancy models for large data sets. Ecology 94:801–808CrossRefGoogle Scholar
  24. Kéry M, Schaub M (2012) Bayesian population analysis using WinBUGS. Academic Press, WalthamGoogle Scholar
  25. Kéry M, Dorazio RM, Soldaat L, van Strien A, Zuiderwijk A, Royle JA (2009) Trend estimation in populations with imperfect detection. J Appl Ecol 46:1163–1172Google Scholar
  26. King R, Morgan BJT, Gimenez O, Brooks SP (2010) Bayesian analysis for population ecology. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  27. Laird NM, Louis TA (1987) Empirical Bayes confidence intervals based on bootstrap samples (with discussion). J Am Stat Assoc 82:739–757CrossRefGoogle Scholar
  28. Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974PubMedCrossRefGoogle Scholar
  29. Laplace PS (1774a) Memoir on the probability of the causes of events. Stat Sci 1:364–378 (English translation of the French original by S. M. Stigler in 1986) Google Scholar
  30. Laplace PS (1774b) A philosophical essay on probabilities. John Wiley & Sons, New York (English translation of the French original by F. W. Truscott and F. L. Emory in 1902)Google Scholar
  31. Lindley DV (2000) The philosophy of statistics (with discussion). Statist 49:293–337Google Scholar
  32. Link WA, Barker RJ (2010) Bayesian inference. Academic Press, AmsterdamGoogle Scholar
  33. Little R (2011) Calibrated Bayes, for statistics in general, and missing data in particular. Stat Sci 26:162–174CrossRefGoogle Scholar
  34. Little RJ (2006) Calibrated Bayes: a Bayes/frequentist roadmap. Am Stat 60:213–223CrossRefGoogle Scholar
  35. Little RJA, Rubin DB (2002) Statistical analysis with missing data, 2nd edn. Wiley, HobokenGoogle Scholar
  36. MacKenzie DI, Nichols JD, Lachman GB, Droege S, Royle JA, Langtimm CA (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248–2255CrossRefGoogle Scholar
  37. MacKenzie DI, Nichols JD, Royle JA, Pollock KH, Bailey LL, Hines JE (2006) Occupancy estimation and modeling. Elsevier, AmsterdamGoogle Scholar
  38. McCarthy M (2007) Bayesian methods for ecology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  39. McCarthy MA, Masters P (2005) Profiting from prior information in Bayesian analyses of ecological data. J Appl Ecol 42:1012–1019CrossRefGoogle Scholar
  40. Morris CN (1983) Parametric empirical Bayes inference: theory and applications (with discussion). J Am Stat Assoc 78:47–65CrossRefGoogle Scholar
  41. Morris WK, Vesk PA, McCarthy MA (2013) Profiting from prior studies: analysing mortality using Bayesian models with informative priors. Basic Appl Ecol 14:81–89CrossRefGoogle Scholar
  42. Nichols JD, Pollock KH, Hines JE (1984) The use of a robust capture-recapture design in small mammal population studies: A field example with Microtus pennsylvanicus. Acta Theriol 29:357–365CrossRefGoogle Scholar
  43. Parent E, Rivot E (2013) Introduction to hierarchical Bayesian modeling for ecological data. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  44. Robert C, Casella G (2011) A short history of MCMC: subjective recollections from incomplete data. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo. Chapman & Hall / CRC, Boca Raton, Florida, pp 49–66Google Scholar
  45. Royle JA, Dorazio RM (2006) Hierarchical models of animal abundance and occurrence. J Agr Biol Environ Stat 11:249–263CrossRefGoogle Scholar
  46. Royle JA, Dorazio RM (2008) Hierarchical modeling and inference in ecology. Academic Press, AmsterdamGoogle Scholar
  47. Royle JA, Dorazio RM (2012) Parameter-expanded data augmentation for Bayesian analysis of capture-recapture models. J Ornithol 152:S521–S537CrossRefGoogle Scholar
  48. Royle JA, Wikle CK (2005) Efficient statistical mapping of avian count data. Environ Ecol Stat 12:225–243CrossRefGoogle Scholar
  49. Rubin DB (1984) Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann Stat 12:1151–1172CrossRefGoogle Scholar
  50. Schaub M, Abadi F (2011) Integrated population models: a novel analysis framework for deeper insights into population dynamics. J Ornithol 152:S227–S237CrossRefGoogle Scholar
  51. Tanner MA (1996) Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 3rd edn. Springer-Verlag, New YorkCrossRefGoogle Scholar
  52. Tyre AJ, Tenhumberg B, Field SA, Niejalke D, Parris K, Possingham HP (2003) Improving precision and reducing bias in biological surveys: estimating false-negative error rates. Ecol Appl 13:1790–1801CrossRefGoogle Scholar
  53. Walters JR, Beissinger SR, Fitzpatrick JW, Greenberg R, Nichols JD, Pulliam HR, Winkler DW (2000) The AOU conservation committee review of the biology, status, and management of Cape Sable seaside sparrows: final report. Auk 117:1093–1115Google Scholar
  54. Wikle CK (2003) Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 84:1382–1394CrossRefGoogle Scholar
  55. Wikle CK (2010) Hierarchical modeling with spatial data. In: Gelfand AE, Diggle PJ, Fuentes M, Guttorp P (eds) Handbook of spatial statistics. Chapman & Hall / CRC, Boca Raton, Florida, pp 89–106CrossRefGoogle Scholar
  56. Williams BK, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic Press, San Diego, CaliforniaGoogle Scholar

Copyright information

© The Society of Population Ecology and Springer Japan (outside the USA)  2015

Authors and Affiliations

  1. 1.U.S. Geological SurveySoutheast Ecological Science CenterGainesvilleUSA

Personalised recommendations