Skip to main content
SpringerLink
Log in

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

  • Special feature: Review
  • Bayesian, Fisherian, error, and evidential statistical approaches for population ecology
  • Published:
Population Ecology

Abstract

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. I use bracket notation (Gelfand and Smith 1990) to specify probability density functions; thus, [x, y] denotes the joint density of random variables X and Y, [x | y] denotes the conditional density of X given \(Y=y\), and [x] denotes the unconditional (marginal) density of X.

References

  • Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc 53:370–418

    Article  Google Scholar 

  • Berger JO (2006) The case for objective Bayesian analysis. Bayesian Anal 1:385–402

    Article  Google Scholar 

  • Box GEP (1980) Sampling and Bayes inference in scientific modelling and robustness (with discussion). J Royal Statist Soc Ser A 143:383–430

    Article  Google Scholar 

  • Box GEP, Tiao GC (1973) Bayesian inference in statistical analysis. Addison-Wesley, Reading

  • Brooks S, Gelman A, Jones GL, Meng XL (eds) (2011) Handbook of Markov chain Monte Carlo. Chapman & Hall / CRC, Boca Raton, Florida

    Google Scholar 

  • Buckland ST, Newman KB, Fernández C, Thomas L, Harwood J (2007) Embedding population dynamics models in inference. Stat Sci 22:44–58

    Article  Google Scholar 

  • Clark JS (2007) Models for ecological data: an introduction. Princeton University Press, Princeton

    Google Scholar 

  • Diggle PJ, Tawn JA, Moyeed RA (1998) Model-based geostatistics (with discussion). Journal of the Royal Statistical Society. C (Applied Statistics) 47:299–350

    Article  Google Scholar 

  • Dorazio RM, Taylor Rodríguez D (2012) A Gibbs sampler for Bayesian analysis of site-occupancy data. Methods Ecol Evol 3:1093–1098

    Article  Google Scholar 

  • Draper D (1996) Utility, sensitivity analysis, and cross-validation in Bayesian model-checking. Stat Sinica 6:760–767

    Google Scholar 

  • Efron B (2005) Bayesians, frequentists, and scientists. J Am Stat Assoc 100:1–5

    Article  CAS  Google Scholar 

  • Flegal JM, Jones GL (2010) Batch means and spectral variance estimators in Markov chain Monte Carlo. Ann Stat 38:1034–1070

    Article  Google Scholar 

  • 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 175–197

    Google Scholar 

  • Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409

    Article  Google Scholar 

  • Gelman A (2011) Induction and deduction in Bayesian data analysis. Rational Markets Morals 2:67–78

    Google Scholar 

  • 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 163–174

    Google Scholar 

  • Gelman A, Meng XL, Stern H (1996) Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Stat Sinica 6:733–807

    Google Scholar 

  • 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 3–48

    Google Scholar 

  • 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 253–293

    Google Scholar 

  • Hooten MB, Hobbs NT (2015) A guide to Bayesian model selection for ecologists. Ecol Monogr 85:3–28

    Article  Google Scholar 

  • 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 15:59–70

    Article  Google Scholar 

  • Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, New York

    Google Scholar 

  • Johnson DS, Conn PB, Hooten MB, Ray JC, Pond BA (2013) Spatial occupancy models for large data sets. Ecology 94:801–808

    Article  Google Scholar 

  • Kéry M, Schaub M (2012) Bayesian population analysis using WinBUGS. Academic Press, Waltham

    Google Scholar 

  • Kéry M, Dorazio RM, Soldaat L, van Strien A, Zuiderwijk A, Royle JA (2009) Trend estimation in populations with imperfect detection. J Appl Ecol 46:1163–1172

    Google Scholar 

  • King R, Morgan BJT, Gimenez O, Brooks SP (2010) Bayesian analysis for population ecology. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  • Laird NM, Louis TA (1987) Empirical Bayes confidence intervals based on bootstrap samples (with discussion). J Am Stat Assoc 82:739–757

    Article  Google Scholar 

  • Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974

    Article  PubMed  CAS  Google Scholar 

  • 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)

  • 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)

  • Lindley DV (2000) The philosophy of statistics (with discussion). Statist 49:293–337

    Google Scholar 

  • Link WA, Barker RJ (2010) Bayesian inference. Academic Press, Amsterdam

    Google Scholar 

  • Little R (2011) Calibrated Bayes, for statistics in general, and missing data in particular. Stat Sci 26:162–174

    Article  Google Scholar 

  • Little RJ (2006) Calibrated Bayes: a Bayes/frequentist roadmap. Am Stat 60:213–223

    Article  Google Scholar 

  • Little RJA, Rubin DB (2002) Statistical analysis with missing data, 2nd edn. Wiley, Hoboken

    Google Scholar 

  • 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 83:2248–2255

    Article  Google Scholar 

  • MacKenzie DI, Nichols JD, Royle JA, Pollock KH, Bailey LL, Hines JE (2006) Occupancy estimation and modeling. Elsevier, Amsterdam

    Google Scholar 

  • McCarthy M (2007) Bayesian methods for ecology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • McCarthy MA, Masters P (2005) Profiting from prior information in Bayesian analyses of ecological data. J Appl Ecol 42:1012–1019

    Article  Google Scholar 

  • Morris CN (1983) Parametric empirical Bayes inference: theory and applications (with discussion). J Am Stat Assoc 78:47–65

    Article  Google Scholar 

  • Morris WK, Vesk PA, McCarthy MA (2013) Profiting from prior studies: analysing mortality using Bayesian models with informative priors. Basic Appl Ecol 14:81–89

    Article  Google Scholar 

  • 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 29:357–365

    Article  Google Scholar 

  • Parent E, Rivot E (2013) Introduction to hierarchical Bayesian modeling for ecological data. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  • 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 49–66

    Google Scholar 

  • Royle JA, Dorazio RM (2006) Hierarchical models of animal abundance and occurrence. J Agr Biol Environ Stat 11:249–263

    Article  Google Scholar 

  • Royle JA, Dorazio RM (2008) Hierarchical modeling and inference in ecology. Academic Press, Amsterdam

    Google Scholar 

  • Royle JA, Dorazio RM (2012) Parameter-expanded data augmentation for Bayesian analysis of capture-recapture models. J Ornithol 152:S521–S537

    Article  Google Scholar 

  • Royle JA, Wikle CK (2005) Efficient statistical mapping of avian count data. Environ Ecol Stat 12:225–243

    Article  Google Scholar 

  • Rubin DB (1984) Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann Stat 12:1151–1172

    Article  Google Scholar 

  • Schaub M, Abadi F (2011) Integrated population models: a novel analysis framework for deeper insights into population dynamics. J Ornithol 152:S227–S237

    Article  Google Scholar 

  • Tanner MA (1996) Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 3rd edn. Springer-Verlag, New York

    Book  Google Scholar 

  • 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 13:1790–1801

    Article  Google Scholar 

  • 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 117:1093–1115

    Google Scholar 

  • Wikle CK (2003) Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 84:1382–1394

    Article  Google Scholar 

  • 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 89–106

    Chapter  Google Scholar 

  • Williams BK, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic Press, San Diego, California

    Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. U.S. Geological Survey, Southeast Ecological Science Center, 7920 NW 71st Street, Gainesville, FL, USA

    Robert M. Dorazio

Authors
  1. Robert M. Dorazio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert M. Dorazio.

Additional information

This manuscript was submitted for the special feature based on a symposium in Tsukuba, Japan, held on 11 October 2014.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 176 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dorazio, R.M. Bayesian data analysis in population ecology: motivations, methods, and benefits. Popul Ecol 58, 31–44 (2016). https://doi.org/10.1007/s10144-015-0503-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10144-015-0503-4

Keywords

Search

Navigation