Environmental and Ecological Statistics

, Volume 14, Issue 1, pp 27–40 | Cite as

Isomorphic chain graphs for modeling spatial dependence in ecological data

  • Alix I. GitelmanEmail author
  • Alan Herlihy
Original Article


Graphical models (alternatively, Bayesian belief networks, path analysis models) are increasingly used for modeling complex ecological systems (e.g., Lee, In: Ferson S, Burgman M(eds) Quantative methods for conservation biology. Springer, Berlin Heilin Heideslperk New York, pp.127–147, 2000; Borsuk et al., J Water Res Plann Manage 129:271–282, 2003). Their implementation in this context leverages their utility in modeling interrelationships in multivariate systems, and in a Bayesian implementation, their intuitive appeal of yielding easily interpretable posterior probability estimates. However, methods for incorporating correlational structure to account for observations collected through time and/or space—features of most ecological data—have not been widely studied; Haas et al. (AI Appl 8:15–27, 1994) is one exception. In this paper, an “isomorphic” chain graph (ICG) model is introduced to account for correlation between samples by linking site-specific Bayes network models. Several results show that the ICG preserves many of the Markov properties (conditional and marginal dependencies) of the site-specific models. The ICG model is compared with a model that does not account for spatial correlation. Data from several stream networks in the Willamette River valley, Oregon (USA) are used. Significant correlation between sites within the same stream network is shown with an ICG model.


Bayesian belief network Graphical model Spatial correlation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersson SA, Madigan D, Perlman MD (2001) An alternative Markov property for chain graphs. Scand J Stat 28:33–86CrossRefGoogle Scholar
  2. Borsuk ME, Stow CA, Reckhow KH (2003) Integrated approach to total maximum daily load development for Neuse River Estuary using Bayesian probability network model (Neu-BERN). J Water Res Plann Manage 129:271–282CrossRefGoogle Scholar
  3. Clarke RT, Furse MT, Wright JF, Moss D (1996) Derivation of a biological quality index for river sites: comparison of the observed with the expected fauna. J Appl Stat 23:311–332CrossRefGoogle Scholar
  4. Congdon P (2003) Applied Bayesian modelling. Wiley, West Sussex, UKGoogle Scholar
  5. Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis 2nd ed. Chapman and Hall, LondonGoogle Scholar
  6. Haas TC, Mowrer HT, Sheppard WD (1994) Modeling aspen stand growth with a temporal Bayes network. AI Appli 8:15–27Google Scholar
  7. Lauritzen SL, Dawid AP, Larsen BN, Leimer H-G (1990) Independence properties of directed Markov fields. Networks 20:491–505Google Scholar
  8. Lee D (2000) Assessing land-use impacts on bull trout using Bayesian belief networks. In: Ferson S, Burgman M (eds) Quantitative methods for conservation biology. Springer, Berlin Heildelbeg New York, pp 127–147CrossRefGoogle Scholar
  9. Ord K (1975) Estimation of methods for models of spatial interaction. J Am Stat Assoc 70:120–126CrossRefGoogle Scholar
  10. Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San MateoGoogle Scholar
  11. Pearl J (2000) Causality: models, reasoning and inference. University of Cambridge, Cambridge, UKGoogle Scholar
  12. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 5:461–464Google Scholar
  13. Spielgelhalter D, Thomas A, Best N, Lunn D (2003) WinBUGS user manual., last accessed April 2005Google Scholar
  14. Spirtes P, Glymour C, Scheines R (1993) Causation, prediction, and search. Springer, Berlin Heidelberg New York; Tetrad 4.3, Department of Philosophy, Carnegie Mellon University,, last accessed April 2005Google Scholar
  15. Van Sickle J, Baker J, Herlihy A, Bayley P, Gregory S, Haggerty P, Ashkenas L, Li J (2004) Projecting the biological condition of streams under alternative scenarios of human land use. Ecol Appl 14:368–380Google Scholar
  16. Verma T, Pearl J (1992) An algorithm for deciding if a set of observed independencies has a causal explanation. In: Dubois D, Wellman M, D’Ambrosio B, Smets P, (eds) Proceedings of the eighth conference on uncertainty in artificial intelligence. Morgan Kaufman, San Francisco, pp 323–330Google Scholar
  17. Wright JF, Furse MT, Armitage PD (1993) RIVPACS: a technique for evaluating the biological water quality of rivers in the UK. Eur Water Pollut Control 3:15–25Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Statistics DepartmentOregon State UniversityCorvallisUSA
  2. 2.Fisheries and Wildlife DepartmentOregon State UniversityCorvallisUSA

Personalised recommendations