Spatial bayesian models of tree density with zero inflation and autocorrelation

Frédéric Mortier; Olivier Flores; Sylvie Gourlet-Fleury

Journal de la société française de statistique (2007)

  • Volume: 148, Issue: 1, page 39-51
  • ISSN: 1962-5197

Abstract

top
Understanding the spatial and temporal dynamics of rain forests is a challenge for assessing the impact of disturbance on forest stands and tree populations. Still few studies address the modelling of spatial patterns of tree density. Here, we present Hierarchical bayesian (HB) models for the local density of juveniles trees in a tropical forest. These models are specifically designed to handle zero inflation and spatial autocorrelation in the data. Height types of models were built and compared through a Hierarchical bayesian approach: Poisson and Negative Binomial generalized linear models, zero-inflated versions of these models and finally a spatial generalization of the four previous models. Spatial dependency in juvenile pattern was modeled through a Conditional Auto Regressive process. An application is presented at the Paracou experimental site (French Guiana). At this site, permanent sample plots settled in a previously undisturbed forest received silvicultural treatments in 1986-1988. Juvenile density of a timber species, Eperua falcata (Caesalpiniaceae), was evaluated in 2003 within 10 m × 10 m cells and served as response in the models. Explanatory variables described three aspects of environmental heterogeneity inside the plots: topography (elevation and slope) was derived from a Digital Elevation Model; stand variables and population variables, either static or dynamic, were calculated from basal area on 20 m-radius circular subplots.

How to cite

top

Mortier, Frédéric, Flores, Olivier, and Gourlet-Fleury, Sylvie. "Spatial bayesian models of tree density with zero inflation and autocorrelation." Journal de la société française de statistique 148.1 (2007): 39-51. <http://eudml.org/doc/93454>.

@article{Mortier2007,
abstract = {Understanding the spatial and temporal dynamics of rain forests is a challenge for assessing the impact of disturbance on forest stands and tree populations. Still few studies address the modelling of spatial patterns of tree density. Here, we present Hierarchical bayesian (HB) models for the local density of juveniles trees in a tropical forest. These models are specifically designed to handle zero inflation and spatial autocorrelation in the data. Height types of models were built and compared through a Hierarchical bayesian approach: Poisson and Negative Binomial generalized linear models, zero-inflated versions of these models and finally a spatial generalization of the four previous models. Spatial dependency in juvenile pattern was modeled through a Conditional Auto Regressive process. An application is presented at the Paracou experimental site (French Guiana). At this site, permanent sample plots settled in a previously undisturbed forest received silvicultural treatments in 1986-1988. Juvenile density of a timber species, Eperua falcata (Caesalpiniaceae), was evaluated in 2003 within 10 m$\times $10 m cells and served as response in the models. Explanatory variables described three aspects of environmental heterogeneity inside the plots: topography (elevation and slope) was derived from a Digital Elevation Model; stand variables and population variables, either static or dynamic, were calculated from basal area on 20 m-radius circular subplots.},
author = {Mortier, Frédéric, Flores, Olivier, Gourlet-Fleury, Sylvie},
journal = {Journal de la société française de statistique},
keywords = {spatial pattern; hierarchical models; zero-inflation; MCMC; conditional autoregressive process},
language = {eng},
number = {1},
pages = {39-51},
publisher = {Société française de statistique},
title = {Spatial bayesian models of tree density with zero inflation and autocorrelation},
url = {http://eudml.org/doc/93454},
volume = {148},
year = {2007},
}

TY - JOUR
AU - Mortier, Frédéric
AU - Flores, Olivier
AU - Gourlet-Fleury, Sylvie
TI - Spatial bayesian models of tree density with zero inflation and autocorrelation
JO - Journal de la société française de statistique
PY - 2007
PB - Société française de statistique
VL - 148
IS - 1
SP - 39
EP - 51
AB - Understanding the spatial and temporal dynamics of rain forests is a challenge for assessing the impact of disturbance on forest stands and tree populations. Still few studies address the modelling of spatial patterns of tree density. Here, we present Hierarchical bayesian (HB) models for the local density of juveniles trees in a tropical forest. These models are specifically designed to handle zero inflation and spatial autocorrelation in the data. Height types of models were built and compared through a Hierarchical bayesian approach: Poisson and Negative Binomial generalized linear models, zero-inflated versions of these models and finally a spatial generalization of the four previous models. Spatial dependency in juvenile pattern was modeled through a Conditional Auto Regressive process. An application is presented at the Paracou experimental site (French Guiana). At this site, permanent sample plots settled in a previously undisturbed forest received silvicultural treatments in 1986-1988. Juvenile density of a timber species, Eperua falcata (Caesalpiniaceae), was evaluated in 2003 within 10 m$\times $10 m cells and served as response in the models. Explanatory variables described three aspects of environmental heterogeneity inside the plots: topography (elevation and slope) was derived from a Digital Elevation Model; stand variables and population variables, either static or dynamic, were calculated from basal area on 20 m-radius circular subplots.
LA - eng
KW - spatial pattern; hierarchical models; zero-inflation; MCMC; conditional autoregressive process
UR - http://eudml.org/doc/93454
ER -

References

top
  1. [1] Banerjee S., Carlin B. and Gelfand A. (2003). Hierarchical modeling and analysis for spatial data. Monographs on Statistics and Applied Probability 101. Chapman & Hall/CRC. Zbl1053.62105
  2. [2] Barry S. and Welsh A. (2002). Generalized additive modelling and zero in-flated count data. Ecological Modelling, 157(2-3), 179-188. 
  3. [3] Besag J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society Series B, 36, 192-236. Zbl0327.60067MR373208
  4. [4] Celeux G., Forbes F., Robert C. P. and Titterington D. M. (2006). Deviance information criteria for missing data models. Bayesian Analysis (in press). Zbl1331.62329MR2282197
  5. [5] Clark J. (2005). Why environmental scientists are becoming bayesians? Ecology Letters, 8, 2-14. 
  6. [6] Collinet F. (1997). Essai de regroupement des principales espèces structurantes d’une forêt dense humide d’après l’analyse de leur répartition spatiale (Forêt de Paracou – Guyane). Ph.D. thesis, Université Claude Bernard – Lyon 1. 
  7. [7] Condit R., Ashton P., Baker P., Bunyavejchewin S., Gunatilleke S., Gunatilleke N., Hubbell S., Foster R., Itoh A., LaFrankie J., Lee H., Losos E., Manokaran N., Sukumar R. and Yamakura T. (2000). Spatial patterns in the distribution of tropical tree species. Science, 288, 1414-1418. 
  8. [8] Favrichon V. (1994). Classification des espèces arborées en groupes fonctionnels en vue de la réalisation d’un modèle de dynamique de peuplement en forêt guyanaise. Revue Ecologie-La Terre et La Vie, 49, 379-403. 
  9. [9] Flores O., Gourlet-Fleury S. and Picard N. (2006). Local disturbance, forest structure and dispersal effects on sapling distribution of light-demanding and shade-tolerant species in a french guianan forest. Acta Oecologica, 29(2), 141-154. 
  10. [10] Gourlet-Fleury S., Guehl J. and Laroussinie O. (2004) Ecology and Management of a Neotropical Rainforest – Lessons drawn from Paracou, a long-term experimental research site in French Guiana. Elsevier, Paris. 
  11. [11] Legendre P. (1993). Spatial autocorrelation: trouble or new paradigm? Ecology, 74(6), 1659-1673. 
  12. [12] McCullagh P. and Nelder J. (1989) Generalized Linear Models. Monographs on Statistics and Applied Probability 37. London, Chapman & Hall edition. Zbl0744.62098MR727836
  13. [13] OAB-OIBT (2003). Principes, critères et indicateurs OAB-OIBT de la gestion durable des forêts tropicales naturelles d’Afrique. Série Développement de politiques OIBT 14, Organisation africaine du bois (OAB), Libreville, Gabon et Organisation internationale des bois tropicaux (OIBT), Yokohama, Japon. 
  14. [14] Plackett R. (1981). The analysis of categorical data. Griffin. Zbl0479.62046MR636258
  15. [15] R Development Core Team (2004). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-00-3. 
  16. [16] Ridout M., Demetrio C. and Hinde J. (1998). Models for count data with many zeros. In International Biometric Conference. Cape Town. 14 Bayesian models of tree density 
  17. [17] Spiegelhalter D., Best N., Carlin B. and Van der Linde A. (2002). Bayesian measures of model complexity and t (with discussion). Journal of the Royal Statistical Society, Series B, 6, 583-639. Zbl1067.62010
  18. [18] Wikle C. (2003). Hierarchical bayesian models for predicting the spread of ecological processes. Ecology, 84, 1382-1394. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.