Modeling spatial patterns and species associations in a Hyrcanian forest using a multivariate log-Gaussian Cox process

Document Type : Original Scientific Paper

Authors

1 Department of Statistics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran

2 Natural Resources and Watershed Management General Office of Kermanshah, ‎, Kermanshah, Iran

3 Department of Forestry, Tarbiat Modares University, Tehran, Iran

Abstract

This paper aims to conduct a model-based analysis of the spatial patterns of three tree species in a Hyrcanian forest and investigate their associations. There are many known and unknown mechanisms that influence the spatial forest structure and species associations. These complex and mainly unobservable mechanisms can be modeled by hidden Gaussian random fields and log-Gaussian Cox process models are appropriate for linking them to the spatial patterns of tree species. We consider a multivariate log-Gaussian Cox process model that can take into account the overall mixed effects of all influential factors on spatial distributions of species and quantify species associations in terms of some parameters. This construction provides a suitable framework for modeling and analyzing spatial patterns of several species. We also discuss modeling tree diameters, parameter estimation and goodness of fit methods and apply them to the data. Results from fitting the model to the data show that there is a significant negative association between two light-demanding species. Finally, a Gamma intensity-dependent model is considered to model spatial correlation in tree diameters of one of the species.

Keywords

Main Subjects

References

Akhavan, R., Sagheb-Talebi, K., Zenner, E. and Safavimanesh, F. (2012). Spatial patterns in different forest development stages of an intact old-growth Oriental beech forest in the Caspian region of Iran. European Journal of Forest Research, 131(5):1355–1366.
Baddeley, A. and Turner, R. (2005). spatstat: An R package for analyzing spatial point patterns. Journal of Statistical Software, 12(6):1–42.
Brix, A. and Møller, J. (2001). Space-time multi type log Gaussian Cox processes with a view to modelling weeds. Scandinavian Journal of Statistics, 28(3):471–488.
Comas, C. and Mateu, J. (2007). Modelling forest dynamics: a perspective from point process methods. Biometrical Journal, 49(2):176–196.
Esmailzadeh, O., Hosseini, S.M., Tabari, M., Baskin, C.C. and Asadi, H. (2011). Persistent soil seed banks and floristic diversity in Fagus orientalis forest communities in the Hyrcanian vegetation region of Iran. Flora - Morphology, Distribution, Functional Ecology of Plants, 206(4):365–372.
Grabarnik, P. and Särkkä, A. (2009). Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions. Ecological Modelling, 220(9):1232–1240.
Hao, Z., Zhang, J., Song, B., Ye, J. and Li, B. (2007). Vertical structure and spatial associations of dominant tree species in an old-growth temperate forest. Forest Ecology and Management, 252(1):1–11.
Hou, J., Mi, X., Liu, C. and Ma, K. (2004). Spatial patterns and associations in a Quercus-Betula forest in northern China. Journal of Vegetation Science, 15(3):407–414.
Illian, J. and Burslem, D. (2007). Contributions of spatial point process modelling to biodiversity theory. Journal de la Société Française de Statistique, 148:9–29.
Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, London.
Illian, J.B., Martino, S., Sørbye, S.H., Gallego-Fernández, J.B., Zunzunegui, M., Esquivias, M.P. and Travis, J.M. (2013). Fitting complex ecological point process models with integrated nested Laplace approximation. Methods in Ecology and Evolution.
Illian, J.B., Møller, J. and Waagepetersen, R.P. (2009). Hierarchical spatial point process analysis for a plant community with high biodiversity. Environmental and Ecological Statistics, 16(3):389–405.
Illian, J.B., Sørbye, S.H. and Rue, H. (2012). A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA). The Annals of Applied Statistics, 6(4):1499–1530.
Jalilian, A., Guan, Y. and Waagepetersen, R. (2012). Decomposition of variance for spatial Cox processes. Scandinavian Journal of Statistics, 40(1):119–137.
Law, R., Illian, J., Burslem, D.F., Gratzer, G., Gunatilleke, C. and Gunatilleke, I. (2009). Ecological information from spatial patterns of plants: insights from point process theory. Journal of Ecology, 97(4):616–628.
Lee, K., Kim, S., Shin, Y. and Choung, Y. (2012). Spatial pattern and association of tree species in a mixed Abies holophylla-broadleaved deciduous forest in Odaesan National Park. Journal of Plant Biology, 55(3):242–250.
Luo, Z.R., Ming, J.Y., Chen, D.L., Wu, Y.G. and Ding, B.Y. (2012). Spatial associations of tree species in a subtropical evergreen broad-leaved forest. Journal of Plant Ecology, 5(3):346–355.
Martínez, I., Wiegand, T., González-Taboada, F. and Obeso, J.R. (2010). Spatial associations among tree species in a temperate forest community in north-western Spain. Forest Ecology and Management, 260(4):456–465.
Møller, J., Syversveen, A.R. and Waagepetersen, R.P. (1998). Log Gaussian Cox processes. Scandinavian Journal of Statistics, 25:451–482.
Møller, J. and Waagepetersen, R.P. (2004). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton.
Møller, J. and Waagepetersen, R.P. (2007). Modern statistics for spatial point processes. Scandinavian Journal of Statistics, 34(4):643–684.
Myllymäki, M., Grabarnik, P., Seijo, H. and Stoyan, D. (2015). Deviation test construction and power comparison for marked spatial point patterns. Spatial Statistics, 11:19–34.
Myllymäki, M. and Penttinen, A. (2009). Conditionally heteroscedastic intensity-dependent marking of log Gaussian Cox processes. Statistica Neerlandica, 63(4):450–473.
Pautasso, M., Aas, G., Queloz, V. and Holdenrieder, O. (2013). European ash (Fraxinus excelsior) dieback – a conservation biology challenge. Biological Conservation, 158:37–49.
Picard, N., Bar-Hen, A., Mortier, F. and Chadœuf, J. (2009). The multi-scale marked area-interaction point process: A model for the spatial pattern of trees. Scandinavian Journal of Statistics, 36(1):23–41.
Pommerening, A. and Särkkä, A. (2013). What mark variograms tell about spatial plant interactions. Ecological Modelling, 251:64–72.
R Core Team (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
Ramezani, E., Mohadjer, M.R.M., Knapp, H.-D., Theuerkauf, M., Manthey, M. and Joosten, H. (2013). Pollen–vegetation relationships in the central Caspian (Hyrcanian) forests of northern Iran. Review of Palaeobotany and Palynology, 189:38–49.
Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2):319–392.
Salehi, A., Ghorbanzadeh, N., Kahneh, E. et al. (2013). Earthworm biomass and abundance, soil chemical and physical properties under different poplar plantations in the north of Iran. Journal of Forest Science, 59(6):223–229.
Sheykholislami, A., Ahmadi, T. et al. (2009). The study of Caucasian walnut (Pterocarya frexinifolia (Lam.) Spach.) in forests of Mashelak (Noshahr, Iran). Botany Research Journal, 2(2):28–33.
Stoyan, D. and Penttinen, A. (2000). Recent applications of point process methods in forestry statistics. Statistical Science, 15(1):61–78.
Taylor, B.M., Davies, T.M., Rowlingson, B.S. and Diggle, P.J. (2013). lgcp: An R package for inference with spatial and spatio-temporal log-Gaussian Cox processes. Journal of Statistical Software, 52(4):1–40.
Waagepetersen, R., Guan, Y., Jalilian, A. and Mateu, J. (2016). Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes. Journal of the Royal Statistical Society: Series C (Applied Statistics), 65(1):77–96.
Waagepetersen, R.P. (2007). An estimating function approach to inference for inhomogeneous Neyman–Scott processes. Biometrics, 63(1):252–258.
Wiegand, T., Gunatilleke, S. and Gunatilleke, N. (2007). Species associations in a heterogeneous Sri Lankan dipterocarp forest. The American Naturalist, 170(4):E77–E95.
Wiegand, T. and Moloney, K.A. (2004). Rings, circles, and null-models for point pattern analysis in ecology. Oikos, 104(2):209–229.
Zhang, J., Song, B., Li, B.-H., Ye, J., Wang, X.-G. and Hao, Z.-Q. (2010). Spatial patterns and associations of six congeneric species in an old-growth temperate forest. Acta Oecologica, 36(1):29–38.

Files

History

  • Receive Date: 26 October 2019
  • Revise Date: 18 December 2018
  • Accept Date: 11 February 2020

Share

How to cite

Statistics