Abdollah Jalilian - Department of Statistics, Razi University, Kermanshah, Iran
Amir Safari - Natural Resources and Watershed Management General Office of Kermanshah, Iran
Hormoz Sohrabi - Department of forestry, Tarbiat Modares University, Tehran, Iran

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.

Cross-pair correlation function, Hidden Gaussian random field, Intensity dependent marking model, Mark variogram