Analysis of Multispecies Point Patterns by Using Multivariate Log-Gaussian Cox Processes

Abstract

Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multispecies point patterns of tree locations. In particular we address the problems of identifying parsimonious models and of extracting biologically relevant information from the fitted models. The latent multivariate Gaussian field is decomposed into components given in terms of random fields common to all species and components which are species specific. This allows a decomposition of variance that can be used to quantify to which extent the spatial variation of a species is governed by common respectively species specific factors. Crossvalidation is used to select the number of common latent fields in order to obtain a suitable trade-off between parsimony and fit of the data. The selected number of common latent fields provides an index of complexity of the multivariate covariance structure. Hierarchical clustering is used to identify groups of species with similar patterns of dependence on the common latent fields.

Detecting Multivariate Interactions in Spatial Point Patterns with Gibbs Models and Variable Selection

“…In the context of potentially inhomogeneous patterns, a popular null model, especially in ecology, is some form of the inhomogeneous Poisson process (IPP) (Wiegand et al ., ). A common asymmetric version can be simulated by keeping type i locations fixed while sampling type j locations from the IPP independently from all other data.…”

“…We implement the IPP simulations following Wiegand et al . (): for each type i =1,…, p , an intensity field is kernel estimated on a 2 m×2 m grid using the border‐corrected Epanechnikov kernel with bandwidth fixed to 30 m (this is of course not optimal for all types; we simply emulate Wiegand et al . ()).…”

“…Spatial point patterns are a common form of observation in plant ecology (Waagepetersen et al, 2016), epidemiology (Diggle et al, 2005), astrophysics (Stoica et al, 2007), seismology (Schoenberg, 2003), social science (Amburgey, 1986), medicine (Olsbo et al, 2013) and criminology (Mohler et al, 2011). Although understanding single, univariate spatial point patterns and their generating point processes is important, frequently we observe labelled point processes or, more precisely, multiple types of points.…”

“…Early approaches to modelling and analysing more than one point process focused on bivariate representation and analysis (Diggle and Milne, 1983;Amburgey, 1986;Brix and Møller, 2001;Gelfand et al, 2004;Shimatani, 2001;Diggle et al, 2005), and going much beyond the bivariate case has proved very challenging. To the best of our knowledge the most diverse model-based analysis of multivariate point patterns to date is of nine rainforest tree species by Waagepetersen et al (2016), who used a multivariate log-Gaussian Cox process model, and fitted the model by using non-parametric least squares. The reason given for confining studies to only nine species by them was to limit the computational burden of analysis.…”

A New Graphical Approach to Classify Spatial Point Patterns Based on Hierarchical Cluster Analysis

“…Recently, the analytical methods for SPPs are extended to spatio-temporal analysis (Diggle, 2013) and multivariate SPPs (Waagepetersen et al, 2016). There are two important graphical methods that are similar to our proposed method: the G-function (Diggle, 2003) and the K-function (Ripley, 1977).…”