Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches

Abstract

We compared two methodological approaches – principal coordinate analysis of neighbour matrices (PCNM) and geostatistics – that both aim at extracting several spatial scales in order to identify spatial relationships between organisms and environmental variables at multiple scales. From a statistical point of view, PCNM analysis and geostatistics come from “two different worlds”– PCNM is based on classical “data analysis” while geostatistical modelling is developed in a probabilistic context. These two methods were used to investigate the spatial relationships between defoliation caused by spruce budworm Choristoneura fumiferana and bioclimatic conditions in Ontario since 1941 through a wide range of scales. On the one hand, PCNM variables related to defoliation frequency were partitioned into four spatial submodels representing respectively four spatial scales: very broad scale (ca>300 km), broad scale (ca 180 km), fine (ca 100 km), and very fine (<80 km). On the other hand, nested variogram modelling was used to identify the relevant scales. The nested variogram model was composed of four variograms with different characteristic scales close to those of the PCNM spatial submodels. Maps of PCNM submodels and kriging components revealed similar spatial patterns of defoliation frequency at very broad and broad scales while spatial patterns at fine and very fine scales looked quite different. Both methods showed that defoliation by spruce budworm occurs at the broader spatial scales but may be explained by fluctuations at the smaller scales. Finally, results based on geostatistics using a Linear Model of Coregionalisation suggested that climatic conditions can be considered to act at the level of outbreak dynamics while the tree community of spruce budworm's principal hosts controls local population dynamics.