Multivariate geostatistical methods for analysis of relationships between ecological indicators and environmental factors at multiple spatial scales

As all biodiversity-related variables, ecological indicators are influenced by environmental factors working at different spatial scales. However, assessing the relationship between environmental factors and ecological indicators is limited to a set of spatial scales determined a priori. This a priori assumption can hide important relationships, especially for ecological indicators with a complex spatial structure that can be driven, for example, by the influence of multiple pollutants with different dispersion ranges or by the influence of local and regional factors such as land-cover and climate. To relate ecological indicators and environmental factors without assuming a priori spatial scales of analysis, we used a Linear Model of Coregionalization. This method has been used in literature to analyze the joint distribution of biodiversity variables. Here we show that it can be used to gain insight into spatial patterns of relationships between ecological indicators and underlying environmental factors. We applied this method to a region of south-west Europe, relating data from land-cover, altitude and climate with an ecological indicator, the abundance of fruticose lichen species, known to be very sensitive to multiple environmental factors. Based on variogram analysis we identified distinct spatial scales of relationships between the ecological indicator and environmental factors. For each spatial scale we described relationships using Principal Component Analysis applied to the coregionalization matrices. This way we could assess how strong the relationship between each environmental factor and ecological indicator at each spatial scale was: at medium scales (c. 15 km) open spaces areas (a proxy for particle emissions) were more important; at larger scales (c. 45 km) open spaces, artificial areas (a proxy for gaseous pollutants) and also climate were preponderant. Thus, multivariate geostatistics provided a tool to improve knowledge on relationships between ecological indicators and environmental factors at multiple spatial scales without setting a priori spatial scales of analysis.