Spatial non-stationarity, anisotropy and scale: The interactive visualisation of spatial turnover

Abstract

Spatial data analysis is often focussed on the identification of spatial patterns across some geographic extent (Laffan, 2002). Properties of these spatial patterns of particular interest are: (1) the spatial scale of the process, which is essentially the extent of a set of locally related values; (2) spatial anisotropy, where the relationship of a location to other locations changes as a function of direction between them; and (3) spatial non-stationarity, where the scale and anisotropy vary across the geographic extent of the data set. All of these are inter-related and are associated with both abrupt and gradual transitions, often with both occurring within the one geographic region. There are numerous analytical methods of exploring these spatial properties, but core to them is visualisation. Visualisation is an integral part of the data analysis process. For spatial analyses of compositional turnover, where the data consists of sets of labels or objects at each location rather than singular values, such visualisation has been difficult. This is due to issues of complexity, large number of spatial associations and computational limitations. An additional cause of this difficulty has been a lack of available software, with GIS software focussing on analyses of layers of single values per location, with compositional data stored as one layer per label or object. This paper contains a description of the interactive visualisation of compositional turnover across geographic data sets, developed as an extension to the Biodiverse software (Laffan et al., 2010). This represents an important step towards improved understanding of spatial turnover patterns in compositional data, particularly for spatial non-stationarity, scale and anisotropy. There is also the potential to use this approach in analyses of distributional breaks and gradational transitions, and of anomalies.