The Geometry of Spatial Analyses: Implications for Conservation Biologists

Abstract

Most conservation biology is about the management of space and therefore requires spatial analyses. However, recent debates in the literature have focused on a limited range of issues related to spatial analyses that are not always of primary interest to conservation biologists, especially autocorrelation and spatial confounding. Explanations of how these analyses work, and what they do, are permeated with mathematical formulas and statistical concepts that are outside the experience of most working conservationists. Here, we describe the concepts behind these analyses using simple simulations to exemplify their main goals, functions and assumptions, and graphically illustrate how processes combine to generate common spatial patterns. Understanding these concepts will allow conservation biologists to make better decisions about the analyses most appropriate for their problems.

Eight (and a half) deadly sins of spatial analysis

“…That is, in non-stationary data the single, semilocal regression coefficients (sensu Fotheringham et al, 2002) generated by spatial regression cannot be interpreted with confidence because a unique local coefficient does not exist in the data. Much like spatial autocorrelation itself, this fundamental property of geographical data was largely ignored until recently (Foody, 2004;Bickford & Laffan, 2006;Cassemiro et al, 2007;Beale et al, 2010;Landeiro & Magnusson, 2011), and it remains very uncommon for geographical ecology papers to report that they have determined whether their data are stationary or not. This is despite the fact that nonstationarity is common in broad-scale data; e.g.…”

“…But the pattern is not the process [see also Landeiro & Magnusson (2011) for discussion of pattern and process in spatial data with respect to conservation biology]. For example, distance of a place from a Pleistocene refugium may pop up in a statistical model accounting for the presence or absence of a plant, but the reason why has to be explained by an interaction of biology and environment; for example, seed size and prevailing wind direction, movement patterns of animal seed-dispersers that are themselves influenced by the environment, the presence of intervening rivers, ocean or mountains and the ability of seeds to get over or around them, the rate of establishment of source populations increasingly nearer the target site as influenced by winter temperatures, summer rainfall and edaphics, and so on.…”

Key environmental determinants of global and regional richness and endemism patterns for a wild bee subfamily

“…However, the relatively large sample size (see Table S1.2 in Online Resource 1) releases the requirement of normality and renders highly significant coefficients (p \ 0.001) reliable (Lumley et al 2002). Autocorrelation is the lack of independence between pairs of observations at given distances in time and space, a common issue in ecological data (Landeiro and Magnusson 2011;Legendre 1993). In the presence of autocorrelation, type I errors (i.e.…”

Geographical Patterns in Biodiversity: Towards an Integration of Concepts and Methods from Genes to Species Diversity

“…The establishment of a clear theoretical basis for this "strong integration" would allow more comprehensive analyses and interpretation of biodiversity patterns. This task would be facilitated by biodiversity and environmental data acquisition using GIS and remote sensing techniques (Graham et al 2004;Kozak et al 2008) and by the use of statistical analyses of geographic and evolutionary patterns with direct conservation implications (Epperson 2003;Diniz-Filho & Telles 2002Landeiro & Magnusson 2011). However, we still lack the tools and the theoretical background to effectively work across the different hierarchical levels represented by FBUs, taking complex processes into account.…”