Abstract
In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.
Highlights
The focus of this study is spatially explicit predictive models designed to support decisionmaking, which should have reliable, probabilistic, and mappable results
Virtual landscapes with irregular geometry were created in five different ways
Three virtual landscapes were approximations to the Dirichlet landscape, but based on a raster grid, with irregular cells composed of a mean of four, nine, or 16 squares (Figure 1E, 1F, and 1G, respectively) and called the coarse-grain Dirichlet (CGD) landscapes
Summary
The focus of this study is spatially explicit predictive models designed to support decisionmaking (e.g., population establishment and spread, climate change, and flood risk), which should have reliable, probabilistic, and mappable results. We focus on the use of cells in a mosaic-based model [2] to represent processes in space, which requires the subdivision of space into a tessellation of discrete, internally homogeneous patches within which a process occurs. This is an elegant, abstract concept, the use of cells to represent uncertain spatial processes is often desirable in real-world applications. By modelling processes at scales significantly larger than that of the underlying data, these problems become statistically tractable (e.g., Land Cover 2000 [3]) In many such models, the attribute values of cells are directly calculable from habitat or Editor: Stephen Paul Rushton, University of Newcastle upon Tyne, United Kingdom
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