Landscape as a Model: The Importance of Geometry

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. : Many different areas of science try to simulate and predict (model) how processes act across virtual landscapes. Sometimes these models are abstract, but often they are based on real-world landscapes and are used to make real-world planning or management decisions. We considered two separate issues: how movement occurs across landscapes and how uncertainty in spatial data can be represented in the model. Most studies represent the landscape using regular geometries (e.g., squares and hexagons), but we generated landscapes of irregular shapes. We tested and compared how the shapes that make up a landscape affected cell-to-cell movement across it. All of the virtual landscapes formed with regular geometries had the potential to bias the direction and distance of movement. Those formed with irregular geometry did not. We have also shown that describing whole real-world landscapes with regular geometries will lead to errors and bias, whereas virtual landscapes formed with irregular geometries are free from both. We recommend the use of multiple versions of virtual landscapes formed using irregular geometries for all spatially explicit models as a way of minimizing this source of bias and error; this is especially relevant in predictive models (e.g., climate change) that are difficult to test and are designed to help make decisions.