Underestimating the effects of spatial heterogeneity due to individual movement and spatial scale: infectious disease as
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RESEARCH ARTICLE
Underestimating the effects of spatial heterogeneity due to individual movement and spatial scale: infectious disease as an example Paul C. Cross • Damien Caillaud Dennis M. Heisey
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Received: 2 May 2012 / Accepted: 19 November 2012 / Published online: 30 November 2012 Ó Springer Science+Business Media Dordrecht (outside the USA) 2012
Abstract Many ecological and epidemiological studies occur in systems with mobile individuals and heterogeneous landscapes. Using a simulation model, we show that the accuracy of inferring an underlying biological process from observational data depends on movement and spatial scale of the analysis. As an example, we focused on estimating the relationship between host density and pathogen transmission. Observational data can result in highly biased inference about the underlying process when individuals move among sampling areas. Even without sampling error, the effect of host density on disease transmission is underestimated by approximately 50 % when one in ten hosts move
Electronic supplementary material The online version of this article (doi:10.1007/s10980-012-9830-4) contains supplementary material, which is available to authorized users. P. C. Cross (&) U.S. Geological Survey, Northern Rocky Mountain Science Center, 2327 University Way, Suite 2, Bozeman, MT 59715, USA e-mail: [email protected] D. Caillaud Section of Integrative Biology, University of Texas at Austin, 1 University Station C4500, Austin, TX 78712, USA e-mail: [email protected] D. M. Heisey U. S. Geological Survey, National Wildlife Health Center, 6006 Schroeder Road, Madison, WI 53711-6223, USA e-mail: [email protected]
among sampling areas per lifetime. Aggregating data across larger regions causes minimal bias when host movement is low, and results in less biased inference when movement rates are high. However, increasing data aggregation reduces the observed spatial variation, which would lead to the misperception that a spatially targeted control effort may not be very effective. In addition, averaging over the local heterogeneity will result in underestimating the importance of spatial covariates. Minimizing the bias due to movement is not just about choosing the best spatial scale for analysis, but also about reducing the error associated with using the sampling location as a proxy for an individual’s spatial history. This error associated with the exposure covariate can be reduced by choosing sampling regions with less movement, including longitudinal information of individuals’ movements, or reducing the window of exposure by using repeated sampling or younger individuals. Keywords Source-sink metapopulation Epidemiological model Observational bias Disease transmission Host density Modifiable areal unit problem
Introduction Understanding the factors that determine habitat quality and create ‘hotspots’ is critical to effective conservation efforts as well as the control of invasive species and infectious diseases. The link between the observed
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