The effects of scale and sample size on the accuracy of spatial predictions of tiger beetle (Cicindelidae) species richness

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Abstract
We apply geostatistical modeling techniques to investigate spatial patterns of species richness. Unlike most other statistical modeling techniques that are valid only when observations are independent, geostatistical methods are designed for applications involving spatially dependent observations. When spatial dependencies, which are sometimes called autocorrelations, exist, geostatistical techniques can be applied to produce optimal predictions in areas (typically proximate to observed data) where no observed data exist. Using tiger beetle species (Cicindelidae) data collected in western North America, we investigate the characteristics of spatial relationships in species numbers data, First, we compare the accuracy of spatial predictions of species richness when data from grid squares of two different sizes (scales) are used to form the predictions. Next we examine how prediction accuracy varies as a function of areal extent of the region under investigation. Then we explore the relationship between the number of observations used to build spatial prediction models and prediction accuracy. Our results indicate that, within the taxon of tiger beetles and for the two scales we investigate, the accuracy of spatial predictions is unrelated to scale and that prediction accuracy is not obviously related lo the areal extent of the region under investigation. We also provide information about the relationship between sample size and prediction accuracy, and, finally, we show that prediction accuracy may be substantially diminished if spatial correlations in the data are ignored.

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