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Spatial Autocorrelation Overview _Zur

Spatial Autocorrelation Overview _Zur - Spatial...

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Spatial Autocorrelation Andrea Zuur Introduction The goal of this presentation is to provide ecology students with an understandable primer on spatial autocorrelation within the context of ecology. The assumptions of spatial and classical statistics are compared, spatial autocorrelation is defined, and the most common spatial autocorrelation functions are reviewed. Spatial statistics is a huge topic. As such, topics such as experimental design, scale, data type, and time-series analysis are not covered. References and resources including software are presented at the end for those interested in more information. Spatial Analysis The distribution of species, a driving force in ecology and conservation biology, often occurs in patterns such as gradients and or clusters. These patterns are the geographic result of the interaction of geologic, climatic, topographic, and biological variables. Spatial statistics provides tools with which these patterns can be analyzed. The origin of spatial statistics is attributed to South African mining engineer D. W. Krige, who developed techniques to predict the location of ores within geologic formations. Kriging, a method of interpolation developed by Matheron (1963) further developed the techniques and named them after Krige. The techniques developed by Krige, Matheron and others have their home in geostatistics and are now applied in fields ranging from epidemiology to ecology to analyze data distributed in space. The space in which the data are measured can be geographic, such as distances between ores in a geological formation, trees in a forest, points in the human brain, or more abstract, where distance is genetic and based on allele frequencies rather than geographic distance. Variables are measured at finite locations within a coordinate system. Measuring variables at specific coordinates allows the calculation of distances between measurements, and hence the analysis of spatial patterns within the data. Assumptions of Classical and Spatial Statistics Randomness One of the goals of statistics is to characterize a population based on a sampling of that population. Both classical and spatial statistics are based on the assumption that samples are randomly chosen from the population. If samples are not randomly chosen, the sample population may be biased. Statistics calculated from a biased sample population will not accurately characterize the population of interest. Independence VS Dependence Classical statistical tests rely on the assumption that subjects are independent of one another. For example, if sampling to determine the distribution of a plant, a researcher randomly places quadrats throughout the study area; all individuals within each quadrat are counted to determine how abundance. The subject is the quadrat and the response variable is species abundance. Each quadrat must be chosen such that it is independent of all other quadrats. Each independent unit, in this case each quadrat,
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counts as a degree of freedom. If the quadrats are not independent of one another, the
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