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26 Spatial Statistics There are three kinds of problems that you might tackle with spatial statistics: point processes (locations and spatial patterns of individuals); maps of a continuous response variable (kriging); spatially explicit responses affected by the identity, size and proximity of neighbours. 26.1 Point processes There are three broad classes of spatial pattern on a continuum from complete regularity (evenly spaced hexagons where every individual is the same distance from its nearest neighbour) to complete aggregation (all the individuals clustered into a single clump): we call these regular, random and aggregated patterns and they look like this: regular random aggregated In their simplest form, the data consist of sets of x and y coordinates within some sampling frame such as a square or a circle in which the individuals have been mapped. The first question is often whether there is any evidence to allow rejection of the null hypothesis of complete spatial randomness (CSR). In a random pattern the distribution of each individual is completely independent of the distribution of every The R Book, Second Edition. Michael J. Crawley. © 2013 John Wiley Sons, Ltd. Published 2013 by John Wiley Sons, Ltd. 826 THE R BOOK other. Individuals neither inhibit nor promote one another. In a regular pattern individuals are more spaced out than in a random one, presumably because of some mechanism (such as competition) that eliminates individuals that are too close together. In an aggregated pattern, individual are more clumped than in a random one, pr