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Scale Effects and the Information Content of Frequency Arrays Obtained by Quadrat Methods

This paper examines the ways in which information statistics can be used to describe frequency arrays obtained by quadrat analysis of the same point-pattern with different cell sizes. The paper begins by reviewing those aspects of information theory that are pertinent to quadrat analysis, and then a series of results are described which relate the behaviour of the redundancy index to variations in the number of cells used to census the pattern. In particular, it is shown how critical cell sizes correspond to limiting values of the redundancy index, which enables the index value to be interpreted as a pure scale-effect. Last, these methods are illustrated with reference to changing factory-location patterns on Merseyside between 1966 and 1972.