A Test for Random Mingling of the Phases of a Mosaic

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Abstract
Suppose an n-phase vegetation mosaic is sampled at equidistant points along a line transect. The observed sequence of symbols (a different symbol for each phase) is then "collapsed"; i.e., any run of 2 or more identical symbols is replaced by a single symbol of the same kind. The resulting sequence is then such that no 2 adjacent symbols are the same. If the patches of the several species (or phases) in the mosaic are randomly mingled with one another, the observed sequence of symbols is a realization of an n-state Markov chain for which a balls-in-boxes model may be constructed. It is shown how one may test the fit of the model to an observed collapsed sequence. This provides a method for testing whether the species in a mosaic are randomly mingled whatever the sizes of the component patches may be. Examples are given of applications of the test to 2 mosaics of ground vegetation.

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