The Relation Between Mean Square and Block Size in the Analysis of Similar Patterns

The analysis of data for pattern in plant communities is a standard procedure in quantitative ecology, and the methods used are described by Greig-Smith (1964) and Kershaw (1964). The analysis depends upon a series of contiguous quadrats or groups of points, each series having a number of units which is a power of 2. One unit is conveniently termed 'Block size 1'. The data from adjacent pairs are combined to give 'Block size 2', from adjacent pairs of pairs to give 'Block size 4', and so on. The method of analysis is analogous to that of a multiple split-plot experiment, with the interest focused upon the estimated error variance of the block sizes (subplots). Most work has concentrated upon the analysis of parallel transects of samples, each transect having the number of units a multiple of 2. Kershaw (1957) experimented with a number of artificial communities, which consisted of clumps of 100% cover being laid out on graph paper. Both Kershaw and Greig-Smith, Kershaw & Anderson (1963) demonstrate the power of this method of analysis. Kershaw discussed the relation between the scale of the heterogeneity and the size of the basic sampling unit. Greig-Smith (1964, p. 88) quotes his results thus: 'If sample size, i.e. total number of grid units, is inadequate, the peaks tend to drift one block size to the right, owing to patches overlapping two blocks of their own size. This drift can be cancelled by an increase in sample size.' The problem of the drift of a peak to the right is important, since this weakens a potentially strong analysis. Both Kershaw's study and the published field studies have started transects or grids at a randomly selected point.