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neighbouring samples usually assume similar values, may arise from gradients or
patches exceeding the diameter of inter-sample distances. Significant positive
autocorrelation (high Moran's i and low Geary's c) at distance class 1 therefore
implies a patch size of between 1-1.5m2 and at distance class 2, a patch size of 1.5-
2m2.
Generally, there were very good agreements between the two autocorrelation
coefficients used: Geary's coefficient was nearly always significant when Moran's
coefficient was significant and both gave similar estimates of patch sizes in most
cases. Cliff and Ord (1973) proposed that i was generally better than c, although the
margin of the advantage was slight. Therefore, patch sizes are given here as indicated
by Moran's coefficient.
The density plots (Figures 2.5(i-vii)) suggest that all of the species with significantly
non-random distributions formed areas of increased densities, or patches, of either less
than 1m2 (e.g., M. balthica and E. cf flava) or between 1-2m 2 (e.g., P. elegans, A.
marina, L. conchilega, G. duebeni and B. sarsi) with very low abundances outside the
patches. However, mapping only gives a guide to spatial patterns, they do not confirm
them. The patterns indicated in Figures 2.5(i-vii) are supported by their correlograms.
For example, patch sizes smaller than inter-sample distances (or lag, in this case 1m)
are not revealed by spatial autocorrelation analysis and therefore M. balthica and E. cf
flava had non-significant correlograms. For these species, smaller inter-sample
distances would have been needed to determine their underlying spatial structure. The
significant correlograms with positive autocorrelation at distance class 1 indicate that
P. elegans, A. marina, L. conchilega and G. duebeni formed patches of 1-1.5m2 while
the positive autocorrelation at distance class 2 suggests that B. sarsi formed patches of
1.5-2m2. For P. elegans, 2 patches were sampled wholly within the 8x8m grid, with 3
others on the edge. These corresponded to the positions of areas of smooth, raised
sediment (pers. obs.) and therefore confirm that these areas did indeed contain
significantly increased numbers of P. elegans. Furthermore, Figure 2.5(i) shows that
although the patch sizes were approximately equal, the inter-patch distances varied
suggesting that the P. elegans patches were randomly distributed at this scale.
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