Seriation (Phuket coral transects)

The Phuket coral-reef assemblages at equi-spaced positions down an onshore-offshore gradient (transect A) from Phuket Island, were seen previously in Sections 8, 9 and 11. Open the workspace Phuket ws, or if not available open just Phuket coral cover 83-87 from C:\Examples v7\Phuket corals, square-root transform, calculate similarity and create nMDS plots such as that of Section 8, separately for the two years 1983 and 1987. Do this by selecting the 12 samples along the transect in 1983, with Select>Samples>(•Factor levels)>(Factor name: Year>Levels>(Include: 83) – note that Select works in just the same way on a resemblance matrix as a data sheet – then take Tools>Duplicate to make a copy of this smaller resemblance matrix, renaming it B-C 1983. Analyse>MDS>Non-metric MDS with default options, except (✓Fix collapse)>(Metric proportion: 0.05). This is needed to avoid the collapse of the nMDS plot because of the outlying first point on the transect (as seen in Section 8). With Graph>Special>Overlay>(✓Overlay trajectory)>(Numeric trajectory factor: Position), the serial change in coral community over the transect positions is clear. Repeat these steps for 1987, giving resemblance B-C 1987. The choice of (✓Fix collapse) is not necessary here but if you run the nMDS with and without this option you will see that it makes no difference at all to the outcome – the metric proportion of the minimised combined stress function is so small that it cannot influence the plot unless there really is no non-metric information to use, as for Position 1 in 1983, when the metric stress kicks in. (You may want to use the Procrustes routine, Graph>Align Graph on one of these plots, specifying the other as the (Configuration Plot:       ) to match to – see Section 8 Align graphs automatically – to see they are indeed identical).

The serial change along the transect in 1983 has largely disappeared in 1987, with sedimentation impact from nearby dredging for a deep-water port. This is reflected in the RELATE tests shown above, with $\rho$ declining from 0.651 to 0.193, e.g. on B-C 1983, Analyse>RELATE>(Secondary Data•Result of seriation) & (Max permutations: 9999), with defaults for the other choices, gives a histogram and results window with observed $\rho$ = 0.651 greater than for any of the 9999 simulated values, so the null hypothesis of no seriation at all ($\rho \approx$ 0) is decisively rejected, p<0.01%. Note that the strong outlier has not wrecked this test, though it somewhat degrades the match to a model of equi-stepped change, as is seen by $\rho$ rising to 0.75 if this first transect position is omitted. [Since we have not provided the factor Position when using the (•Result of seriation) option, the routine has to assume that samples are in the desired equi-stepped serial order – a different order, or a wish to fit unequal steps, perhaps by omission of an intermediate transect sample, must be handled by a Model Matrix.] The $\rho$ = 0.193 for 1987 is more in the body of the null distribution however, and there is no clear evidence in the RELATE test for any serial structure (p $\approx$ 7.5%). In this simple case, there is a very close link with the ordered, unreplicated 1-way ANOSIM test on factor Position (see Section 9), with R (not $\rho$) statistics of R$^{\text Os}$ = 0.655 (p<0.01%) and 0.194 (p $\approx$ 7.0%) for 1983 and 87.