A long time ago I was having problems trying to understand what SLOTSEQ.FOR (Birks, 1979) was doing in its attempt to correlate (slot) two pollen sequences. The algorithm was constructing a "least-cost" route through a matrix of dissimilarity coefficients (DC) based on the Manhattan metric. To help visualize the problem, I wrote SLOTSEE.BAS which let me see the SLOTSEQ solution on a color-coded map of the DC matrix; I added a couple of other DCs as well (Maher, 1990). Later I combined the automatic solution of SLOTSEQ with some manual constraints in the program SLOTDEEP (Maher, 1993).
SLOTDEEP allows the user to get a pretty good insight into the distribution of the dissimilarity coefficients in the matrix map by typing in a number that lights up all DCs with that or lower (better) values. But geologists often combine map views with profiles in the hope that the two different ways of viewing things will provide more information than either method alone. I have incorporated DC profiles in the VGA version of SLOTDEEP v. 1.8. (I seem to be the only one who still owns a computer with EGA graphics; the EGA version of SLOTDEEP will be kept in the INQUA File Boutique, but it is not being upgraded further.)
To illustrate the DC profiles I will use the same pollen sites (Wisconsin's Devils Lake and Kellners Lake) that I used in Maher (1997). Kellners Lake is located about 110 miles (177 km) northeast of Devils Lake. The two sites are on opposite sides of Wisconsin's Tension Zone.
Figure 1 shows abbreviated pollen diagrams of 19 wind-pollinated taxa from the two lakes. Kellners Lake is treated as the subordinate site; the ticks at its margins represent depth in meters extending from the sediment surface to 1145 cm. Devils Lake is treated as the principal site; its ticks represent 1000s of 14C years BP. Both sites cover the entire Holocene ranging from the Picea zone at the base to the Ambrosia zone at the top. Although the diagrams are generally similar they differ in detail.
SLOTDEEP's menu item 3 allows one to view the DC matrix map. Many SLOTDEEP screens do not provide any instructions in case one wants to use a "screen grabber" to obtain a copy of the image. By touching the space key, one can generally get instructions, and these are shown at the base of Figure 2 surrounding the "DC = CHD" (Chord Distance) label. Kellners Lake's 69 sample levels extend along the X-axis with a tick mark every ten samples. Devils Lake's 122 sample levels extend along the Y-axis. The maximum DC shown on the figure is 0.35. The scale is at the right side of the figure; DC values between 0 and 0.1 are shown in white, 0.1+ to 0.2 in red, 0.2+ to 0.3 in yellow, etc. The purple line extending from the core tops (upper left) to the core bases (lower right) traces out the automatic SLOTSEQ solution for slotting the two cores.
The area of rather good correlations (DC < 0.3; reds and yellows) extends from the core bases at the lower right to level 56 of Devils Lake and level 30 of Kellners Lake. In this region the SLOTSEQ solution does an adequate job. However in the upper parts of the cores, the SLOTSEQ solution generally runs horizontally or vertically rather than-as we would hope-diagonally across the matrix map. Figure 2 shows that there is greater dissimilarity in the upper parts of the cores, and this can be seen in Figure 1 as well. There are several vertical stripes of yellows and greens in the "northwest" quadrant of the matrix map; the most pronounced one-which appears to guide the SLOTSEQ solution-is caused by level 31 of Kellners Lake. Figure 1 shows that Kellners level 31 just happens to combine higher than average Quercus, with lower than average Pinus and Betula. This singularity makes Kellners level 31 more like the upper part of Devils Lake, and it confounds the SLOTSEQ solution.
Now that we have examined the matrix map of Figure 2, we can elect to study some DC profiles. The profiles will extend north-south across the figure comparing any level in the subordinate site (Kellners Lake) with all the levels of the principal site. We should first decide which profiles we want to see. For this example let us look at Kellners level 69 (the base), level 20, and level 31. We then touch "P" to view the profiles. We will be asked the level number of Kellners for which we want a DC plot.
Figure 3 shows the DC profile comparing Kellners level 69 with all the levels of Devils Lake. The top level of Devils Lake is at the left; the base is at the right. The transect extends along the right margin of Figure 2's matrix map. The profile's vertical dimension is in dissimilarity units. The Manhattan metric and 1-Rs DCs can range up to a maximum of 2.0 if none of the grains in one sample are found in the other. The maximum DC value for the Chord metric is 1.414 (square root of 2). The horizontal dotted blue line marks the value of the DC chosen to plot on the matrix map-here 0.35.
I find it helpful to think of the DC profile as a geologic section with the blue line representing a water table. Where the water table lies below the surface it is ground water; where it extends above the profile's surface it represents a river or lake that appears as the patch of color on the matrix map. Using this analogy, the profile's upland surface (DC = 1) shows that the upper 90 levels of Devils Lake are very different from level 69 of Kellners Lake. Devils Lake levels 100-110 (DC about 0.5) form a "flood plain"-a zone where the Devils Lake levels are vaguely similar to the Kellners Lake sample. The low DC in the "under-water" part of the valley suggest the Kellners Lake best matches levels, say, 111 to 118 of Devils Lake.
There are no lakes or streams along the profile that contains Kellners sample 20 (depth 380 cm) in Figure 4; that is to say, at a chord dissimilarity of 0.35, it does not match any level of Devils Lake. It has a vague resemblance (DC = 0.5) to Devils Lake levels 5 through 93-the pre-settlement part of the Holocene.
Lastly, Figure 5 shows the profile associated with Kellners sample 31 (depth 600 cm), the anomalous sample referred to earlier. It contains a vast marshy region in Devils levels 5 through 93. Level 31's higher than average Quercus, and lower than average Pinus and Betula reduces its dissimilarity with Devils Lake, but we should resist the temptation to use it for correlation.
Although I still prefer to compare sites by using the DC map, I must admit I have gained helpful information by using both map and profiles. In case you might wish to try it, I have placed SLOTDEEP v. 1.8 (VGA version only) in the INQUA File Boutique in a self-extracting file with some example data.
References.
Birks, H.J.B. 1979. Numerical methods for the zonation and correlation of biostratigraphical data, 99-123 + Appendix 2, 15 p. (The SLOTSEQ.FOR listing appears on 13-15 of Appendix 2). In Bjorn E. Berglund, Ed., Vol I. General Project Descriptions. Subproject B: Lake and Mire Environments. Project 158: Palaeohydrological Changes in the Temperate Zone in the Last 15,000 Years. International Geological Correlation Programme, Lund, Sweden. 143 pp. + 2 Appendices.