I believe most pollen analysts share a common mixed emotion when they complete their first fossil core. Although it is good to be finished, they realize the reliability of the first-counted samples are not nearly as good as those counted last. Counting technique and pollen recognition tend to improve with experience. When we decide to "bite the bullet" and recount those first slides, we always find that our suspicion was correct; the recount does not match the original. Because we are now more sure of our taxa, we attribute the difference to earlier inexperience. After all, we were working at expensive microscopes with marvelous optics and finely-crafted vernier controls, so why else would the counts differ?
It is true that identifying taxa correctly will produce more consistent and thus better results. But we make a serious mistake attributing count differences solely to experience, because that kind of reasoning reinforces a very dangerous attitude: my data will be perfect if I identify every pollen grain correctly. Thus once our pollen recognition improves, we start to believe what we calculate from our counts. This leads to statements like "Because Acer decreased by half (from 5.61 % to 2.80 %) upward across the stratigraphic boundary, it is clear the Younger Dryas cooling event is recorded at this site." We must always keep in mind that our labor-intensive counts are nothing but estimates of what is in our sample vials.
Until a few years ago I was never really able to drive that point home with my students. I would provide the class a vial of processed pollen, and each member would make a slide and count the pollen on it. When the results were pooled, I tried to introduce and test some of the ideas about sample variance. But I never had much luck; the students were not consistent with their identifications, and there was a lot of "noise" in the results. Even when I fabricated samples containing but three or four modern taxa of very distinct types, there was sure to be several who reported 10 to 15 different taxa. It was then that I hit on a plan to strip away all the subtle complexity of taxonomy, the intricacies of microscope manipulation, and the hours of counting time needed to gather the data.
I decided to write a program to generate a synthetic pollen slide printed on a sheet of paper. The user has the choice of sending output to one of several different printers, or to disk--where it can be printed later using one's own word processor. There are only three taxa represented by a dot, a plus mark, and a circle. (It would be easy to have many "taxa," but we are striving for simplicity, and three will suffice.) The instructor gets to assign nominal percentage values for the dot and for the plus mark; the circle is then automatically allotted a value such that the sum of all three will equal 100 per cent. The program prints a heading consisting of the date and a random four-digit serial number, such as the 5434 of Fig. 1. The program then uses an algorithm that will print the three taxa randomly but at about the requested proportions. Blank spaces will be printed about 80% of the time so the synthetic pollen grains appear suspended in a transparent medium as they do in real slides. After the slide is printed, the stipulated and actual percentages and the actual number of each taxon printed are summarized on a second sheet. This printout serves as an instructor key which the student need not see. In the case of Fig. 1, the summary is:
SYNTHETIC POLLEN SLIDE 12-13-1994 Serial No: 5434 POLLEN 1 (.) IN SAMPLE = 206 GRAINS ( 21.28099 %) POLLEN 2 (+) IN SAMPLE = 530 GRAINS ( 54.75207 %) POLLEN 3 (0) IN SAMPLE = 232 GRAINS ( 23.96694 %) Stipulated % : '.'= 20 ,'+'= 55 , 'O'= 25
SYNTHETIC POLLEN SLIDE 12-13-1994 Serial No: 5434
0+ .. . 0 0 + . + + . 0
+ + + . ++++ + + . . + .0 0
00+ + . . . + 0 . + + . 0 + + 0 +
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Figure 1. Synthetic Pollen Slide.
In addition to observing that the taxon proportions and the actual numbers observed vary between traverses, the student also begins to wrestle with the problem of what to do with grains lying only partly in the view. I remember arguing about this with contemporaries when I was a student. Some count any grain they recognize, others count grains that intersect the top of the view and ignore those at the bottom. Others record any grain lying partly out of the view as half of a grain.
(Because the printer works in a rectilinear world of rows and columns, traverses exactly horizontal or vertical on the page should be avoided. Otherwise all grains at one or both margins may lie partly out of view.)
In most cases it does not really seem to matter how one deals with this problem. However a bias occurs when the objects differ substantially in size. Figure 2 illustrates an extreme example. There is only one bisaccate grain on the slide, but it will be seen and counted on nearly every traverse. The large grain will seem to be more common in the slide than it really is; the principle applies any time the counted objects differ in size.
The students' assignment is to predict the true relative abundance of the three taxa on the slide without counting all its grains. They cannot escape the fact that the estimates based on larger counts tend to cluster better than those based on smaller counts. They can then refer to Mosimann (1965) to set confidence limits on their estimates as well as doing Chi-square tests to see if their fellow students' counts are sufficiently alike to accept the null hypothesis that they all were drawn from a single population. In addition to these "inside-the-sum" counts, the students can define one of the taxa as an artificially introduced exotic marker grain and examine the statistics of counts "outside-the-sum." My simple programs MOSLIMIT.BAS and MOSITEST.EXE help with the computation.
Students who do this exercise never expect repeat counts of real pollen slides will yield exactly the same proportions. In fact they cannot understand why anyone would ever believe they should! If MOSITEST shows they can accept the null hypothesis, they then combine their counts to reduce the confidence limits and go on their way. (I do not stress to them that these tests do not show their identifications were correct--only that they have been consistent in naming the objects.)
You can also use synthetic slides to illustrate the problems of documenting up-core-changes in pollen abundance. Make up three or four synthetic slides in which you specify subtle uni-directional changes in one or two of the taxa. Define the slides as coming from discrete depths in the core, and see if the students can determine what is really happening through time.
I have put the files SYNSLIDE.BAS, MOSLIMIT.BAS, and MOSITEST.EXE in a self-extracting zipped file named SYNSLIDZ.EXE, and put it in the INQUA File Boutique. You can get it by anonymous ftp at geology.wisc.edu in the subdirectory /pub/inqua. If you use Mosaic, you can reach them at URL http://geology.wisc.edu/~maher/inqua.html (select the Mosaic Option, "Recover to Disk" before you click on SYNSLIDZ.EXE).
Mosimann, J. E. 1965. Statistical Methods for the Pollen Analyst, in B. Kummel and D. Raup (Eds.). Handbook of Paleontological Techniques: Freeman and Co., San Francisco, pp. 636-673.