Below are two items by Louis J. Maher that are particularly relevant to palynologists:

**Statistics for Lycopodium Tablets**

by

Louis J. Maher

Department of Geology & Geophysics

University of Wisconsin – Madison, USA

Pollen analysts often add *Lycopodium* tablets (obtained from Lund University, Sweden) to pollen preparations during processing, in order to calculate microfossil concentrations (see Stockmarr 1971). Each batch of tablets comes with an estimate of the spore content, given usually as the mean and standard deviation of five tablets. Depending on the characteristics of the sample, it is not always necessary to use five *Lycopodium* tablets. So palynologists may need to calculate statistics for other numbers of tablets. Taking Batch 710961 as an example and assuming that Lund is correct in their statistics that five of their *Lycopodium* tables in this batch contain (mean ± standard deviation) 69,556 ± 1541 spores, then what are the statistics for one, two, or three tablets?

The mean number of grains in a group of N tablets = N times the mean number of grains per tablet (Y). Lund determined that their five-tablet mean was 69,556, so a single tablet’s mean is 13,911, as they indicate.

The standard deviation of a group of N tablets = square root of N times the standard deviation of the individual tablet; that is SQR(N) x s. (See Maher 1981, pp. 158-159). So the standard deviation for a single tablet is 689. Similar computations can be done for other numbers of tablets, as shown in the table below.

Number of Tablets |
Group Mean |
Group S.D. |
Coefficient of Variation |
---|---|---|---|

1 | 13,911 | 689 | 4.95% |

2 | 27,822 | 975 | 3.50% |

3 | 41,733 | 1193 | 2.90% |

4 | 55,644 | 1378 | 2.50% |

5 | 69,556 | 1541 | 2.20% |

10 | 139,110 | 2179 | 1.60% |

**References**

Maher, L. J., 1981. Statistics for Microfossil Concentration Measurements Employing Samples Spiked with Marker Grains. *Review of Palaeobotany and Palynology* 32:153-191.

Stockmarr, J., 1971. Tablets with Spores used in Absolute Pollen Analysis. *Pollen et Spores* 13:615-621.

**Editor’s note**

This item was elicited in response to a recent question by Martin Head posted on the POLPAL discussion list. It is reproduced here, in slightly modified form, with permission from Dr Maher.

For more information on *Lycopodium* spore tablets, including details about where to order them from, please take a look at Equipment and Laboratory Supplies.

This article first appeared in *CAP Newsletter* 20(2):26, 1997.

**How to Compute Age-Depth Relationships for a Core**

by

Louis J. Maher

Department of Geology & Geophysics,

University of Wisconsin – Madison, USA

In Quaternary pollen analysis, it is common practice to estimate age-depth relationships for a core, based on radiocarbon dates, and use these data in the computation of, for example, pollen accumulation rates (PAR). Recently, there has been considerable discussion on the TILIA-L discussion list about the best method for fitting radiocarbon dates to depths in a core. I tend to agree with the comments made by other researchers that there is no a priori ‘BEST’ method for this. Nonetheless, cores are routinely ‘dated.’ Some procedures work well with one core and provide unsatisfactory results with another. I have always felt it was a pity to choose a particular fitting method without ever examining other possibilities. That is why I produced a simple computer program that lets one read an ASCII file of the core’s dates, plot the points on the screen, and then fit the data with a variety of different assumptions. DEP-AGE.EXE is a DOS program, but it runs well in a DOS window of WINDOWS. It can be picked up from Keith Bennett’s INQUA File Boutique (http://www.kv.geo.uu.se/inqua) or from my mirror site at the University of Wisconsin (http://www.geology.wisc.edu/~maher/inqua.html).

Download a copy of DEP-AGEZ.EXE, a self-extracting zipped version of the program DEP-AGE.EXE. It is designed to facilitate the conversion of core depths (cm) into estimates of their equivalent age in C-14 years. (It fits by linear segments, cubic splines, exponential functions, power functions, and by best-fit polynomials of orders 1, 2, 3, ….) You can save the resulting data and formulae so that they can be used elsewhere.

Many people routinely use TILIA and TILIA. GRAPH for computations on their raw pollen data and to display the results as a pollen diagram. There was some interest in whether the results obtained with DEP-AGE could be imported into TILIA’s spreadsheet and used in the construction of the final diagram. I have now modified DEP-AGE (Version 3.9) to allow that transfer.

TILIA allows you to export your data as a WISCONSIN format data file (TILIA menu item D, F). The WISCONSIN format uses the name extension ‘.RAW’ (e.g, BLUELAKE.RAW). Put that file in the directory with DEP-AGE before running DEP-AGE. Then run DEP-AGE with the BLUELAKE.C14 file for your site, select your favoured rate model, and save it as BLUELAKE.RAT. Return to DEP-AGE’s main menu, and choose item 3. Item 3 allows you to try a few values to test the general results of the function. Pressing “enter” or “carriage return” without specifying a depth, gets you back to the initial menu, but you are first given the opportunity of exporting the results to TILIA.

DEP-AGE will load the BLUELAKE.RAW file and change it by appending each level’s age (yr) and its apparent sedimentation rate (cm/yr). For purposes of documentation, the RATe file (BLUELAKE.RAT) on which those dates were based is appended to the end of the *.RAW file. The file is then saved with either the same or a new name. The revised *.RAW file can then be imported back into TILIA (menu item C, F) and used in that program.

DEP-AGEZ.EXE includes sample files, and a short article expressing my philosophy on the subject… free! The revised DEP-AGE.EXE (version 3.9) is now available on Keith Bennett’s INQUA File Boutique (http://www.kv.geo.uu.se/inqua) and my mirror site at: http://www.geology.wisc.edu/~maher/inqua

Contact: Louis J. Maher, Geology & Geophysics, University of Wisconsin – Madison, Madison, Wisconsin, WI 53706, USA, Tel: (608) 262-9595, Fax: (608) 262-0693, E-mail: maher[at]geology[dot]wisc[dot]edu

[This article first appeared in *CAP Newsletter* 21(2):27-28, 1998.]