INQUA Working Group on Data-Handling Methods

Newsletter 13: January 1995

RAREFACTION ANALYSIS AND MICROFOSSIL COUNT SIZE

Alexander P. Wolfe
Laboratoire Jacques-Rousseau
Département de géographie
Université de Montréal
C.P. 6128 Centre Ville
Montréal H3C 3J7
E-mail: wolfea@ere.umontreal.ca

Paleoecologists usually target a standard count size when enumerating microfossils. Examples of typical and widely used sums include 300 pollen grains or 500 diatom valves per sample. Although the practice of noting each taxon's first appearance in the course of a count is undertaken in some laboratories, this doubtfully applies to most of us during routine analyses. Clearly, it is advantageous to have some knowledge of the taxonomic structure of assemblages, particularly if count size is to be modified for specific purposes (for example: Renberg, 1990).

Rarefaction analysis (for applications to pollen data, see Birks & Line, 1992; Birks et al., 1988) produces distribution-free measures of species richness (number of taxa, t), that are standardised to a specified sample size n, where n<N, n being a random sample drawn without replacement from N specimens of T total species. In other terms, rarefaction analysis provides a simple to interpret yet robust diversity index that predicts species richness for a standardized sample size (i.e. count) throughout the data set (e.g. the core). This number (n) is usually designated as the smallest sample size (count) in the data set. This provides richness estimates, unbiased by sample size, that allow for direct comparisons between samples over a given sequence. Additional statistical and ecological characteristics of rarefaction analysis are given by Birks & Line (1992).

Another application of this technique, using Birks & Line's FORTRAN program RAREPOLL (available from the INQUA file boutique), is the calculation of rarefaction-estimated species richness (E(Tn)) for a series of samples using progressively smaller values of n. From the underlying structure of the assemblage, this models a posteriori how rapidly taxa were encountered in the enumeration of samples. During high resolution diatom analyses on 60 continuous samples 2.5 mm thick, I used this approach to establish what degree of taxonomic richness would be lost by reducing the count size (Wolfe, 1994a). Counts >500 valves on samples representing the different diatom zones in the same core (from Wolfe, 1994b) were used for the exercise. For comparative purposes, I show the diatom results alongside those from four pollen assemblages (Holocene) in a core from Lac Ébron, Gaspésie, Québec (counts from N. Morasse & P.J.H Richard, Université de Montréal).

Figure 1
Figure 1. Relationships between assemblage size (n) and rarefaction-estimated richness (E(Tn)) for sample diatom and pollen data.
The asymptotic shape of curves on Figure 1 is well known to paleoecologists. What should be sought is a count size for which these curves begin to level off, as this indicates an appropriate count size to account for the presence of infrequent, but often important, taxa (although not necessarily their stabilized frequencies). Another option is to consider the percentage of taxa that are retained in samples of reduced size relative to the estimated richness for n=500 (Table 1). Together, these simple exercises are useful ways to ponder retrospectively questions such as "did I count enough?" or "did I need to count so many?" In some instances, the rates at which new taxa are accounted for may seem surprising, indicating that, often, smaller counts can be sufficient for the detection of even subtle paleoecological changes. If this is the case, equal counting effort can be spread over a larger number of samples. In my own investigation, I settled on counting 200 diatom valves, knowing that, despite cutting my normal count size by more than 60%, I only lost about 20% of the taxonomic richness of each sample, which was clearly offset by the larger number of total samples counted, as well as their greater stratigraphic resolution.
Table 1. Percentages of the rarefaction-estimated richness for n=500 (E(T500)) accounted for by counts (n) of smaller size. 
          Amarok L. diatoms       Lac Ébron pollen
 n     min    max   mean        min    max   mean
 50   49.7   64.9   54.9       41.5   48.4   44.9
100   62.9   79.0   68.8       55.2   64.4   59.2
200   75.7   90.4   82.1       72.4   80.4   75.4
300   85.0   95.3   89.8       83.1   89.4   85.8
400   92.8   98.1   95.4       92.0   95.4   93.6

References.

Birks, H.J.B. & J.M. Line, 1992. The use of rarefaction analysis for estimating palynological richness from Quaternary pollen-analytical data. The Holocene 2: 1-10.

Birks, H.J.B., Line, J.M. & T. Persson, 1988. Quantitative estimation of human impact on cultural landscape development. In: H.H. Birks, H.J.B. Birks, P.E. Kaland & D. Moe (eds.), The Cultural Landscape Past, Present and Future. Cambridge University Press, Cambridge, 229-240.

Renberg, I., 1990. A 12 600 year perspective of the acidification of Lilla Öresjön. Philosophical Transactions of the Royal Society of London Series B 327: 357-361.

Wolfe, A.P., 1994a. A paleolimnological assessment of late Quaternary environmental change on southwestern Cumberland Peninsula, Baffin Island, N.W.T. Ph.D. thesis, Department of Geography, Queen's University, Kingston, Canada, 161 pp.

Wolfe, A.P., 1994b. Late Wisconsinan and Holocene diatom stratigraphy from Amarok Lake, Baffin Island, N.W.T. Journal of Paleolimnology 10: 129-139.

Copyright © 1995 Alexander P. Wolfe
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