Computer Applications in the Earth Sciences pp 63-103 | Cite as

# Quantitative Biostratigraphy, 1830–1980

## Abstract

Charles Lyell (1830–1833) became the first quantitative biostratigrapher when he proposed his method for determining the relative age of Tertiary fossil assemblages by calculating the percent of living species in them. Quantitative biostratigraphy languished for about 125 years but a major renaissance began in the late 1950’s which is continuing at an accelerating pace.

Methods of quantitative biostratigraphy can be grouped into several categories. The first category consists of the quantification of the index-fossil concept including measurement of the attributes of an index fossil as well as the relative biostratigraphic values of the species concerned.

The second category represents the treatment of assemblage zones with multivariate analysis. The basic data may represent proportions of different species in a series of samples but presence-absence data also are used. The unweighted presence-absence data may be analyzed but the presences also can be weighted by the amount of biostratigraphic information conveyed by the species involved. Most of the techniques applied here are well-known multivariate methods such as cluster analysis, multidimensional scaling and some forms of archeological seriation.

In the third category, the biostratigrapher is faced with a plethora of methods for determining the most likely sequence of biostratigraphic events based on observations from numerous stratigraphic sections. Most schemes are concerned with point events which consist of the highest and lowest occurrences of the species treated. Several techniques are concerned with entire range zones. Sequencing algorithms produce either average sequences or are intended to give the stratigraphically highest possible estimate of the top of a range zone and the stratigraphically lowest possible estimate of the base of that range zone. Once the most likely sequence of events is ascertained, it can serve to correlate the individual samples and stratigraphic sections. Some of the techniques are elaborate whereas others are simplicity carried to the ultimate.

Although numerous methods of quantitative biostratigraphy have been proposed which do produce excellent results, most biostratigraphers have resisted successfully the impact of quantification. There are several reasons for this. First, most practicing biostratigraphers are basically nonquantitative. Secondly, many of the methods involve logic and algorithms which are not familiar to biostratigraphy. Thirdly, biostratigraphers learn that nonquantitative techniques produce acceptable results although only after long periods of time and much effort. Essentially quantitative biostratigraphy has proven unpalatable to the intended consumers.

Therefore, in the fourth category, we have cast about for super-simple methods of quantitative biostratigraphy, almost without numbers, which closely replicate the logic of biostratigraphers. One such technique is archeological seriation which can work directly on a species by samples data matrix to simultaneously produce a range chart as well as correlation of the samples. Both additive and nonadditive models are applicable. Another is a sequencing method which involves comparison of lists of events in a series of stratigraphie sections and resolving the inconsistencies between the different sections in such a manner as to produce a composite zonation.

Lastly, paleontologists have studied evolutionary sequences in a numerical context using a smorgasbord of techniques for many years. The statistical methods range from the simplest univariate to the most complicated multivariate types with or without the aid of time-series analysis. Although evolution provides the basis for biostratigraphy, it is surprising that many evolutionary sequences are approached through a strictly biological point of view rather than in a biostratigraphic context.

Through the past 150 years, biostratigraphers have proposed many numerical schemes for quantitative correlation. It is unfortunate that most of these methods have not been tested rigorously on numerous actual and simulated data sets. Hopefully, during the next decade quantitative biostratigraphers will evaluate systematically the available algorithms by case studies to ascertain which techniques provide the best results with various types of data. Thus the 1980’s should represent an interval of consolidation instead of a decade in which a new horde of algorithms will be invented.

## Keywords

Assemblage Zone Stratigraphic Section Composite Section Association Matrix Range Zone## Preview

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