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The quality of the information yielded by stratigraphic and paleoecologic studies based on microfossils is often poor due to the spotty recovery of the taxa. Thus, downcore sequences contain many null records between the first appearance (FA) and the last appearance (LA) of the species. Cheetham and Deboo (1963) suggested the use of the range-through method (i.e., a species is considered present in a sample if found both above and below it, even if it was not found within the sample) as a means of smoothing these spotty data sets and, when biostratigraphic conclusions are sought, to counteract the effect of environmental influences (Hazel, 1970). The technique was subsequently adopted in many reports and incorporated in numerical methods for biostratigraphic work (e.g., see review in Brower, 1985). This procedure, however, has a distorting effect on the data in such a way that faunal similarities between the samples compared are artificially increased toward the middle of the column. This is due to the fact that, while in the original species x samples array the probability of filling any cell is mainly a function of the species' abundance and of the number of specimens scanned in that particular sample, in the matrix resulting from the range-through principle it also depends upon the number of samples checked both above and below the level in question. Since the number of these samples is highest for the central part of the sequence, and decreases toward the top and bottom, the central section will have artificially enhanced specific cooccurrences and, hence, faunal similarities. This distortion is subsequently reflected in the results attained after processing the indices such as, for example, in cluster analysis (Figure 1). This bias influences primarily the relative magnitude of the level at which the elements and groups of elements compared are associated and the makeup of the groups themselves, which can invalidate analyses aimed at the assessment of parameters such as faunistic breaks, turnovers, etc. Some other applications of the method, like the correlation of dated and undated samples (e.g., Tway et al., 1985), may not be greatly affected by range-through modifications of the original data matrix. The numbers of FA's and LA's of taxa at different levels in the sedimentary column have sometimes been used for the analysis of paleoecological and biostratigraphic events (e.g., Thomas, 1985). Yet, unless the total interval sampled is considerably longer than the life-span of the taxa involved and null records are due to actual absences (rather than to undersampling), the long-ranging and scarce organisms will tend to have their FA's and LA's closer to the ends of the sequence, than to its center (Figure 2.1). An extreme situation of this type is illustrated in Figure 2.2, where the 100 "taxa" are distributed at random in the 100 "samples" (i.e., all span the entire interval "sampled"). In both cases the problems involved are most significant when dealing with long-ranging taxa in highly diversified assemblages, like deep-sea benthic Foraminifera, which yield samples x species arrays with high percentages of null records between the FA's and the LA's of many species. Eliminating these rare species mitigates the drawback, but the problem is not solved altogether. In addition, given the usually high correlation between abundance and occurrence, the most abundant taxa are often also the most long-ranging (e.g., in deep-sea benthic Foraminifera) and, therefore, have limited use for biostratigraphic applications.

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