The geological record represents the only source of data available for documenting long-term historical patterns of extinction intensity and extinction susceptibility. Such data are critical for testing hypotheses of extinction causality in the modern world as well as in deep time. The study of extinction is relatively new. Prior to 1800, extinctions were not accepted as a feature of the natural environment. Even after extinctions were recognized to have occurred in Earth's geological past, they were deemed to have played a minor role in mediating evolutionary processes until the 1950s. Global extinction events are now recognized as having been a recurring feature of the history of life and to have played an important role in promoting biotic diversification. Interpretation of the geological extinction record is rendered complex as a result of several biasing factors that have to do with the spatial and temporal resolutions at which the data used to study extinctions have been recorded: fluctuations in sediment accumulation rates, the presence of hiatuses in the stratigraphic sections/cores from which fossils are collected, and variation in the volumes of sediments that can be searched for fossils of different ages. The action of these factors conspires to render the temporal and geographic records of fossil occurrences incomplete in many local stratigraphic sections and cores. In some cases, these stratigraphic and sampling uncertainties can be quantified and taken into account in interpretations of that record. However, their effects can never be eliminated entirely. Testing hypotheses of global extinction causality requires acknowledgment of the uncertainties inherent in extinction data, the search for unique predictions of historical patterns of variation or associations that can, in principle, be preserved in the fossil record and tied logically to the operation of specific causal processes, and to adoption of an explicitly comparative approach that establishes the presence of multiple instances of the predicted cause-effect couplets within a well-documented chronostratigraphic context.

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Abstract Accurate estimation of the line of correlation (LOC) is an important goal of graphic correlation. Since wide variety of both qualitative and quantitative methods are currently available to guide LOC estimation, it is crucial that the procedure used to infer a working LOC be completely specified and, thus, reproducible. The most popular LOC estimation technique, termed “splitting tops and bases,” takes advantage of inherent differences in the chronostratigraphic implications of biostratigraphic first and last appearance datums (FADs and LADs, respectively). This method takes, as its starting point, a Standard Reference Section (SRS) that contains occurrences of a large number of species distributed over a long stratigraphic interval with no obvious gaps, hiatuses, or structural complications. If the SRS is well-chosen, a large number of its constituent taxa may occur at horizons corresponding to their global FADs and LADs. In such instances, graphic comparison of the SRS with datum positions from other sections or cores will result in the grouping of FADs and LADs on opposite sides of the true LOC. Using this relationship, the geometry of the LOC can be inferred by finding that line which divides FADs from LADs in the most efficient manner. Adjunct criteria that may be useful in establishing a qualitatively-defined LOC or distinguishing between alternative LOC geometries include consideration of key beds, datum weighting, and parsimony. Regression analysis can also be used to quantitatively estimate LOC positions. Unlike qualitative LOC estimation, regression-based techniques make no assumptions with respect to differences between biostratigraphic datum types. Least squares linear regression has a long history of use in graphic correlation as a LOC estimation technique. However, least-squares methods make a necessary distinction between independent and dependent variables ( = sections or cores). This distinction, along with its implicit corollary of a cause and effect relationship between variables, seems out of place in the context of a graphic correlation problem. Reduced major axis and major axis regression models provide a much closer match between the assumptions of the regression model and the nature of stratigraphic data, in addition to providing a better estimate of the bivariate linear trend. Reduced major axis regressions have the added advantage of being much easier to calculate than either least squares or major axis regressions. These alternative regression algorithms can be modified to take key beds and weighted data into consideration. Significance tests are available for least squares and major axis regressions, but these are, at best, indirect tests of the quality of the fit between the estimated LOC and the underlying data. Analysis of residual deviations from the LOC provides the best indication of this fit. Linear regression methods minimizē standard measures of fit between the LOC and the underlying data. While minimization of these parameters usually involves straightforward computations, these numerical recipes often fail to respect the stratigraphic implications of the minimization procedures, specifically those involving the inferred extension of local stratigraphic ranges. The sum of all local range extensions implied by a LOC has been termed the “economy of fit.” No deterministic formula leads directly from the raw stratigraphic data to the LOC exhibiting the best economy of fit. However, iterative constrained optimization procedures are available to efficiently search for LOCs with very good economy of fit characteristics. In most instances, LOCs with the best economy of fit or smallest net range extension exhibit a piecewise linear geometry. Constrained optimization search strategies can also be combined with a multivariate representation of raw stratigraphic data to locate highly economica! LOCs for all sections simultaneously.

Abstract Since the original MacLeod and Keller (1991a, b) graphic correlation study of Cretaceous/Tertiary (K/T) boundary sections and cores, new biostratigraphic data have become available for lowermost Danian successions in high latitudes (Nye Kj0v, ODP sites 690 and 738) and from sequences proximal to the proposed Chicxulub impact structure (Millers Ferry, Mimbral). Graphic analysis of these data provides an opportunity lo test the prediction that rising eustatic sea level during the tians-K/T interval played a major role in Controlling pattems of sediment accumulation in neritic and bathyal settings. In addition, restricling the empirical basis for development of a lowermost Danian Composite Standard (LD-CS) from all available biostratigraphic data (used in the previous study) to only datums from widely-accepled Danian and K/T survivor laxa enables determination of the extent to which previous results were biased by inclusion of data from controversial “Cretaceous” survivor taxa. Results indicate that sequences from neritic and upper bathyal settings (Nye Kİ0V, Mimbral) are temporally complete within their lowermost Danian intervals while sections/cores from very shallow inner neritic settings (Millers Ferry) and the deep sea (ODP Site 690, ODP Site 738) contain incomplete lower Danian stratigraphic records. These findings are consistent wilh results of traditional zone-based biostratigraphic analyses and with predictions of the sequence stratigraphic model. Moreover, this revised LD-CS is essentially identical to the previous K/T-CS (MacLeod and Keller, 1991b) based on total biotic data. Data from a large number of organismal groups now confirm that biotic, sedimentologic, and geochemical studies based solely on deep-sea and very shallow neritic successions are biased toward catastrophic paneras of change as a result of missing section (= time). Biotic patterns from inner neritic through upper bathyal settings have the best chance of preserving temporally complete sequences of lower Danian events. The faunal record from these sequences reveals the lower Danian succession to be characterized by progressive rather than instantaneous turnover in biotic, sedimentologic, and geochemical variables occurring over at least 500,000 years.