phy has focused on the completeness of local taxon ranges (Paul 1982; McKinney 1986a,b;. Springer and Lilje 1988; Strauss and Sadler. 1989; Marshall 1990a ...
Paleobiology, 16(4), 1990, pp. 512-520
The effect of random range truncations on patterns of evolution in the fossil record MarkS. Springer
Abstract.-Both fossil preservation and sampling methods affect perceived patterns of biotic diversity. Artificial range truncations, for example, may lead to incongruences between apparent- and actual-diversity curves. Thus, a catastrophic extinction event may appear gradual. Recent advances in biostratigraphic-gap analysis provide models for the distribution of gap lengths between fossil occurrence horizons and provide methods to place confidence intervals on local taxon ranges and remove the biases caused by artificial range truncations. Confidence intervals for a set of local taxon ranges may then be evaluated collectively to test a hypothesis of co-extinction/co-emigration or coorigination/co-immigration. In the case of terminal Cretaceous ammonites from Seymour Island, range-chart data are compatible with an abrupt extinction event, although the test statistic is not minimized at the stratigraphic horizon that was suggested by Macellari (1986). Mark S. Springer. Division of Biology, California Institute of Technology, 101 Dahlia, Corona del Mar, California 92625
Accepted:
June 10, 1990
Introduction The importance of fossil preservation and sampling effects that bias the fossil record has been documented by numerous authors (Raup 1972, 1976a,b, 1986; Signor and Lipps 1982; Paul1982; McKinney 1986a; Koch 1978, 1987). Preservation and sampling affect the observed extent of taxon ranges and can cause apparent patterns of biotic diversity, extinction, and multispecies evolution to differ from corresponding actual patterns. In short, sampling and preservation bias can create misleading patterns and obscure patterns that reflect important biological phenomena. In addition, patterns of evolution in the fossil record are affected by sedimentation regimes and stratigraphic completeness. Hence, disentangling the effects of preservation, sampling, sedimentation, and stratigraphic completeness is a necessary endeavor if we are to elucidate underlying patterns of evolution. Recent work in quantitative biostratigraphy has focused on the completeness of local taxon ranges (Paul 1982; McKinney 1986a,b; Springer and Lilje 1988; Strauss and Sadler 1989; Marshall 1990a,b). Methods have been developed to place confidence intervals on the ends of these ranges, where it may be assumed that fossil-occurrence horizons are © 1990 The Paleontological Society. All rights reserved.
randomly distributed. Springer and Lilje (1988), Strauss and Sadler (1989), and Marshall (1990b) have suggested appropriate tests for this assumption. Paul (1982) and Springer and Lilje (1988) have modeled gap-length frequencies as an exponential function and Springer and Lilje (1988) have provided the following equation to place confidence intervals on the stratigraphic extent of local taxon ranges: x
= ln
P0 (x)!(-m),
(1)
where P 0 is the probability of zero events, x is the length of the confidence interval, and m is the mean number of occurrence horizons per unit of length of stratigraphic section. A major shortcoming of this approach is that it does not take into account the standard error of parameter m, as well as its reciprocal, mean gap length (H). Fortunately, two different methods of placing confidence intervals on local taxon ranges that incorporate the effects of sample size have been developed by Strauss and Sadler (1989). The first method employs a standard statistical distribution known as the Dirichlet distribution. Specifically, confidence intervals on either end of the stratigraphic range may be calculated using the following equation: 0094-8373/90 I 1604-0008/$1.00
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