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Biostratigraphy and Gap Analysis: The Expected Sequence of Biostratigraphic Events

The distribution of gaps within taxon range zones has been suggested to fit Poisson as well as exponential distributions. If the distribution of fossil occurrence horizons is controlled by a Poisson random variable, the distribution of gap length frequencies will be exponential. An exponential model of gap length frequencies allows us to place confidence intervals on the expected extent of taxon range zones and on the observed order of any two biostratigraphic events. By examining all pairs of biostratigraphic events, it becomes possible to estimate the corresponding sequence of biologic events. Sequences of biologic events determined in this fashion may be compared with the results of other quantitative biostratigraphic techniques. The utility of an exponential model assumes that (1) the distribution of fossil occurrence horizons in taxon range zones is random, and (2) sampling is random. If these assumptions are violated, an exponential model of gap length frequencies should not be used to place confidence intervals on the expected endpoints of taxon range zones. However, the problem of nonrandom sampling may be alleviated through additional collecting.