For much of the geologic time scale, resolving power appears to be limited by the duration of biostratigraphic zones and subzones. Yet these zones exploit the appearance and disappearance events of only a small fraction of the species they span. Computer algorithms can sequence an order of magnitude more events and make explicit the uncertainties that arise when calibrating the resulting time line. An illustrative case history builds an Ordovician and Silurian time scale from the geologic record of the entire graptolite clade—over 1900 species from more than 400 localities and sections worldwide. The same approach can be applied to any stratigraphic interval with detailed biostratigraphic observations. It provides the foundation for time scales and paleobiologic time lines.

Using logic similar to graphic correlation, optimizing algorithms search for a composite sequence of species first- and last-appearance events that minimizes the implied shortcomings of all the field observations. The algorithms minimize the number of species coexistences that are implied, but never observed, and the net adjustments needed to bring local range charts into agreement with a single composite sequence of events. After total section thicknesses have been rescaled to help normalize for variation in depositional rate, mean stratigraphic thicknesses are used to scale the intervals between adjacent events in the composite sequence. The resulting scaled composite sequence is converted to a relative geologic time scale by identifying stage and zone boundaries within the sequence of graptolite events. This relative scale is, in turn, calibrated by dated volcanic ash beds that were incorporated in the search for the optimal sequence. These dated events are also used to test for linearity of the scaled composite.

The final time scale has a potential resolving power of 0.02–0.1 m.y., more than ten times better than can be achieved by traditional zones. Graptolite zones vary widely in duration from as short as 0.1 m.y. to nearly 5.0 m.y. The mean duration of zones or zonal groupings calibrated here is 1.44 m.y. in the Ordovician and 0.91 m.y. in the Silurian. The average uncertainty in locating zone boundaries in a single composite sequence is about one-fourth of the mean zone duration. The variance resulting from differences in time scales developed from differing numbers of field observations and in response to changes in the optimization criteria gives a very conservative measure of the overall robustness of the method. These differences indicate an average uncertainty in the age of graptolite zone boundaries that is more nearly equal to the mean zone duration. For zone duration, the mean uncertainty amounts to about one-half of the length of an average zone.

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