POTENTIAL RESOLVING POWER OF CALIBRATED BIOSTRATIGRAPHIC TIME LINES FOR PALEOZOIC DEEP TIME

Optimization algorithms can build ordered composite sequences for thousands of first- and last-appearance events of fossil taxa. The optimal order is determined from evidence of superposition, coexistence, and spacing in all available stratigraphic sections. Isotopically dated events find their best-fit position during the ordering process, as determined by taxa found in the same stratigraphic sections as the dated beds. Because the composite sequence resembles an exceptionally complete stratigraphic section, regional biozones may be fit to the sequence using diagnostic taxa. The spacing of dated events in the scaled composite allows the age of other events to be estimated by interpolation. Geochronologic limits to resolving power derive from the number of dated events and their analytic uncertainty. Stratigraphic limits to resolving power have three sources: the number of paleontologic events; the adequacy of the superpositional constraints, and the difficulties of recognizing local zones in a global composite of all biologic provinces.

We applied constrained optimization to sequence 3,408 Ordovician to earliest Devonian graptolite appearance and disappearance events, using 14,921 observed range ends in 402 localities worldwide. Calibration was attempted down to the scale of individual zones and subzones to quantify the stratigraphic limits of resolving power for correlation. There is not a complete and unique best sequence for these events: the algorithms cannot separately resolve every event. The best ordered composite sequence contains just over 1,300 individual events and irresolvable clusters of events. This compares with 60-70 traditional zones and still leaves a potential average resolving power of 0.05 myr.; i.e. an order of magnitude better than needed to resolve the average graptolite zone. The calibrated time scale shows that traditional graptolite zones and subzones vary in duration from more than 5.0 myr. to less than 0.1 myr. The average stratigraphic uncertainty in locating zone boundaries in the composite sequence is 0.53+/- 0.42 myr. (or 41% +/- 28 of the zone duration) in the Ordovician and 0.23 +/- 0.25 myr. (24% +/- 25) in the Silurian.