Paleobiologic diversity is most often measured at or between the boundaries of biostratigraphic zones and stages. This adds to the biases and low resolution that afflict many diversity curves: the estimates of diversity are few and irregularly spaced. In modern biostratigraphy, however, computer-assisted methods of correlation avoid the limitations of biozones in favor of composite sequences of the first and last appearances of fossil taxa. The constrained optimization algorithms in CONOP9, for example, seek a parsimonious sequence that best fits all the direct field observations, in the sense that all the local range charts can be made to fit the sequence with the minimum net adjustment to observed taxon ranges. Because CONOP9 can incorporate all available taxa, not just those found in multiple sections, the order of individual origination and extinction events in a resulting best-fit sequence leads directly to an interval-free estimate of diversity history. A stack of the set of all the equally most parsimonious sequences provides a natural tolerance interval for the diversity curve. Fossiliferous dated tuffs may be included from the beginning of the optimization; they emerge in optimal positions in the best-fit sequences; and they provide time calibration.

CONOP9 algorithms have facilitated the sequencing of first and last occurrences for 1136 graptolite taxa, from 198 stratigraphic sections ranging from latest Cambrian to early Devonian. Twenty two dated tuffs provide time calibration. The resulting curves include over 2200 estimates of graptolite diversity and mean longevity in a time interval of about 100 million years. Because this interval captures the entire clade, artificial edge effects are eliminated. The robustness of individual peaks and troughs was tested by stacking multiple best-fit curves, by correcting for the number of stratigraphic sections that span each estimate, and by examining how soon a feature disappears as the optimization is progressively relaxed.