Even range charts from the best graptoloid-bearing sections can be improved by adding information from nearby sections. Traditionally this is achieved on a scale of discrete biozones. Zonal composites improve upon the taxon richness of individual sections but lose resolving power; they artificially cluster range-end events at zone boundaries. Graphical and numerical methods allow composite sections to be constructed on continuous scales that match or exceed the resolving power of individual sections. Using a database of 582 graptoloid-bearing sections that together preserve 2214 distinct graptoloid taxa, we show that constrained optimization algorithms can construct objective, reproducible, global time-lines for the entire Ordovician to early Devonian graptoloid clade. The underlying database of locally observed ranges allows standardization for sampling unevenness. The quality and geographic origins of support for composite taxon ranges are explicitly revealed. A high precision, interval-free, standing species richness curve derived by this approach reveals the diversity trajectory of the graptoloid clade and of the families of which it is composed. Major reorganizations of the clade at the family level took place after diversity minima in the late Darriwilian and Hirnantian. Glacial events recognized on sedimentological evidence coincide with diversity minima.