Quantitative analyses of global diversity in the marine fossil record over Phanerozoic time reveal an historically ordered pattern of sequential dominance and increasing diversity. Explanatory models applied to this empirical pattern lead to irreconcilable differences of interpretation. The issue may be resolved by determining the expected distributions and limits of temporal covariation among clades generated by a random branching process. Results also challenge the claim that asymmetries in intra-clade diversity variation provide a directional arrow for the history of life.