Figure 4. Graphical model for analysis of the time of origin of Archaeoceti, assuming that all uncertainty is in the left or origination tail of the confidence interval (compare work sheet in Table 2). Sample space is three-dimensional and composed of five volumes: A is the partially-stippled volume preceding inferred origination and diversification of the taxon of interest; B is the thin wedge-shaped origination volume (hatched) reflecting the density of potential fossils during diversification; C is the volume representing the density of the known fossil record (cross-hatched); D is negligible because we are not concerned with extinction here; and E is the partially-stippled volume succeeding inferred extinction or conversion to another taxon. For comparison with other figures, tables, and text, volume C is the observed temporal density OTD, and volumes B + C together are the expected temporal density ETD. The sample space shown here reflects the exponentially declining availability of older fossil-bearing sedimentary rocks at the earth's surface (F), and diversification of Archaeoceti at a constant rate in the d dimension from the time they are first inferred to have existed until they are first found as fossils. Simulation built into the analysis tests analytical assumptions by repeatedly drawing samples of size n = 42 from B + C (or ETD) and counting the number of times all fall in C (or OTD) in 1000 trials (one sample is shown in simulation bar at bottom of figure). All samples drawn from B + C fell in C in 53 of 1000 simulation trials, which is close to the 50/1000 times expected with a critical likelihood l = 0.05.