TIME OF ORIGIN OF ARCHAEOCETES

There are approximately 42 independently sampled sites yielding archaeocete whales distributed on six continents (Table 1). These range in age from late Priabonian (t₃, ca. 36 Ma) to late Ypresian (t₂, ca. 49.5 Ma), for an observed temporal range t₂ - t₃ = 13.5 m.y. Calculation of ETD from equation 3 yields an expected temporal range of 14.78 m.y., and adding the difference between expected and observed ranges to the oldest stratigraphic record at 49.5 yields a classical 95% confidence limit for the time of origin of archaeocetes and hence all whales at 50.78 Ma, an extension of about 1.3 m.y. beyond the earliest stratigraphic record known to date.

Likelihood calculation of the time of origin of whales is outlined in the work sheet of Table 2 and shown graphically in Figure 4. Here the origination volume OTD is successively incremented by 0.001 units until critical likelihoods l = 0.5 and l = 0.05 are reached and exceeded. Hypothesized times of origin are interpolated at 49.99 and 51.64 Ma, respectively, with the latter, an extension of about 2.1 m.y. beyond the earliest stratigraphic record, being the likelihood equivalent of a 95% confidence limit. This limit at 51.64 Ma is almost 1 m.y. earlier in time than the classical confidence interval of Strauss and Sadler (1989) based on a uniform distribution of potential fossils. The difference is due to assumptions built into our geometric model of increasing density and diversity of whales during their initial diversification and to the exponentially increasing availability of fossil-bearing sedimentary rocks in more recent geological times.

The likelihood function calculated for the time of origin of Archaeoceti is shown in Figure 5. Both of the confidence limits calculated here, a 50% limit at 49.99 Ma and a 95% limit at 51.64 Ma, fall comfortably within the early Eocene on the Haq et al. (1987) time scale used here. Thus we can be confident, given present evidence, that whales originated in the early Eocene. Any discovery older than the known temporal range of archaeocetes would of course extend both the range and the ages associated with all critical likelihoods.