If everyone agreed that whales became whales when they first showed evidence of the evolutionary transition in grade from terrestrial to aquatic life, then it would still be possible to view the origin of whales in different ways, depending on whether one assumed a predominantly comparative or predominantly historical perspective. We do not view such a dichotomy as necessary so much as matter-of-factly descriptive of perspectives colleagues have.
To comparative biologists concerned solely with living organisms, a whale is a whale after the time of separation of Cetacea from its closest living noncetacean relative. Flower (1883) interpreted an elongated larynx, complex stomach, simple liver, reproductive organs, and fetal membranes as linking Cetacea to Artiodactyla anatomically, but later authors did not find this convincing (Kellogg 1936; Simpson 1945). We owe our present understanding that extant Artiodactyla are the sister-group of extant Cetacea to comparative immunology (Boyden and Gemeroy 1950), to the fossil record (Van Valen 1966, 1969), and more recently to molecular gene sequencing (Arnason et al. 1991; Irwin et al. 1991; Milinkovitch 1992; Krettek et al. 1995; D'Erchia et al. 1996). Claims that (1) sperm whales are mysticetes (Milinkovitch et al. 1993, 1994; Douzery 1993; Milinkovitch 1995; Milinkovitch et al. 1995; but see Ohland et al. 1995 and Messenger and McGuire 1998); (2) Cetacea originated within Artiodactyla as the sister-group of extant camels (Goodman et al. 1985), hippopotami (Sarich 1993; Irwin and Arnason 1994; Arnason and Gullberg 1996), ruminants (Graur 1993; Graur and Higgins 1994), or suids (Kumar and Hedges 1998); and (3) whales are the sister group of perissodactyls (McKenna 1987) cast doubt on the efficacy of molecular systematics, but we accept that Artiodactyla is probably the closest living sister-group to Cetacea. If true, then to a comparative biologist the time of origin of Cetacea is the time Cetacea diverged from Artiodactyla.
To paleontologists like us concerned with both living and extinct organisms, a whale is not a whale until it has both (1) separated from its closest living sister taxon (Artiodactyla), becoming a distinct clade, and (2) acquired one or more characteristics of Cetacea, achieving a distinctive grade. Cetacea and Artiodactyla can be traced back in geological time to different stem groups within Condylarthra (Mesonychia and Arctocyonia, respectively; Van Valen 1966, 1971, 1978; Rose 1996). Consequently, there is a possibly-significant interval of time between events (1) and (2) that we consider here. In the following analyses we first estimate the time of origin of whales as conceived by paleontologists, based on the fossil record, where Cetacea is not only a distinct clade but also a distinct grade. We then estimate the time of divergence of Cetacea from Artiodactyla by estimating the time of origin of Mesonychia and comparing that to the ranges of Arctocyonia and Artiodactyla in the fossil record.
One way to evaluate the time of origin of whales is to consider it to be close to the time of first preservation of whales in the fossil record. This is reasonable because whales are relatively large animals with well-ossified skeletons, most whales have distinctive dental and osteological characteristics related to aquatic or partially aquatic adaptations enabling them to be identified, and life in water enhances preservation potential in the fossil record. We can then consider the distribution of ages of known fossils and estimate an acceptable confidence limit for this distribution.
In the following calculations we use the fossil record of Archaeoceti to estimate the time of origin of Cetacea as a whole. We do this because Archaeoceti represents the Eocene initial diversification of whales and is thus the subgroup having the greatest bearing on the time of origin of the order. We concentrate on Archaeoceti too because this is the group for which we can best determine the number of independently-sampled site records. Occurrences of non-cetaceans, even when thought to be broadly ancestral (like mesonychians for example), contribute little in constraining the time of origin of cetaceans, just as the stratigraphic distribution of Archaeoceti contributes little to knowledge of the time of origin of later Odontoceti or Mysticeti.
Calculations similar to those presented here can be carried out for Cetacea as a whole (and for Artiodactyla and other orders of mammals) when counts of independently-sampled site records are known, but these are not yet available. If we can generalize based on what we demonstrate here about the statistical power of even modest numbers of independent sites, the temporal ranges of all of the better known orders of mammals are already closely constrained by the known fossil record.