TABLE 1. Independent records of archaeocete Cetacea. Records from different geological formations are considered independent; records from the same geological formation are considered independent of they come from different states, provinces, or countries.
Country/State Formation Age Ref.
North America      
1. Canada (B.C.) Nootka Conglomerate L. Eocene Kellogg (1936)
2. U.S.A. (N. Car.) Castle Hayne L. Eocene (Bart.-Priab.) Kellogg (1936)
3. U.S.A. (S. Car.) Harleyville Formation M. Eocene (Bartonian) Sanders (1974)
4. U.S.A. (S. Car.) Santee Limestone M. Eocene (E. Bart.) Albright (1996)
5. U.S.A. (Georgia) Twiggs Clay L. Eocene (L. Priab.) Case (1975)
6. U.S.A. (Georgia) Barnwell Sand L. Eocene (Bart.-Priab.) Cooke and Shearer (1918)
7. U.S.A. (Georgia) Clinchfield L. Eocene (L. Bart.) Westgate (1994)
8. U.S.A. (Georgia) McBean M. Eocene (E. Bart.) Petkewich and Lancaster (1984)
9. U.S.A. (Florida) Ocala Limestone L. Eocene (L. Bart.-Priab.) Morgan (1978)
10. U.S.A. (Alabama) Jackson/Ocala L. Eocene (L. Bart.-Priab.) Kellogg (1936)
11. U.S.A. (Miss.) Yazoo L. Eocene (L. Bart.-Priab.) Daly (1992)
12. U.S.A. (Miss.) Moodys Branch M. Eocene (M. Bart.) Dockery (1974)
13. U.S.A. (Ark.) Jackson L. Eocene (Priabonian) Palmer (1939)
14. U.S.A. (Tenn.) Jackson L. Eocene (Priabonian) Corgan (1976)
15. U.S.A. (Louis.) Cook Mountain M. Eocene (E. Bart.) Maher and Jones (1949)
16. U.S.A. (Louis.) Jackson L. Eocene (L. Bart.-Priab.) Lancaster (1986)
17. U.S.A. (Texas) Yegua (basal) M. Eocene (E. Bart.) Ball (1931)
18. U.S.A. (Texas) Cook Mountain M. Eocene (L. Lut.) Gimbrede (1962)
Europe      
19. England Middle Headon Beds L. Eocene (L. Priab.) Hooker et al. (1980)
20. England Barton Clay M. Eocene (Bartonian) Hooker et al. (1980)
21. Germany Braunschweig Phosphates L. Eocene (reworked) Kuhn (1935)
22. Italy Not reported M. to l. Eocene Pilleri and Cig.-Ful. (1989)
23. Spain Not reported M. to l. Eocene Pilleri (1989)
Asia      
24. India (Kutch) Gypsiferous Clay M. Eocene (Lutetian) Kumar and Sahni (1986)
25. India (Kutch) Chocolate Limestone M. Eocene (Lutetian) Kumar and Sahni (1986)
26. India (Kashmir) Subathu E.-M. Eocene Kumar and Sahni (1985)
27. Pakistan (Punj.) Drazinda M. Eocene (Lutetian) Gingerich et al. (1995b)
28. Pakistan (Punj.) Domanda M. Eocene (Lutetian) Gingerich et al. (1994)
29. Pakistan (Punj.) Habib Rahi M. Eocene (Lutetian) Gingerich (1991)
30. Pakistan (Punj.) Kuldana E. Eocene (L. Ypr.) West (1980)
31. Pakistan (NWFP) Kuldana E. Eocene (L. Ypr.) Gingerich and Russell (1981)
Africa      
32. Egypt (Fayum) Qasr el-Sagha L. Eocene (M.-L. Priab.) Stromer (1903)
33. Egypt (Fayum) Birket Qarun L. Eocene (E. Priab.) Andrews (1906)
34. Egypt (Fayum) Gehannam M. Eocene (L. Bart.) Gingerich (1992)
35. Egypt (E. desert) Mokattam M. Eocene (L. Lut.?) Blanckenhorn (1900)
36. Egypt (Cairo) Mokattam M. Eocene (Lut.-E. Bart.) Fraas (1904)
37. Nigeria Ameki M. Eocene (Lutetian) Andrews (1919)
38. Senegal Not reported M. to l. Eocene Elouard (1981)
39. Togo Kpogamé Phosphates M. Eocene (L. Lut.) Gingerich et al. (1992)
Australia      
40. New Zealand Opuha River Sandstone M. to l. Eocene Fordyce (1985)
41. New Zealand Waihao Greensands L. Eocene Fordyce (1985)
Antarctica      
42. Seymour Island La Meseta L. Eocene(?) Borsuk-Bialynicka (1988)
Table 2. Work sheet for likelihood estimation of the time of origin of Archaeoceti. The fossil record of archaeocetes begins at about 49.5 Ma and ends at about 36 Ma, an interval of about 13.5 m.y. (Haq et al. 1987 temporal calibration). There are 42 independently-sampled fossil localities known from sites on six continents (Table 1). Analysis here takes account of exponentially decreasing area of sedimentary rocks of older ages exposed at the earth's surface and linear diversification through the inferred temporal range of archaeocetes before their earliest fossil record (see Fig. 4). Interpolated 50% and 5% likelihood limits for the time of origin of mesonychians are shown in bold face. Results are not accurate to more than one decimal place and must be interpreted in context of the particular temporal calibration used to quantify the geological time scale (50.0 and 51.6 Ma are both late early Eocene).
1. Increment of origination volume
2. Hypothesized time of origin
3. Origination volume B
4. Fossil record volume C
5. Extinction volume D
6. Hypothesized time of extinction
7. Volume quotient (probability)
8. Exponentiated quotient (probability)
9. Likelihood ratio
1. 2. 3. 4. 5. 6. 7. 8. 9.
                 
0.0000 49.5000 0.0000 0.0583 0.0000 36.0000 1.0000 1.0000 1.0000
--- 49.9869 --- --- --- --- --- --- 0.5000
0.0010 49.9899 0.0010 0.0583 0.0000 36.0000 0.9831 0.4979 0.4979
0.0020 50.4698 0.0020 0.0583 0.0000 36.0000 0.9668 0.2508 0.2508
0.0030 50.9498 0.0030 0.0583 0.0000 36.0000 0.9511 0.1278 0.1278
0.0040 51.4297 0.0040 0.0583 0.0000 36.0000 0.9358 0.0658 0.0658
--- 51.6352 --- --- --- --- --- --- 0.0500
0.0050 51.9196 0.0050 0.0583 0.0000 36.0000 0.9210 0.0343 0.0343

Volume quotient is the fossil record volume (C here and in Fig. 4) divided by the sum of the hypothesized origination volume plus the fossil record volume (B + C here and in Fig. 4). Exponentiated quotient is (B / B + C)n where n is the number of independent samples drawn from B + C and falling in C (here n = 42).

Table 3. Independent records of Mesonychia (here Mesonychidae plus Hapalodectidae). Records from different geological formations are considered independent; records from the same geological formation are considered independent of they come from different states, provinces, or countries.
Country/State Formation Age Ref.
North America      
1. Mexico (B. Cal.) Tetas de Cabra Early Eocene (Wasatchian) Novacek et al. (1991)
2. USA (Colorado) Huerfano Middle Eocene (Bridger.) Robinson (1966)
3. USA (Colorado) Wasatch Early Eocene (Wasatchian) McKenna (1960)
4. USA (Colorado) DeBeque Late Paleocene (Clarkfork.) Kihm (1984)
5. USA (Colorado) San Jose Late Paleocene (Tiffanian) Granger (1917)
6. USA (Montana) Fort Union Late Paleocene (Clarkfork.) Simpson (1929)
7. USA (Montana) Tongue River Late Paleocene (Tiffanian) Zhou (1995)
8. USA (Montana) Lebo Middle Paleocene (Torrejon.) Simpson (1937)
9. USA (New Mexico) San Jose Early Eocene (Wasatchian) Cope (1874)
10. USA (New Mexico) Nacimiento Middle Paleocene (Torrejon.) Osborn and Earle (1895)
11. USA (Texas) Comena Middle Eocene (Uintan) Gustafson (1986)
12. USA (Texas) Devils Graveyard Middle Eocene (Uintan) Gustafson (1986)
13. USA (Utah) Duchesne River Late Eocene (Duchesnian) Peterson (1931)
14. USA (Utah) Uinta Middle Eocene (Uintan) Osborn (1895)
15. USA (Wyoming) Washakie Middle Eocene (Bridgerian) Cope (1872b)
16. USA (Wyoming) Bridger Middle Eocene (Bridgerian) Cope (1872a)
17. USA (Wyoming) Aycross Middle Eocene (Bridgerian) Bown (1982)
18. USA (Wyoming) Wasatch Early Eocene (Wasatchian) Gazin (1952)
19. USA (Wyoming) Wind River Early Eocene (Wasatchian) Matthew (1909)
20. USA (Wyoming) Willwood Early Eocene (Wasatchian) Osborn and Wortman (1892)
21. USA (Wyoming) Fort Union Late Paleocene (Tiffanian) Rose (1981)
Europe      
22. Belgium Landen Early Eocene (Sparnacian) Russell (1982)
23. France (Herault) Marnes Jaunes et Rouges Middle Eocene (Lutetian) Stehlin (1926)
24. France (Marne) Lignites de Soissonais Early Eocene (Sparnacian) Lemoine (1891)
25. France (B. Rhône) Lentille de Marne Early Eocene (Sparnacian) Godinot et al. (1987)
26. France (H. Seine) Argile Plastique Early Eocene (Sparnacian) Boule (1903)
27. France (Marne) Conglomérat de Cernay Late Paleocene (Thanetian) Lemoine (1891)
28. Spain (Lérida) Tremp or Montañana Middle Eocene (Lutetian) Crusafont and Golpe (1968)
29. Spain (Huesca) Tremp or Montañana Early Eocene (Cuisian) Crusafont and Golpe (1973)
Asia      
30. China (Anhui) Tujinshan Late Paleocene (Nongshanian) Zhou et al. (1995)
31. China (Anhui) Shuangtasi Late Paleocene (Nongshanian) Yan and Tang (1976)
32. China (Gwangdong) Nongshan Late Paleocene (Nongshanian) Wang (1976)
33. China (Guangdong) Shanghu Middle Paleocene (Shanghuan) Chow et al. (1973)
34. China (Henan) Dacangfang Middle Eocene (Irdinmanhan) Xu et al. (1979)
35. China (Henan) Lushi Middle Eocene (Irdinmanhan) Chow (1965)
36. China (Hunan) Lingcha Early Eocene (Bumbanian) Ting and Li (1987)
37. China (Hunan) Zaoshi Middle Paleocene (Shanghuan) Wang (1975)
38. China (Jiangxi) Chijiang Late Paleocene (Nongshanian) Zhang et al. (1979)
39. China (Nei Mong.) Chaganbulage Early Oligocene (Ergilian) Qi (1975)
40. China (Nei Mong.) Ulan Gochu Early Oligocene (Ergilian) Szalay and Gould (1966)
41. China (Nei Mong.) Shara Murun Late Eocene (Sharamurunian) Matthew and Granger (1925)
42. China (Nei Mong.) Ulan Shireh Middle Eocene (Irdinmanhan) Szalay and Gould (1966)
43. China (Nei Mong.) Irdin Manha Middle Eocene (Irdinmanhan) Matthew and Granger (1925)
44. China (Nei Mong.) Arshanto Middle Eocene(Irdinmanhan) Qi (1987)
45. China (Nei Mong.) Nomogen Late Paleocene (Nongshanian) Chow and Qi (1978)
46. China (Shaanxi) Fangou Middle Paleocene (Shanghuan) Qi and Huang (1982)
47. China (Yunnan) Lumeiyi Middle Eocene (Irdin.-Shar.) Zheng et al. (1978)
48. China (Yunnan) Xiangshan Middle Eocene (Irdin.-Shar.) Zhang et al. (1978)
49. India (Kashmir) Subathu Early to middle Eocene Ranga Rao (1973)
50. Kazakhstan Sargamys Svita Middle Eocene (Irdinmanhan) Gabunia (1982)
51. Kirgizistan Alay Svita Middle Eocene (Irdinmanhan) Reshetov (Russ. and Zhai 1987)
52. Korea Hosan coal Middle to late Eocene Shikama (1943)
53. Mongolia (Zaal.) Khaychin Svita Middle to late Eocene Dashzeveg (1976)
54. Mongolia (Dorn.) Unnamed Svita Middle Eocene (Irdinmanhan) Dashzeveg (Russ.and Zhai 1987)
55. Mongolia (Omon.) Naran-Bulak Svita Late Paleocene (Nongshanian) Gromova (1952)
56. Mongolia (Omon.) Khashat Svita Late Paleocene (Nongshanian) Szalay and McKenna (1971)
Table 4. Work sheet for likelihood estimation of the time of origin of Mesonychia (here Mesonychidae and Hapalodectidae). The fossil record of Mesonychia begins at about 63 Ma and ends at about 33 Ma, an interval of about 30 m.y. (Haq et al. 1987 temporal calibration). There are some 56 independently-sampled fossil localities known from northern continents (Table 3). Analysis takes account of exponentially decreasing area of sedimentary rocks of older ages exposed at the earth's surface and linear diversification through the inferred temporal range of mesonychians before their earliest fossil record (see Fig. 6). Interpolated 50% and 5% likelihood limits for the time of origin of mesonychians are shown in bold face. Results are not accurate to more than one decimal place and must be interpreted in context of the particular temporal calibration used to quantify the geological time scale (63.8 Ma is early Paleocene and 66.7 Ma is very latest Cretaceous).
1. Increment of origination volume
2. Hypothesized time of origin
3. Origination volume B
4. Fossil record volume C
5. Extinction volume D
6. Hypothesized time of extinction
7. Volume quotient (probability)
8. Exponentiated quotient (probability)
9. Likelihood ratio
1. 2. 3. 4. 5. 6. 7. 8. 9.
                 
0.0000 63.0000 0.0000 0.1260 0.0000 33.0000 1.0000 1.0000 1.0000
0.0010 63.5199 0.0010 0.1260 0.0000 33.0000 0.9921 0.6474 0.6474
--- 63.8308 --- --- --- --- --- --- 0.5000
0.0020 64.0398 0.0020 0.1260 0.0000 33.0000 0.9844 0.4206 0.4206
0.0030 64.5600 0.0030 0.1260 0.0000 33.0000 0.9767 0.2741 0.2741
0.0040 65.0801 0.0040 0.1260 0.0000 33.0000 0.9692 0.1793 0.1793
0.0050 65.6002 0.0050 0.1260 0.0000 33.0000 0.9618 0.1176 0.1176
0.0060 66.1303 0.0060 0.1260 0.0000 33.0000 0.9545 0.0774 0.0774
0.0070 66.6504 0.0070 0.1260 0.0000 33.0000 0.9474 0.0511 0.0511
--- 66.6781 --- --- --- --- --- --- 0.0500
0.0080 67.1705 0.0080 0.1260 0.0000 33.0000 0.9403 0.0339 0.0339

Volume quotient is the fossil record volume (C here and in Fig. 6) divided by the sum of the hypothesized origination volume plus the fossil record volume (B + C here and in Fig. 6). Exponentiated quotient is (B / B + C)n where n is the number of independent samples drawn from B + C and falling in C (here n = 56).