TABLE 1 Paleontological dates and numbers of replacements

 

Amino acid differences

Sister groups

Mya

Replacements

Observed SOD

Simulated

D. nebulosa–D. melanogaster

55 ± 5

33

18 ± 2

18 ± 2

D. hydei–D. melanogaster

60 ± ?

36

19 ± 3

20 ± 4

Chymomyza–D. melanogaster

65 ± ?

39

23 ± 2

20 ± 4

Homo sapiens–Bos taurus

70 ± 10

42

27 ± 2

22 ± 4

Ceratitis–D. melanogaster

100 ± ?

60

31 ± 2

28 ± 3

Monocot–dicot

125 ± ?

74

28 ± 3

31 ± 5

Angiosperm–gymnosperm

220 ± ?

132

29 ± 7

42 ± 5

Frog–mammals

350 ± 10

210

49 ± 2

53 ± 6

Fish–tetrapods

400 ± 20

240

44 ± 4

56 ± 7

Yeast–Neurospora

?

 

46 ± 1

 

Insect–vertebrate

580 ± 20

348

59 ± 3

60 ± 6

Fungi–metazoans

1000 ± ?

600

67 ± 4

66 ± 7

Replacements refer to the number of replacements used in the simulation, which is equivalent to six replacements every 10 Myr. Observed is the average number of amino acid differences observed between members of the two sister groups shown. The sister group names (e.g., Drosophila nebulosa–Drosophila melanogaster) should be understood as indicating the groups to which these species belong and not just two individual species. Simulated is the observed number of amino acid differences obtained after the number of replacements shown had been incorporated. The plus/minus values are crude estimates of error for Mya but are SDs for observed and simulated differences. The simulated values are based on 40 simulated instances for each entry. See Methods for details of the simulation. D. stands for Drosophila.

number of differences. It was soon recognized that changes could occur at positions where changes had already occurred. Margoliash and Smith (1965) introduced a correction as follows

where r is the number of replacements, n is the number of variable positions in the sequence, and d is the number of divergent positions (differences). It is interesting that Margoliash and Smith contemplated the possibility of invariable positions so early, even though the concern that this might be an important consideration was not present in the field for nearly 20 years, except for Fitch (Fitch and Markowitz, 1970; Shoemaker and Fitch, 1989).

1  

The equation they said they used was r = n In(n/d), which would be incorrect, but their results are those obtained by the correct equation shown.



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