Letter to the Editor
The Relative-Rate Test of the Molecular Clock Hypothesis:
A Note of Caution1
Se&ied
Scherer
Department of Biochemistry, Virginia Polytechnic Institute and State University
Molecular
Clock and Relative-Rate
Test
Arguments dealing with empirical and theoretical considerations
have been raised
in order to challenge or to defend the molecular clock hypothesis (e.g., see Langley
and Fitch 1974; Fitch 1976; Wilson et al. 1977; Goodman et al. 1982; Gillespie 1986;
Kimura
1987; Scherer, accepted).
An important
role in the controversy
has been
assigned to the relative-rate
test of molecular evolution (Sarich and Wilson 1973),
since it can be applied without referring to geological time (for review, see Wilson et
al. 1977). This test has been used widely as ultima ratio in order to support the rateconstancy hypothesis of molecular evolution (for recent examples, see, e.g., Bledsoe
1987; Easteal 1988), although it was pointed out more than 10 years ago that the
relative-rate test cannot detect changes in the evolutionary
rate if proteins change their
rates proportionally
(Fitch 1976). In the present letter, the potential failure of the
relative-rate test to support the rate-constancy
hypothesis is emphasized using Cu-Zn
superoxide dismutase ( SOD), since this protein has been considered to be a very poor
evolutionary
clock (for a detailed discussion of nine sequences, see Lee et al. 1985;
Ayala et al. 1986).
The Relative-Rate
Test of SOD Favors Rate Constancy
The difference matrix based on 12 amino acid sequences of SOD is shown in
figure 1. The boxed numbers indicate different pairs of species that should be separated
by approximately
the same number of amino acid differences in order to support the
rate-constancy
hypothesis. Ideally, the distances should be identical (equidistances),
since the times of divergence are assumed to be identical. However, the statistical
nature of mutational
events inevitably will produce deviations, which are summarized
in table 1 and which range between 2.0% and 3.8% of the average distance. Whether
these deviations observed for a particular group can be assigned to the statistical nature
of or provide evidence for a nonlinear behavior of molecular evolution can be evaluated
by the x2 test, which was performed according to a method described in detail by
Fitch ( 1976). The test yielded x2 values between 0 and 3.36, with averages ranging
from 0.17 to 0.78 (table 1). The relative-rate test was also applied using a difference
matrix that was transformed
by a logarithmic function in order to correct for multiple
replacements
according to the methods of Margoliash and Fitch ( 1968) and Dickerson ( 197 1) . Considerably
higher x2 values, with averages ranging between 0.53 and
2.22, have been found in this case. However, application
of the x2 test presupposes a
normally distributed
set of numbersin the present case, amino acid differences. It
is doubtful whether the x2 test is justified after transformation
of the difference matrix
by a logarithmic
function, since this results in a major distortion of the normal curve
1. Key words: molecular clock, relative-rate test, superoxide dismutase, molecular evolution, rate constancy. Abbreviations: df = degree of freedom; Photobact. = Photobacterium leiognathi; SOD = Cu-Zn
superoxide dismutase.
Address for correspondence and reprints: Dr. Siegfried Scherer, Fakultit fur Biologie, Universitat
GieBberg, D-7750 Konstanz, Federal Republic of Germany.
Mol. Biol. Evol. 6(4):436-441. 1989.
0 1989 by The University of Chicago. All rights reserved.
0737-4038/89/0604-0010$02.00
436
Letter to the Editor
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Man
437
24
24
26
24
7
6
5
4
4
22
24
25
25
8
7
5
4
4
20
23
24
7
7
5
4
4
Cattle
7
5
4
4
Horse
7
5
4
4
7
5
4
4
8
5
4
4
5
5
5
4
4
Rat
26
Rabbit
22
Pig
25
l-l
27
30
28
29
27
23
27
26
22
31
36
31
36
27
1 50
53
46
44
50
49 ]
1 64
68
63
65
69
66
69 1
Mould
73
70
72
71
68
69
69
68
76
70
65
70
70
69
65
78
Yeast
70
68
69
72
67
73
71
77
Photobact
1107
Swordfish
Fruitfly
Cabbage
104 102
7
102 104 103 101106
L
72
75
?
47
102 106 1061
FIG. 1.-Amino
acid differences (lower left) and evolutionary rates (expressed as amino acid differences/
100 residues and/ 100 Mya; upper right) of SOD sequences. Sequences are taken from Steffens et al. ( 1986)
and Reinecke et al. ( 1988), using their alignment.
Photobacterium leiognathi exhibited five parts of its
sequence that either miss or have more than one residue as compared with all other sequences. These have
been counted as only one difference each, thus assuming either deletions or insertions. Evolutionary
rates
have been calculated assuming the following divergence times: Man vs. rat = 60 Mya; rat vs. rabbit = 75
Mya; rabbit-rat-man
vs. cattle-pig-horse
= 75 Mya; mammals vs. swordfish = 450 Mya; vertebrates vs.
fi-uitfly = 600 Mya; animals vs. cabbage = 900 Mya; animals-cabbage
vs. fungi = 1,200 Mya (see also Ayala
1986). Since not even a crude estimate based on the fossil record exists regarding the divergence time from
P. leiognathi or the split between yeast and mold, no evolutionary rates have been calculated in these cases.
The correction for multiple substitutions
yielded a maximum
and minimum evolutionary
rate of 45 and
5.7 amino acid differences/ 100 residues and / 100 Mya, respectively (see text).
(also see Fitch 1976). To elucidate the significance of the test, the distribution
of the
x2 values, rather than their averages, has to be considered (fig. 2). The critical x2 value
that is necessary for rejection of the rate-constancy
hypothesis with 95% confidence
[ 1 degree of freedom (df)] is 3.84. Of 368 x2 tests performed, all 184 (original data)
and 169 of 184 (transformed
data) are lower than this critical value. The majority are
found between 0 and 0.4. The data, therefore, do not warrant rejecting the interpretation
of the “quasi equidistances”
as representing the rate constancy of molecular evolution
(it should, however, be kept in mind that any x2 test does not warrant asserting the
correctness of the rate-constancy
hypothesis in a strict sense, either).
438
Letter to the Editor
Table 1
Relative-Rate Test of the SOD Molecular Clock
OUTGROUP DISTANCES
(Mean f SD)
OUTGROUP vs. SISTER
GROUPS’
Procaryote vs. eucaryotes (11)
Fungi (2) vs. animals (8) .
Cabbage vs. animals (8) .
Fruitfly vs. vertebrates (7)
..
Swordfish vs. mammals (6)
Ungulates (3) vs.
nonungulates (3)
Original
Data
104.1
71.1
69.7
66.8
49.2
f
f
f
f
f
2.0
3.0
3.8
2.1
3.3
27.3 f 2.1
SD AS % OF MEAN
Original
Data
Transformed
Datad
MEAN x2 c
No. OF x2
TESTS
PERFORMED
6.7
6.2
8.0
5.0
4.8
1.9
4.2
5.4
3.1
6.7
3.8
6.4
8.3
5.7
8.1
0.170
0.367
0.770
0.386
0.784
55
56
28
21
15
30.2 f 2.5
7.6
8.3
0.362
9
Transformed
Datad
182.2
96.6
94.6
88.2
59.1
f
f
+
f
f
a Numbers in parentheses are number of species in the groups compared.
b Compare fig. 1, boxed figures.
’ As calculated for the original data. Each x2 test (1 df) was performed by comparing one member of the outgroup
with a sister group consisting of two species.
d Difference matrix transformed by a logarithmical function (see text).
An “Empirical Test” of Rate Constancy
A closer evaluation
of the difference matrix presented in figure 1 led to the construction of the phenogram depicted in figure 3. Ideally, this phenogram should reflect
the natural classification of the organisms involved, since the relative-rate test favored
a constant rate of evolutionary
change. However, the overall topology does not seem
to be satisfactory (note that both the mammalian
cluster and the cluster consisting of
fruitfly, cabbage, and yeast cannot be resolved unequivocally
by the data), and the
relative distances do not seem to cope with expectations
that are based on either
classical taxonomy
or the fossil record. To highlight the latter inconsistency
in more
detail, the molecular-clock
hypothesis was subjected to an “empirical
test” by comparing amino acid differences with times of divergence derived from the fossil record
(fig. 1, upper right). The rates of molecular evolution vary between 4 and 36 amino
acid differences/ 100 residues/ 100 Mya. The correction of the amino acid-difference
matrix for multiple changes at the same position (see above) did not change this result
significantly
(see legend to fig. 1). This was also found when Ayala ( 1986) applied
four other correction formulas.
Relative-Rate Test and Empirical Test of Rate Constancy Yield
Contradictory Results
For comparison,
an “average” evolutionary
rate of (4 + 36)/2 = 20 amino acid
differences/ 100 residues and per 100 Mya may be assumed. Then, the evolutionary
rate varies by *80%, whereas SDS from average distances range only between 2% and
8% (table 1). Although some of the divergence times given in the legend to figure 1
might be subject to discussion, most authors would not consider the fossil record to
be as fallacious as the relative-rate
test would require it to be in order to support the
rate-constancy
hypothesis. Similar conclusions
have emerged (data not shown) from
the study of ferredoxin, plastocyanin,
and plant cytochrome c, which likewise cannot
be used as molecular clocks (Scherer and Binder 1986; Scherer, accepted). Recently,
Hayasaka et al. ( 1988) compared 12 sequences of a 0.9-kb fragment of primate mtDNA.
The relative-rate test revealed no differences in evolutionary
rates, yet the molecular
Letter to the Editor
I
439
I
.
00
,
8
0.0.
B
1
Chi square
(~2)
I
3
FIG. 2.-A, x2 Distribution as calculated for the original data. n = cumulative number of x2 values
within the range indicated. B, x2 Distribution for the transformed difference matrix. n, = number of x2
values within 0.2 units as plotted against their average. Each plot is based on 184 x2 tests.
clock based on the fossil record indicated changes of evolutionary
rates by a factor of
three. The cause for the quasi equidistances
revealed by the comparison
of sequences
remains, however, to be elucidated. Hitherto, the assumption
of independent but simultanous changes in evolutionary
rates in all lineages leading finally to the quasi
equidistances
observed today would solve the problem but is yet without theoretical
foundation.
Conclusion
ments
SOD has been shown to have large differences in its rate of amino acid replacewhen the fossil record is used for calibration
of the molecular clock. It does
440
Letter to the Editor
Amino
0
20
I
I
I
acid differences
40
60
I
I
I
I
80
I
100
I
I
I
Man
Rabbit
Rat
5
Cattle
Pig
Horse
Swordfish
Fruitfly
Cabbage
Yeast
Moul d
Photobact
I
5
4
1
11
3
2
1
1
1
I
0
0.4
0.8
Billions of years
1.2
I
1.4
FIG. 3.-Average
linkage phenogram
of SOD sequences, based on the amino acid differences given in
fig. 1. Note that only one of several possible phenograms
is shown, since the branching order indicated by
the dotted areas cannot be resolved unequivocally.
The time scale is set as would be true if fungi-zoophyte
divergence occurred 1.2 billion years ago and if the rate was clocklike. Numbers just above the time scale
indicate where the corresponding
nodes (see arrows) in the phylogeny should plot based on estimates from
the fossil record.
not, however, reveal such disparities when the relative-rate test is applied. This means
that passing the relative-rate
test does not guarantee a uniform rate of molecular
evolution.
Acknowledgment
I thank Dr. Walter M. Fitch, University of Southern California, for critical comments and valuable suggestions and Dr. Eberhard Bertsch, Universitat
Bochum, for
helpful discussions concerning
the use of the x2 test.
Letter to the Editor 441
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WALTER M. FITCH, reviewing
Received
February
editor
1, 1989; revision
received
March
15, 1989