Evolution__3rd_Edition

Box 7.2
The Relative Rate Test
The relative rate test is a method of testing whether a molecule (or,
in principle, any other character) evolves at a constant rate in two
independent lineages. It was first used by Sarich and Wilson in
1973. Suppose we know the sequence of a protein in three species,
a, b, and c, and we also know the order of phylogenetic branching
of the three species (Figure B7.1). We can now infer the amounts
of change in the two lines from the common ancestor of a and b to
the modern species (x and y in Figure B7.1). If the protein evolved
at the same rate in the two lineages, the number of amino acid
changes between the common ancestor and a (x) should equal the
number of changes between the common ancestor and b (y); that is,
x = y. x and y can be inferred by simple simultaneous equations. We
know the differences between the protein sequences in a and b (k),
b and c (l), and a and c (m). Thus
k = x + y
l = y + z
m = x + z
We have three equations with three unknowns and can solve for x,
y, and z. We then test whether the rates were the same by seeing
whether x = y. Notice that we do not need to know the absolute
date (or the identity) of the common ancestors.
The relative rate test can only show that a molecule evolved at
the same rate in the two lineages connecting the two modern
species with their common ancestor. This does not prove that the
molecule always has a constant rate; it does not, in other words,
confirm the molecular clock. If identity of relative rate is shown for
many pairs of species, with common ancestors of very different
antiquities, that is suggestive of (and consistent with) a molecular
clock, but it is not conclusive evidence. We can see why in a
counterexample (Figure B7.2). Suppose that a molecule evolves
at the same rate in all lineages at any one time, but that it has been
gradually slowing down through evolutionary history. A pair of
Figure B7.2
(a) The rate of evolution of a
molecule has slowed down
gradually through time; but the
rate of evolution is always the
same in all lineages at any one
time. The molecule does not
evolve like a clock (which
would show up as a flat graph
of rate against time). (b) Then,
for any pair of species, with
common ancestors at any time,
the amount of change will be
the same in both lineages.
Rate of evolution
of all lineages
species with a common ancestor 100 million years ago will then
show rate constancy according to the relative rate test (because
the molecule evolves at the same rate in all lineages at any one
time); and any other species pair, for instance with a common
ancestor 50 million years ago, will also show relative rate
constancy. However, there is no molecular clock because the rate
slows down through time. The relative rate test will not detect that
the more recent species pair have a smaller absolute number of
changes: absolute dates would be needed for that. The same point
would apply if there were any trend in evolutionary rate with time,
and it does not have to be directional. The molecule could speed up
and slow down many times in evolution; but so long as the speeding
up and slowing down apply to all lineages, the relative rate test will
show equal rates of evolution in the two lineages. The relative rate
test, therefore, cannot conclusively test the molecular clock
hypothesis.
(a) (b)
Time
z
Time
50
100
x
y
Species
a
Figure B7.1
Phylogeny of three species: a, b, and c. k, l, and m are the
observed number of amino acid differences between the
three species. The amounts of evolution (x, y, z) in the three
parts of the tree can be simply inferred, as the text explains.
b
c
k
l
m
p q r s
r = s
p = q
..