Evolution__3rd_Edition

444 PART 4 / Evolution and Diversity
Box 15.1
Models of Sequence Evolution
A DNA sequence is made up of four kinds of nucleotide. Evolution
consists of changes among the four nucleotide states. In the
simplest model of evolution, we assume that the chance of any
change, from one nucleotide to another, is the same, and has
probability p. (p could be defined as the chance that a nucleotide
at a site will change from one kind of nucleotide to another kind,
per million years, in a population. In practice p is usually an
instantaneous rate, rather than a rate per million years, but that
does not matter here.) Figure B15.1 shows the evolutionary
possibilities.
An A, for example, can change to a C, G, or T. In all, there are
12 kinds of change. The simplest model assumes that the chance
of all 12 is the same, p. This model is a “one-parameter” model,
called the Jukes–Cantor model after its originators. If two species
have the same nucleotide at a site, it could be that the nucleotide
has not changed (chance 1 − 3p). Or it could have changed and
then changed back (A → C → A, for instance), which has chance p 2 .
(The probabilities would need to be multiplied by an amount of time
if they have been evolving apart for something other than 1 million
years.) If the two species have different nucleotides (such as A in
one species and C in the other) at a site, there could have been one
change (chance p) or two (for instance A → G → C), with chance p 2 .
We can think through all the possibilities, and calculate the total
probabilities that a site will be identical, or different, in the two
species, when we sum over all the ways that a site can end up
identical, or different.
The one-parameter Jukes–Cantor model is the simplest. In
practice, the chance of transitions differs from the chance of
transversions. This leads to the “two-parameter” model, first
discussed by Kimura. We assume that the four transitions in
Figure B15.1 have one chance, p 1 , and the eight transversions
have some other chance, p 2 . More complex models allow for
the possibility that some transitions are more likely than other
transitions. Figure B15.1 has 12 arrows, and a complex model
could have 12 parameters, one for each kind of nucleotide
change. Models for maximum likelihood (see Box 15.2) usually
also take account of differences in the rate of evolution between
different sites.
For any given model of sequence evolution, we can use the
sequence data to estimate the value of p (or of p 1 and p 2 ). Several
statistical procedures are used, which can be found in an advanced
text. The estimated value of p can then be used for various
Transitions
Transversions
Transitions
A G
C T
Figure B15.1
Possible kinds of evolutionary change between the four
kinds of nucleotide.
purposes, such as correcting for multiple hits, or the calculation
of maximum likelihood.
Inferences that employ models of sequence evolution are more
or less accurate, depending on how good the model is and how
well the parameters are estimated. For instance, if transition and
transversion frequencies differ, then the use of the one-parameter
Jukes–Cantor model would give misleading results, and might lead
to a faulty phylogenetic inference. Also, the parameters (such as p)
are estimated from sequence data, using a statistical model such
as the Poisson or gamma distribution. The quality of the estimate
depends on how good the data are a whether the stretch of
sequence is long enough, for instance a and on whether the
correct statistical model has been picked. Controversies in
molecular phylogenetics can turn on details of these statistical
models. In general, a trade-off exists between the quantity of data
needed to estimate the parameters, and the accuracy of the model
that can be used. A model with two parameters should be better
than a model with one parameter, but requires more sequence data
to estimate the parameters.
Further reading: Swofford et al. (1996), Page & Holmes (1998),
Graur & Li (2000).
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