Page 232 - Applied Probability

10. Molecular Phylogeny
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5 root 2
1

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eubacterium halobacterium eukaryote eocyte
FIGURE 10.7. Best Rooted Tree for the Evolution of Eukaryotes
with the tree depicted in Figure 10.7.
Without the assumption of stationarity, two other rooted trees reducing
to the E tree have nearly the same loglikelihoods (−4537.3 and −4537.4)
as the best rooted tree. Apparently, distinguishing rooted trees in practice
is much harder than distinguishing them in theory. On the other hand, the
best rooted tree corresponding to either an F or G tree has a much lower
loglikelihood than that (−4544.2) of the best rooted tree.

10.8 Codon Models

Except for regulatory regions, codons rather than nucleotides are the units
of evolution. Because there are 61 non-stop codons compared to 4 nu-
cleotides, codon models are much more computationally demanding than
nucleotide models. Nonetheless, taking variation at the codon level into ac-
count can substantially improve reconstruction of evolutionary trees [9, 25].
It also helps identify conserved domains within proteins. The most natural
method of turning a nucleotide substitution model into a codon substitu-
tion model is to penalize nonsynonymous codon changes. For example,
suppose ω bd is the infinitesimal transition rate from base b to base d. On the
codon level, the infinitesimal transition rate from codon (a, b, c)tocodon
(a, d, c) is still ω bd, assuming sites mutate independently. If two codons are
nonsynonymous, then one can penalize transitions between them by replac-
ing ω bd by ρè bd for ρ< 1. Here we can view ρ as the probability that a
proposed evolutionary change is accepted. If the destination codon is one
of the three stop codons, the acceptance probability is 0. The acceptance
probability for a synonymous change is 1. In the presence of strong positive
selection, a value of ρ> 1 is plausible. In this case, we simply interpret the
product ρè bd as a rate.
Besides accounting for nonsynonymous codon changes in a parsimonious
manner, this codon model possesses the attractive property of turning a