Gerhart,
The first striking example of saturation of the Ts/Tv ratio was
described by Brown et al. in 1982 (see below). If we make a distinction
between the Ts/Tv substitution *rate* [R(s/v)] versus the ratio of
*observed* transitions and transversions [O(s/v)], they found that their
most closely related sequences had O(s/v)=~9, while the more distant ones
were just below unity. They explained this by supposing that the ratio of
the intrinsic rates R(s/v) was actually about 9, but that this ratio was
obscured by occasional transversions over time. For example, imagine a
particular nucleotide position changing in the following manner, over
enough evolutionary time to have resulted in six substitutions:
A -> G ->A -> G ->C -> T -> C
The observer will only see the initial A changing to a final C, i.e. a
transversion; but the actual sequence of events shows five transitions and
a single transversion having occurred, which makes R(s/v)=5; the relatively
rare transversion event obscures the more frequent transitions.
This was analyzed very elegantly by Walter Fitch (see his 1986 work,
below), graphically showing the interdependence of O(s/v), R(s/v) and
substitution rates. Whatever the actual value of R(s/v), the value of
O(s/v) tends toward 0.5 with increasing time (for any given nucleotide
there are two possible transversions but only a single transition).
For algorithms (tree-making or otherwise) that take into account the
transition/transversion ratio, the value that should be used is R(s/v),
assuming it is relatively constant, not O(s/v), which is highly dependent
on time of divergence. The best estimate of this is O(s/v) for the most
closely related sequences available. If your values range from 1-3.5, the
higher value is probably your best bet, and may itself be an underestimate,
depending on how close your closest sequences are.
Cheers,
George Gutman
Refences:
Brown WM; Prager EM; Wang A; Wilson AC. (1982) Mitochondrial DNA sequences
of primates: tempo and mode of evolution. J. Mol. Evol. 18:225-39.
Fitch WM. (1986) An estimation of the number of invariable sites is
necessary for the accurate estimation of the number of nucleotide
substitutions since a common ancestor. in: Evolutionary prespectives and
the new genetics, pp. 149-159, Alan R. Liss Inc.
*****************************************************************
* George A. Gutman *
* Department of Microbiology Tel:(714)824-6593 *
* and Molecular Genetics FAX:(714)824-8598 *
* University of California INTERNET: GAGUTMAN at UCI.EDU *
* Irvine CA 92717 *
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