Transitions and transversions in evolutionary descent: An approach to understanding |
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Authors: | Richard Holmquist |
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Institution: | (1) Space Sciences Laboratory, University of California at Berkeley, 1414 Harbour Way South, 94804 Richmond, CA, USA |
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Abstract: | Summary In this paper I lay a quantitative theoretical groundwork for understanding the proportions of the possible types of base
substitutions observed between 12 genes sharing a common ancestor and isolated from extant species. The experimentally observed
types of base substitution between two sequenced genes do not give a direct measure of the types of base substitutions that
occur during evolutionary descent. However, by use of a statistical assemblage of these observations, we can recover, without
the assumption of parsimony, the conditional base substitution probabilities that determine this descent. Three methods—direct
count, regression, and informational entropy maximization—are described by which these probabilities can be estimated from
experimental data. The methods are complementary in that each is most useful for somewhat different types of experimental
data. These methods are used to study the ratio of transversions to transitions during gene divergence. Though this ratio
is not constant during divergence, it does approach a stable limiting value that in principle can vary from zero, corresponding
to 100% transition differences, to infinity, corresponding to 0% transition differences. In practice the limiting ratio tends
to hover around a value of two, which is expected on a random basis. However, base substitution pathways that are very nonrandom
also may lead to a limiting ratio of exactly two, so that such a value is not diagnostic for random pathways. The limiting
ratio can be directly calculated from a knowledge of the twelve conditional probabilities for each type of base substitution,
or from a knowledge of the equilibrium base composition of the DNAs compared. An expression is given for this calculation.
Fifteen years ago Jean Derancourt, Andrew Lebor and Emile Zuckerkandl (1967), analyzing the amino acid sequence of globin
chains coded by nuclear genes, made the original observation that the proportion of transition differences decreases with
increasing evolutionary time. Recently Brown et al. (1982) and Brown and Simpson (1982) have reported a decrease in the observed
proportion of transition differences in mitochondrial DNA with increasing evolutionary divergence. The conditions that must
be satisfied for this type of behavior to occur at stable base composition and with stable base substitution probabilities
are defined. Multiple substitutionsper se do not lead to a decrease in transition differences with increasing evolutionary divergence. |
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Keywords: | Base substitutions Transitions and Transversions Gene evolution Evolutionary theory Maximum entropy inference |
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