# Transitions and transversions in evolutionary descent: An approach to understanding

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DOI: 10.1007/BF02300751

- Cite this article as:
- Holmquist, R. J Mol Evol (1983) 19: 134. doi:10.1007/BF02300751

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## 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 substitutions*per se* do not lead to a decrease in transition differences with increasing evolutionary divergence.