Theory of compensatory substitutions

From the individual sequence viewpoint complementary mutations are a two-step process typically involving a U-G or a G-U pair as a transition state. These pairs are thermodynamically less stable than Waston-Crick pairs but they are still more likely to arise than any other mismatches. Nonetheless, in phylogenetic studies we are not considering individual copies of a gene but we are rather modelling consensus sequences for a large number of individuals. From the population genetics viewpoint, evolution in stems can either occur by two single substitutions or by simultaneous compensatory substitutions, (see, e.g., Savill et al., 2001; Higgs, 1998). The first mechanism is by fixation of the slightly deleterious UG or GU pair in the population before the second mutation occurs. The second mechanism happens when natural selection against intermediate mutants is too strong. In such a case, deleterious pairs are kept low in frequency until a second mutation takes place in one of the sporadic mutant sequences by chance. Afterwards, the new neutral variant may replace the original one due to drift in gene frequencies (see figure 2.4).

Figure 2.4: Substitution mechanisms for paired-sites

Therefore, even if simultaneous mutations are very unlikely to occur in a single organism, it is reasonable, although not compulsory, to allow double substitutions in models from the population point of view. The experimental results you can have with PHASE confirm that. Since natural selection against intermediate mutants with any other mismatch pairs than U-G or G-U is usually much stronger, one can notice two groups of states in which rapid interchange occurs, while interchange between the two groups, although possible, is really slow (see figure 2.5).

Figure 2.5: Mutation rate between paired-sites