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Transitions are base mutations of purine to purine (A <-> G) or pyrimidine to pyrimidine (C <-> T). Transversions are purine to pyrimidine or vice versa (A <-> C, A <-> T, G <-> C, G <-> T). And it is well-known that transitions are more common than transversions in the populations.

So what is the condition in the evolution of duplicated genes? Suppose a gene A is duplicated with two copies A1 and A2 in the same genome (not two alleles in different sets of chromosomes, or the same gene in two different cells/organisms). At first A1 and A2 had the same sequence, but then they went through an evolution process and each got some mutations. Now let's check the sequence of A1 and A2 again, are the differences between A1 and A2 mainly transitions instead of transversions?

Although I think it would not be surprising to find that transitions are more common in this condition, I've searched some papers focusing on the evolution of duplicated genes to look for some support. However, they mainly discuss what happened to their functions instead of sequences.

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If we consider that the biochemical impact of transitions vs transversions is constant across the two scenarios, then the only discrepancy can be due to the level of purifying selection, or the level of positive diversifying selection, or both, between the two duplicates.

By far the most common fate to one duplicate copy is for purifying selection to be relaxed, leading to accruing deleterious mutations and eventually loss. This means that fixation of non-synonymous mutations are more common, and as transversions are more likely to be non-synonymous, this implies that the rate of fixation for transversions would increase.

Similarly, one might expect functional change leading to positive diversifying selection, which implies a greater rate of fixation of non-synonymous mutations and, following the same logic as above, a greater rate of transversions.

Whether or not this contributing increase to the rate of fixation of transversions mean that transversions actually outnumber transitions, or instead merely decreases the ratio of transition:transversion, will be dependent on the particular gene and selective scenario.

As a final note, while the first cause I identified (biochemical) actually changes the rate of mutation, the selection-specific factors are changes to rate of fixation, which is a population-level process. So while the relative rates of transition and transversion may stay the same, the fixation rates of these two categories of mutation between the two duplicate copies are the important difference.

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