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If a sequence is under selection will it acquire more changes over time because of faster fixation than if changes were neutral? Is this true or am I missing something?

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Generally speaking, there are sequences that are under purifying selection (where new mutations are often deleterious) and there are sequences that are neutral. Sequences under constant positive selection do not really exist. So, when you ask

If a sequence is under selection will it acquire more changes over time because of faster fixation than if changes were neutral?

No! If a sequence is under selection, then it is under purifying selection. As such the rate of fixation will be lower than for a neutral sequence.

If you have a sequence, where most mutations are beneficial, then it the sequence would fix new mutations at a higher rate then a neutral sequence. However such sequence don't really exist! If it were to exist, then mutations would quickly fix such that new mutations would then be deleterious again.

Of course, a single beneficial mutation has a higher chance of fixation than a neutral mutation. Also, when a mutation is under selection (whether purifying or not), the expected change in heterozygosity in the population is higher than if the mutation is neutral (the expected change in allele frequency is equal to the additive genetic variance for fitness at this locus). But those are not details you are asking about.

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