The other side of the nearly neutral theory, evidence of slightly advantageous back-mutations.

We argue that if there is a category of slightly deleterious mutations, then there should be a category of slightly advantageous back-mutations. We show that when there are both slightly deleterious and advantageous back-mutations, there is likely to be an increase in the rate of evolution after a population size expansion. This increase in the rate of evolution is short-lived. However, we show how its signature can be captured by comparing the rate of evolution in species that have undergone population size expansion versus contraction. We test our model by comparing the pattern of evolution in pairs of island and mainland species in which the colonization event was either island-to-mainland (population size expansion) or mainland-to-island (contraction). We show that the predicted pattern of evolution is observed.