A note on the arrival probability, first arrival time and age of a mutant gene in a finite population

Abstract

It is pointed out that the arrival or fixation probability of a mutant gene can be easily inferred analytically. The mean first arrival time for a single overdominant mutation to reach frequency y attains its maximum when x is close to but still slightly less than y/2, where x is the equilibrium frequency of the mutant gene in an infinitely large population. For an advantageous mutation, the mean first arrival time decreases with an increasing degree of dominance if selection is strong, but it first increases, after reaching a maximum, then decreases as the degree of dominance increases, if selection is weak. Contrary to our intuition, the mean age of an advantageous mutant gene increases with increasing degree of dominance, except when selection is very strong. A simple explanation is given in terms of the sojourn time at a particular gene frequency.