Each of the 2N genes in the original population has an equal chance of being the lucky one

Any one gene in the population, therefore, has a 1/( 2N ) chance of eventual fixation by random drift (and a ( 2N -1)/( 2N ) chance of being lost by it). Because the same argument applies to any gene in the population, it also applies to a new, unique, neutral mutation.

When the mutation arises, it will be one gene in a population of 2N genes at its locus (i.e., its frequency will be 1/(2/N )), and it has the same 1/(2N ) chance of eventual fixation as does every other gene in the population. It is therefore most likely that the mutation will be lost but it does have a small chance of success. The probability that a neutral mutation will eventually be fixed is 1/(2N ).

The rate of evolution equals the probability that a mutation is fixed, multiplied by the rate at which mutations appear. We define the rate at which neutral mutations arise as µ per gene per generation. (µ is the rate at which new selectively neutral mutations arise, not the total mutation rate. We are here considering only those mutations that are neutral.) At each locus, there are 2N genes in the population: the total number of neutral mutations arising in the population will be 2N µ per generation.

The rate of neutral evolution is 1/(2N ) x 2Nµ = µ. It is equal to the neutral mutation rate.