## Effective size of the population

In describing the dynamics of *fixation of mutations*, it is necessary to consider not only the *probability* with which a mutation will become fixed in a population of a certain size, but also the *time required on an average for fixation of a mutation.* The probability that a newly formed mutation will be fixed is equal to **1/2N.** Similarly, the average time required for *fixation* of one mutation is proportional to the size of the population. However, this is a case of direct proportionality. M. Kimura derived that the average time for fixation of a mutation by *genetic drift* is equal to **4 N_{e }generations**, where

*N*

_{e}is the

*effective size of the population*(the effective size of the population is a term that will be explained in Section V.3.2.1) For a population with an

*effective size*of 30,

*fixation*of a neutral mutation will thus require an average of 120 generation periods.

The graph describing the shape of the time distribution required for *fixation* of a mutation by *genetic drift* is highly asymmetric. The asymmetry of the graph reflects the fact that it is highly improbable that a mutation will become fixed sooner than in **0.8 N_{e }**generation periods and a great many mutations require substantially more time than the average

**4**generation periods.

*N*_{e}