Relationship of Effective to Census Size in Fluctuating Populations

The effective size of a population (   N_e    ) rather than the census size (   N) determines its rate of genetic drift. Knowing the ratio of effective to census size, N_e   /  N, is useful for estimating the effective size of a population from census data and for examining how different ecological factors influence effective size. Two different multigenerational ratios have been used in the literature based on either the arithmetic mean or the harmonic mean in the denominator. We clarify the interpretation and meaning of these ratios. The arithmetic mean N_e   /  N ratio compares the total number of real individuals to the long-term effective size of the population. The harmonic mean N_e   /  N ratio summarizes variation in the N_e   /  N ratio for each generation. In addition, we show that the ratio of the harmonic mean population size to the arithmetic mean population size provides a useful measure of how much fluctuation in size reduced the effective size of a population. We discuss applications of these ratios and emphasize how to use the harmonic mean N_e   /  N ratio to estimate the effective size of a population over a period of time for which census counts have been collected.