Population genetics theory predicts the heterozygosity (H) of a finite population maintained for t generations at a constant size of 2N each generation, with a random distribution of family size, as:

where H ₀ is the heterozygosity of the population before the bottleneck, H _t is the heterozygosity after t generations of maintenance with 2N individuals and F is the inbreeding coefficient (Falconer & Mackay, Reference Falconer and Mackay1996). Clearly heterozygosity decreases, and inbreeding increases, as N decreases; and these effects accumulate over time. However, no real population fits the ideal model on which this theory is based, which includes self-fertilization in random amounts. The concept of effective population size enables us to utilize this expression by replacing the N in the equation with N _e, where N _e, the effective population size, is the number of individuals that would give rise to the same variance in gene frequency or rate of inbreeding as an ideal population of that size (Falconer & Mackay, Reference Falconer and Mackay1996). Major departures from the ideal population model that affect N _e are unequal numbers of males and females, unequal numbers of individuals in different generations, non-random distribution of family size, and overlapping generations. Analytical expressions relating the census size of the population (N) to the effective population size have been derived for each of these cases (Frankham, Reference Frankham1995; Falconer & Mackay, Reference Falconer and Mackay1996); under most scenarios N _e<N. Knowledge of the ratio of N _e to N is critical in wildlife populations and particularly endangered species, if we are to predict the rate of inbreeding and loss of heterozygosity. In this meta-analysis, Frankham (Reference Frankham1995) synthesizes data from 192 estimates of N _e/N from 102 species.

The estimates of N _e/N from insects, molluscs, amphibians, reptiles, birds, mammals and plants ranged from 10⁻⁶ in Pacific oysters to 0·99 in humans, and averaged 0·34 overall. However, these studies differed in whether they included fluctuating population size, variable family size and/or different numbers of males and females – less than one-third of the studies included all three of these factors. In addition, different measures of census size were used as the denominator. Some studies utilized the total census size (N _T, the total number of adults and juveniles), some the number of adults (N _A, the number of breeding plus senescent adults), while others counted only the number of breeding individuals (N _B). Finally, both genetic and demographic methods were used. Frankham (Reference Frankham1995) capitalized on this variability to perform stepwise regression analyses in order to determine the major variables affecting N _e/N. The significant variables, in decreasing order of importance, were fluctuating population size, variable family size, method of determining census number, taxonomic group, and the sex ratio. The most striking conclusion was that the comprehensive estimates of N _e/N in wild species, including all variables, were of the order of 10%. This is much smaller than had been thought previously and a cause for concern in terms of long-term population viability. This influential review stimulated many studies estimating N _e/N in a wide variety of wild species.