Editing Effective population size (section)

==== Variance in reproductive success ====

If population size is to remain constant, each individual must contribute on average two [[gamete]]s to the next generation.  An idealized population assumes that this follows a [[Poisson distribution]] so that the [[variance]] of the number of gametes contributed, ''k'' is equal to the [[mean]] number contributed, i.e. 2:

:<math>\operatorname{var}(k) = \bar{k} = 2.</math>

However, in natural populations the variance is often larger than this. The vast majority of individuals may have no offspring, and the next generation stems only from a small number of individuals, so

:<math>\operatorname{var}(k) > 2.</math>

The effective population size is then smaller, and given by:

:<math>N_e^{(v)} = {4 N - 2D \over 2 + \operatorname{var}(k)}</math>

Note that if the variance of ''k'' is less than 2,  ''N''<sub>''e''</sub> is greater than ''N''.  In the extreme case of a population experiencing no variation in family size, in a laboratory population in which the number of offspring is artificially controlled, ''V''<sub>''k''</sub> = 0 and ''N''<sub>''e''</sub> = 2''N''.