## N

term in this equation predicts the decline in heterozygosity through time by genetic drift. Additive genetic variation is greater when heterozygosity is greater because alleles are at intermediate frequencies.

Next we can predict the balance between the additive genotypic variation lost by drift and new additive variation gained due to new mutations at the loci that influence a quantitative trait. Let's start by reworking the equation for decline in VA over an arbitrary time interval to instead predict the change in additive genotypic variation each generation due to drift:

as an estimate of the effective population size expected to maintain a heritability of about one-half.

A 2N

This equation is obtained from equation 9.23 by setting t = 1, multiplying the right side out, and then subtracting V0A from both sides. Then assume that the amount of new additive genotypic variance caused by mutation each generation is Vm. The sum of additive variation lost by drift and additive variation gained by mutation is aa =- Ai-

A 2N

This defines the net change in additive genotypic variation due to the action of both drift and mutation. If we assume that a population is at drift-mutation equilibrium then AVa = 0, allowing equation 9.21 to be rearranged to give

V=2NVM

(see Lynch & Hill 1986; Bürger & Lande 1994).

The expected additive genotypic variance for a neutral quantitative trait at drift-mutation equilibrium was the basis of a much debated recommendation that Ne = 500 would be sufficient to maintain additive genotypic variation in populations of endangered species (Franklin 1980; Lande 1995). This recommendation came from rearranging equation 9.26 to solve for the effective population size:

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