QLE

Kirkpatrick M, Johnson T & Barton N 2002 General models of multilocus evolution. Genetics 161:1727-1750.

• D_ij = e_ij pq_ij / r_ij + O(a²) ... (A5)
• [Watterson?]

• we derive approximate expressions for the associations and changes in allele frequencies when the population is in a state of QLE
• the concept was introduced by Kimura (1965) and greatly generalized by Nagylaki (1993) and Nagylaki et al. (1999)
• a concise summary of those results is given in Bürger (2000, p. 82)
• the first fundamental assumption we must make is that all the associations D are of order a
• this condition is met when the forces that generate associations within a sex (epistasis, migration, etc.) are weak relative to recombination and when nonrandom mating is not strong
• the second assumption needed for the QLE approximation is that all the selection coefficients a are ≪1
• when these two conditions hold, a population rapidly settles into a state where the allele frequencies are changing slowly, and the associations are close to the equilibrium values they would reach if the allele frequencies were in fact stationary